Abstract

A frequency doubled I/Q modulator based optical single-sideband (OSSB) laser system is demonstrated for atomic physics research, specifically for atom interferometry where the presence of additional sidebands causes parasitic transitions. The performance of the OSSB technique and the spectrum after second harmonic generation are measured and analyzed. The additional sidebands are removed with better than 20 dB suppression, and the influence of parasitic transitions upon stimulated Raman transitions at varying spatial positions is shown to be removed beneath experimental noise. This technique will facilitate the development of compact atom interferometry based sensors with improved accuracy and reduced complexity.

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2017 (1)

A. Hinton, M. Perea-Ortiz, J. Winch, J. Briggs, S. Freer, D. Moustoukas, S. Powell-Gill, C. Squire, A. Lamb, C. Rammeloo, B. Stray, G. Voulazeris, L. Zhu, A. Kaushik, Y.-H. Lien, A. Niggebaum, A. Rodgers, A. Stabrawa, D. Boddice, S. R. Plant, G. W. Tuckwell, K. Bongs, N. Metje, and M. Holynski, “A portable magneto-optical trap with prospects for atom interferometry in civil engineering,” Phil. Trans. R. Soc. A 375, 20160238 (2017).
[Crossref] [PubMed]

2016 (3)

C. Freier, M. Hauth, V. Schkolnik, B. Leykauf, M. Schilling, H. Wziontek, H.-G. Scherneck, J. Müller, and A. Peters, “Mobile quantum gravity sensor with unprecedented stability,” J. Phys.: Conf. Ser. 723, 012050 (2016).

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

V. Schkolnik, O. Hellmig, A. Wenzlawski, J. Grosse, A. Kohfeldt, K. Döringshoff, A. Wicht, P. Windpassinger, K. Sengstock, C. Braxmaier, M. Krutzik, and A. Peters, “A compact and robust diode laser system for atom interferometry on a sounding rocket,” Appl. Phys. B: Lasers Opt. 122, 217 (2016)
[Crossref]

2015 (3)

F. Theron, O. Carraz, G. Renon, N. Zahzam, Y. Bidel, M. Cadoret, and A. Bresson, “Narrow linewidth single laser source system for onboard atom interferometry,” Appl. Phys. B: Lasers Opt. 118, 1–5 (2015).
[Crossref]

B. Altschul, Q. G. Bailey, L. Blanchet, K. Bongs, P. Bouyer, L. Cacciapuoti, S. Capozziello, N. Gaaloul, D. Giulini, J. Hartwig, L. Iess, P. Jetzer, A. Landragin, E. Rasel, S. Reynaud, S. Schiller, C. Schubert, F. Sorrentino, U. Sterr, J. D. Tasson, G. M. Tino, P. Tuckey, and P. Wolf, “Quantum tests of the Einstein equivalence principle with the STE-QUEST space mission,” Adv. Space Res. 55, 501– 524 (2015).
[Crossref]

K. Bongs, M. Holynski, and Y. Singh, “ψ in the sky,” Nat. Phys. 11, 615–617 (2015).
[Crossref]

2014 (2)

S. Merlet, L. Volodimer, M. Lours, and F. Pereira dos Santos, “A simple laser system for atom interferometry,” Appl. Phys. B: Lasers Opt. 117, 749 (2014).
[Crossref]

A. Hangauer, G. Spinner, M. Nikodem, and G. Wysocki, “High frequency modulation capabilities and quasi single-sideband emission from a quantum cascade laser,” Opt. Express 22, 23439 (2014).
[Crossref] [PubMed]

2012 (1)

O. Carraz, R. Charrière, M. Cadoret, N. Zahzam, Y. Bidel, and A. Bresson, “Phase shift in an atom interferometer induced by the additional laser lines of a Raman laser generated by modulation,” Phys. Rev. A 86, 033605 (2012).
[Crossref]

2011 (1)

2010 (2)

F. Sorrentino, Y.-H. Lien, G. Rosi, L. Cacciapuoti, M. Prevedelli, and G. M. Tino, “Sensitive gravity-gradiometry with atom interferometry: progress towards an improved determination of the gravitational constant,” New J. Phys. 12, 095009 (2010).
[Crossref]

D. M. S. Johnson, J. M. Hogan, S.-W. Chiow, and M. A. Kasevich, “Broadband optical serrodyne frequency shifting,” Opt. Lett. 35, 745–747 (2010).
[Crossref] [PubMed]

2009 (1)

J. Le Gouët, J. Kim, C. Bourassin-Bouchet, M. Lours, A. Landragin, and F. Pereira dos Santos, “Wide bandwidth phase-locked diode laser with an intra-cavity electro-optic modulator,” Opt. Commun. 282, 977 (2009).
[Crossref]

2006 (1)

P. Cheinet, F. Pereira dos Santos, T. Petelski, J. Le Gouët, J. Kim, K. T. Therkildsen, A. Clairon, and A. Landragin, “Compact laser system for atom interferometry,” Appl. Phys. B: Lasers Opt. 84, 643 (2006).
[Crossref]

2004 (1)

2001 (2)

A. Peters, K. Y. Chung, and S. Chu, “High-precision gravity measurements using atom interferometry,” Metrologia 38, 25 (2001).
[Crossref]

S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, “Single side-band modulation performance of a LiNbO3 integrated modulator consisting of four-phase modulator waveguides,” IEEE Photonics Technol. Lett. 13, 364 (2001).
[Crossref]

2000 (1)

T. L. Gustavson, A. Landragin, and M. A. Kasevich, “Rotation sensing with a dual atom-interferometer sagnac gyroscope,” Class. Quantum Grav. 17, 2385 (2000).
[Crossref]

1996 (1)

1991 (2)

M. Kasevich, D. S. Weiss, E. Riis, K. Moler, S. Kasapi, and S. Chu, “Atomic velocity selection using stimulated Raman transitions,” Phys. Rev. Lett. 66, 2297 (1991).
[Crossref] [PubMed]

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

1989 (2)

1981 (1)

M. Izutsu, S. Shikama, and T. Sueta, “Integrated optical SSB modulator/frequency shifter,” IEEE J. Quantum Electron. 17, 2225 (1981).
[Crossref]

1970 (1)

P. Page and H. Pursey, “Tunable single sideband electro-optic ring modulator,” Opto-electronics 2, 1 (1970).
[Crossref]

1962 (1)

C. F. Buhrer, D. Baird, and E. M. Conwell, “Optical frequency shifting by electro-optic effect,” Appl. Phys. Lett. 1, 46 (1962).
[Crossref]

Altschul, B.

B. Altschul, Q. G. Bailey, L. Blanchet, K. Bongs, P. Bouyer, L. Cacciapuoti, S. Capozziello, N. Gaaloul, D. Giulini, J. Hartwig, L. Iess, P. Jetzer, A. Landragin, E. Rasel, S. Reynaud, S. Schiller, C. Schubert, F. Sorrentino, U. Sterr, J. D. Tasson, G. M. Tino, P. Tuckey, and P. Wolf, “Quantum tests of the Einstein equivalence principle with the STE-QUEST space mission,” Adv. Space Res. 55, 501– 524 (2015).
[Crossref]

Bailey, Q. G.

B. Altschul, Q. G. Bailey, L. Blanchet, K. Bongs, P. Bouyer, L. Cacciapuoti, S. Capozziello, N. Gaaloul, D. Giulini, J. Hartwig, L. Iess, P. Jetzer, A. Landragin, E. Rasel, S. Reynaud, S. Schiller, C. Schubert, F. Sorrentino, U. Sterr, J. D. Tasson, G. M. Tino, P. Tuckey, and P. Wolf, “Quantum tests of the Einstein equivalence principle with the STE-QUEST space mission,” Adv. Space Res. 55, 501– 524 (2015).
[Crossref]

Baird, D.

C. F. Buhrer, D. Baird, and E. M. Conwell, “Optical frequency shifting by electro-optic effect,” Appl. Phys. Lett. 1, 46 (1962).
[Crossref]

Battelier, B.

Bidel, Y.

F. Theron, O. Carraz, G. Renon, N. Zahzam, Y. Bidel, M. Cadoret, and A. Bresson, “Narrow linewidth single laser source system for onboard atom interferometry,” Appl. Phys. B: Lasers Opt. 118, 1–5 (2015).
[Crossref]

O. Carraz, R. Charrière, M. Cadoret, N. Zahzam, Y. Bidel, and A. Bresson, “Phase shift in an atom interferometer induced by the additional laser lines of a Raman laser generated by modulation,” Phys. Rev. A 86, 033605 (2012).
[Crossref]

Blanchet, L.

B. Altschul, Q. G. Bailey, L. Blanchet, K. Bongs, P. Bouyer, L. Cacciapuoti, S. Capozziello, N. Gaaloul, D. Giulini, J. Hartwig, L. Iess, P. Jetzer, A. Landragin, E. Rasel, S. Reynaud, S. Schiller, C. Schubert, F. Sorrentino, U. Sterr, J. D. Tasson, G. M. Tino, P. Tuckey, and P. Wolf, “Quantum tests of the Einstein equivalence principle with the STE-QUEST space mission,” Adv. Space Res. 55, 501– 524 (2015).
[Crossref]

Boddice, D.

