Abstract

We report on an original and simple formulation of the phase shift in N-light-pulse atom interferometers. We consider atomic interferometers based on two-photon transitions (Raman transitions or Bragg pulses). Starting from the exact analytical phase shift formula obtained from the atom optics ABCD formalism, we use a power series expansion in time of the position of the atomic wave packet with respect to the initial condition. The result of this expansion leads to a formulation of the interferometer phase shift, where the leading coefficient in the phase terms up to Tk dependences (k0) in the time separation T between pulses can be simply expressed in terms of a product between a Vandermonde matrix and a vector characterizing the two-photon pulse sequence of the interferometer. This simple coefficient dependence of the phase shift reflects very well the atom interferometer’s sensitivity to a specific inertial field in the presence of multiple gravito-inertial effects. Consequently, we show that this formulation is well suited when looking for selective atomic sensors of accelerations, rotations, or photon recoil only, which can be obtained by simply zeroing some specific coefficients. We give a theoretical application of our formulation to the photon recoil measurement.

© 2016 Optical Society of America

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References

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  1. M. Kasevich and S. Chu, “Atomic interferometry using stimulated Raman transitions,” Phys. Rev. Lett. 67, 181–184 (1991).
    [Crossref]
  2. F. Riehle, T. Kisters, A. Witte, J. Helmcke, and C. J. Borde, “Optical Ramsey spectroscopy in a rotating frame—Sagnac effect in a matter-wave interferometer,” Phys. Rev. Lett. 67, 177–180 (1991).
    [Crossref]
  3. G. Rosi, F. Sorrentino, L. Cacciapuoti, M. Prevedelli, and G. M. Tino, “Precision measurement of the Newtonian gravitational constant using cold atoms,” Nature 510, 518–521 (2014).
    [Crossref]
  4. M. Cadoret, E. De Mirandes, P. Cladé, S. Guellati-Khelifa, C. Schwob, F. Nez, L. Julien, and F. Biraben, “Combination of Bloch oscillations with a Ramsey–Bordé interferometer: new determination of the fine structure constant,” Phys. Rev. Lett. 101, 230801 (2008).
    [Crossref]
  5. R. Bouchendira, P. Cladé, S. Guellati-Khelifa, F. Nez, and F. Biraben, “New determination of the fine structure constant and test of the quantum electrodynamics,” Phys. Rev. Lett. 106, 080801 (2011).
    [Crossref]
  6. A. Peters, K. Y. Chung, and S. Chu, “Measurement of gravitational acceleration by dropping atoms,” Nature 400, 849–852 (1999).
    [Crossref]
  7. J. L. Gouët, T. Mehlstäubler, J. Kim, S. Merlet, A. Clairon, A. Landragin, and F. P. DosSantos, “Limits to the sensitivity of a low noise compact atomic gravimeter,” Appl. Phys. B 92, 133–144 (2008).
    [Crossref]
  8. J. M. McGuirk, G. T. Foster, J. B. Fixler, M. J. Snadden, and M. A. Kasevich, “Sensitive absolute-gravity gradiometry using atom interferometry,” Phys. Rev. A 65, 033608 (2002).
    [Crossref]
  9. F. Sorrentino, Q. Bodart, L. Cacciapuoti, Y. H. Lien, M. Prevedelli, G. Rosi, L. Salvi, and G. M. Tino, “Sensitivity limits of a Raman atom interferometer as a gravity gradiometer,” Phys. Rev. A 89, 023607 (2014).
    [Crossref]
  10. T. L. Gustavson, P. Bouyer, and M. A. Kasevich, “Precision rotation measurements with an atom interferometer gyroscope,” Phys. Rev. Lett. 78, 2046–2049 (1997).
    [Crossref]
  11. J. K. Stockton, K. Takase, and M. A. Kasevich, “Absolute geodetic rotation measurement using atom interferometry,” Phys. Rev. Lett. 107, 133001 (2011).
    [Crossref]
  12. I. Dutta, D. Savoie, B. Fang, B. Venon, C. L. Garrido Alzar, R. Geiger, and A. Landragin, “Continuous cold-atom inertial sensor with 1nrad/s rotation stability,” Phys. Rev. Lett. 116, 183003 (2016).
    [Crossref]
  13. S. Dimopoulos, P. W. Graham, J. M. Hogan, and M. A. Kasevich, “Testing general relativity with atom interferometry,” Phys. Rev. Lett. 98, 111102 (2007).
    [Crossref]
  14. S. Dimopoulos, P. W. Graham, J. M. Hogan, M. A. Kasevich, and S. Rajendran, “Gravitational wave detection with atom interferometry,” Phys. Lett. B 678, 37–40 (2009).
    [Crossref]
  15. W. Chaibi, R. Geiger, B. Canuel, A. Bertoldi, A. Landragin, and P. Bouyer, “Low frequency gravitational wave detection with ground-based atom interferometer arrays,” Phys. Rev. D 93, 021101(R) (2016).
    [Crossref]
  16. P. Wolf, P. Lemonde, A. Lambrecht, S. Bize, A. Landragin, and A. Clairon, “From optical lattice clocks to the measurement of forces in the Casimir regime,” Phys. Rev. A 75, 063608 (2007).
    [Crossref]
  17. A. Bonnin, N. Zahzam, Y. Bidel, and A. Bresson, “Simultaneous dual-species matter-wave accelerometer,” Phys. Rev. A 88, 043615 (2013).
    [Crossref]
  18. K. Bongs, R. Launay, and M. A. Kasevich, “High-order inertial phase shifts for time domain atom interferometers,” Appl. Phys. B 84, 599–602 (2006).
    [Crossref]
  19. B. Dubetsky and M. A. Kasevich, “Atom interferometer as a selective sensor of rotation or gravity,” Phys. Rev. A 74, 023615 (2006).
    [Crossref]
  20. C. J. Bordé, “Atomic clocks and inertial sensors,” Metrologia 39, 435–463 (2002).
    [Crossref]
  21. C. J. Bordé, “Propagation of laser beams and of atomic systems,” in Fundamental Systems in Quantum Optics, J. Dalibard, J.-M. Raimond, and J. Zinn-Justin, eds., Les Houches Lectures Session LIII 1990 (Elsevier, 1991).
  22. C. Antoine and C. J. Bordé, “Quantum theory of atomic clocks and gravito-inertial sensors: an update,” J. Opt. B 5, S199–S203 (2003).
    [Crossref]
  23. P. Wolf and P. Tourrenc, “Gravimetry using atom interferometers: some systematic effects,” Phys. Lett. A 251, 241–246 (1999).
    [Crossref]
  24. P. Berman, Atom Interferometry (Academic, 1996).
  25. P. Storey and C. Cohen-Tannoudji, “The Feynman path-integral approach to atomic interferometry: a tutorial,” J. Phys. II 4, 1999–2027 (1994).
    [Crossref]
  26. T. M. Niebauer, G. S. Sasagawa, J. E. Faller, R. Hilt, and F. Klopping, “A new generation of absolute gravimeters,” Metrologia 32, 159–180 (1995).
    [Crossref]
  27. T. Lévéque, A. Gauguet, F. Michaud, F. Pereira Dos Santos, and A. Landragin, “Enhancing the area of a Raman atom interferometer using a versatile double-diffraction technique,” Phys. Rev. Lett. 103, 080405 (2009).
    [Crossref]
  28. J. E. Debs, P. A. Altin, T. H. Barter, D. Doring, G. R. Dennis, G. McDonald, R. P. Anderson, J. D. Close, and N. P. Robins, “Cold-atom gravimetry with a Bose–Einstein condensate,” Phys. Rev. A 84, 033610 (2011).
    [Crossref]
  29. C. J. Bordé, “Atomic interferometry with internal state labelling,” Phys. Lett. A 140, 10–12 (1989).
    [Crossref]
  30. H. Müller, S.-W. Chiow, Q. Long, S. Herrmann, and S. Chu, “Atom interferometry with up to 24-photon-momentum-transfer beam splitters,” Phys. Rev. Lett. 100, 180405 (2008).
    [Crossref]
  31. R. Charriére, M. Cadoret, N. Zahzam, Y. Bidel, and A. Bresson, “Local gravity measurement with the combination of atom interferometry and Bloch oscillations,” Phys. Rev. A 85, 013639 (2012).
    [Crossref]
  32. M. Andia, R. Jannin, F. Nez, F. Biraben, S. Guellati-Khélifa, and P. Cladé, “Compact atomic gravimeter based on a pulsed and accelerated optical lattice,” Phys. Rev. A 88, 031605 (2013).
    [Crossref]
  33. D. S. Weiss, B. C. Young, and S. Chu, “Precision measurement of the photon recoil of an atom using atom interferometry,” Phys. Rev. Lett. 70, 2706–2709 (1993).
    [Crossref]
  34. O. Carraz, C. Siemes, L. Massotti, R. Haagmans, and P. Silvestrin, “A spaceborne gravity gradiometer concept based on cold atom interferometers for measuring Earth’s gravity field,” Microgravity Sci. Technol. 26, 139–145 (2014).
    [Crossref]
  35. Y. Bidel, O. Carraz, R. Charrière, M. Cadoret, N. Zahzam, and A. Bresson, “Compact cold atom gravimeter for field applications,” Appl. Phys. Lett 102, 144107 (2013).
    [Crossref]
  36. S.-W. Chiow, S. Herrmann, S. Chu, and H. Muller, “Noise-immune conjugate large-area atom interferometers,” Phys. Rev. Lett. 103, 050402 (2011).
    [Crossref]
  37. T. Trebst, T. Binnewies, J. Helmcke, and M. F. Riehle, “Suppression of spurious phase shifts in an optical frequency standard,” IEEE Trans. Instrum. Meas. 50, 535–538 (2001).
    [Crossref]
  38. T. Aoki, T. Shinohara, and M. A. Morinaga, “High-finesse atomic multiple-beam interferometer comprised of copropagating stimulated Raman-pulse fields,” Phys. Rev. A 63, 063611 (2001).
    [Crossref]
  39. T. Aoki, M. Yasuhara, and M. A. Morinaga, “Atomic multiple-wave interferometer phase-shifted by the scalar Aharanov–Bohm effect,” Phys. Rev. A 67, 053602 (2003).
    [Crossref]

2016 (2)

I. Dutta, D. Savoie, B. Fang, B. Venon, C. L. Garrido Alzar, R. Geiger, and A. Landragin, “Continuous cold-atom inertial sensor with 1nrad/s rotation stability,” Phys. Rev. Lett. 116, 183003 (2016).
[Crossref]

W. Chaibi, R. Geiger, B. Canuel, A. Bertoldi, A. Landragin, and P. Bouyer, “Low frequency gravitational wave detection with ground-based atom interferometer arrays,” Phys. Rev. D 93, 021101(R) (2016).
[Crossref]

2014 (3)

F. Sorrentino, Q. Bodart, L. Cacciapuoti, Y. H. Lien, M. Prevedelli, G. Rosi, L. Salvi, and G. M. Tino, “Sensitivity limits of a Raman atom interferometer as a gravity gradiometer,” Phys. Rev. A 89, 023607 (2014).
[Crossref]

