Abstract

We present a method to engineer the frequency splitting of polarization eigenmodes in fiber Fabry-Perot (FFP) cavities. Using specific patterns of multiple CO2 laser pulses, we machine paraboloidal micromirrors with controlled elliptical shape in a large range of radii of curvature. This method is versatile and can be used to produce cavities with maximized or near-zero polarization mode splitting. In addition, we realize dual-wavelength FFP cavities with finesse exceeding 40 000 at 780 nm and at 1559 nm in the telecom range. We provide direct evidence that the birefringent frequency splitting in FFP cavities is governed only by the geometrical shape of the mirrors, and that the astigmatism of the cavity modes needs to be taken into account for specific cavities.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Millimeter-long fiber Fabry-Perot cavities

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    [Crossref]
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2018 (1)

J.-M. Cui, K. Zhou, M.-S. Zhao, M.-Z. Ai, C.-K. Hu, Q. Li, B.-H. Liu, J.-L. Peng, Y.-F. Huang, C.-F. Li, and G.-C. Guo, “Polarization nondegenerate fiber Fabry-Perot cavities with large tunable splittings,” Appl. Phys. Lett. 112, 171105 (2018).
[Crossref]

2017 (1)

H. Zhong, G. Fläschner, A. Schwarz, R. Wiesendanger, P. Christoph, T. Wagner, A. Bick, C. Staarmann, B. Abeln, K. Sengstock, and C. Becker, “A millikelvin all-fiber cavity optomechanical apparatus for merging with ultra-cold atoms in a hybrid quantum system,” Rev. Sci. Instrum. 88, 023115 (2017).
[Crossref] [PubMed]

2016 (7)

H. Kaupp, T. Hümmer, M. Mader, B. Schlederer, J. Benedikter, P. Haeusser, H. C. Chang, H. Fedder, T. W. Hänsch, and D. Hunger, “Purcell-enhanced single-photon emission from nitrogen-vacancy centers coupled to a tunable microcavity,” Phys. Rev. Appl. 6, 054010 (2016).
[Crossref]

A. Jeantet, Y. Chassagneux, C. Raynaud, P. Roussignol, J. S. Lauret, B. Besga, J. Estève, J. Reichel, and C. Voisin, “Widely tunable single-photon source from a carbon nanotube in the Purcell regime,” Phys. Rev. Lett. 116, 247402 (2016).
[Crossref] [PubMed]

T. Hümmer, J. Noe, M. S. Hofmann, T. W. Hänsch, A. Högele, and D. Hunger, “Cavity-enhanced Raman microscopy of individual carbon nanotubes,” Nat. Commun. 7, 12155 (2016).
[Crossref] [PubMed]

J. Gallego, S. Ghosh, S. K. Alavi, W. Alt, M. Martinez-Dorantes, D. Meschede, and L. Ratschbacher, “High-finesse fiber Fabry-Perot cavities: stabilization and mode matching analysis,” Appl. Phys. B 122, 47 (2016).
[Crossref]

A. D. Kashkanova, A. B. Shkarin, C. D. Brown, N. E. Flowers-Jacobs, L. Childress, S. W. Hoch, L. Hohmann, K. Ott, J. Reichel, and J. G. E. Harris, “Superfluid Brillouin optomechanics,” Nat. Phys. 13, 74–79 (2016).
[Crossref]

A. J. Fleisher, D. A. Long, Q. Liu, and J. T. Hodges, “Precision interferometric measurements of mirror birefringence in high-finesse optical resonators,” Phys. Rev. A 93, 013833 (2016).
[Crossref]

K. Ott, S. Garcia, R. Kohlhaas, K. Schüppert, P. Rosenbusch, R. Long, and J. Reichel, “Millimeter-long fiber Fabry-Perot cavities,” Opt. Express 24, 9839–9853 (2016).
[Crossref] [PubMed]

2015 (4)

A. A. P. Trichet, P. R. Dolan, D. M. Coles, G. M. Hughes, and J. M. Smith, “Topographic control of open-access microcavities at the nanometer scale,” Opt. Express 23, 17205–17216 (2015).
[Crossref] [PubMed]

L. C. Flatten., A. A. P. Trichet, and J. M. Smith, “Spectral engineering of coupled open-access microcavities,” Laser Photonics Rev. 10, 257–263 (2015).
[Crossref]