A. Hinton, M. Perea-Ortiz, J. Winch, J. Briggs, S. Freer, D. Moustoukas, S. Powell-Gill, C. Squire, A. Lamb, C. Rammeloo, B. Stray, G. Voulazeris, L. Zhu, A. Kaushik, Y.-H. Lien, A. Niggebaum, A. Rodgers, A. Stabrawa, D. Boddice, S. R. Plant, G. W. Tuckwell, K. Bongs, N. Metje, and M. Holynski, “A portable magneto-optical trap with prospects for atom interferometry in civil engineering,” Phil. Trans. R. Soc. A 375, 20160238 (2017).
[Crossref] [PubMed]

Bongs, K.

A. Hinton, M. Perea-Ortiz, J. Winch, J. Briggs, S. Freer, D. Moustoukas, S. Powell-Gill, C. Squire, A. Lamb, C. Rammeloo, B. Stray, G. Voulazeris, L. Zhu, A. Kaushik, Y.-H. Lien, A. Niggebaum, A. Rodgers, A. Stabrawa, D. Boddice, S. R. Plant, G. W. Tuckwell, K. Bongs, N. Metje, and M. Holynski, “A portable magneto-optical trap with prospects for atom interferometry in civil engineering,” Phil. Trans. R. Soc. A 375, 20160238 (2017).
[Crossref] [PubMed]

K. Bongs, M. Holynski, and Y. Singh, “ψ in the sky,” Nat. Phys. 11, 615–617 (2015).
[Crossref]

B. Altschul, Q. G. Bailey, L. Blanchet, K. Bongs, P. Bouyer, L. Cacciapuoti, S. Capozziello, N. Gaaloul, D. Giulini, J. Hartwig, L. Iess, P. Jetzer, A. Landragin, E. Rasel, S. Reynaud, S. Schiller, C. Schubert, F. Sorrentino, U. Sterr, J. D. Tasson, G. M. Tino, P. Tuckey, and P. Wolf, “Quantum tests of the Einstein equivalence principle with the STE-QUEST space mission,” Adv. Space Res. 55, 501– 524 (2015).
[Crossref]

Bourassin-Bouchet, C.

J. Le Gouët, J. Kim, C. Bourassin-Bouchet, M. Lours, A. Landragin, and F. Pereira dos Santos, “Wide bandwidth phase-locked diode laser with an intra-cavity electro-optic modulator,” Opt. Commun. 282, 977 (2009).
[Crossref]

Bouyer, P.

B. Altschul, Q. G. Bailey, L. Blanchet, K. Bongs, P. Bouyer, L. Cacciapuoti, S. Capozziello, N. Gaaloul, D. Giulini, J. Hartwig, L. Iess, P. Jetzer, A. Landragin, E. Rasel, S. Reynaud, S. Schiller, C. Schubert, F. Sorrentino, U. Sterr, J. D. Tasson, G. M. Tino, P. Tuckey, and P. Wolf, “Quantum tests of the Einstein equivalence principle with the STE-QUEST space mission,” Adv. Space Res. 55, 501– 524 (2015).
[Crossref]

V. Ménoret, R. Geiger, G. Stern, N. Zahzam, B. Battelier, A. Bresson, A. Landragin, and P. Bouyer, “Dual-wavelength laser source for onboard atom interferometry,” Opt. Lett. 36, 4128 (2011).
[Crossref] [PubMed]

P. Bouyer, T. L. Gustavson, K. G. Haritos, and M. A. Kasevich, “Microwave signal generation with optical injection locking,” Opt. Lett. 21, 1502 (1996).
[Crossref] [PubMed]

Braxmaier, C.

V. Schkolnik, O. Hellmig, A. Wenzlawski, J. Grosse, A. Kohfeldt, K. Döringshoff, A. Wicht, P. Windpassinger, K. Sengstock, C. Braxmaier, M. Krutzik, and A. Peters, “A compact and robust diode laser system for atom interferometry on a sounding rocket,” Appl. Phys. B: Lasers Opt. 122, 217 (2016)
[Crossref]

Bresson, A.

F. Theron, O. Carraz, G. Renon, N. Zahzam, Y. Bidel, M. Cadoret, and A. Bresson, “Narrow linewidth single laser source system for onboard atom interferometry,” Appl. Phys. B: Lasers Opt. 118, 1–5 (2015).
[Crossref]

O. Carraz, R. Charrière, M. Cadoret, N. Zahzam, Y. Bidel, and A. Bresson, “Phase shift in an atom interferometer induced by the additional laser lines of a Raman laser generated by modulation,” Phys. Rev. A 86, 033605 (2012).
[Crossref]

V. Ménoret, R. Geiger, G. Stern, N. Zahzam, B. Battelier, A. Bresson, A. Landragin, and P. Bouyer, “Dual-wavelength laser source for onboard atom interferometry,” Opt. Lett. 36, 4128 (2011).
[Crossref] [PubMed]

Briggs, J.

A. Hinton, M. Perea-Ortiz, J. Winch, J. Briggs, S. Freer, D. Moustoukas, S. Powell-Gill, C. Squire, A. Lamb, C. Rammeloo, B. Stray, G. Voulazeris, L. Zhu, A. Kaushik, Y.-H. Lien, A. Niggebaum, A. Rodgers, A. Stabrawa, D. Boddice, S. R. Plant, G. W. Tuckwell, K. Bongs, N. Metje, and M. Holynski, “A portable magneto-optical trap with prospects for atom interferometry in civil engineering,” Phil. Trans. R. Soc. A 375, 20160238 (2017).
[Crossref] [PubMed]

Buch, P.

Buhrer, C. F.

C. F. Buhrer, D. Baird, and E. M. Conwell, “Optical frequency shifting by electro-optic effect,” Appl. Phys. Lett. 1, 46 (1962).
[Crossref]

Cacciapuoti, L.

B. Altschul, Q. G. Bailey, L. Blanchet, K. Bongs, P. Bouyer, L. Cacciapuoti, S. Capozziello, N. Gaaloul, D. Giulini, J. Hartwig, L. Iess, P. Jetzer, A. Landragin, E. Rasel, S. Reynaud, S. Schiller, C. Schubert, F. Sorrentino, U. Sterr, J. D. Tasson, G. M. Tino, P. Tuckey, and P. Wolf, “Quantum tests of the Einstein equivalence principle with the STE-QUEST space mission,” Adv. Space Res. 55, 501– 524 (2015).
[Crossref]

F. Sorrentino, Y.-H. Lien, G. Rosi, L. Cacciapuoti, M. Prevedelli, and G. M. Tino, “Sensitive gravity-gradiometry with atom interferometry: progress towards an improved determination of the gravitational constant,” New J. Phys. 12, 095009 (2010).
[Crossref]

Cadoret, M.

F. Theron, O. Carraz, G. Renon, N. Zahzam, Y. Bidel, M. Cadoret, and A. Bresson, “Narrow linewidth single laser source system for onboard atom interferometry,” Appl. Phys. B: Lasers Opt. 118, 1–5 (2015).
[Crossref]

O. Carraz, R. Charrière, M. Cadoret, N. Zahzam, Y. Bidel, and A. Bresson, “Phase shift in an atom interferometer induced by the additional laser lines of a Raman laser generated by modulation,” Phys. Rev. A 86, 033605 (2012).
[Crossref]

Capozziello, S.

B. Altschul, Q. G. Bailey, L. Blanchet, K. Bongs, P. Bouyer, L. Cacciapuoti, S. Capozziello, N. Gaaloul, D. Giulini, J. Hartwig, L. Iess, P. Jetzer, A. Landragin, E. Rasel, S. Reynaud, S. Schiller, C. Schubert, F. Sorrentino, U. Sterr, J. D. Tasson, G. M. Tino, P. Tuckey, and P. Wolf, “Quantum tests of the Einstein equivalence principle with the STE-QUEST space mission,” Adv. Space Res. 55, 501– 524 (2015).
[Crossref]

Carraz, O.

F. Theron, O. Carraz, G. Renon, N. Zahzam, Y. Bidel, M. Cadoret, and A. Bresson, “Narrow linewidth single laser source system for onboard atom interferometry,” Appl. Phys. B: Lasers Opt. 118, 1–5 (2015).
[Crossref]

O. Carraz, R. Charrière, M. Cadoret, N. Zahzam, Y. Bidel, and A. Bresson, “Phase shift in an atom interferometer induced by the additional laser lines of a Raman laser generated by modulation,” Phys. Rev. A 86, 033605 (2012).
[Crossref]

Charrière, R.

O. Carraz, R. Charrière, M. Cadoret, N. Zahzam, Y. Bidel, and A. Bresson, “Phase shift in an atom interferometer induced by the additional laser lines of a Raman laser generated by modulation,” Phys. Rev. A 86, 033605 (2012).
[Crossref]

Cheinet, P.

P. Cheinet, F. Pereira dos Santos, T. Petelski, J. Le Gouët, J. Kim, K. T. Therkildsen, A. Clairon, and A. Landragin, “Compact laser system for atom interferometry,” Appl. Phys. B: Lasers Opt. 84, 643 (2006).
[Crossref]

Chiow, S.-W.

Chu, S.

A. Peters, K. Y. Chung, and S. Chu, “High-precision gravity measurements using atom interferometry,” Metrologia 38, 25 (2001).
[Crossref]

M. Kasevich, D. S. Weiss, E. Riis, K. Moler, S. Kasapi, and S. Chu, “Atomic velocity selection using stimulated Raman transitions,” Phys. Rev. Lett. 66, 2297 (1991).
[Crossref] [PubMed]

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

Chung, K. Y.