G. Rosi, F. Sorrentino, L. Cacciapuoti, M. Prevedelli, and G. M. Tino, “Precision measurement of the Newtonian gravitational constant using cold atoms,” Nature 510, 518–521 (2014).
[Crossref]

O. Carraz, C. Siemes, L. Massotti, R. Haagmans, and P. Silvestrin, “A spaceborne gravity gradiometer concept based on cold atom interferometers for measuring Earth’s gravity field,” Microgravity Sci. Technol. 26, 139–145 (2014).
[Crossref]

2013 (3)

Y. Bidel, O. Carraz, R. Charrière, M. Cadoret, N. Zahzam, and A. Bresson, “Compact cold atom gravimeter for field applications,” Appl. Phys. Lett 102, 144107 (2013).
[Crossref]

A. Bonnin, N. Zahzam, Y. Bidel, and A. Bresson, “Simultaneous dual-species matter-wave accelerometer,” Phys. Rev. A 88, 043615 (2013).
[Crossref]

M. Andia, R. Jannin, F. Nez, F. Biraben, S. Guellati-Khélifa, and P. Cladé, “Compact atomic gravimeter based on a pulsed and accelerated optical lattice,” Phys. Rev. A 88, 031605 (2013).
[Crossref]

2012 (1)

R. Charriére, M. Cadoret, N. Zahzam, Y. Bidel, and A. Bresson, “Local gravity measurement with the combination of atom interferometry and Bloch oscillations,” Phys. Rev. A 85, 013639 (2012).
[Crossref]

2011 (4)

J. E. Debs, P. A. Altin, T. H. Barter, D. Doring, G. R. Dennis, G. McDonald, R. P. Anderson, J. D. Close, and N. P. Robins, “Cold-atom gravimetry with a Bose–Einstein condensate,” Phys. Rev. A 84, 033610 (2011).
[Crossref]

S.-W. Chiow, S. Herrmann, S. Chu, and H. Muller, “Noise-immune conjugate large-area atom interferometers,” Phys. Rev. Lett. 103, 050402 (2011).
[Crossref]

R. Bouchendira, P. Cladé, S. Guellati-Khelifa, F. Nez, and F. Biraben, “New determination of the fine structure constant and test of the quantum electrodynamics,” Phys. Rev. Lett. 106, 080801 (2011).
[Crossref]

J. K. Stockton, K. Takase, and M. A. Kasevich, “Absolute geodetic rotation measurement using atom interferometry,” Phys. Rev. Lett. 107, 133001 (2011).
[Crossref]

2009 (2)

S. Dimopoulos, P. W. Graham, J. M. Hogan, M. A. Kasevich, and S. Rajendran, “Gravitational wave detection with atom interferometry,” Phys. Lett. B 678, 37–40 (2009).
[Crossref]

T. Lévéque, A. Gauguet, F. Michaud, F. Pereira Dos Santos, and A. Landragin, “Enhancing the area of a Raman atom interferometer using a versatile double-diffraction technique,” Phys. Rev. Lett. 103, 080405 (2009).
[Crossref]

2008 (3)

H. Müller, S.-W. Chiow, Q. Long, S. Herrmann, and S. Chu, “Atom interferometry with up to 24-photon-momentum-transfer beam splitters,” Phys. Rev. Lett. 100, 180405 (2008).
[Crossref]

J. L. Gouët, T. Mehlstäubler, J. Kim, S. Merlet, A. Clairon, A. Landragin, and F. P. DosSantos, “Limits to the sensitivity of a low noise compact atomic gravimeter,” Appl. Phys. B 92, 133–144 (2008).
[Crossref]

M. Cadoret, E. De Mirandes, P. Cladé, S. Guellati-Khelifa, C. Schwob, F. Nez, L. Julien, and F. Biraben, “Combination of Bloch oscillations with a Ramsey–Bordé interferometer: new determination of the fine structure constant,” Phys. Rev. Lett. 101, 230801 (2008).
[Crossref]

2007 (2)

P. Wolf, P. Lemonde, A. Lambrecht, S. Bize, A. Landragin, and A. Clairon, “From optical lattice clocks to the measurement of forces in the Casimir regime,” Phys. Rev. A 75, 063608 (2007).
[Crossref]

S. Dimopoulos, P. W. Graham, J. M. Hogan, and M. A. Kasevich, “Testing general relativity with atom interferometry,” Phys. Rev. Lett. 98, 111102 (2007).
[Crossref]

2006 (2)

K. Bongs, R. Launay, and M. A. Kasevich, “High-order inertial phase shifts for time domain atom interferometers,” Appl. Phys. B 84, 599–602 (2006).
[Crossref]

B. Dubetsky and M. A. Kasevich, “Atom interferometer as a selective sensor of rotation or gravity,” Phys. Rev. A 74, 023615 (2006).
[Crossref]

2003 (2)

C. Antoine and C. J. Bordé, “Quantum theory of atomic clocks and gravito-inertial sensors: an update,” J. Opt. B 5, S199–S203 (2003).
[Crossref]

T. Aoki, M. Yasuhara, and M. A. Morinaga, “Atomic multiple-wave interferometer phase-shifted by the scalar Aharanov–Bohm effect,” Phys. Rev. A 67, 053602 (2003).
[Crossref]

2002 (2)

C. J. Bordé, “Atomic clocks and inertial sensors,” Metrologia 39, 435–463 (2002).
[Crossref]

J. M. McGuirk, G. T. Foster, J. B. Fixler, M. J. Snadden, and M. A. Kasevich, “Sensitive absolute-gravity gradiometry using atom interferometry,” Phys. Rev. A 65, 033608 (2002).
[Crossref]

2001 (2)

T. Trebst, T. Binnewies, J. Helmcke, and M. F. Riehle, “Suppression of spurious phase shifts in an optical frequency standard,” IEEE Trans. Instrum. Meas. 50, 535–538 (2001).
[Crossref]

T. Aoki, T. Shinohara, and M. A. Morinaga, “High-finesse atomic multiple-beam interferometer comprised of copropagating stimulated Raman-pulse fields,” Phys. Rev. A 63, 063611 (2001).
[Crossref]

1999 (2)

P. Wolf and P. Tourrenc, “Gravimetry using atom interferometers: some systematic effects,” Phys. Lett. A 251, 241–246 (1999).
[Crossref]

A. Peters, K. Y. Chung, and S. Chu, “Measurement of gravitational acceleration by dropping atoms,” Nature 400, 849–852 (1999).
[Crossref]

1997 (1)

T. L. Gustavson, P. Bouyer, and M. A. Kasevich, “Precision rotation measurements with an atom interferometer gyroscope,” Phys. Rev. Lett. 78, 2046–2049 (1997).
[Crossref]

1995 (1)

T. M. Niebauer, G. S. Sasagawa, J. E. Faller, R. Hilt, and F. Klopping, “A new generation of absolute gravimeters,” Metrologia 32, 159–180 (1995).
[Crossref]

1994 (1)

P. Storey and C. Cohen-Tannoudji, “The Feynman path-integral approach to atomic interferometry: a tutorial,” J. Phys. II 4, 1999–2027 (1994).
[Crossref]

1993 (1)

D. S. Weiss, B. C. Young, and S. Chu, “Precision measurement of the photon recoil of an atom using atom interferometry,” Phys. Rev. Lett. 70, 2706–2709 (1993).
[Crossref]

1991 (2)

M. Kasevich and S. Chu, “Atomic interferometry using stimulated Raman transitions,” Phys. Rev. Lett. 67, 181–184 (1991).
[Crossref]

F. Riehle, T. Kisters, A. Witte, J. Helmcke, and C. J. Borde, “Optical Ramsey spectroscopy in a rotating frame—Sagnac effect in a matter-wave interferometer,” Phys. Rev. Lett. 67, 177–180 (1991).
[Crossref]

1989 (1)

C. J. Bordé, “Atomic interferometry with internal state labelling,” Phys. Lett. A 140, 10–12 (1989).
[Crossref]

Altin, P. A.

J. E. Debs, P. A. Altin, T. H. Barter, D. Doring, G. R. Dennis, G. McDonald, R. P. Anderson, J. D. Close, and N. P. Robins, “Cold-atom gravimetry with a Bose–Einstein condensate,” Phys. Rev. A 84, 033610 (2011).
[Crossref]

Anderson, R. P.

J. E. Debs, P. A. Altin, T. H. Barter, D. Doring, G. R. Dennis, G. McDonald, R. P. Anderson, J. D. Close, and N. P. Robins, “Cold-atom gravimetry with a Bose–Einstein condensate,” Phys. Rev. A 84, 033610 (2011).
[Crossref]

Andia, M.

M. Andia, R. Jannin, F. Nez, F. Biraben, S. Guellati-Khélifa, and P. Cladé, “Compact atomic gravimeter based on a pulsed and accelerated optical lattice,” Phys. Rev. A 88, 031605 (2013).
[Crossref]

Antoine, C.

C. Antoine and C. J. Bordé, “Quantum theory of atomic clocks and gravito-inertial sensors: an update,” J. Opt. B 5, S199–S203 (2003).
[Crossref]

Aoki, T.

T. Aoki, M. Yasuhara, and M. A. Morinaga, “Atomic multiple-wave interferometer phase-shifted by the scalar Aharanov–Bohm effect,” Phys. Rev. A 67, 053602 (2003).
[Crossref]

T. Aoki, T. Shinohara, and M. A. Morinaga, “High-finesse atomic multiple-beam interferometer comprised of copropagating stimulated Raman-pulse fields,” Phys. Rev. A 63, 063611 (2001).
[Crossref]

Barter, T. H.

J. E. Debs, P. A. Altin, T. H. Barter, D. Doring, G. R. Dennis, G. McDonald, R. P. Anderson, J. D. Close, and N. P. Robins, “Cold-atom gravimetry with a Bose–Einstein condensate,” Phys. Rev. A 84, 033610 (2011).
[Crossref]

Berman, P.

P. Berman, Atom Interferometry (Academic, 1996).

Bertoldi, A.

W. Chaibi, R. Geiger, B. Canuel, A. Bertoldi, A. Landragin, and P. Bouyer, “Low frequency gravitational wave detection with ground-based atom interferometer arrays,” Phys. Rev. D 93, 021101(R) (2016).
[Crossref]

Bidel, Y.

A. Bonnin, N. Zahzam, Y. Bidel, and A. Bresson, “Simultaneous dual-species matter-wave accelerometer,” Phys. Rev. A 88, 043615 (2013).
[Crossref]

Y. Bidel, O. Carraz, R. Charrière, M. Cadoret, N. Zahzam, and A. Bresson, “Compact cold atom gravimeter for field applications,” Appl. Phys. Lett 102, 144107 (2013).
[Crossref]

R. Charriére, M. Cadoret, N. Zahzam, Y. Bidel, and A. Bresson, “Local gravity measurement with the combination of atom interferometry and Bloch oscillations,” Phys. Rev. A 85, 013639 (2012).
[Crossref]

Binnewies, T.