G. Barontini, L. Hohmann, F. Haas, J. Esteve, and J. Reichel, “Deterministic generation of multiparticle entanglement by quantum Zeno dynamics,” Science 349, 1317–1321 (2015).
[Crossref] [PubMed]

M. Uphoff, M. Brekenfeld, G. Rempe, and S. Ritter, “Frequency splitting of polarization eigenmodes in microscopic Fabry-Perot cavities,” New J. Phys. 17, 013053 (2015).
[Crossref]

2014 (3)

L. Greuther, S. Starosielec, D. Najer, A. Ludwig, L. Duempelmann, D. Rohner, and R. J. Warburton, “A small mode volume tunable microcavity: Development and characterization,” Appl. Phys. Lett. 105, 121105 (2014).
[Crossref]

A. Reiserer, N. Kalb, G. Rempe, and S. Ritter, “A quantum gate between a flying optical photon and a single trapped atom,” Nature 508, 237–240 (2014).
[Crossref] [PubMed]

H. Takahashi, J. Morphew, F. Oručević, A. Noguchi, E. Kassa, and M. Keller, “Novel laser machining of optical fibers for long cavities with low birefringence,” Opt. Express 22, 31317–31328 (2014).
[Crossref]

2013 (4)

B. Brandstätter, A. McClung, K. Schüppert, B. Casabone, K. Friebe, A. Stute, P. O. Schmidt, C. Deutsch, J. Reichel, R. Blatt, and T. E. Northup, “Integrated fiber-mirror ion trap for strong ion-cavity coupling,” Rev. Sci. Instrum. 84, 123104 (2013).
[Crossref]

M. Steiner, H. M. Meyer, C. Deutsch, J. Reichel, and M. Köhl, “Single ion coupled to an optical fiber cavity,” Phys. Rev. Lett. 110, 043003 (2013).
[Crossref] [PubMed]

J. Miguel-Sánchez, A. Reinhard, E. Togan, T. Volz, A. Imamoglu, B. Besga, J. Reichel, and J. Estève, “Cavity quantum electrodynamics with charge-controlled quantum dots coupled to a fiber Fabry-Perot cavity,” New J. Phys. 15, 045002 (2013).
[Crossref]

R. Albrecht, A. Bommer, C. Deutsch, J. Reichel, and C. Becher, “Coupling of a single nitrogen-vacancy center in diamond to a fiber-based microcavity,” Phys. Rev. Lett. 110, 243602 (2013).
[Crossref] [PubMed]

2012 (4)

N. E. Flowers-Jacobs, S. W. Hoch, J. C. Sankey, A. Kashkanova, A. M. Jayich, C. Deutsch, J. Reichel, and J. G. E. Harris, “Fiber-cavity-based optomechanical device,” Appl. Phys. Lett. 101, 221109 (2012).
[Crossref]

H. Weber, “Rays and fields in general astigmatic resonators,” J. Mod. Opt. 59, 740–770 (2012).
[Crossref]

D. Hunger, C. Deutsch, R. J. Barbour, R. J. Warburton, and J. Reichel, “Laser micro-fabrication of concave, low-roughness features in silica,” AIP Adv. 2, 012119 (2012).
[Crossref]

A. Stute, B. Casabone, P. Schindler, T. Monz, P. O. Schmidt, B. Brandstätter, T. E. Northup, and R. Blatt, “Tunable ion-photon entanglement in an optical cavity,” Nature 485, 482–485 (2012).
[Crossref] [PubMed]

2011 (3)

J. Volz, R. Gehr, G. Dubois, J. Estève, and J. Reichel, “Measurement of the internal state of a single atom without energy exchange,” Nature 475, 210–213 (2011).
[Crossref] [PubMed]

R. J. Barbour, P. A. Dalgarno, A. Curran, K. M. Nowak, H. J. Baker, D. R. Hall, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “A tunable microcavity,” J. Appl. Phys. 110, 053107 (2011).
[Crossref]

B. Petrak, K. Konthasinghe, S. Perez, and A. Muller, “Feedback-controlled laser fabrication of micromirror substrates,” Rev. Sci. Instrum. 82, 123112 (2011).
[Crossref]

2010 (4)

C. Toninelli, Y. Delley, T. Stöferle, A. Renn, S. Götzinger, and V. Sandoghdar, “A scanning microcavity for in situ control of single-molecule emission,” Appl. Phys. Lett. 97, 021107 (2010).
[Crossref]