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I. Dutta, D. Savoie, B. Fang, B. Venon, C. Garrido Alzar, R. Geiger, and A. Landragin, “Continuous cold-atom inertial sensor with 1 nrad/sec rotation stability,” Phys. Rev. Lett. 116, 183003 (2016).
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A. Hinton, M. Perea-Ortiz, J. Winch, J. Briggs, S. Freer, D. Moustoukas, S. Powell-Gill, C. Squire, A. Lamb, C. Rammeloo, B. Stray, G. Voulazeris, L. Zhu, A. Kaushik, Y.-H. Lien, A. Niggebaum, A. Rodgers, A. Stabrawa, D. Boddice, S. R. Plant, G. W. Tuckwell, K. Bongs, N. Metje, and M. Holynski, “A portable magneto-optical trap with prospects for atom interferometry in civil engineering,” Phil. Trans. R. Soc. A 375, 20160238 (2017).
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C. Freier, M. Hauth, V. Schkolnik, B. Leykauf, M. Schilling, H. Wziontek, H.-G. Scherneck, J. Müller, and A. Peters, “Mobile quantum gravity sensor with unprecedented stability,” J. Phys.: Conf. Ser. 723, 012050 (2016).

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B. Altschul, Q. G. Bailey, L. Blanchet, K. Bongs, P. Bouyer, L. Cacciapuoti, S. Capozziello, N. Gaaloul, D. Giulini, J. Hartwig, L. Iess, P. Jetzer, A. Landragin, E. Rasel, S. Reynaud, S. Schiller, C. Schubert, F. Sorrentino, U. Sterr, J. D. Tasson, G. M. Tino, P. Tuckey, and P. Wolf, “Quantum tests of the Einstein equivalence principle with the STE-QUEST space mission,” Adv. Space Res. 55, 501– 524 (2015).
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Garrido Alzar, C.

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

I. Dutta, D. Savoie, B. Fang, B. Venon, C. Garrido Alzar, R. Geiger, and A. Landragin, “Continuous cold-atom inertial sensor with 1 nrad/sec rotation stability,” Phys. Rev. Lett. 116, 183003 (2016).
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V. Ménoret, R. Geiger, G. Stern, N. Zahzam, B. Battelier, A. Bresson, A. Landragin, and P. Bouyer, “Dual-wavelength laser source for onboard atom interferometry,” Opt. Lett. 36, 4128 (2011).
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Grosse, J.

V. Schkolnik, O. Hellmig, A. Wenzlawski, J. Grosse, A. Kohfeldt, K. Döringshoff, A. Wicht, P. Windpassinger, K. Sengstock, C. Braxmaier, M. Krutzik, and A. Peters, “A compact and robust diode laser system for atom interferometry on a sounding rocket,” Appl. Phys. B: Lasers Opt. 122, 217 (2016)
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Gustavson, T. L.

T. L. Gustavson, A. Landragin, and M. A. Kasevich, “Rotation sensing with a dual atom-interferometer sagnac gyroscope,” Class. Quantum Grav. 17, 2385 (2000).
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Hangauer, A.

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B. Altschul, Q. G. Bailey, L. Blanchet, K. Bongs, P. Bouyer, L. Cacciapuoti, S. Capozziello, N. Gaaloul, D. Giulini, J. Hartwig, L. Iess, P. Jetzer, A. Landragin, E. Rasel, S. Reynaud, S. Schiller, C. Schubert, F. Sorrentino, U. Sterr, J. D. Tasson, G. M. Tino, P. Tuckey, and P. Wolf, “Quantum tests of the Einstein equivalence principle with the STE-QUEST space mission,” Adv. Space Res. 55, 501– 524 (2015).
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Hauth, M.

C. Freier, M. Hauth, V. Schkolnik, B. Leykauf, M. Schilling, H. Wziontek, H.-G. Scherneck, J. Müller, and A. Peters, “Mobile quantum gravity sensor with unprecedented stability,” J. Phys.: Conf. Ser. 723, 012050 (2016).

Hellmig, O.

V. Schkolnik, O. Hellmig, A. Wenzlawski, J. Grosse, A. Kohfeldt, K. Döringshoff, A. Wicht, P. Windpassinger, K. Sengstock, C. Braxmaier, M. Krutzik, and A. Peters, “A compact and robust diode laser system for atom interferometry on a sounding rocket,” Appl. Phys. B: Lasers Opt. 122, 217 (2016)
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A. Hinton, M. Perea-Ortiz, J. Winch, J. Briggs, S. Freer, D. Moustoukas, S. Powell-Gill, C. Squire, A. Lamb, C. Rammeloo, B. Stray, G. Voulazeris, L. Zhu, A. Kaushik, Y.-H. Lien, A. Niggebaum, A. Rodgers, A. Stabrawa, D. Boddice, S. R. Plant, G. W. Tuckwell, K. Bongs, N. Metje, and M. Holynski, “A portable magneto-optical trap with prospects for atom interferometry in civil engineering,” Phil. Trans. R. Soc. A 375, 20160238 (2017).
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Hogan, J. M.

Holynski, M.

A. Hinton, M. Perea-Ortiz, J. Winch, J. Briggs, S. Freer, D. Moustoukas, S. Powell-Gill, C. Squire, A. Lamb, C. Rammeloo, B. Stray, G. Voulazeris, L. Zhu, A. Kaushik, Y.-H. Lien, A. Niggebaum, A. Rodgers, A. Stabrawa, D. Boddice, S. R. Plant, G. W. Tuckwell, K. Bongs, N. Metje, and M. Holynski, “A portable magneto-optical trap with prospects for atom interferometry in civil engineering,” Phil. Trans. R. Soc. A 375, 20160238 (2017).
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Izutsu, M.

S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, “Single side-band modulation performance of a LiNbO3 integrated modulator consisting of four-phase modulator waveguides,” IEEE Photonics Technol. Lett. 13, 364 (2001).
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B. Altschul, Q. G. Bailey, L. Blanchet, K. Bongs, P. Bouyer, L. Cacciapuoti, S. Capozziello, N. Gaaloul, D. Giulini, J. Hartwig, L. Iess, P. Jetzer, A. Landragin, E. Rasel, S. Reynaud, S. Schiller, C. Schubert, F. Sorrentino, U. Sterr, J. D. Tasson, G. M. Tino, P. Tuckey, and P. Wolf, “Quantum tests of the Einstein equivalence principle with the STE-QUEST space mission,” Adv. Space Res. 55, 501– 524 (2015).
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Johnson, D. M. S.

Kasapi, S.

M. Kasevich, D. S. Weiss, E. Riis, K. Moler, S. Kasapi, and S. Chu, “Atomic velocity selection using stimulated Raman transitions,” Phys. Rev. Lett. 66, 2297 (1991).
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Kasevich, M.

M. Kasevich, D. S. Weiss, E. Riis, K. Moler, S. Kasapi, and S. Chu, “Atomic velocity selection using stimulated Raman transitions,” Phys. Rev. Lett. 66, 2297 (1991).
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M. Kasevich and S. Chu, “Atomic interferometry using stimulated Raman transitions,” Phys. Rev. Lett. 67, 181 (1991).
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Kasevich, M. A.

Kaushik, A.

A. Hinton, M. Perea-Ortiz, J. Winch, J. Briggs, S. Freer, D. Moustoukas, S. Powell-Gill, C. Squire, A. Lamb, C. Rammeloo, B. Stray, G. Voulazeris, L. Zhu, A. Kaushik, Y.-H. Lien, A. Niggebaum, A. Rodgers, A. Stabrawa, D. Boddice, S. R. Plant, G. W. Tuckwell, K. Bongs, N. Metje, and M. Holynski, “A portable magneto-optical trap with prospects for atom interferometry in civil engineering,” Phil. Trans. R. Soc. A 375, 20160238 (2017).
[Crossref] [PubMed]

Kawanishi, T.

S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, “Single side-band modulation performance of a LiNbO3 integrated modulator consisting of four-phase modulator waveguides,” IEEE Photonics Technol. Lett. 13, 364 (2001).
[Crossref]

Kim, J.

J. Le Gouët, J. Kim, C. Bourassin-Bouchet, M. Lours, A. Landragin, and F. Pereira dos Santos, “Wide bandwidth phase-locked diode laser with an intra-cavity electro-optic modulator,” Opt. Commun. 282, 977 (2009).
[Crossref]

P. Cheinet, F. Pereira dos Santos, T. Petelski, J. Le Gouët, J. Kim, K. T. Therkildsen, A. Clairon, and A. Landragin, “Compact laser system for atom interferometry,” Appl. Phys. B: Lasers Opt. 84, 643 (2006).
[Crossref]

Kohfeldt, A.

V. Schkolnik, O. Hellmig, A. Wenzlawski, J. Grosse, A. Kohfeldt, K. Döringshoff, A. Wicht, P. Windpassinger, K. Sengstock, C. Braxmaier, M. Krutzik, and A. Peters, “A compact and robust diode laser system for atom interferometry on a sounding rocket,” Appl. Phys. B: Lasers Opt. 122, 217 (2016)
[Crossref]

Krutzik, M.

V. Schkolnik, O. Hellmig, A. Wenzlawski, J. Grosse, A. Kohfeldt, K. Döringshoff, A. Wicht, P. Windpassinger, K. Sengstock, C. Braxmaier, M. Krutzik, and A. Peters, “A compact and robust diode laser system for atom interferometry on a sounding rocket,” Appl. Phys. B: Lasers Opt. 122, 217 (2016)
[Crossref]

Kubodera, K.