T. Trebst, T. Binnewies, J. Helmcke, and M. F. Riehle, “Suppression of spurious phase shifts in an optical frequency standard,” IEEE Trans. Instrum. Meas. 50, 535–538 (2001).
[Crossref]

Biraben, F.

M. Andia, R. Jannin, F. Nez, F. Biraben, S. Guellati-Khélifa, and P. Cladé, “Compact atomic gravimeter based on a pulsed and accelerated optical lattice,” Phys. Rev. A 88, 031605 (2013).
[Crossref]

R. Bouchendira, P. Cladé, S. Guellati-Khelifa, F. Nez, and F. Biraben, “New determination of the fine structure constant and test of the quantum electrodynamics,” Phys. Rev. Lett. 106, 080801 (2011).
[Crossref]

M. Cadoret, E. De Mirandes, P. Cladé, S. Guellati-Khelifa, C. Schwob, F. Nez, L. Julien, and F. Biraben, “Combination of Bloch oscillations with a Ramsey–Bordé interferometer: new determination of the fine structure constant,” Phys. Rev. Lett. 101, 230801 (2008).
[Crossref]

Bize, S.

P. Wolf, P. Lemonde, A. Lambrecht, S. Bize, A. Landragin, and A. Clairon, “From optical lattice clocks to the measurement of forces in the Casimir regime,” Phys. Rev. A 75, 063608 (2007).
[Crossref]

Bodart, Q.

F. Sorrentino, Q. Bodart, L. Cacciapuoti, Y. H. Lien, M. Prevedelli, G. Rosi, L. Salvi, and G. M. Tino, “Sensitivity limits of a Raman atom interferometer as a gravity gradiometer,” Phys. Rev. A 89, 023607 (2014).
[Crossref]

Bongs, K.

K. Bongs, R. Launay, and M. A. Kasevich, “High-order inertial phase shifts for time domain atom interferometers,” Appl. Phys. B 84, 599–602 (2006).
[Crossref]

Bonnin, A.

A. Bonnin, N. Zahzam, Y. Bidel, and A. Bresson, “Simultaneous dual-species matter-wave accelerometer,” Phys. Rev. A 88, 043615 (2013).
[Crossref]

Borde, C. J.

F. Riehle, T. Kisters, A. Witte, J. Helmcke, and C. J. Borde, “Optical Ramsey spectroscopy in a rotating frame—Sagnac effect in a matter-wave interferometer,” Phys. Rev. Lett. 67, 177–180 (1991).
[Crossref]

Bordé, C. J.

C. Antoine and C. J. Bordé, “Quantum theory of atomic clocks and gravito-inertial sensors: an update,” J. Opt. B 5, S199–S203 (2003).
[Crossref]

C. J. Bordé, “Atomic clocks and inertial sensors,” Metrologia 39, 435–463 (2002).
[Crossref]

C. J. Bordé, “Atomic interferometry with internal state labelling,” Phys. Lett. A 140, 10–12 (1989).
[Crossref]

C. J. Bordé, “Propagation of laser beams and of atomic systems,” in Fundamental Systems in Quantum Optics, J. Dalibard, J.-M. Raimond, and J. Zinn-Justin, eds., Les Houches Lectures Session LIII 1990 (Elsevier, 1991).

Bouchendira, R.

R. Bouchendira, P. Cladé, S. Guellati-Khelifa, F. Nez, and F. Biraben, “New determination of the fine structure constant and test of the quantum electrodynamics,” Phys. Rev. Lett. 106, 080801 (2011).
[Crossref]

Bouyer, P.

W. Chaibi, R. Geiger, B. Canuel, A. Bertoldi, A. Landragin, and P. Bouyer, “Low frequency gravitational wave detection with ground-based atom interferometer arrays,” Phys. Rev. D 93, 021101(R) (2016).
[Crossref]

T. L. Gustavson, P. Bouyer, and M. A. Kasevich, “Precision rotation measurements with an atom interferometer gyroscope,” Phys. Rev. Lett. 78, 2046–2049 (1997).
[Crossref]

Bresson, A.

A. Bonnin, N. Zahzam, Y. Bidel, and A. Bresson, “Simultaneous dual-species matter-wave accelerometer,” Phys. Rev. A 88, 043615 (2013).
[Crossref]

Y. Bidel, O. Carraz, R. Charrière, M. Cadoret, N. Zahzam, and A. Bresson, “Compact cold atom gravimeter for field applications,” Appl. Phys. Lett 102, 144107 (2013).
[Crossref]

R. Charriére, M. Cadoret, N. Zahzam, Y. Bidel, and A. Bresson, “Local gravity measurement with the combination of atom interferometry and Bloch oscillations,” Phys. Rev. A 85, 013639 (2012).
[Crossref]

Cacciapuoti, L.

F. Sorrentino, Q. Bodart, L. Cacciapuoti, Y. H. Lien, M. Prevedelli, G. Rosi, L. Salvi, and G. M. Tino, “Sensitivity limits of a Raman atom interferometer as a gravity gradiometer,” Phys. Rev. A 89, 023607 (2014).
[Crossref]

G. Rosi, F. Sorrentino, L. Cacciapuoti, M. Prevedelli, and G. M. Tino, “Precision measurement of the Newtonian gravitational constant using cold atoms,” Nature 510, 518–521 (2014).
[Crossref]

Cadoret, M.

Y. Bidel, O. Carraz, R. Charrière, M. Cadoret, N. Zahzam, and A. Bresson, “Compact cold atom gravimeter for field applications,” Appl. Phys. Lett 102, 144107 (2013).
[Crossref]

R. Charriére, M. Cadoret, N. Zahzam, Y. Bidel, and A. Bresson, “Local gravity measurement with the combination of atom interferometry and Bloch oscillations,” Phys. Rev. A 85, 013639 (2012).
[Crossref]

M. Cadoret, E. De Mirandes, P. Cladé, S. Guellati-Khelifa, C. Schwob, F. Nez, L. Julien, and F. Biraben, “Combination of Bloch oscillations with a Ramsey–Bordé interferometer: new determination of the fine structure constant,” Phys. Rev. Lett. 101, 230801 (2008).
[Crossref]

Canuel, B.

W. Chaibi, R. Geiger, B. Canuel, A. Bertoldi, A. Landragin, and P. Bouyer, “Low frequency gravitational wave detection with ground-based atom interferometer arrays,” Phys. Rev. D 93, 021101(R) (2016).
[Crossref]

Carraz, O.

O. Carraz, C. Siemes, L. Massotti, R. Haagmans, and P. Silvestrin, “A spaceborne gravity gradiometer concept based on cold atom interferometers for measuring Earth’s gravity field,” Microgravity Sci. Technol. 26, 139–145 (2014).
[Crossref]

Y. Bidel, O. Carraz, R. Charrière, M. Cadoret, N. Zahzam, and A. Bresson, “Compact cold atom gravimeter for field applications,” Appl. Phys. Lett 102, 144107 (2013).
[Crossref]

Chaibi, W.

W. Chaibi, R. Geiger, B. Canuel, A. Bertoldi, A. Landragin, and P. Bouyer, “Low frequency gravitational wave detection with ground-based atom interferometer arrays,” Phys. Rev. D 93, 021101(R) (2016).
[Crossref]

Charriére, R.

R. Charriére, M. Cadoret, N. Zahzam, Y. Bidel, and A. Bresson, “Local gravity measurement with the combination of atom interferometry and Bloch oscillations,” Phys. Rev. A 85, 013639 (2012).
[Crossref]

Charrière, R.

Y. Bidel, O. Carraz, R. Charrière, M. Cadoret, N. Zahzam, and A. Bresson, “Compact cold atom gravimeter for field applications,” Appl. Phys. Lett 102, 144107 (2013).
[Crossref]

Chiow, S.-W.

S.-W. Chiow, S. Herrmann, S. Chu, and H. Muller, “Noise-immune conjugate large-area atom interferometers,” Phys. Rev. Lett. 103, 050402 (2011).
[Crossref]

H. Müller, S.-W. Chiow, Q. Long, S. Herrmann, and S. Chu, “Atom interferometry with up to 24-photon-momentum-transfer beam splitters,” Phys. Rev. Lett. 100, 180405 (2008).
[Crossref]

Chu, S.

S.-W. Chiow, S. Herrmann, S. Chu, and H. Muller, “Noise-immune conjugate large-area atom interferometers,” Phys. Rev. Lett. 103, 050402 (2011).
[Crossref]

H. Müller, S.-W. Chiow, Q. Long, S. Herrmann, and S. Chu, “Atom interferometry with up to 24-photon-momentum-transfer beam splitters,” Phys. Rev. Lett. 100, 180405 (2008).
[Crossref]

A. Peters, K. Y. Chung, and S. Chu, “Measurement of gravitational acceleration by dropping atoms,” Nature 400, 849–852 (1999).
[Crossref]

D. S. Weiss, B. C. Young, and S. Chu, “Precision measurement of the photon recoil of an atom using atom interferometry,” Phys. Rev. Lett. 70, 2706–2709 (1993).
[Crossref]

M. Kasevich and S. Chu, “Atomic interferometry using stimulated Raman transitions,” Phys. Rev. Lett. 67, 181–184 (1991).
[Crossref]

Chung, K. Y.

A. Peters, K. Y. Chung, and S. Chu, “Measurement of gravitational acceleration by dropping atoms,” Nature 400, 849–852 (1999).
[Crossref]

Cladé, P.

M. Andia, R. Jannin, F. Nez, F. Biraben, S. Guellati-Khélifa, and P. Cladé, “Compact atomic gravimeter based on a pulsed and accelerated optical lattice,” Phys. Rev. A 88, 031605 (2013).
[Crossref]

R. Bouchendira, P. Cladé, S. Guellati-Khelifa, F. Nez, and F. Biraben, “New determination of the fine structure constant and test of the quantum electrodynamics,” Phys. Rev. Lett. 106, 080801 (2011).
[Crossref]

M. Cadoret, E. De Mirandes, P. Cladé, S. Guellati-Khelifa, C. Schwob, F. Nez, L. Julien, and F. Biraben, “Combination of Bloch oscillations with a Ramsey–Bordé interferometer: new determination of the fine structure constant,” Phys. Rev. Lett. 101, 230801 (2008).
[Crossref]

Clairon, A.

J. L. Gouët, T. Mehlstäubler, J. Kim, S. Merlet, A. Clairon, A. Landragin, and F. P. DosSantos, “Limits to the sensitivity of a low noise compact atomic gravimeter,” Appl. Phys. B 92, 133–144 (2008).
[Crossref]

P. Wolf, P. Lemonde, A. Lambrecht, S. Bize, A. Landragin, and A. Clairon, “From optical lattice clocks to the measurement of forces in the Casimir regime,” Phys. Rev. A 75, 063608 (2007).
[Crossref]

Close, J. D.