D. Hunger, T. Steinmetz, Y. Colombe, C. Deutsch, T. W. Hänsch, and J. Reichel, “A fiber Fabry-Perot cavity with high finesse,” New J. Phys. 12, 065038 (2010).
[Crossref]

R. Gehr, J. Volz, G. Dubois, T. Steinmetz, Y. Colombe, B. L. Lev, R. Long, J. Estève, and J. Reichel, “Cavity-based single atom preparation and high-fidelity hyperfine state readout,” Phys. Rev. Lett. 104, 203602 (2010).
[Crossref] [PubMed]

A. Muller, E. B. Flagg, J. R. Lawall, and G. S. Solomon, “Ultrahigh-finesse, low-mode-volume Fabry-Perot microcavity,” Opt. Lett. 35, 2293–2295 (2010).
[Crossref] [PubMed]

2009 (1)

F. Bielsa, A. Dupays, M. Fouché, R. Battesti, C. Robilliard, and C. Rizzo, “Birefringence of interferential mirrors at normal incidence,” Appl. Phys. B 97, 457–463 (2009).
[Crossref]

2007 (2)

S. J. Habraken and G. Nienhuis, “Modes of a twisted optical cavity,” Phys. Rev. A 75, 033819 (2007).
[Crossref]

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom-field coupling for Bose-Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (2007).
[Crossref] [PubMed]

1997 (1)

1969 (1)

1941 (1)

Abeln, B.

H. Zhong, G. Fläschner, A. Schwarz, R. Wiesendanger, P. Christoph, T. Wagner, A. Bick, C. Staarmann, B. Abeln, K. Sengstock, and C. Becker, “A millikelvin all-fiber cavity optomechanical apparatus for merging with ultra-cold atoms in a hybrid quantum system,” Rev. Sci. Instrum. 88, 023115 (2017).
[Crossref] [PubMed]

Ai, M.-Z.

J.-M. Cui, K. Zhou, M.-S. Zhao, M.-Z. Ai, C.-K. Hu, Q. Li, B.-H. Liu, J.-L. Peng, Y.-F. Huang, C.-F. Li, and G.-C. Guo, “Polarization nondegenerate fiber Fabry-Perot cavities with large tunable splittings,” Appl. Phys. Lett. 112, 171105 (2018).
[Crossref]

Alavi, S. K.

J. Gallego, S. Ghosh, S. K. Alavi, W. Alt, M. Martinez-Dorantes, D. Meschede, and L. Ratschbacher, “High-finesse fiber Fabry-Perot cavities: stabilization and mode matching analysis,” Appl. Phys. B 122, 47 (2016).
[Crossref]

Albrecht, R.

R. Albrecht, A. Bommer, C. Deutsch, J. Reichel, and C. Becher, “Coupling of a single nitrogen-vacancy center in diamond to a fiber-based microcavity,” Phys. Rev. Lett. 110, 243602 (2013).
[Crossref] [PubMed]

Alt, W.

J. Gallego, S. Ghosh, S. K. Alavi, W. Alt, M. Martinez-Dorantes, D. Meschede, and L. Ratschbacher, “High-finesse fiber Fabry-Perot cavities: stabilization and mode matching analysis,” Appl. Phys. B 122, 47 (2016).
[Crossref]

Arnaud, J. A.

Baker, H. J.

R. J. Barbour, P. A. Dalgarno, A. Curran, K. M. Nowak, H. J. Baker, D. R. Hall, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “A tunable microcavity,” J. Appl. Phys. 110, 053107 (2011).
[Crossref]

Barbour, R. J.

D. Hunger, C. Deutsch, R. J. Barbour, R. J. Warburton, and J. Reichel, “Laser micro-fabrication of concave, low-roughness features in silica,” AIP Adv. 2, 012119 (2012).
[Crossref]

R. J. Barbour, P. A. Dalgarno, A. Curran, K. M. Nowak, H. J. Baker, D. R. Hall, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “A tunable microcavity,” J. Appl. Phys. 110, 053107 (2011).
[Crossref]

Barontini, G.

G. Barontini, L. Hohmann, F. Haas, J. Esteve, and J. Reichel, “Deterministic generation of multiparticle entanglement by quantum Zeno dynamics,” Science 349, 1317–1321 (2015).
[Crossref] [PubMed]

Battesti, R.