S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, “Single side-band modulation performance of a LiNbO3 integrated modulator consisting of four-phase modulator waveguides,” IEEE Photonics Technol. Lett. 13, 364 (2001).
[Crossref]

Lam, P. K.

Lamb, A.

A. Hinton, M. Perea-Ortiz, J. Winch, J. Briggs, S. Freer, D. Moustoukas, S. Powell-Gill, C. Squire, A. Lamb, C. Rammeloo, B. Stray, G. Voulazeris, L. Zhu, A. Kaushik, Y.-H. Lien, A. Niggebaum, A. Rodgers, A. Stabrawa, D. Boddice, S. R. Plant, G. W. Tuckwell, K. Bongs, N. Metje, and M. Holynski, “A portable magneto-optical trap with prospects for atom interferometry in civil engineering,” Phil. Trans. R. Soc. A 375, 20160238 (2017).
[Crossref] [PubMed]

Landragin, A.

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

B. Altschul, Q. G. Bailey, L. Blanchet, K. Bongs, P. Bouyer, L. Cacciapuoti, S. Capozziello, N. Gaaloul, D. Giulini, J. Hartwig, L. Iess, P. Jetzer, A. Landragin, E. Rasel, S. Reynaud, S. Schiller, C. Schubert, F. Sorrentino, U. Sterr, J. D. Tasson, G. M. Tino, P. Tuckey, and P. Wolf, “Quantum tests of the Einstein equivalence principle with the STE-QUEST space mission,” Adv. Space Res. 55, 501– 524 (2015).
[Crossref]

V. Ménoret, R. Geiger, G. Stern, N. Zahzam, B. Battelier, A. Bresson, A. Landragin, and P. Bouyer, “Dual-wavelength laser source for onboard atom interferometry,” Opt. Lett. 36, 4128 (2011).
[Crossref] [PubMed]

J. Le Gouët, J. Kim, C. Bourassin-Bouchet, M. Lours, A. Landragin, and F. Pereira dos Santos, “Wide bandwidth phase-locked diode laser with an intra-cavity electro-optic modulator,” Opt. Commun. 282, 977 (2009).
[Crossref]

P. Cheinet, F. Pereira dos Santos, T. Petelski, J. Le Gouët, J. Kim, K. T. Therkildsen, A. Clairon, and A. Landragin, “Compact laser system for atom interferometry,” Appl. Phys. B: Lasers Opt. 84, 643 (2006).
[Crossref]

T. L. Gustavson, A. Landragin, and M. A. Kasevich, “Rotation sensing with a dual atom-interferometer sagnac gyroscope,” Class. Quantum Grav. 17, 2385 (2000).
[Crossref]

Le Gouët, J.

J. Le Gouët, J. Kim, C. Bourassin-Bouchet, M. Lours, A. Landragin, and F. Pereira dos Santos, “Wide bandwidth phase-locked diode laser with an intra-cavity electro-optic modulator,” Opt. Commun. 282, 977 (2009).
[Crossref]

P. Cheinet, F. Pereira dos Santos, T. Petelski, J. Le Gouët, J. Kim, K. T. Therkildsen, A. Clairon, and A. Landragin, “Compact laser system for atom interferometry,” Appl. Phys. B: Lasers Opt. 84, 643 (2006).
[Crossref]

Lett, P. D.

Leykauf, B.

C. Freier, M. Hauth, V. Schkolnik, B. Leykauf, M. Schilling, H. Wziontek, H.-G. Scherneck, J. Müller, and A. Peters, “Mobile quantum gravity sensor with unprecedented stability,” J. Phys.: Conf. Ser. 723, 012050 (2016).

Lien, Y.-H.

A. Hinton, M. Perea-Ortiz, J. Winch, J. Briggs, S. Freer, D. Moustoukas, S. Powell-Gill, C. Squire, A. Lamb, C. Rammeloo, B. Stray, G. Voulazeris, L. Zhu, A. Kaushik, Y.-H. Lien, A. Niggebaum, A. Rodgers, A. Stabrawa, D. Boddice, S. R. Plant, G. W. Tuckwell, K. Bongs, N. Metje, and M. Holynski, “A portable magneto-optical trap with prospects for atom interferometry in civil engineering,” Phil. Trans. R. Soc. A 375, 20160238 (2017).
[Crossref] [PubMed]

F. Sorrentino, Y.-H. Lien, G. Rosi, L. Cacciapuoti, M. Prevedelli, and G. M. Tino, “Sensitive gravity-gradiometry with atom interferometry: progress towards an improved determination of the gravitational constant,” New J. Phys. 12, 095009 (2010).
[Crossref]

Lours, M.

S. Merlet, L. Volodimer, M. Lours, and F. Pereira dos Santos, “A simple laser system for atom interferometry,” Appl. Phys. B: Lasers Opt. 117, 749 (2014).
[Crossref]

J. Le Gouët, J. Kim, C. Bourassin-Bouchet, M. Lours, A. Landragin, and F. Pereira dos Santos, “Wide bandwidth phase-locked diode laser with an intra-cavity electro-optic modulator,” Opt. Commun. 282, 977 (2009).
[Crossref]

Ménoret, V.

Merlet, S.

S. Merlet, L. Volodimer, M. Lours, and F. Pereira dos Santos, “A simple laser system for atom interferometry,” Appl. Phys. B: Lasers Opt. 117, 749 (2014).
[Crossref]

Metje, N.

A. Hinton, M. Perea-Ortiz, J. Winch, J. Briggs, S. Freer, D. Moustoukas, S. Powell-Gill, C. Squire, A. Lamb, C. Rammeloo, B. Stray, G. Voulazeris, L. Zhu, A. Kaushik, Y.-H. Lien, A. Niggebaum, A. Rodgers, A. Stabrawa, D. Boddice, S. R. Plant, G. W. Tuckwell, K. Bongs, N. Metje, and M. Holynski, “A portable magneto-optical trap with prospects for atom interferometry in civil engineering,” Phil. Trans. R. Soc. A 375, 20160238 (2017).
[Crossref] [PubMed]

Mitsugi, N.

S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, “Single side-band modulation performance of a LiNbO3 integrated modulator consisting of four-phase modulator waveguides,” IEEE Photonics Technol. Lett. 13, 364 (2001).
[Crossref]

Moler, K.

M. Kasevich, D. S. Weiss, E. Riis, K. Moler, S. Kasapi, and S. Chu, “Atomic velocity selection using stimulated Raman transitions,” Phys. Rev. Lett. 66, 2297 (1991).
[Crossref] [PubMed]

Moustoukas, D.

A. Hinton, M. Perea-Ortiz, J. Winch, J. Briggs, S. Freer, D. Moustoukas, S. Powell-Gill, C. Squire, A. Lamb, C. Rammeloo, B. Stray, G. Voulazeris, L. Zhu, A. Kaushik, Y.-H. Lien, A. Niggebaum, A. Rodgers, A. Stabrawa, D. Boddice, S. R. Plant, G. W. Tuckwell, K. Bongs, N. Metje, and M. Holynski, “A portable magneto-optical trap with prospects for atom interferometry in civil engineering,” Phil. Trans. R. Soc. A 375, 20160238 (2017).
[Crossref] [PubMed]

Müller, J.

C. Freier, M. Hauth, V. Schkolnik, B. Leykauf, M. Schilling, H. Wziontek, H.-G. Scherneck, J. Müller, and A. Peters, “Mobile quantum gravity sensor with unprecedented stability,” J. Phys.: Conf. Ser. 723, 012050 (2016).

Niggebaum, A.

A. Hinton, M. Perea-Ortiz, J. Winch, J. Briggs, S. Freer, D. Moustoukas, S. Powell-Gill, C. Squire, A. Lamb, C. Rammeloo, B. Stray, G. Voulazeris, L. Zhu, A. Kaushik, Y.-H. Lien, A. Niggebaum, A. Rodgers, A. Stabrawa, D. Boddice, S. R. Plant, G. W. Tuckwell, K. Bongs, N. Metje, and M. Holynski, “A portable magneto-optical trap with prospects for atom interferometry in civil engineering,” Phil. Trans. R. Soc. A 375, 20160238 (2017).
[Crossref] [PubMed]

Nikodem, M.

Oikawa, S.

S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, “Single side-band modulation performance of a LiNbO3 integrated modulator consisting of four-phase modulator waveguides,” IEEE Photonics Technol. Lett. 13, 364 (2001).
[Crossref]

Page, P.

P. Page and H. Pursey, “Tunable single sideband electro-optic ring modulator,” Opto-electronics 2, 1 (1970).
[Crossref]

Perea-Ortiz, M.

A. Hinton, M. Perea-Ortiz, J. Winch, J. Briggs, S. Freer, D. Moustoukas, S. Powell-Gill, C. Squire, A. Lamb, C. Rammeloo, B. Stray, G. Voulazeris, L. Zhu, A. Kaushik, Y.-H. Lien, A. Niggebaum, A. Rodgers, A. Stabrawa, D. Boddice, S. R. Plant, G. W. Tuckwell, K. Bongs, N. Metje, and M. Holynski, “A portable magneto-optical trap with prospects for atom interferometry in civil engineering,” Phil. Trans. R. Soc. A 375, 20160238 (2017).
[Crossref] [PubMed]

Pereira dos Santos, F.