J. E. Debs, P. A. Altin, T. H. Barter, D. Doring, G. R. Dennis, G. McDonald, R. P. Anderson, J. D. Close, and N. P. Robins, “Cold-atom gravimetry with a Bose–Einstein condensate,” Phys. Rev. A 84, 033610 (2011).
[Crossref]

Cohen-Tannoudji, C.

P. Storey and C. Cohen-Tannoudji, “The Feynman path-integral approach to atomic interferometry: a tutorial,” J. Phys. II 4, 1999–2027 (1994).
[Crossref]

De Mirandes, E.

M. Cadoret, E. De Mirandes, P. Cladé, S. Guellati-Khelifa, C. Schwob, F. Nez, L. Julien, and F. Biraben, “Combination of Bloch oscillations with a Ramsey–Bordé interferometer: new determination of the fine structure constant,” Phys. Rev. Lett. 101, 230801 (2008).
[Crossref]

Debs, J. E.

J. E. Debs, P. A. Altin, T. H. Barter, D. Doring, G. R. Dennis, G. McDonald, R. P. Anderson, J. D. Close, and N. P. Robins, “Cold-atom gravimetry with a Bose–Einstein condensate,” Phys. Rev. A 84, 033610 (2011).
[Crossref]

Dennis, G. R.

J. E. Debs, P. A. Altin, T. H. Barter, D. Doring, G. R. Dennis, G. McDonald, R. P. Anderson, J. D. Close, and N. P. Robins, “Cold-atom gravimetry with a Bose–Einstein condensate,” Phys. Rev. A 84, 033610 (2011).
[Crossref]

Dimopoulos, S.

S. Dimopoulos, P. W. Graham, J. M. Hogan, M. A. Kasevich, and S. Rajendran, “Gravitational wave detection with atom interferometry,” Phys. Lett. B 678, 37–40 (2009).
[Crossref]

S. Dimopoulos, P. W. Graham, J. M. Hogan, and M. A. Kasevich, “Testing general relativity with atom interferometry,” Phys. Rev. Lett. 98, 111102 (2007).
[Crossref]

Doring, D.

J. E. Debs, P. A. Altin, T. H. Barter, D. Doring, G. R. Dennis, G. McDonald, R. P. Anderson, J. D. Close, and N. P. Robins, “Cold-atom gravimetry with a Bose–Einstein condensate,” Phys. Rev. A 84, 033610 (2011).
[Crossref]

DosSantos, F. P.

J. L. Gouët, T. Mehlstäubler, J. Kim, S. Merlet, A. Clairon, A. Landragin, and F. P. DosSantos, “Limits to the sensitivity of a low noise compact atomic gravimeter,” Appl. Phys. B 92, 133–144 (2008).
[Crossref]

Dubetsky, B.

B. Dubetsky and M. A. Kasevich, “Atom interferometer as a selective sensor of rotation or gravity,” Phys. Rev. A 74, 023615 (2006).
[Crossref]

Dutta, I.

I. Dutta, D. Savoie, B. Fang, B. Venon, C. L. Garrido Alzar, R. Geiger, and A. Landragin, “Continuous cold-atom inertial sensor with 1nrad/s rotation stability,” Phys. Rev. Lett. 116, 183003 (2016).
[Crossref]

Faller, J. E.

T. M. Niebauer, G. S. Sasagawa, J. E. Faller, R. Hilt, and F. Klopping, “A new generation of absolute gravimeters,” Metrologia 32, 159–180 (1995).
[Crossref]

Fang, B.

I. Dutta, D. Savoie, B. Fang, B. Venon, C. L. Garrido Alzar, R. Geiger, and A. Landragin, “Continuous cold-atom inertial sensor with 1nrad/s rotation stability,” Phys. Rev. Lett. 116, 183003 (2016).
[Crossref]

Fixler, J. B.

J. M. McGuirk, G. T. Foster, J. B. Fixler, M. J. Snadden, and M. A. Kasevich, “Sensitive absolute-gravity gradiometry using atom interferometry,” Phys. Rev. A 65, 033608 (2002).
[Crossref]

Foster, G. T.

J. M. McGuirk, G. T. Foster, J. B. Fixler, M. J. Snadden, and M. A. Kasevich, “Sensitive absolute-gravity gradiometry using atom interferometry,” Phys. Rev. A 65, 033608 (2002).
[Crossref]

Garrido Alzar, C. L.

I. Dutta, D. Savoie, B. Fang, B. Venon, C. L. Garrido Alzar, R. Geiger, and A. Landragin, “Continuous cold-atom inertial sensor with 1nrad/s rotation stability,” Phys. Rev. Lett. 116, 183003 (2016).
[Crossref]

Gauguet, A.

T. Lévéque, A. Gauguet, F. Michaud, F. Pereira Dos Santos, and A. Landragin, “Enhancing the area of a Raman atom interferometer using a versatile double-diffraction technique,” Phys. Rev. Lett. 103, 080405 (2009).
[Crossref]

Geiger, R.

I. Dutta, D. Savoie, B. Fang, B. Venon, C. L. Garrido Alzar, R. Geiger, and A. Landragin, “Continuous cold-atom inertial sensor with 1nrad/s rotation stability,” Phys. Rev. Lett. 116, 183003 (2016).
[Crossref]

W. Chaibi, R. Geiger, B. Canuel, A. Bertoldi, A. Landragin, and P. Bouyer, “Low frequency gravitational wave detection with ground-based atom interferometer arrays,” Phys. Rev. D 93, 021101(R) (2016).
[Crossref]

Gouët, J. L.

J. L. Gouët, T. Mehlstäubler, J. Kim, S. Merlet, A. Clairon, A. Landragin, and F. P. DosSantos, “Limits to the sensitivity of a low noise compact atomic gravimeter,” Appl. Phys. B 92, 133–144 (2008).
[Crossref]

Graham, P. W.

S. Dimopoulos, P. W. Graham, J. M. Hogan, M. A. Kasevich, and S. Rajendran, “Gravitational wave detection with atom interferometry,” Phys. Lett. B 678, 37–40 (2009).
[Crossref]

S. Dimopoulos, P. W. Graham, J. M. Hogan, and M. A. Kasevich, “Testing general relativity with atom interferometry,” Phys. Rev. Lett. 98, 111102 (2007).
[Crossref]

Guellati-Khelifa, S.

R. Bouchendira, P. Cladé, S. Guellati-Khelifa, F. Nez, and F. Biraben, “New determination of the fine structure constant and test of the quantum electrodynamics,” Phys. Rev. Lett. 106, 080801 (2011).
[Crossref]

M. Cadoret, E. De Mirandes, P. Cladé, S. Guellati-Khelifa, C. Schwob, F. Nez, L. Julien, and F. Biraben, “Combination of Bloch oscillations with a Ramsey–Bordé interferometer: new determination of the fine structure constant,” Phys. Rev. Lett. 101, 230801 (2008).
[Crossref]

Guellati-Khélifa, S.

M. Andia, R. Jannin, F. Nez, F. Biraben, S. Guellati-Khélifa, and P. Cladé, “Compact atomic gravimeter based on a pulsed and accelerated optical lattice,” Phys. Rev. A 88, 031605 (2013).
[Crossref]

Gustavson, T. L.

T. L. Gustavson, P. Bouyer, and M. A. Kasevich, “Precision rotation measurements with an atom interferometer gyroscope,” Phys. Rev. Lett. 78, 2046–2049 (1997).
[Crossref]

Haagmans, R.

O. Carraz, C. Siemes, L. Massotti, R. Haagmans, and P. Silvestrin, “A spaceborne gravity gradiometer concept based on cold atom interferometers for measuring Earth’s gravity field,” Microgravity Sci. Technol. 26, 139–145 (2014).
[Crossref]

Helmcke, J.

T. Trebst, T. Binnewies, J. Helmcke, and M. F. Riehle, “Suppression of spurious phase shifts in an optical frequency standard,” IEEE Trans. Instrum. Meas. 50, 535–538 (2001).
[Crossref]

F. Riehle, T. Kisters, A. Witte, J. Helmcke, and C. J. Borde, “Optical Ramsey spectroscopy in a rotating frame—Sagnac effect in a matter-wave interferometer,” Phys. Rev. Lett. 67, 177–180 (1991).
[Crossref]

Herrmann, S.

S.-W. Chiow, S. Herrmann, S. Chu, and H. Muller, “Noise-immune conjugate large-area atom interferometers,” Phys. Rev. Lett. 103, 050402 (2011).
[Crossref]

H. Müller, S.-W. Chiow, Q. Long, S. Herrmann, and S. Chu, “Atom interferometry with up to 24-photon-momentum-transfer beam splitters,” Phys. Rev. Lett. 100, 180405 (2008).
[Crossref]

Hilt, R.

T. M. Niebauer, G. S. Sasagawa, J. E. Faller, R. Hilt, and F. Klopping, “A new generation of absolute gravimeters,” Metrologia 32, 159–180 (1995).
[Crossref]

Hogan, J. M.

S. Dimopoulos, P. W. Graham, J. M. Hogan, M. A. Kasevich, and S. Rajendran, “Gravitational wave detection with atom interferometry,” Phys. Lett. B 678, 37–40 (2009).
[Crossref]

S. Dimopoulos, P. W. Graham, J. M. Hogan, and M. A. Kasevich, “Testing general relativity with atom interferometry,” Phys. Rev. Lett. 98, 111102 (2007).
[Crossref]

Jannin, R.

M. Andia, R. Jannin, F. Nez, F. Biraben, S. Guellati-Khélifa, and P. Cladé, “Compact atomic gravimeter based on a pulsed and accelerated optical lattice,” Phys. Rev. A 88, 031605 (2013).
[Crossref]

Julien, L.

M. Cadoret, E. De Mirandes, P. Cladé, S. Guellati-Khelifa, C. Schwob, F. Nez, L. Julien, and F. Biraben, “Combination of Bloch oscillations with a Ramsey–Bordé interferometer: new determination of the fine structure constant,” Phys. Rev. Lett. 101, 230801 (2008).
[Crossref]

Kasevich, M.

M. Kasevich and S. Chu, “Atomic interferometry using stimulated Raman transitions,” Phys. Rev. Lett. 67, 181–184 (1991).
[Crossref]

Kasevich, M. A.

J. K. Stockton, K. Takase, and M. A. Kasevich, “Absolute geodetic rotation measurement using atom interferometry,” Phys. Rev. Lett. 107, 133001 (2011).
[Crossref]

S. Dimopoulos, P. W. Graham, J. M. Hogan, M. A. Kasevich, and S. Rajendran, “Gravitational wave detection with atom interferometry,” Phys. Lett. B 678, 37–40 (2009).
[Crossref]

S. Dimopoulos, P. W. Graham, J. M. Hogan, and M. A. Kasevich, “Testing general relativity with atom interferometry,” Phys. Rev. Lett. 98, 111102 (2007).
[Crossref]

K. Bongs, R. Launay, and M. A. Kasevich, “High-order inertial phase shifts for time domain atom interferometers,” Appl. Phys. B 84, 599–602 (2006).
[Crossref]

B. Dubetsky and M. A. Kasevich, “Atom interferometer as a selective sensor of rotation or gravity,” Phys. Rev. A 74, 023615 (2006).
[Crossref]

J. M. McGuirk, G. T. Foster, J. B. Fixler, M. J. Snadden, and M. A. Kasevich, “Sensitive absolute-gravity gradiometry using atom interferometry,” Phys. Rev. A 65, 033608 (2002).
[Crossref]

T. L. Gustavson, P. Bouyer, and M. A. Kasevich, “Precision rotation measurements with an atom interferometer gyroscope,” Phys. Rev. Lett. 78, 2046–2049 (1997).
[Crossref]

Kim, J.