F. Bielsa, A. Dupays, M. Fouché, R. Battesti, C. Robilliard, and C. Rizzo, “Birefringence of interferential mirrors at normal incidence,” Appl. Phys. B 97, 457–463 (2009).
[Crossref]

Becher, C.

R. Albrecht, A. Bommer, C. Deutsch, J. Reichel, and C. Becher, “Coupling of a single nitrogen-vacancy center in diamond to a fiber-based microcavity,” Phys. Rev. Lett. 110, 243602 (2013).
[Crossref] [PubMed]

Becker, C.

H. Zhong, G. Fläschner, A. Schwarz, R. Wiesendanger, P. Christoph, T. Wagner, A. Bick, C. Staarmann, B. Abeln, K. Sengstock, and C. Becker, “A millikelvin all-fiber cavity optomechanical apparatus for merging with ultra-cold atoms in a hybrid quantum system,” Rev. Sci. Instrum. 88, 023115 (2017).
[Crossref] [PubMed]

Benedikter, J.

H. Kaupp, T. Hümmer, M. Mader, B. Schlederer, J. Benedikter, P. Haeusser, H. C. Chang, H. Fedder, T. W. Hänsch, and D. Hunger, “Purcell-enhanced single-photon emission from nitrogen-vacancy centers coupled to a tunable microcavity,” Phys. Rev. Appl. 6, 054010 (2016).
[Crossref]

Berger, V.

Besga, B.

A. Jeantet, Y. Chassagneux, C. Raynaud, P. Roussignol, J. S. Lauret, B. Besga, J. Estève, J. Reichel, and C. Voisin, “Widely tunable single-photon source from a carbon nanotube in the Purcell regime,” Phys. Rev. Lett. 116, 247402 (2016).
[Crossref] [PubMed]

J. Miguel-Sánchez, A. Reinhard, E. Togan, T. Volz, A. Imamoglu, B. Besga, J. Reichel, and J. Estève, “Cavity quantum electrodynamics with charge-controlled quantum dots coupled to a fiber Fabry-Perot cavity,” New J. Phys. 15, 045002 (2013).
[Crossref]

Bick, A.

H. Zhong, G. Fläschner, A. Schwarz, R. Wiesendanger, P. Christoph, T. Wagner, A. Bick, C. Staarmann, B. Abeln, K. Sengstock, and C. Becker, “A millikelvin all-fiber cavity optomechanical apparatus for merging with ultra-cold atoms in a hybrid quantum system,” Rev. Sci. Instrum. 88, 023115 (2017).
[Crossref] [PubMed]

Bielsa, F.

F. Bielsa, A. Dupays, M. Fouché, R. Battesti, C. Robilliard, and C. Rizzo, “Birefringence of interferential mirrors at normal incidence,” Appl. Phys. B 97, 457–463 (2009).
[Crossref]

Blatt, R.

B. Brandstätter, A. McClung, K. Schüppert, B. Casabone, K. Friebe, A. Stute, P. O. Schmidt, C. Deutsch, J. Reichel, R. Blatt, and T. E. Northup, “Integrated fiber-mirror ion trap for strong ion-cavity coupling,” Rev. Sci. Instrum. 84, 123104 (2013).
[Crossref]

A. Stute, B. Casabone, P. Schindler, T. Monz, P. O. Schmidt, B. Brandstätter, T. E. Northup, and R. Blatt, “Tunable ion-photon entanglement in an optical cavity,” Nature 485, 482–485 (2012).
[Crossref] [PubMed]

Bommer, A.

R. Albrecht, A. Bommer, C. Deutsch, J. Reichel, and C. Becher, “Coupling of a single nitrogen-vacancy center in diamond to a fiber-based microcavity,” Phys. Rev. Lett. 110, 243602 (2013).
[Crossref] [PubMed]

Brandstätter, B.

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L. C. Flatten., A. A. P. Trichet, and J. M. Smith, “Spectral engineering of coupled open-access microcavities,” Laser Photonics Rev. 10, 257–263 (2015).
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M. Uphoff, M. Brekenfeld, G. Rempe, and S. Ritter, “Frequency splitting of polarization eigenmodes in microscopic Fabry-Perot cavities,” New J. Phys. 17, 013053 (2015).
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J. Miguel-Sánchez, A. Reinhard, E. Togan, T. Volz, A. Imamoglu, B. Besga, J. Reichel, and J. Estève, “Cavity quantum electrodynamics with charge-controlled quantum dots coupled to a fiber Fabry-Perot cavity,” New J. Phys. 15, 045002 (2013).
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D. Hunger, C. Deutsch, R. J. Barbour, R. J. Warburton, and J. Reichel, “Laser micro-fabrication of concave, low-roughness features in silica,” AIP Adv. 2, 012119 (2012).
[Crossref]

R. J. Barbour, P. A. Dalgarno, A. Curran, K. M. Nowak, H. J. Baker, D. R. Hall, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “A tunable microcavity,” J. Appl. Phys. 110, 053107 (2011).
[Crossref]

Weber, H.