S. Merlet, L. Volodimer, M. Lours, and F. Pereira dos Santos, “A simple laser system for atom interferometry,” Appl. Phys. B: Lasers Opt. 117, 749 (2014).
[Crossref]

J. Le Gouët, J. Kim, C. Bourassin-Bouchet, M. Lours, A. Landragin, and F. Pereira dos Santos, “Wide bandwidth phase-locked diode laser with an intra-cavity electro-optic modulator,” Opt. Commun. 282, 977 (2009).
[Crossref]

P. Cheinet, F. Pereira dos Santos, T. Petelski, J. Le Gouët, J. Kim, K. T. Therkildsen, A. Clairon, and A. Landragin, “Compact laser system for atom interferometry,” Appl. Phys. B: Lasers Opt. 84, 643 (2006).
[Crossref]

Petelski, T.

P. Cheinet, F. Pereira dos Santos, T. Petelski, J. Le Gouët, J. Kim, K. T. Therkildsen, A. Clairon, and A. Landragin, “Compact laser system for atom interferometry,” Appl. Phys. B: Lasers Opt. 84, 643 (2006).
[Crossref]

Peters, A.

V. Schkolnik, O. Hellmig, A. Wenzlawski, J. Grosse, A. Kohfeldt, K. Döringshoff, A. Wicht, P. Windpassinger, K. Sengstock, C. Braxmaier, M. Krutzik, and A. Peters, “A compact and robust diode laser system for atom interferometry on a sounding rocket,” Appl. Phys. B: Lasers Opt. 122, 217 (2016)
[Crossref]

C. Freier, M. Hauth, V. Schkolnik, B. Leykauf, M. Schilling, H. Wziontek, H.-G. Scherneck, J. Müller, and A. Peters, “Mobile quantum gravity sensor with unprecedented stability,” J. Phys.: Conf. Ser. 723, 012050 (2016).

A. Peters, K. Y. Chung, and S. Chu, “High-precision gravity measurements using atom interferometry,” Metrologia 38, 25 (2001).
[Crossref]

Phillips, W. D.

Plant, S. R.

A. Hinton, M. Perea-Ortiz, J. Winch, J. Briggs, S. Freer, D. Moustoukas, S. Powell-Gill, C. Squire, A. Lamb, C. Rammeloo, B. Stray, G. Voulazeris, L. Zhu, A. Kaushik, Y.-H. Lien, A. Niggebaum, A. Rodgers, A. Stabrawa, D. Boddice, S. R. Plant, G. W. Tuckwell, K. Bongs, N. Metje, and M. Holynski, “A portable magneto-optical trap with prospects for atom interferometry in civil engineering,” Phil. Trans. R. Soc. A 375, 20160238 (2017).
[Crossref] [PubMed]

Powell-Gill, S.

A. Hinton, M. Perea-Ortiz, J. Winch, J. Briggs, S. Freer, D. Moustoukas, S. Powell-Gill, C. Squire, A. Lamb, C. Rammeloo, B. Stray, G. Voulazeris, L. Zhu, A. Kaushik, Y.-H. Lien, A. Niggebaum, A. Rodgers, A. Stabrawa, D. Boddice, S. R. Plant, G. W. Tuckwell, K. Bongs, N. Metje, and M. Holynski, “A portable magneto-optical trap with prospects for atom interferometry in civil engineering,” Phil. Trans. R. Soc. A 375, 20160238 (2017).
[Crossref] [PubMed]

Prevedelli, M.

F. Sorrentino, Y.-H. Lien, G. Rosi, L. Cacciapuoti, M. Prevedelli, and G. M. Tino, “Sensitive gravity-gradiometry with atom interferometry: progress towards an improved determination of the gravitational constant,” New J. Phys. 12, 095009 (2010).
[Crossref]

Pursey, H.

P. Page and H. Pursey, “Tunable single sideband electro-optic ring modulator,” Opto-electronics 2, 1 (1970).
[Crossref]

Rammeloo, C.

A. Hinton, M. Perea-Ortiz, J. Winch, J. Briggs, S. Freer, D. Moustoukas, S. Powell-Gill, C. Squire, A. Lamb, C. Rammeloo, B. Stray, G. Voulazeris, L. Zhu, A. Kaushik, Y.-H. Lien, A. Niggebaum, A. Rodgers, A. Stabrawa, D. Boddice, S. R. Plant, G. W. Tuckwell, K. Bongs, N. Metje, and M. Holynski, “A portable magneto-optical trap with prospects for atom interferometry in civil engineering,” Phil. Trans. R. Soc. A 375, 20160238 (2017).
[Crossref] [PubMed]

Rasel, E.

B. Altschul, Q. G. Bailey, L. Blanchet, K. Bongs, P. Bouyer, L. Cacciapuoti, S. Capozziello, N. Gaaloul, D. Giulini, J. Hartwig, L. Iess, P. Jetzer, A. Landragin, E. Rasel, S. Reynaud, S. Schiller, C. Schubert, F. Sorrentino, U. Sterr, J. D. Tasson, G. M. Tino, P. Tuckey, and P. Wolf, “Quantum tests of the Einstein equivalence principle with the STE-QUEST space mission,” Adv. Space Res. 55, 501– 524 (2015).
[Crossref]

Renon, G.

F. Theron, O. Carraz, G. Renon, N. Zahzam, Y. Bidel, M. Cadoret, and A. Bresson, “Narrow linewidth single laser source system for onboard atom interferometry,” Appl. Phys. B: Lasers Opt. 118, 1–5 (2015).
[Crossref]

Reynaud, S.

B. Altschul, Q. G. Bailey, L. Blanchet, K. Bongs, P. Bouyer, L. Cacciapuoti, S. Capozziello, N. Gaaloul, D. Giulini, J. Hartwig, L. Iess, P. Jetzer, A. Landragin, E. Rasel, S. Reynaud, S. Schiller, C. Schubert, F. Sorrentino, U. Sterr, J. D. Tasson, G. M. Tino, P. Tuckey, and P. Wolf, “Quantum tests of the Einstein equivalence principle with the STE-QUEST space mission,” Adv. Space Res. 55, 501– 524 (2015).
[Crossref]

Riis, E.

M. Kasevich, D. S. Weiss, E. Riis, K. Moler, S. Kasapi, and S. Chu, “Atomic velocity selection using stimulated Raman transitions,” Phys. Rev. Lett. 66, 2297 (1991).
[Crossref] [PubMed]

Rodgers, A.

A. Hinton, M. Perea-Ortiz, J. Winch, J. Briggs, S. Freer, D. Moustoukas, S. Powell-Gill, C. Squire, A. Lamb, C. Rammeloo, B. Stray, G. Voulazeris, L. Zhu, A. Kaushik, Y.-H. Lien, A. Niggebaum, A. Rodgers, A. Stabrawa, D. Boddice, S. R. Plant, G. W. Tuckwell, K. Bongs, N. Metje, and M. Holynski, “A portable magneto-optical trap with prospects for atom interferometry in civil engineering,” Phil. Trans. R. Soc. A 375, 20160238 (2017).
[Crossref] [PubMed]

Rolston, S. L.

Rosi, G.

F. Sorrentino, Y.-H. Lien, G. Rosi, L. Cacciapuoti, M. Prevedelli, and G. M. Tino, “Sensitive gravity-gradiometry with atom interferometry: progress towards an improved determination of the gravitational constant,” New J. Phys. 12, 095009 (2010).
[Crossref]

Saitou, T.

S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, “Single side-band modulation performance of a LiNbO3 integrated modulator consisting of four-phase modulator waveguides,” IEEE Photonics Technol. Lett. 13, 364 (2001).
[Crossref]

Savoie, D.

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

Scherneck, H.-G.

C. Freier, M. Hauth, V. Schkolnik, B. Leykauf, M. Schilling, H. Wziontek, H.-G. Scherneck, J. Müller, and A. Peters, “Mobile quantum gravity sensor with unprecedented stability,” J. Phys.: Conf. Ser. 723, 012050 (2016).

Schiller, S.

B. Altschul, Q. G. Bailey, L. Blanchet, K. Bongs, P. Bouyer, L. Cacciapuoti, S. Capozziello, N. Gaaloul, D. Giulini, J. Hartwig, L. Iess, P. Jetzer, A. Landragin, E. Rasel, S. Reynaud, S. Schiller, C. Schubert, F. Sorrentino, U. Sterr, J. D. Tasson, G. M. Tino, P. Tuckey, and P. Wolf, “Quantum tests of the Einstein equivalence principle with the STE-QUEST space mission,” Adv. Space Res. 55, 501– 524 (2015).
[Crossref]

Schilling, M.

C. Freier, M. Hauth, V. Schkolnik, B. Leykauf, M. Schilling, H. Wziontek, H.-G. Scherneck, J. Müller, and A. Peters, “Mobile quantum gravity sensor with unprecedented stability,” J. Phys.: Conf. Ser. 723, 012050 (2016).

Schkolnik, V.

C. Freier, M. Hauth, V. Schkolnik, B. Leykauf, M. Schilling, H. Wziontek, H.-G. Scherneck, J. Müller, and A. Peters, “Mobile quantum gravity sensor with unprecedented stability,” J. Phys.: Conf. Ser. 723, 012050 (2016).