J. L. Gouët, T. Mehlstäubler, J. Kim, S. Merlet, A. Clairon, A. Landragin, and F. P. DosSantos, “Limits to the sensitivity of a low noise compact atomic gravimeter,” Appl. Phys. B 92, 133–144 (2008).
[Crossref]

Kisters, T.

F. Riehle, T. Kisters, A. Witte, J. Helmcke, and C. J. Borde, “Optical Ramsey spectroscopy in a rotating frame—Sagnac effect in a matter-wave interferometer,” Phys. Rev. Lett. 67, 177–180 (1991).
[Crossref]

Klopping, F.

T. M. Niebauer, G. S. Sasagawa, J. E. Faller, R. Hilt, and F. Klopping, “A new generation of absolute gravimeters,” Metrologia 32, 159–180 (1995).
[Crossref]

Lambrecht, A.

P. Wolf, P. Lemonde, A. Lambrecht, S. Bize, A. Landragin, and A. Clairon, “From optical lattice clocks to the measurement of forces in the Casimir regime,” Phys. Rev. A 75, 063608 (2007).
[Crossref]

Landragin, A.

I. Dutta, D. Savoie, B. Fang, B. Venon, C. L. Garrido Alzar, R. Geiger, and A. Landragin, “Continuous cold-atom inertial sensor with 1nrad/s rotation stability,” Phys. Rev. Lett. 116, 183003 (2016).
[Crossref]

W. Chaibi, R. Geiger, B. Canuel, A. Bertoldi, A. Landragin, and P. Bouyer, “Low frequency gravitational wave detection with ground-based atom interferometer arrays,” Phys. Rev. D 93, 021101(R) (2016).
[Crossref]

T. Lévéque, A. Gauguet, F. Michaud, F. Pereira Dos Santos, and A. Landragin, “Enhancing the area of a Raman atom interferometer using a versatile double-diffraction technique,” Phys. Rev. Lett. 103, 080405 (2009).
[Crossref]

J. L. Gouët, T. Mehlstäubler, J. Kim, S. Merlet, A. Clairon, A. Landragin, and F. P. DosSantos, “Limits to the sensitivity of a low noise compact atomic gravimeter,” Appl. Phys. B 92, 133–144 (2008).
[Crossref]

P. Wolf, P. Lemonde, A. Lambrecht, S. Bize, A. Landragin, and A. Clairon, “From optical lattice clocks to the measurement of forces in the Casimir regime,” Phys. Rev. A 75, 063608 (2007).
[Crossref]

Launay, R.

K. Bongs, R. Launay, and M. A. Kasevich, “High-order inertial phase shifts for time domain atom interferometers,” Appl. Phys. B 84, 599–602 (2006).
[Crossref]

Lemonde, P.

P. Wolf, P. Lemonde, A. Lambrecht, S. Bize, A. Landragin, and A. Clairon, “From optical lattice clocks to the measurement of forces in the Casimir regime,” Phys. Rev. A 75, 063608 (2007).
[Crossref]

Lévéque, T.

T. Lévéque, A. Gauguet, F. Michaud, F. Pereira Dos Santos, and A. Landragin, “Enhancing the area of a Raman atom interferometer using a versatile double-diffraction technique,” Phys. Rev. Lett. 103, 080405 (2009).
[Crossref]

Lien, Y. H.

F. Sorrentino, Q. Bodart, L. Cacciapuoti, Y. H. Lien, M. Prevedelli, G. Rosi, L. Salvi, and G. M. Tino, “Sensitivity limits of a Raman atom interferometer as a gravity gradiometer,” Phys. Rev. A 89, 023607 (2014).
[Crossref]

Long, Q.

H. Müller, S.-W. Chiow, Q. Long, S. Herrmann, and S. Chu, “Atom interferometry with up to 24-photon-momentum-transfer beam splitters,” Phys. Rev. Lett. 100, 180405 (2008).
[Crossref]

Massotti, L.

O. Carraz, C. Siemes, L. Massotti, R. Haagmans, and P. Silvestrin, “A spaceborne gravity gradiometer concept based on cold atom interferometers for measuring Earth’s gravity field,” Microgravity Sci. Technol. 26, 139–145 (2014).
[Crossref]

McDonald, G.

J. E. Debs, P. A. Altin, T. H. Barter, D. Doring, G. R. Dennis, G. McDonald, R. P. Anderson, J. D. Close, and N. P. Robins, “Cold-atom gravimetry with a Bose–Einstein condensate,” Phys. Rev. A 84, 033610 (2011).
[Crossref]

McGuirk, J. M.

J. M. McGuirk, G. T. Foster, J. B. Fixler, M. J. Snadden, and M. A. Kasevich, “Sensitive absolute-gravity gradiometry using atom interferometry,” Phys. Rev. A 65, 033608 (2002).
[Crossref]

Mehlstäubler, T.

J. L. Gouët, T. Mehlstäubler, J. Kim, S. Merlet, A. Clairon, A. Landragin, and F. P. DosSantos, “Limits to the sensitivity of a low noise compact atomic gravimeter,” Appl. Phys. B 92, 133–144 (2008).
[Crossref]

Merlet, S.

J. L. Gouët, T. Mehlstäubler, J. Kim, S. Merlet, A. Clairon, A. Landragin, and F. P. DosSantos, “Limits to the sensitivity of a low noise compact atomic gravimeter,” Appl. Phys. B 92, 133–144 (2008).
[Crossref]

Michaud, F.

T. Lévéque, A. Gauguet, F. Michaud, F. Pereira Dos Santos, and A. Landragin, “Enhancing the area of a Raman atom interferometer using a versatile double-diffraction technique,” Phys. Rev. Lett. 103, 080405 (2009).
[Crossref]

Morinaga, M. A.

T. Aoki, M. Yasuhara, and M. A. Morinaga, “Atomic multiple-wave interferometer phase-shifted by the scalar Aharanov–Bohm effect,” Phys. Rev. A 67, 053602 (2003).
[Crossref]

T. Aoki, T. Shinohara, and M. A. Morinaga, “High-finesse atomic multiple-beam interferometer comprised of copropagating stimulated Raman-pulse fields,” Phys. Rev. A 63, 063611 (2001).
[Crossref]

Muller, H.

S.-W. Chiow, S. Herrmann, S. Chu, and H. Muller, “Noise-immune conjugate large-area atom interferometers,” Phys. Rev. Lett. 103, 050402 (2011).
[Crossref]

Müller, H.

H. Müller, S.-W. Chiow, Q. Long, S. Herrmann, and S. Chu, “Atom interferometry with up to 24-photon-momentum-transfer beam splitters,” Phys. Rev. Lett. 100, 180405 (2008).
[Crossref]

Nez, F.

M. Andia, R. Jannin, F. Nez, F. Biraben, S. Guellati-Khélifa, and P. Cladé, “Compact atomic gravimeter based on a pulsed and accelerated optical lattice,” Phys. Rev. A 88, 031605 (2013).
[Crossref]

R. Bouchendira, P. Cladé, S. Guellati-Khelifa, F. Nez, and F. Biraben, “New determination of the fine structure constant and test of the quantum electrodynamics,” Phys. Rev. Lett. 106, 080801 (2011).
[Crossref]

M. Cadoret, E. De Mirandes, P. Cladé, S. Guellati-Khelifa, C. Schwob, F. Nez, L. Julien, and F. Biraben, “Combination of Bloch oscillations with a Ramsey–Bordé interferometer: new determination of the fine structure constant,” Phys. Rev. Lett. 101, 230801 (2008).
[Crossref]

Niebauer, T. M.

T. M. Niebauer, G. S. Sasagawa, J. E. Faller, R. Hilt, and F. Klopping, “A new generation of absolute gravimeters,” Metrologia 32, 159–180 (1995).
[Crossref]

Pereira Dos Santos, F.

T. Lévéque, A. Gauguet, F. Michaud, F. Pereira Dos Santos, and A. Landragin, “Enhancing the area of a Raman atom interferometer using a versatile double-diffraction technique,” Phys. Rev. Lett. 103, 080405 (2009).
[Crossref]

Peters, A.

A. Peters, K. Y. Chung, and S. Chu, “Measurement of gravitational acceleration by dropping atoms,” Nature 400, 849–852 (1999).
[Crossref]

Prevedelli, M.

G. Rosi, F. Sorrentino, L. Cacciapuoti, M. Prevedelli, and G. M. Tino, “Precision measurement of the Newtonian gravitational constant using cold atoms,” Nature 510, 518–521 (2014).
[Crossref]

F. Sorrentino, Q. Bodart, L. Cacciapuoti, Y. H. Lien, M. Prevedelli, G. Rosi, L. Salvi, and G. M. Tino, “Sensitivity limits of a Raman atom interferometer as a gravity gradiometer,” Phys. Rev. A 89, 023607 (2014).
[Crossref]

Rajendran, S.

S. Dimopoulos, P. W. Graham, J. M. Hogan, M. A. Kasevich, and S. Rajendran, “Gravitational wave detection with atom interferometry,” Phys. Lett. B 678, 37–40 (2009).
[Crossref]

Riehle, F.

F. Riehle, T. Kisters, A. Witte, J. Helmcke, and C. J. Borde, “Optical Ramsey spectroscopy in a rotating frame—Sagnac effect in a matter-wave interferometer,” Phys. Rev. Lett. 67, 177–180 (1991).
[Crossref]

Riehle, M. F.

T. Trebst, T. Binnewies, J. Helmcke, and M. F. Riehle, “Suppression of spurious phase shifts in an optical frequency standard,” IEEE Trans. Instrum. Meas. 50, 535–538 (2001).
[Crossref]

Robins, N. P.

J. E. Debs, P. A. Altin, T. H. Barter, D. Doring, G. R. Dennis, G. McDonald, R. P. Anderson, J. D. Close, and N. P. Robins, “Cold-atom gravimetry with a Bose–Einstein condensate,” Phys. Rev. A 84, 033610 (2011).
[Crossref]

Rosi, G.

G. Rosi, F. Sorrentino, L. Cacciapuoti, M. Prevedelli, and G. M. Tino, “Precision measurement of the Newtonian gravitational constant using cold atoms,” Nature 510, 518–521 (2014).
[Crossref]

F. Sorrentino, Q. Bodart, L. Cacciapuoti, Y. H. Lien, M. Prevedelli, G. Rosi, L. Salvi, and G. M. Tino, “Sensitivity limits of a Raman atom interferometer as a gravity gradiometer,” Phys. Rev. A 89, 023607 (2014).
[Crossref]

Salvi, L.