H. Weber, “Rays and fields in general astigmatic resonators,” J. Mod. Opt. 59, 740–770 (2012).
[Crossref]

Wiesendanger, R.

H. Zhong, G. Fläschner, A. Schwarz, R. Wiesendanger, P. Christoph, T. Wagner, A. Bick, C. Staarmann, B. Abeln, K. Sengstock, and C. Becker, “A millikelvin all-fiber cavity optomechanical apparatus for merging with ultra-cold atoms in a hybrid quantum system,” Rev. Sci. Instrum. 88, 023115 (2017).
[Crossref] [PubMed]

Zhao, M.-S.

J.-M. Cui, K. Zhou, M.-S. Zhao, M.-Z. Ai, C.-K. Hu, Q. Li, B.-H. Liu, J.-L. Peng, Y.-F. Huang, C.-F. Li, and G.-C. Guo, “Polarization nondegenerate fiber Fabry-Perot cavities with large tunable splittings,” Appl. Phys. Lett. 112, 171105 (2018).
[Crossref]

Zhong, H.

H. Zhong, G. Fläschner, A. Schwarz, R. Wiesendanger, P. Christoph, T. Wagner, A. Bick, C. Staarmann, B. Abeln, K. Sengstock, and C. Becker, “A millikelvin all-fiber cavity optomechanical apparatus for merging with ultra-cold atoms in a hybrid quantum system,” Rev. Sci. Instrum. 88, 023115 (2017).
[Crossref] [PubMed]

Zhou, K.

J.-M. Cui, K. Zhou, M.-S. Zhao, M.-Z. Ai, C.-K. Hu, Q. Li, B.-H. Liu, J.-L. Peng, Y.-F. Huang, C.-F. Li, and G.-C. Guo, “Polarization nondegenerate fiber Fabry-Perot cavities with large tunable splittings,” Appl. Phys. Lett. 112, 171105 (2018).
[Crossref]

AIP Adv. (1)

D. Hunger, C. Deutsch, R. J. Barbour, R. J. Warburton, and J. Reichel, “Laser micro-fabrication of concave, low-roughness features in silica,” AIP Adv. 2, 012119 (2012).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (2)

F. Bielsa, A. Dupays, M. Fouché, R. Battesti, C. Robilliard, and C. Rizzo, “Birefringence of interferential mirrors at normal incidence,” Appl. Phys. B 97, 457–463 (2009).
[Crossref]

J. Gallego, S. Ghosh, S. K. Alavi, W. Alt, M. Martinez-Dorantes, D. Meschede, and L. Ratschbacher, “High-finesse fiber Fabry-Perot cavities: stabilization and mode matching analysis,” Appl. Phys. B 122, 47 (2016).
[Crossref]

Appl. Phys. Lett. (4)

C. Toninelli, Y. Delley, T. Stöferle, A. Renn, S. Götzinger, and V. Sandoghdar, “A scanning microcavity for in situ control of single-molecule emission,” Appl. Phys. Lett. 97, 021107 (2010).
[Crossref]

N. E. Flowers-Jacobs, S. W. Hoch, J. C. Sankey, A. Kashkanova, A. M. Jayich, C. Deutsch, J. Reichel, and J. G. E. Harris, “Fiber-cavity-based optomechanical device,” Appl. Phys. Lett. 101, 221109 (2012).
[Crossref]

L. Greuther, S. Starosielec, D. Najer, A. Ludwig, L. Duempelmann, D. Rohner, and R. J. Warburton, “A small mode volume tunable microcavity: Development and characterization,” Appl. Phys. Lett. 105, 121105 (2014).
[Crossref]