V. Schkolnik, O. Hellmig, A. Wenzlawski, J. Grosse, A. Kohfeldt, K. Döringshoff, A. Wicht, P. Windpassinger, K. Sengstock, C. Braxmaier, M. Krutzik, and A. Peters, “A compact and robust diode laser system for atom interferometry on a sounding rocket,” Appl. Phys. B: Lasers Opt. 122, 217 (2016)
[Crossref]

Schubert, C.

B. Altschul, Q. G. Bailey, L. Blanchet, K. Bongs, P. Bouyer, L. Cacciapuoti, S. Capozziello, N. Gaaloul, D. Giulini, J. Hartwig, L. Iess, P. Jetzer, A. Landragin, E. Rasel, S. Reynaud, S. Schiller, C. Schubert, F. Sorrentino, U. Sterr, J. D. Tasson, G. M. Tino, P. Tuckey, and P. Wolf, “Quantum tests of the Einstein equivalence principle with the STE-QUEST space mission,” Adv. Space Res. 55, 501– 524 (2015).
[Crossref]

Sengstock, K.

V. Schkolnik, O. Hellmig, A. Wenzlawski, J. Grosse, A. Kohfeldt, K. Döringshoff, A. Wicht, P. Windpassinger, K. Sengstock, C. Braxmaier, M. Krutzik, and A. Peters, “A compact and robust diode laser system for atom interferometry on a sounding rocket,” Appl. Phys. B: Lasers Opt. 122, 217 (2016)
[Crossref]

Shaddock, D. A.

Sheard, B. S.

Shikama, S.

M. Izutsu, S. Shikama, and T. Sueta, “Integrated optical SSB modulator/frequency shifter,” IEEE J. Quantum Electron. 17, 2225 (1981).
[Crossref]

Shimotsu, S.

S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, “Single side-band modulation performance of a LiNbO3 integrated modulator consisting of four-phase modulator waveguides,” IEEE Photonics Technol. Lett. 13, 364 (2001).
[Crossref]

Singh, Y.

K. Bongs, M. Holynski, and Y. Singh, “ψ in the sky,” Nat. Phys. 11, 615–617 (2015).
[Crossref]

Sorrentino, F.

B. Altschul, Q. G. Bailey, L. Blanchet, K. Bongs, P. Bouyer, L. Cacciapuoti, S. Capozziello, N. Gaaloul, D. Giulini, J. Hartwig, L. Iess, P. Jetzer, A. Landragin, E. Rasel, S. Reynaud, S. Schiller, C. Schubert, F. Sorrentino, U. Sterr, J. D. Tasson, G. M. Tino, P. Tuckey, and P. Wolf, “Quantum tests of the Einstein equivalence principle with the STE-QUEST space mission,” Adv. Space Res. 55, 501– 524 (2015).
[Crossref]

F. Sorrentino, Y.-H. Lien, G. Rosi, L. Cacciapuoti, M. Prevedelli, and G. M. Tino, “Sensitive gravity-gradiometry with atom interferometry: progress towards an improved determination of the gravitational constant,” New J. Phys. 12, 095009 (2010).
[Crossref]

Spinner, G.

Squire, C.

A. Hinton, M. Perea-Ortiz, J. Winch, J. Briggs, S. Freer, D. Moustoukas, S. Powell-Gill, C. Squire, A. Lamb, C. Rammeloo, B. Stray, G. Voulazeris, L. Zhu, A. Kaushik, Y.-H. Lien, A. Niggebaum, A. Rodgers, A. Stabrawa, D. Boddice, S. R. Plant, G. W. Tuckwell, K. Bongs, N. Metje, and M. Holynski, “A portable magneto-optical trap with prospects for atom interferometry in civil engineering,” Phil. Trans. R. Soc. A 375, 20160238 (2017).
[Crossref] [PubMed]

Stabrawa, A.

A. Hinton, M. Perea-Ortiz, J. Winch, J. Briggs, S. Freer, D. Moustoukas, S. Powell-Gill, C. Squire, A. Lamb, C. Rammeloo, B. Stray, G. Voulazeris, L. Zhu, A. Kaushik, Y.-H. Lien, A. Niggebaum, A. Rodgers, A. Stabrawa, D. Boddice, S. R. Plant, G. W. Tuckwell, K. Bongs, N. Metje, and M. Holynski, “A portable magneto-optical trap with prospects for atom interferometry in civil engineering,” Phil. Trans. R. Soc. A 375, 20160238 (2017).
[Crossref] [PubMed]

Stern, G.

Sterr, U.

B. Altschul, Q. G. Bailey, L. Blanchet, K. Bongs, P. Bouyer, L. Cacciapuoti, S. Capozziello, N. Gaaloul, D. Giulini, J. Hartwig, L. Iess, P. Jetzer, A. Landragin, E. Rasel, S. Reynaud, S. Schiller, C. Schubert, F. Sorrentino, U. Sterr, J. D. Tasson, G. M. Tino, P. Tuckey, and P. Wolf, “Quantum tests of the Einstein equivalence principle with the STE-QUEST space mission,” Adv. Space Res. 55, 501– 524 (2015).
[Crossref]

Stray, B.

A. Hinton, M. Perea-Ortiz, J. Winch, J. Briggs, S. Freer, D. Moustoukas, S. Powell-Gill, C. Squire, A. Lamb, C. Rammeloo, B. Stray, G. Voulazeris, L. Zhu, A. Kaushik, Y.-H. Lien, A. Niggebaum, A. Rodgers, A. Stabrawa, D. Boddice, S. R. Plant, G. W. Tuckwell, K. Bongs, N. Metje, and M. Holynski, “A portable magneto-optical trap with prospects for atom interferometry in civil engineering,” Phil. Trans. R. Soc. A 375, 20160238 (2017).
[Crossref] [PubMed]

Sueta, T.

M. Izutsu, S. Shikama, and T. Sueta, “Integrated optical SSB modulator/frequency shifter,” IEEE J. Quantum Electron. 17, 2225 (1981).
[Crossref]

Takase, K.

K. Takase, “Precision rotation rate measurements with a mobile atom interferometer,” Ph.D. thesis, University of Stanford (2008).

Tanner, C. E.

Tasson, J. D.

B. Altschul, Q. G. Bailey, L. Blanchet, K. Bongs, P. Bouyer, L. Cacciapuoti, S. Capozziello, N. Gaaloul, D. Giulini, J. Hartwig, L. Iess, P. Jetzer, A. Landragin, E. Rasel, S. Reynaud, S. Schiller, C. Schubert, F. Sorrentino, U. Sterr, J. D. Tasson, G. M. Tino, P. Tuckey, and P. Wolf, “Quantum tests of the Einstein equivalence principle with the STE-QUEST space mission,” Adv. Space Res. 55, 501– 524 (2015).
[Crossref]

Therkildsen, K. T.

P. Cheinet, F. Pereira dos Santos, T. Petelski, J. Le Gouët, J. Kim, K. T. Therkildsen, A. Clairon, and A. Landragin, “Compact laser system for atom interferometry,” Appl. Phys. B: Lasers Opt. 84, 643 (2006).
[Crossref]

Theron, F.

F. Theron, O. Carraz, G. Renon, N. Zahzam, Y. Bidel, M. Cadoret, and A. Bresson, “Narrow linewidth single laser source system for onboard atom interferometry,” Appl. Phys. B: Lasers Opt. 118, 1–5 (2015).
[Crossref]

Tino, G. M.

B. Altschul, Q. G. Bailey, L. Blanchet, K. Bongs, P. Bouyer, L. Cacciapuoti, S. Capozziello, N. Gaaloul, D. Giulini, J. Hartwig, L. Iess, P. Jetzer, A. Landragin, E. Rasel, S. Reynaud, S. Schiller, C. Schubert, F. Sorrentino, U. Sterr, J. D. Tasson, G. M. Tino, P. Tuckey, and P. Wolf, “Quantum tests of the Einstein equivalence principle with the STE-QUEST space mission,” Adv. Space Res. 55, 501– 524 (2015).
[Crossref]

F. Sorrentino, Y.-H. Lien, G. Rosi, L. Cacciapuoti, M. Prevedelli, and G. M. Tino, “Sensitive gravity-gradiometry with atom interferometry: progress towards an improved determination of the gravitational constant,” New J. Phys. 12, 095009 (2010).
[Crossref]

Tuckey, P.

B. Altschul, Q. G. Bailey, L. Blanchet, K. Bongs, P. Bouyer, L. Cacciapuoti, S. Capozziello, N. Gaaloul, D. Giulini, J. Hartwig, L. Iess, P. Jetzer, A. Landragin, E. Rasel, S. Reynaud, S. Schiller, C. Schubert, F. Sorrentino, U. Sterr, J. D. Tasson, G. M. Tino, P. Tuckey, and P. Wolf, “Quantum tests of the Einstein equivalence principle with the STE-QUEST space mission,” Adv. Space Res. 55, 501– 524 (2015).
[Crossref]

Tuckwell, G. W.

A. Hinton, M. Perea-Ortiz, J. Winch, J. Briggs, S. Freer, D. Moustoukas, S. Powell-Gill, C. Squire, A. Lamb, C. Rammeloo, B. Stray, G. Voulazeris, L. Zhu, A. Kaushik, Y.-H. Lien, A. Niggebaum, A. Rodgers, A. Stabrawa, D. Boddice, S. R. Plant, G. W. Tuckwell, K. Bongs, N. Metje, and M. Holynski, “A portable magneto-optical trap with prospects for atom interferometry in civil engineering,” Phil. Trans. R. Soc. A 375, 20160238 (2017).
[Crossref] [PubMed]

Venon, B.