F. Sorrentino, Q. Bodart, L. Cacciapuoti, Y. H. Lien, M. Prevedelli, G. Rosi, L. Salvi, and G. M. Tino, “Sensitivity limits of a Raman atom interferometer as a gravity gradiometer,” Phys. Rev. A 89, 023607 (2014).
[Crossref]

Sasagawa, G. S.

T. M. Niebauer, G. S. Sasagawa, J. E. Faller, R. Hilt, and F. Klopping, “A new generation of absolute gravimeters,” Metrologia 32, 159–180 (1995).
[Crossref]

Savoie, D.

I. Dutta, D. Savoie, B. Fang, B. Venon, C. L. Garrido Alzar, R. Geiger, and A. Landragin, “Continuous cold-atom inertial sensor with 1nrad/s rotation stability,” Phys. Rev. Lett. 116, 183003 (2016).
[Crossref]

Schwob, C.

M. Cadoret, E. De Mirandes, P. Cladé, S. Guellati-Khelifa, C. Schwob, F. Nez, L. Julien, and F. Biraben, “Combination of Bloch oscillations with a Ramsey–Bordé interferometer: new determination of the fine structure constant,” Phys. Rev. Lett. 101, 230801 (2008).
[Crossref]

Shinohara, T.

T. Aoki, T. Shinohara, and M. A. Morinaga, “High-finesse atomic multiple-beam interferometer comprised of copropagating stimulated Raman-pulse fields,” Phys. Rev. A 63, 063611 (2001).
[Crossref]

Siemes, C.

O. Carraz, C. Siemes, L. Massotti, R. Haagmans, and P. Silvestrin, “A spaceborne gravity gradiometer concept based on cold atom interferometers for measuring Earth’s gravity field,” Microgravity Sci. Technol. 26, 139–145 (2014).
[Crossref]

Silvestrin, P.

O. Carraz, C. Siemes, L. Massotti, R. Haagmans, and P. Silvestrin, “A spaceborne gravity gradiometer concept based on cold atom interferometers for measuring Earth’s gravity field,” Microgravity Sci. Technol. 26, 139–145 (2014).
[Crossref]

Snadden, M. J.

J. M. McGuirk, G. T. Foster, J. B. Fixler, M. J. Snadden, and M. A. Kasevich, “Sensitive absolute-gravity gradiometry using atom interferometry,” Phys. Rev. A 65, 033608 (2002).
[Crossref]

Sorrentino, F.

F. Sorrentino, Q. Bodart, L. Cacciapuoti, Y. H. Lien, M. Prevedelli, G. Rosi, L. Salvi, and G. M. Tino, “Sensitivity limits of a Raman atom interferometer as a gravity gradiometer,” Phys. Rev. A 89, 023607 (2014).
[Crossref]

G. Rosi, F. Sorrentino, L. Cacciapuoti, M. Prevedelli, and G. M. Tino, “Precision measurement of the Newtonian gravitational constant using cold atoms,” Nature 510, 518–521 (2014).
[Crossref]

Stockton, J. K.

J. K. Stockton, K. Takase, and M. A. Kasevich, “Absolute geodetic rotation measurement using atom interferometry,” Phys. Rev. Lett. 107, 133001 (2011).
[Crossref]

Storey, P.

P. Storey and C. Cohen-Tannoudji, “The Feynman path-integral approach to atomic interferometry: a tutorial,” J. Phys. II 4, 1999–2027 (1994).
[Crossref]

Takase, K.

J. K. Stockton, K. Takase, and M. A. Kasevich, “Absolute geodetic rotation measurement using atom interferometry,” Phys. Rev. Lett. 107, 133001 (2011).
[Crossref]

Tino, G. M.

F. Sorrentino, Q. Bodart, L. Cacciapuoti, Y. H. Lien, M. Prevedelli, G. Rosi, L. Salvi, and G. M. Tino, “Sensitivity limits of a Raman atom interferometer as a gravity gradiometer,” Phys. Rev. A 89, 023607 (2014).
[Crossref]

G. Rosi, F. Sorrentino, L. Cacciapuoti, M. Prevedelli, and G. M. Tino, “Precision measurement of the Newtonian gravitational constant using cold atoms,” Nature 510, 518–521 (2014).
[Crossref]

Tourrenc, P.

P. Wolf and P. Tourrenc, “Gravimetry using atom interferometers: some systematic effects,” Phys. Lett. A 251, 241–246 (1999).
[Crossref]

Trebst, T.

T. Trebst, T. Binnewies, J. Helmcke, and M. F. Riehle, “Suppression of spurious phase shifts in an optical frequency standard,” IEEE Trans. Instrum. Meas. 50, 535–538 (2001).
[Crossref]

Venon, B.

I. Dutta, D. Savoie, B. Fang, B. Venon, C. L. Garrido Alzar, R. Geiger, and A. Landragin, “Continuous cold-atom inertial sensor with 1nrad/s rotation stability,” Phys. Rev. Lett. 116, 183003 (2016).
[Crossref]

Weiss, D. S.

D. S. Weiss, B. C. Young, and S. Chu, “Precision measurement of the photon recoil of an atom using atom interferometry,” Phys. Rev. Lett. 70, 2706–2709 (1993).
[Crossref]

Witte, A.

F. Riehle, T. Kisters, A. Witte, J. Helmcke, and C. J. Borde, “Optical Ramsey spectroscopy in a rotating frame—Sagnac effect in a matter-wave interferometer,” Phys. Rev. Lett. 67, 177–180 (1991).
[Crossref]

Wolf, P.

P. Wolf, P. Lemonde, A. Lambrecht, S. Bize, A. Landragin, and A. Clairon, “From optical lattice clocks to the measurement of forces in the Casimir regime,” Phys. Rev. A 75, 063608 (2007).
[Crossref]

P. Wolf and P. Tourrenc, “Gravimetry using atom interferometers: some systematic effects,” Phys. Lett. A 251, 241–246 (1999).
[Crossref]

Yasuhara, M.

T. Aoki, M. Yasuhara, and M. A. Morinaga, “Atomic multiple-wave interferometer phase-shifted by the scalar Aharanov–Bohm effect,” Phys. Rev. A 67, 053602 (2003).
[Crossref]

Young, B. C.

D. S. Weiss, B. C. Young, and S. Chu, “Precision measurement of the photon recoil of an atom using atom interferometry,” Phys. Rev. Lett. 70, 2706–2709 (1993).
[Crossref]

Zahzam, N.

A. Bonnin, N. Zahzam, Y. Bidel, and A. Bresson, “Simultaneous dual-species matter-wave accelerometer,” Phys. Rev. A 88, 043615 (2013).
[Crossref]

Y. Bidel, O. Carraz, R. Charrière, M. Cadoret, N. Zahzam, and A. Bresson, “Compact cold atom gravimeter for field applications,” Appl. Phys. Lett 102, 144107 (2013).
[Crossref]

R. Charriére, M. Cadoret, N. Zahzam, Y. Bidel, and A. Bresson, “Local gravity measurement with the combination of atom interferometry and Bloch oscillations,” Phys. Rev. A 85, 013639 (2012).
[Crossref]

Appl. Phys. B (2)

J. L. Gouët, T. Mehlstäubler, J. Kim, S. Merlet, A. Clairon, A. Landragin, and F. P. DosSantos, “Limits to the sensitivity of a low noise compact atomic gravimeter,” Appl. Phys. B 92, 133–144 (2008).
[Crossref]

K. Bongs, R. Launay, and M. A. Kasevich, “High-order inertial phase shifts for time domain atom interferometers,” Appl. Phys. B 84, 599–602 (2006).
[Crossref]

Appl. Phys. Lett (1)

Y. Bidel, O. Carraz, R. Charrière, M. Cadoret, N. Zahzam, and A. Bresson, “Compact cold atom gravimeter for field applications,” Appl. Phys. Lett 102, 144107 (2013).
[Crossref]

IEEE Trans. Instrum. Meas. (1)

T. Trebst, T. Binnewies, J. Helmcke, and M. F. Riehle, “Suppression of spurious phase shifts in an optical frequency standard,” IEEE Trans. Instrum. Meas. 50, 535–538 (2001).
[Crossref]

J. Opt. B (1)

C. Antoine and C. J. Bordé, “Quantum theory of atomic clocks and gravito-inertial sensors: an update,” J. Opt. B 5, S199–S203 (2003).
[Crossref]

J. Phys. II (1)

P. Storey and C. Cohen-Tannoudji, “The Feynman path-integral approach to atomic interferometry: a tutorial,” J. Phys. II 4, 1999–2027 (1994).
[Crossref]

Metrologia (2)

T. M. Niebauer, G. S. Sasagawa, J. E. Faller, R. Hilt, and F. Klopping, “A new generation of absolute gravimeters,” Metrologia 32, 159–180 (1995).
[Crossref]

C. J. Bordé, “Atomic clocks and inertial sensors,” Metrologia 39, 435–463 (2002).
[Crossref]

Microgravity Sci. Technol. (1)

O. Carraz, C. Siemes, L. Massotti, R. Haagmans, and P. Silvestrin, “A spaceborne gravity gradiometer concept based on cold atom interferometers for measuring Earth’s gravity field,” Microgravity Sci. Technol. 26, 139–145 (2014).
[Crossref]

Nature (2)

A. Peters, K. Y. Chung, and S. Chu, “Measurement of gravitational acceleration by dropping atoms,” Nature 400, 849–852 (1999).
[Crossref]

G. Rosi, F. Sorrentino, L. Cacciapuoti, M. Prevedelli, and G. M. Tino, “Precision measurement of the Newtonian gravitational constant using cold atoms,” Nature 510, 518–521 (2014).
[Crossref]

Phys. Lett. A (2)

C. J. Bordé, “Atomic interferometry with internal state labelling,” Phys. Lett. A 140, 10–12 (1989).
[Crossref]

P. Wolf and P. Tourrenc, “Gravimetry using atom interferometers: some systematic effects,” Phys. Lett. A 251, 241–246 (1999).
[Crossref]

Phys. Lett. B (1)

S. Dimopoulos, P. W. Graham, J. M. Hogan, M. A. Kasevich, and S. Rajendran, “Gravitational wave detection with atom interferometry,” Phys. Lett. B 678, 37–40 (2009).
[Crossref]

Phys. Rev. A (10)

P. Wolf, P. Lemonde, A. Lambrecht, S. Bize, A. Landragin, and A. Clairon, “From optical lattice clocks to the measurement of forces in the Casimir regime,” Phys. Rev. A 75, 063608 (2007).
[Crossref]

A. Bonnin, N. Zahzam, Y. Bidel, and A. Bresson, “Simultaneous dual-species matter-wave accelerometer,” Phys. Rev. A 88, 043615 (2013).
[Crossref]

B. Dubetsky and M. A. Kasevich, “Atom interferometer as a selective sensor of rotation or gravity,” Phys. Rev. A 74, 023615 (2006).
[Crossref]