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

Volodimer, L.

S. Merlet, L. Volodimer, M. Lours, and F. Pereira dos Santos, “A simple laser system for atom interferometry,” Appl. Phys. B: Lasers Opt. 117, 749 (2014).
[Crossref]

Voulazeris, G.

A. Hinton, M. Perea-Ortiz, J. Winch, J. Briggs, S. Freer, D. Moustoukas, S. Powell-Gill, C. Squire, A. Lamb, C. Rammeloo, B. Stray, G. Voulazeris, L. Zhu, A. Kaushik, Y.-H. Lien, A. Niggebaum, A. Rodgers, A. Stabrawa, D. Boddice, S. R. Plant, G. W. Tuckwell, K. Bongs, N. Metje, and M. Holynski, “A portable magneto-optical trap with prospects for atom interferometry in civil engineering,” Phil. Trans. R. Soc. A 375, 20160238 (2017).
[Crossref] [PubMed]

Watts, R. N.

Weiss, D. S.

M. Kasevich, D. S. Weiss, E. Riis, K. Moler, S. Kasapi, and S. Chu, “Atomic velocity selection using stimulated Raman transitions,” Phys. Rev. Lett. 66, 2297 (1991).
[Crossref] [PubMed]

Wenzlawski, A.

V. Schkolnik, O. Hellmig, A. Wenzlawski, J. Grosse, A. Kohfeldt, K. Döringshoff, A. Wicht, P. Windpassinger, K. Sengstock, C. Braxmaier, M. Krutzik, and A. Peters, “A compact and robust diode laser system for atom interferometry on a sounding rocket,” Appl. Phys. B: Lasers Opt. 122, 217 (2016)
[Crossref]

Westbrook, C. I.

Whitcomb, S. E.

Wicht, A.

V. Schkolnik, O. Hellmig, A. Wenzlawski, J. Grosse, A. Kohfeldt, K. Döringshoff, A. Wicht, P. Windpassinger, K. Sengstock, C. Braxmaier, M. Krutzik, and A. Peters, “A compact and robust diode laser system for atom interferometry on a sounding rocket,” Appl. Phys. B: Lasers Opt. 122, 217 (2016)
[Crossref]

Winch, J.

A. Hinton, M. Perea-Ortiz, J. Winch, J. Briggs, S. Freer, D. Moustoukas, S. Powell-Gill, C. Squire, A. Lamb, C. Rammeloo, B. Stray, G. Voulazeris, L. Zhu, A. Kaushik, Y.-H. Lien, A. Niggebaum, A. Rodgers, A. Stabrawa, D. Boddice, S. R. Plant, G. W. Tuckwell, K. Bongs, N. Metje, and M. Holynski, “A portable magneto-optical trap with prospects for atom interferometry in civil engineering,” Phil. Trans. R. Soc. A 375, 20160238 (2017).
[Crossref] [PubMed]

Windpassinger, P.

V. Schkolnik, O. Hellmig, A. Wenzlawski, J. Grosse, A. Kohfeldt, K. Döringshoff, A. Wicht, P. Windpassinger, K. Sengstock, C. Braxmaier, M. Krutzik, and A. Peters, “A compact and robust diode laser system for atom interferometry on a sounding rocket,” Appl. Phys. B: Lasers Opt. 122, 217 (2016)
[Crossref]

Wolf, P.

B. Altschul, Q. G. Bailey, L. Blanchet, K. Bongs, P. Bouyer, L. Cacciapuoti, S. Capozziello, N. Gaaloul, D. Giulini, J. Hartwig, L. Iess, P. Jetzer, A. Landragin, E. Rasel, S. Reynaud, S. Schiller, C. Schubert, F. Sorrentino, U. Sterr, J. D. Tasson, G. M. Tino, P. Tuckey, and P. Wolf, “Quantum tests of the Einstein equivalence principle with the STE-QUEST space mission,” Adv. Space Res. 55, 501– 524 (2015).
[Crossref]

Wysocki, G.

Wziontek, H.

C. Freier, M. Hauth, V. Schkolnik, B. Leykauf, M. Schilling, H. Wziontek, H.-G. Scherneck, J. Müller, and A. Peters, “Mobile quantum gravity sensor with unprecedented stability,” J. Phys.: Conf. Ser. 723, 012050 (2016).

Zahzam, N.

F. Theron, O. Carraz, G. Renon, N. Zahzam, Y. Bidel, M. Cadoret, and A. Bresson, “Narrow linewidth single laser source system for onboard atom interferometry,” Appl. Phys. B: Lasers Opt. 118, 1–5 (2015).
[Crossref]

O. Carraz, R. Charrière, M. Cadoret, N. Zahzam, Y. Bidel, and A. Bresson, “Phase shift in an atom interferometer induced by the additional laser lines of a Raman laser generated by modulation,” Phys. Rev. A 86, 033605 (2012).
[Crossref]

V. Ménoret, R. Geiger, G. Stern, N. Zahzam, B. Battelier, A. Bresson, A. Landragin, and P. Bouyer, “Dual-wavelength laser source for onboard atom interferometry,” Opt. Lett. 36, 4128 (2011).
[Crossref] [PubMed]

Zhu, L.

A. Hinton, M. Perea-Ortiz, J. Winch, J. Briggs, S. Freer, D. Moustoukas, S. Powell-Gill, C. Squire, A. Lamb, C. Rammeloo, B. Stray, G. Voulazeris, L. Zhu, A. Kaushik, Y.-H. Lien, A. Niggebaum, A. Rodgers, A. Stabrawa, D. Boddice, S. R. Plant, G. W. Tuckwell, K. Bongs, N. Metje, and M. Holynski, “A portable magneto-optical trap with prospects for atom interferometry in civil engineering,” Phil. Trans. R. Soc. A 375, 20160238 (2017).
[Crossref] [PubMed]

Zhu, M.

Adv. Space Res. (1)

B. Altschul, Q. G. Bailey, L. Blanchet, K. Bongs, P. Bouyer, L. Cacciapuoti, S. Capozziello, N. Gaaloul, D. Giulini, J. Hartwig, L. Iess, P. Jetzer, A. Landragin, E. Rasel, S. Reynaud, S. Schiller, C. Schubert, F. Sorrentino, U. Sterr, J. D. Tasson, G. M. Tino, P. Tuckey, and P. Wolf, “Quantum tests of the Einstein equivalence principle with the STE-QUEST space mission,” Adv. Space Res. 55, 501– 524 (2015).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B: Lasers Opt. (4)

V. Schkolnik, O. Hellmig, A. Wenzlawski, J. Grosse, A. Kohfeldt, K. Döringshoff, A. Wicht, P. Windpassinger, K. Sengstock, C. Braxmaier, M. Krutzik, and A. Peters, “A compact and robust diode laser system for atom interferometry on a sounding rocket,” Appl. Phys. B: Lasers Opt. 122, 217 (2016)
[Crossref]

P. Cheinet, F. Pereira dos Santos, T. Petelski, J. Le Gouët, J. Kim, K. T. Therkildsen, A. Clairon, and A. Landragin, “Compact laser system for atom interferometry,” Appl. Phys. B: Lasers Opt. 84, 643 (2006).
[Crossref]

S. Merlet, L. Volodimer, M. Lours, and F. Pereira dos Santos, “A simple laser system for atom interferometry,” Appl. Phys. B: Lasers Opt. 117, 749 (2014).
[Crossref]

F. Theron, O. Carraz, G. Renon, N. Zahzam, Y. Bidel, M. Cadoret, and A. Bresson, “Narrow linewidth single laser source system for onboard atom interferometry,” Appl. Phys. B: Lasers Opt. 118, 1–5 (2015).
[Crossref]

Appl. Phys. Lett. (1)

C. F. Buhrer, D. Baird, and E. M. Conwell, “Optical frequency shifting by electro-optic effect,” Appl. Phys. Lett. 1, 46 (1962).
[Crossref]

Class. Quantum Grav. (1)

T. L. Gustavson, A. Landragin, and M. A. Kasevich, “Rotation sensing with a dual atom-interferometer sagnac gyroscope,” Class. Quantum Grav. 17, 2385 (2000).
[Crossref]

IEEE J. Quantum Electron. (1)

M. Izutsu, S. Shikama, and T. Sueta, “Integrated optical SSB modulator/frequency shifter,” IEEE J. Quantum Electron. 17, 2225 (1981).
[Crossref]

IEEE Photonics Technol. Lett. (1)

S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, “Single side-band modulation performance of a LiNbO3 integrated modulator consisting of four-phase modulator waveguides,” IEEE Photonics Technol. Lett. 13, 364 (2001).
[Crossref]

J. Opt. Soc. Am. B (2)

J. Phys.: Conf. Ser. (1)

C. Freier, M. Hauth, V. Schkolnik, B. Leykauf, M. Schilling, H. Wziontek, H.-G. Scherneck, J. Müller, and A. Peters, “Mobile quantum gravity sensor with unprecedented stability,” J. Phys.: Conf. Ser. 723, 012050 (2016).