J. M. McGuirk, G. T. Foster, J. B. Fixler, M. J. Snadden, and M. A. Kasevich, “Sensitive absolute-gravity gradiometry using atom interferometry,” Phys. Rev. A 65, 033608 (2002).
[Crossref]

F. Sorrentino, Q. Bodart, L. Cacciapuoti, Y. H. Lien, M. Prevedelli, G. Rosi, L. Salvi, and G. M. Tino, “Sensitivity limits of a Raman atom interferometer as a gravity gradiometer,” Phys. Rev. A 89, 023607 (2014).
[Crossref]

J. E. Debs, P. A. Altin, T. H. Barter, D. Doring, G. R. Dennis, G. McDonald, R. P. Anderson, J. D. Close, and N. P. Robins, “Cold-atom gravimetry with a Bose–Einstein condensate,” Phys. Rev. A 84, 033610 (2011).
[Crossref]

T. Aoki, T. Shinohara, and M. A. Morinaga, “High-finesse atomic multiple-beam interferometer comprised of copropagating stimulated Raman-pulse fields,” Phys. Rev. A 63, 063611 (2001).
[Crossref]

T. Aoki, M. Yasuhara, and M. A. Morinaga, “Atomic multiple-wave interferometer phase-shifted by the scalar Aharanov–Bohm effect,” Phys. Rev. A 67, 053602 (2003).
[Crossref]

R. Charriére, M. Cadoret, N. Zahzam, Y. Bidel, and A. Bresson, “Local gravity measurement with the combination of atom interferometry and Bloch oscillations,” Phys. Rev. A 85, 013639 (2012).
[Crossref]

M. Andia, R. Jannin, F. Nez, F. Biraben, S. Guellati-Khélifa, and P. Cladé, “Compact atomic gravimeter based on a pulsed and accelerated optical lattice,” Phys. Rev. A 88, 031605 (2013).
[Crossref]

Phys. Rev. D (1)

W. Chaibi, R. Geiger, B. Canuel, A. Bertoldi, A. Landragin, and P. Bouyer, “Low frequency gravitational wave detection with ground-based atom interferometer arrays,” Phys. Rev. D 93, 021101(R) (2016).
[Crossref]

Phys. Rev. Lett. (12)

T. L. Gustavson, P. Bouyer, and M. A. Kasevich, “Precision rotation measurements with an atom interferometer gyroscope,” Phys. Rev. Lett. 78, 2046–2049 (1997).
[Crossref]

J. K. Stockton, K. Takase, and M. A. Kasevich, “Absolute geodetic rotation measurement using atom interferometry,” Phys. Rev. Lett. 107, 133001 (2011).
[Crossref]

I. Dutta, D. Savoie, B. Fang, B. Venon, C. L. Garrido Alzar, R. Geiger, and A. Landragin, “Continuous cold-atom inertial sensor with 1nrad/s rotation stability,” Phys. Rev. Lett. 116, 183003 (2016).
[Crossref]

S. Dimopoulos, P. W. Graham, J. M. Hogan, and M. A. Kasevich, “Testing general relativity with atom interferometry,” Phys. Rev. Lett. 98, 111102 (2007).
[Crossref]

M. Cadoret, E. De Mirandes, P. Cladé, S. Guellati-Khelifa, C. Schwob, F. Nez, L. Julien, and F. Biraben, “Combination of Bloch oscillations with a Ramsey–Bordé interferometer: new determination of the fine structure constant,” Phys. Rev. Lett. 101, 230801 (2008).
[Crossref]

R. Bouchendira, P. Cladé, S. Guellati-Khelifa, F. Nez, and F. Biraben, “New determination of the fine structure constant and test of the quantum electrodynamics,” Phys. Rev. Lett. 106, 080801 (2011).
[Crossref]

M. Kasevich and S. Chu, “Atomic interferometry using stimulated Raman transitions,” Phys. Rev. Lett. 67, 181–184 (1991).
[Crossref]

F. Riehle, T. Kisters, A. Witte, J. Helmcke, and C. J. Borde, “Optical Ramsey spectroscopy in a rotating frame—Sagnac effect in a matter-wave interferometer,” Phys. Rev. Lett. 67, 177–180 (1991).
[Crossref]

D. S. Weiss, B. C. Young, and S. Chu, “Precision measurement of the photon recoil of an atom using atom interferometry,” Phys. Rev. Lett. 70, 2706–2709 (1993).
[Crossref]

S.-W. Chiow, S. Herrmann, S. Chu, and H. Muller, “Noise-immune conjugate large-area atom interferometers,” Phys. Rev. Lett. 103, 050402 (2011).
[Crossref]

H. Müller, S.-W. Chiow, Q. Long, S. Herrmann, and S. Chu, “Atom interferometry with up to 24-photon-momentum-transfer beam splitters,” Phys. Rev. Lett. 100, 180405 (2008).
[Crossref]

T. Lévéque, A. Gauguet, F. Michaud, F. Pereira Dos Santos, and A. Landragin, “Enhancing the area of a Raman atom interferometer using a versatile double-diffraction technique,” Phys. Rev. Lett. 103, 080405 (2009).
[Crossref]

Other (2)

P. Berman, Atom Interferometry (Academic, 1996).

C. J. Bordé, “Propagation of laser beams and of atomic systems,” in Fundamental Systems in Quantum Optics, J. Dalibard, J.-M. Raimond, and J. Zinn-Justin, eds., Les Houches Lectures Session LIII 1990 (Elsevier, 1991).

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Figures (10)

Fig. 1.
Fig. 1. Recoil diagram of a two-photon transition: the two-photon transition (Raman or Bragg) couples two momentum states. During the process, the momentum transfer Δ p i = ϵ i k i at time t i . (a) Beam splitter pulse: the atom is put in a coherent superposition of two momentum states. (b) Mirror pulse: the atom’s momentum state is changed with momentum Δ p . Solid and dashed lines correspond to two different momentum states corresponding to the same internal quantum state (Bragg pulse) or different internal quantum states (Raman transition). The two paths are described with vectors ( ϵ⃗ ) and ( ϵ⃗ ) .
Fig. 2.
Fig. 2. Space–time recoil diagram in the absence of gravity of a Mach–Zehnder interferometer consisting of pulse sequence π / 2 π π / 2 .
Fig. 3.
Fig. 3. Nonrotating inertial geocentric reference frame R (i-frame) defined by the fixed stars having its origin at the center of the Earth and Earth reference frame R with local coordinate system ( x , y , z ) , where the z -axis is chosen to point away from the Earth’s center, with rotation rate components Ω⃗ = ( 0 , Ω cos λ , Ω sin λ ) .
Fig. 4.
Fig. 4. Space–time recoil diagrams in the absence of gravity. (a) Ramsey interferometer consisting of two π / 2 pulses separated by a free precession time T = t 2 t 1 . The interferometer is closed in momentum space Δ G 0 = 0 . (b) The Mach–Zehnder interferometer consisting of pulse sequence ( π / 2 , t 1 = 0 ) ( π , t 2 = T ) ( π / 2 , t 3 = 2 T ) . This single-loop interferometer is closed in both momentum and position space. Its sensitivity to acceleration is proportional to the space–time area enclosed by the loop. (c) Double-diffraction atom interferometer: two pairs of Raman beams with effective wave vectors ± k i are shined simultaneously on the atoms at three moments in times separated by time T . DDP1 and DDP3 are double-diffraction pulses that act as splitters, whereas DDP2 acts as a mirror pulse transferring momentum Δ p = 2 k i to ± k i wave packets. The interferometer is totally symmetric, and the scale factor is improved by a factor of 2. In cases (b) and (c), the phase shift does not depend on the initial velocity of the atoms.
Fig. 5.
Fig. 5. Space–time recoil diagrams in the absence of gravity. (a) Symmetric four-pulse Ramsey–Bordé interferometer. (b) Ramsey–Bordé interferometer in a double-diffraction scheme ( M = 1 ). (c) Five-pulse double-loop interferometer closed in both momentum and position space. In this configuration, Δ G 2 = 0 , making the interferometer insensitive to homogeneous acceleration.
Fig. 6.
Fig. 6. Space–time diagram of a double-loop interferometer with nonidentical loops. Assuming t 1 = 0 and total interrogation time t 4 = 1 , in order to eliminate all t 3 terms (i.e., Δ G 3 = 0 ) to the phase shift, one finds t 2,3 = 5 1 4 . Solid and dashed lines correspond to momentum states separated by k .
Fig. 7.
Fig. 7. Space–time diagram showing the Mach–Zehnder interferometer paths in the presence of gravity acceleration. Solid lines: upper and lower interferometer paths ( z i and z i ). Dashed line: classical midpoint positions of the atoms taking into account the recoil effect. Solid line (in blue): parabola in the absence of photon recoil. The trajectories are plotted assuming k 1 = k 2 = k 3 .
Fig. 8.
Fig. 8. Space–time recoil diagram of the six-pulse atom interferometer sensitive to recoil phase shift and insensitive to gravity acceleration. Black line: (upper path) ϵ⃗ = ( 1 , 1 , 1 , 1 , 1 , 1 ) . Red line: (lower path) ϵ⃗ = ( 0 , 0 , 1 , 1 , 0 , 0 ) . S , beam splitter pulse; DDP, double-diffraction pulse.
Fig. 9.
Fig. 9. Space–time recoil diagram of the eight-pulse atom interferometer sensitive to recoil phase shift and insensitive to Earth’s rotation, gravity acceleration, and its gradient. Black line: (upper path) ϵ⃗ = ( 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 ) . Red line: (lower path) ϵ⃗ = ( 0 , 1 , 1 , 0 , 0 , 1 , 1 , 0 ) . S , beam-splitter pulse; M, mirror pulse; DDP, double-diffraction pulse.
Fig. 10.
Fig. 10. Space–time recoil diagram of an eight-pulse atom interferometer sensitive to recoil phase shift and insensitive to Earth’s rotation, gravity acceleration, and its gradient. Black line: (upper path) ϵ⃗ = ( 1 , 1 , 0 , 0 , 0 , 0 , 1 , 1 ) . Red line: (lower path) ϵ⃗ = ( 0 , 1 , 0 , 1 , 1 , 0 , 1 , 0 ) . S , beam-splitter pulse; M, mirror pulse.

Tables (8)

Tables Icon

Table 1. Phase Shift Terms up to the Order k = 4

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Table 2. Examples of Phase Shift Coefficient Values Δ G k k ! for Usual Atomic Interferometers

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Table 3. Recoil Phase Shift Terms up to the Order T 4 ( k = 4 ) Assuming Δ k = 0

Tables Icon

Table 4. Examples of Recoil Phase Shift Coefficient Values Δ A k K ! for Usual Atomic Interferometers

Tables Icon

Table 5. Contribution to the Phase for Atomic Gravimeter of Ref. [35] in the Rotating Earth Frame a

Tables Icon

Table 6. Phase Shift Coefficients of the Six-Light-Pulse Atom Interferometer of Fig. 8

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Table 7. Phase Shift Coefficients of the Eight-Light-Pulse Atom Interferometer of Fig. 9

Tables Icon

Table 8. Phase Shift Coefficients of the Eight-Light-Pulse Atom Interferometer of Fig. 10

Equations (63)

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t i = ( i 1 ) T ( i 1 ) .
k i = k 1 + Δ k ( i 1 ) ,
ω i = ω 1 + Δ ω ( i 1 ) ,
φ i = φ 1 + ω 1 ( i 1 ) T + Δ ω ( i 1 ) 2 T 2 .
G k = i = 1 N ( i 1 ) k ϵ i , G k = i = 1 N ( i 1 ) k ϵ i ,
Δ G k = G k G k = i = 1 N ( i 1 ) k Δ ϵ i = V Δ ϵ i ,
Δ Φ Total = i = 1 N k i Δ ϵ i z i + z i 2 Δ Φ in ertial + i = 1 N φ i Δ ϵ i Δ Φ t .
Δ Φ t = i = 1 N Δ ϵ i ( φ 1 + ω 1 ( i 1 ) T + Δ ω ( i 1 ) 2 T 2 ) = Δ G 0 φ 1 + Δ G 1 ω 1 T + Δ G 2 Δ ω T 2 ,
Δ Φ inertial i = 1 N k i Δ ϵ i z i .
z i = z ( t i ) = k = 0 a k t i k = k = 0 a k T k ( i 1 ) k ,
Δ Φ inertial k = 0 Δ G k k 1 a k T k k = 0 Δ G k k ! k 1 ( d k z d t k ) t = t 1 T k ,
Δ Φ inertial k Δ G k k ! T k × k⃗ 1 · F⃗ k ( R⃗ 1 , v⃗ 1 , + inertial forces ) ,
g⃗ ( R⃗ ) = ( d 2 R⃗ d t 2 ) R ( a ) + 2 Ω⃗ × ( d R⃗ d t ) R ( b ) + Ω⃗ × ( Ω⃗ × R⃗ ) + d Ω⃗ d t × R⃗ ( c ) ,
g⃗ ( R⃗ ) = g⃗ ( R⃗ 1 ) + Γ . ( R⃗ R⃗ 1 ) ,
d d t ( g⃗ ( R⃗ 1 ) + Γ . ( R⃗ R⃗ 1 ) ) R = Γ . ( d R⃗ d t ) R + η Ω⃗ × g⃗ + η Ω⃗ × ( Γ . ( R⃗ R⃗ 1 ) + ( 1 η ) Γ . ( Ω⃗ × R⃗ ) .
a⃗ = g⃗ ( R⃗ 1 ) Ω⃗ × ( Ω⃗ × R⃗ 1 )
Δ Φ inertial = Δ G 0 0 ! k⃗ 1 · R⃗ 1 + Δ G 1 1 ! k⃗ 1 · v⃗ 1 T + Δ G 2 2 ! k⃗ 1 · ( a⃗ 2 Ω⃗ × v⃗ 1 ) T 2 + O ( T 3 ) .
Δ G 3 3 ! k⃗ 1 · ( ( η 3 ) · Ω⃗ × a⃗ + Γ · v⃗ 1 + 3 · Ω⃗ × ( Ω⃗ × v⃗ 1 ) + ( η 1 ) · Ω⃗ × ( Ω⃗ × ( Ω⃗ × R⃗ 1 ) ) ( η 1 ) Γ⃗ · ( Ω⃗ × R⃗ 1 ) )
Δ G 4 4 ! k⃗ 1 · ( Γ · a⃗ + 3 ( η 2 ) · Ω⃗ × a⃗ 4 · Ω⃗ × ( Ω⃗ × ( Ω⃗ × v⃗ 1 ) ) + ( 1 η ) · Γ · ( Ω⃗ × ( Ω⃗ × R⃗ 1 ) ) 4 ( 1 η ) · Ω⃗ × ( Γ · ( Ω⃗ × R⃗ 1 ) ) + 3 ( 1 η ) · Ω⃗ × ( Ω⃗ × ( Ω⃗ × ( Ω⃗ × R⃗ 1 ) ) ) )
Δ ϵ i = Δ ϵ N + 1 i ,
{ Δ G 0 = Δ ϵ 1 + Δ ϵ 2 + Δ ϵ 3 = 0 , Δ G 1 = Δ ϵ 2 + 2 Δ ϵ 3 = 0 .
Δ ϵ i = Δ ϵ N + 1 i .
Δ ϵ = M ( 2 4 2 ) .
Δ ϵ i = 2 ϵ i .
( 1 1 0 0 )
( 1 2 1 0 )
( 2 4 2 0 )
( 1 1 1 1 )
( 1 2 0 2 1 )
Δ ϵ = V 1 Δ G ,
Δ G k ( t ) = i = 1 N Δ ϵ i t i k = V ( t 1 , t 2 , t 3 , , t N ) Δ ϵ .
Δ ϵ = ( V ( t 1 , t 2 , t 3 , t 4 ) ) 1 Δ G .
Δ Φ inertial k = 0 Δ G k + Δ k k 1 Δ G k + 1 k ! · T k k⃗ 1 · F⃗ k ( R⃗ 1 , v⃗ 1 , a⃗ , Ω⃗ , Γ ) ,
z i = z 1 + v 1 ( i 1 ) T + m T j = 1 i 1 ( i j ) k j ϵ j ( a ) + 1 2 g ( i 1 ) 2 T 2 + O ( T 3 ) , z i = z 1 + v 1 ( i 1 ) T + m T j = 1 i 1 ( i j ) k j ϵ j ( b ) + 1 2 g ( i 1 ) 2 T 2 + O ( T 3 ) ,
z i rec = z i + z i 2 = z 1 + v 1 ( i 1 ) T + 1 2 g ( i 1 ) 2 T 2 + 2 m T j = 1 i 1 ( i j ) k j ( ϵ j + ϵ j ) ( c ) ,
Δ Φ inertial = i = 1 N k i Δ ϵ i z i rec = i = 1 N k i Δ ϵ i z i + Δ Φ rec ,
Δ Φ rec = 2 m k 2 T Δ A 1 + 2 m k Δ k T Δ B 1 + 2 m Δ k 2 T Δ C 1 + O ( T 2 ) ,
Δ A k = i = 1 N ( ϵ i ϵ i ) × ( j = 1 i 1 ( i j ) k ( ϵ j + ϵ j ) ) ,
Δ B k = i = 1 N ( ϵ i ϵ i ) × ( j = 1 i 1 ( i 1 + j 1 ) ( i j ) k ( ϵ j + ϵ j ) ) ,
Δ C k = i = 1 N ( ϵ i ϵ i ) × ( j = 1 i 1 ( j 1 ) ( i j ) k ( i 1 ) ( ϵ j + ϵ j ) ) ,
Δ Φ rec = k Δ A k + Δ k k 1 Δ B k + ( Δ k k 1 ) 2 Δ C k k ! · T k × k⃗ 1 · F⃗ k ( 0⃗ , v⃗ r = k⃗ 1 2 m , 0⃗ , Ω⃗ , Γ ) ,
Δ A 3 3 ! k⃗ 1 · ( 3 Ω⃗ × ( Ω⃗ × k⃗ 1 2 m ) + Γ⃗ · ( k⃗ 1 2 m ) ) T 3
2 Δ A 4 4 ! k⃗ 1 · ( ( 2 η ) · Ω⃗ × ( Γ⃗ · k⃗ 1 2 m ) η Γ⃗ · ( Ω⃗ × k⃗ 1 2 m ) ) T 4
( 1 1 )
( 1 0 1 )
( 0 0 0 )
( 1 1 1 1 )
( 1 1 1 1 )
Δ Φ Total = Δ Φ t + Δ Φ inertial ,
Δ Φ Total = Δ G 0 φ 1 + Δ G 1 ω 1 T + Δ G 2 Δ ω T 2 + k Δ G k + Δ k k 1 Δ G k + 1 k ! · T k × k⃗ 1 · F⃗ k ( R⃗ 1 , v⃗ 1 , a⃗ , Ω⃗ , Γ ) + Δ A k + Δ k k 1 Δ B k + ( Δ k k 1 ) 2 Δ C k k ! · T k × k⃗ 1 · F⃗ k ( 0⃗ , v⃗ r = k⃗ 1 2 m , 0⃗ , Ω⃗ , Γ ) ,
Δ Φ MZ = Δ ω T + k Δ G k + Δ k k 1 Δ G k + 1 k ! · T k × F⃗ k ( R⃗ 1 , v⃗ 1 + k⃗ 1 2 m , a⃗ , Ω⃗ , Γ ) ,
g⃗ 1 = g⃗ ( R⃗ 1 ) + Γ · ( R⃗ R⃗ 1 ) ,
g⃗ 1 = a⃗ ( R⃗ 1 ) + Ω⃗ × ( Ω⃗ × R⃗ 1 ) ,
Δ Φ Total = Δ ω T + M 2 ω r T + M k⃗ 1 ( g⃗ 2 Ω⃗ × v⃗ 1 ) T 2 + O ( T 3 ) ,
Δ Φ Total 6 pulse = 2 k 1 2 2 m T = 2 ω r T + O ( T 2 ) ,
Δ ϵ 1 = [ ( t 1 + t 2 + t 3 + t 4 ) t 1 ] Δ G 2 Δ G 3 ( t 2 t 1 ) ( t 3 t 1 ) ( t 4 t 1 ) , Δ ϵ 2 = [ ( t 1 + t 2 + t 3 + t 4 ) t 2 ] Δ G 2 Δ G 3 ( t 2 t 1 ) ( t 3 t 2 ) ( t 4 t 2 ) , Δ ϵ 3 = [ ( t 1 + t 2 + t 3 + t 4 ) t 3 ] Δ G 2 Δ G 3 ( t 3 t 1 ) ( t 3 t 2 ) ( t 4 t 3 ) , Δ ϵ 4 = [ ( t 1 + t 2 + t 3 + t 4 ) t 4 ] Δ G 2 Δ G 3 ( t 4 t 1 ) ( t 4 t 2 ) ( t 4 t 3 ) .
t 2 t 3 = ( t 2 + t 3 + 1 ) Δ G 2 Δ G 3 , 2 t 2 ( t 3 t 2 ) ( 1 t 2 ) = ( 1 + t 3 ) Δ G 2 Δ G 3 , 2 t 3 ( t 3 t 2 ) ( 1 t 3 ) = ( t 2 + 1 ) Δ G 2 Δ G 3 , ( 1 t 2 ) ( 1 t 3 ) = ( t 3 + t 2 ) Δ G 2 Δ G 3 ,
t 2 = t 3 1 2 ,
t 3 ,
Δ G 2 = 2 ( t 3 3 4 ) ,
Δ G 3 = 3 ( t 3 1 5 4 ) ( t 3 1 + 5 4 ) .
{ t 2 = 1 4 t 4 ; t 3 = 3 4 t 4 ; Δ G 3 = 3 16 t 4 3 } .
{ t 2 = 5 1 4 ; t 3 = 5 + 1 4 ; Δ G 2 = ( 1 5 2 ) t 4 2 } .

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