Metrologia (1)

A. Peters, K. Y. Chung, and S. Chu, “High-precision gravity measurements using atom interferometry,” Metrologia 38, 25 (2001).
[Crossref]

Nat. Phys. (1)

K. Bongs, M. Holynski, and Y. Singh, “ψ in the sky,” Nat. Phys. 11, 615–617 (2015).
[Crossref]

New J. Phys. (1)

F. Sorrentino, Y.-H. Lien, G. Rosi, L. Cacciapuoti, M. Prevedelli, and G. M. Tino, “Sensitive gravity-gradiometry with atom interferometry: progress towards an improved determination of the gravitational constant,” New J. Phys. 12, 095009 (2010).
[Crossref]

Opt. Commun. (1)

J. Le Gouët, J. Kim, C. Bourassin-Bouchet, M. Lours, A. Landragin, and F. Pereira dos Santos, “Wide bandwidth phase-locked diode laser with an intra-cavity electro-optic modulator,” Opt. Commun. 282, 977 (2009).
[Crossref]

Opt. Express (1)

Opt. Lett. (3)

Opto-electronics (1)

P. Page and H. Pursey, “Tunable single sideband electro-optic ring modulator,” Opto-electronics 2, 1 (1970).
[Crossref]

Phil. Trans. R. Soc. A (1)

A. Hinton, M. Perea-Ortiz, J. Winch, J. Briggs, S. Freer, D. Moustoukas, S. Powell-Gill, C. Squire, A. Lamb, C. Rammeloo, B. Stray, G. Voulazeris, L. Zhu, A. Kaushik, Y.-H. Lien, A. Niggebaum, A. Rodgers, A. Stabrawa, D. Boddice, S. R. Plant, G. W. Tuckwell, K. Bongs, N. Metje, and M. Holynski, “A portable magneto-optical trap with prospects for atom interferometry in civil engineering,” Phil. Trans. R. Soc. A 375, 20160238 (2017).
[Crossref] [PubMed]

Phys. Rev. A (1)

O. Carraz, R. Charrière, M. Cadoret, N. Zahzam, Y. Bidel, and A. Bresson, “Phase shift in an atom interferometer induced by the additional laser lines of a Raman laser generated by modulation,” Phys. Rev. A 86, 033605 (2012).
[Crossref]

Phys. Rev. Lett. (3)

M. Kasevich, D. S. Weiss, E. Riis, K. Moler, S. Kasapi, and S. Chu, “Atomic velocity selection using stimulated Raman transitions,” Phys. Rev. Lett. 66, 2297 (1991).
[Crossref] [PubMed]

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

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

Other (2)

“Muquans Absolute Quantum Gravimeter,” https://www.muquans.com/index.php/products/aqg

K. Takase, “Precision rotation rate measurements with a mobile atom interferometer,” Ph.D. thesis, University of Stanford (2008).

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Figures (9)

Fig. 1
Fig. 1 Simplified diagram of the apparatus. A simplified 87Rb level diagram is included as an inset. The pair of the counter-propagating beams ks0 ↓ and ks1 ↑ are resonant with a two-photon Raman transition between the magnetically insensitive hyperfine sublevels mF = 0. FS 1: 1560 nm 1:99 fibre splitter. FS 2: 780 nm 1:20 fibre splitter. FPI 1, 2: 1560 nm and 780 nm Fabry-Pérot Interferometer, respectively. All fibers are polarization-maintaining.
Fig. 2
Fig. 2 Simulation of the optical power ratio of the sidebands with respect to the carrier after the SHG. The power ratio where is −3 dB is denoted in dashed line.
Fig. 3
Fig. 3 The FC- and SC-OSSB spectra. (a) and (c) are the 1560 nm spectra of FC- and SC-OSSB, respectively. (b) and (d) are the 780 nm spectra of FC- and SC-OSSB, respectively. The FSRs of FPIs are marked by the blue dash lines.
Fig. 4
Fig. 4 The 780 nm sideband ratio verse the modulation frequency. The ratio ωs1/ωs0 is to −3 dB at 6.834 GHz. The subfigure (b) is the red dash boxed region in (a).
Fig. 5
Fig. 5 The interferometric fringes for determining local gravity. The chirp rate at the stationary phase point is 25, 164, 858 ± 12 Hz, from which the local gravity can be derived to be 9.817239(4) m/s2.
Fig. 6
Fig. 6 The Raman laser system for measuring the spatial dependence of the Raman transition probability.
Fig. 7
Fig. 7 The spatial dependence of the Raman transition probability. The Raman transition probabilities are measured along the beam axis with FC-OSSB and EOM Raman lasers. P1 (yellow) and P2 (green) represent two atom interferometers operate at different locations.
Fig. 8
Fig. 8 The interferometric fringes from different Raman laser schemes. From top to bottom, the EOM(U) scheme assuming single global Rabi frequency, the EOM(C) scheme compensating local Rabi frequency variation, and FC-OSSB.
Fig. 9
Fig. 9 Illustration of the simplified structure of a dual parallel Mach-Zehnder modulator. Sine phase modulator: Δϕs = β sin ωmt. Cosine phase modulator: Δϕc = β cos ωmt. Φ1, 2, 3: optical phase shifter.

Tables (1)

Tables Icon

Table 1 The phase shifts and the contrasts of the interferometric fringes from different Raman laser schemes. The results for P1 and P2 are marked by black and red respectively.

Equations (13)

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Δ Φ RAI = cos 1 ( P 1 P 1 + P 2 ) = ( k eff g α ) T 2
8 ( 1 + e i π / 2 ) J 2 ( β ) J 1 ( β ) e i ( ω 2 + ω 1 ) t
8 e i π / 2 [ J 0 ( β ) J 2 ( β ) e i ( ω 0 + ω 2 ) t J 1 ( β ) J 1 ( β ) e i ( ω 1 + ω 1 ) t ]
E o = E ( 1 ) + E ( 2 ) + ( E ( 3 ) + E ( 4 ) ) e i Φ 3 = E i 2 e i ω c t [ e i ( β sin ω m t ) + e i ( β sin ( ω m t ) + Φ 1 ) + e i ( β cos ( ω m t ) + Φ 3 ) + e i ( β cos ( ω m t ) + Φ 2 + Φ 3 ) ] = E i 2 e i ω c t [ J n ( β ) e i n ω m t + J n ( β ) e i ( n ω m t + Φ 1 ) + J n ( β ) e i ( n ω m t + π / 2 ) + Φ 3 ) ] + J n ( β ) e i ( n ( ω m t + π / 2 ) + Φ 2 + Φ 3 ) = E i 2 e i ω c t { C 0 J 0 ( β ) + n = 1 [ A n J n ( β ) e i n ω m t + B n J n ( β ) e i n ω m t ] }
C 0 = 1 + e i Φ 1 + e i Φ 3 ( 1 + e i Φ 2 )
A n = 1 + ( 1 ) n e i Φ 1 + e i Φ 3 [ e i n π 2 + ( 1 ) n e i ( n π 2 + Φ 2 ) ]
B n = ( 1 ) n + e i Φ 1 + e i Φ 3 [ ( 1 ) n e i n π 2 + e i ( n π 2 + Φ 2 ) ]
E o = E i 2 [ 2 J 0 ( β ) e i ω c t + 2 ( 1 e i π / 2 ) J 1 ( β ) e i ( ω c ω m ) t + 2 e i π / 2 J 2 ( β ) e i ( ω c + 2 ω m t ) + 2 e i π / 2 J 1 ( β ) e i ( ω c 2 ω m t ) 2 ( 1 e i π / 2 ) J 3 ( β ) e i ( ω c 3 ω m t ) + 2 J 4 ( β ) e i ( ω c + 4 ω m t ) + 2 J 4 ( β ) e i ( ω c 4 ω m ) t + ]
E o = E i 2 [ 4 J 1 ( β ) e i ( ω c ω m ) t 4 J 3 ( β ) e i ( ω c 3 ω m ) t + 4 J 5 ( β ) e i ( ω c + 5 ω m ) t + ]
E S FC 0 χ 2 E o 2 0 χ 2 E i 2 4 { [ ( 4 J 0 2 ( β ) 8 J 2 2 ( β ) ) ] e i ω s 0 t + 8 ( 1 e i π / 2 ) J 0 ( β ) J 1 ( β ) e i ω s 1 t + 8 ( 1 + e i π / 2 ) J 2 ( β ) J 1 ( β ) e i ω s 1 t + 8 e i π / 2 [ J 0 ( β ) J 2 ( β ) J 1 ( β ) J 1 ( β ) ] e i ω s 2 t + 8 e i π / 2 [ J 0 ( β ) J 2 ( β ) 2 J 3 ( β ) J 1 ( β ) ] e i ω s 2 t + 8 ( 1 + e i π / 2 ) J 1 ( β ) J 2 ( β ) e i ω s 3 t + 8 ( 1 e i π / 2 ) J 0 ( β ) J 3 ( β ) e i ω s 3 t + [ 8 J 0 ( β ) J 4 ( β ) 4 J 2 2 ( β ) ] e i ω s 4 t + [ 8 J 0 ( β ) J 4 ( β ) 4 J 2 2 ( β ) ] e i ω s 4 t ] }
ω n = ω c + n ω m ω 0 = ω c , ω 1 = ω c + ω m , ω 1 = ω c ω m
ω s n = 2 ω c + n ω m ω s 0 = 2 ω c , ω s 1 = 2 ω c + ω m , ω s 1 = 2 ω c ω m
E S SC 0 χ 2 E o 2 = 0 χ 2 E i 2 4 [ 16 J 1 ( β ) J 1 ( β ) e i ω s 2 t + 32 J 3 ( β ) J 1 ( β ) e i ω s 2 t ]

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