J.-M. Cui, K. Zhou, M.-S. Zhao, M.-Z. Ai, C.-K. Hu, Q. Li, B.-H. Liu, J.-L. Peng, Y.-F. Huang, C.-F. Li, and G.-C. Guo, “Polarization nondegenerate fiber Fabry-Perot cavities with large tunable splittings,” Appl. Phys. Lett. 112, 171105 (2018).
[Crossref]

J. Appl. Phys. (1)

R. J. Barbour, P. A. Dalgarno, A. Curran, K. M. Nowak, H. J. Baker, D. R. Hall, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “A tunable microcavity,” J. Appl. Phys. 110, 053107 (2011).
[Crossref]

J. Mod. Opt. (1)

H. Weber, “Rays and fields in general astigmatic resonators,” J. Mod. Opt. 59, 740–770 (2012).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (1)

Laser Photonics Rev. (1)

L. C. Flatten., A. A. P. Trichet, and J. M. Smith, “Spectral engineering of coupled open-access microcavities,” Laser Photonics Rev. 10, 257–263 (2015).
[Crossref]

Nat. Commun. (1)

T. Hümmer, J. Noe, M. S. Hofmann, T. W. Hänsch, A. Högele, and D. Hunger, “Cavity-enhanced Raman microscopy of individual carbon nanotubes,” Nat. Commun. 7, 12155 (2016).
[Crossref] [PubMed]

Nat. Phys. (1)

A. D. Kashkanova, A. B. Shkarin, C. D. Brown, N. E. Flowers-Jacobs, L. Childress, S. W. Hoch, L. Hohmann, K. Ott, J. Reichel, and J. G. E. Harris, “Superfluid Brillouin optomechanics,” Nat. Phys. 13, 74–79 (2016).
[Crossref]

Nature (4)

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom-field coupling for Bose-Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (2007).
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J. Volz, R. Gehr, G. Dubois, J. Estève, and J. Reichel, “Measurement of the internal state of a single atom without energy exchange,” Nature 475, 210–213 (2011).
[Crossref] [PubMed]

A. Stute, B. Casabone, P. Schindler, T. Monz, P. O. Schmidt, B. Brandstätter, T. E. Northup, and R. Blatt, “Tunable ion-photon entanglement in an optical cavity,” Nature 485, 482–485 (2012).
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A. Reiserer, N. Kalb, G. Rempe, and S. Ritter, “A quantum gate between a flying optical photon and a single trapped atom,” Nature 508, 237–240 (2014).
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New J. Phys. (3)

D. Hunger, T. Steinmetz, Y. Colombe, C. Deutsch, T. W. Hänsch, and J. Reichel, “A fiber Fabry-Perot cavity with high finesse,” New J. Phys. 12, 065038 (2010).
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M. Uphoff, M. Brekenfeld, G. Rempe, and S. Ritter, “Frequency splitting of polarization eigenmodes in microscopic Fabry-Perot cavities,” New J. Phys. 17, 013053 (2015).
[Crossref]

J. Miguel-Sánchez, A. Reinhard, E. Togan, T. Volz, A. Imamoglu, B. Besga, J. Reichel, and J. Estève, “Cavity quantum electrodynamics with charge-controlled quantum dots coupled to a fiber Fabry-Perot cavity,” New J. Phys. 15, 045002 (2013).
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Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. A (2)

A. J. Fleisher, D. A. Long, Q. Liu, and J. T. Hodges, “Precision interferometric measurements of mirror birefringence in high-finesse optical resonators,” Phys. Rev. A 93, 013833 (2016).
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S. J. Habraken and G. Nienhuis, “Modes of a twisted optical cavity,” Phys. Rev. A 75, 033819 (2007).
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Phys. Rev. Appl. (1)

H. Kaupp, T. Hümmer, M. Mader, B. Schlederer, J. Benedikter, P. Haeusser, H. C. Chang, H. Fedder, T. W. Hänsch, and D. Hunger, “Purcell-enhanced single-photon emission from nitrogen-vacancy centers coupled to a tunable microcavity,” Phys. Rev. Appl. 6, 054010 (2016).
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Phys. Rev. Lett. (4)

A. Jeantet, Y. Chassagneux, C. Raynaud, P. Roussignol, J. S. Lauret, B. Besga, J. Estève, J. Reichel, and C. Voisin, “Widely tunable single-photon source from a carbon nanotube in the Purcell regime,” Phys. Rev. Lett. 116, 247402 (2016).
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R. Albrecht, A. Bommer, C. Deutsch, J. Reichel, and C. Becher, “Coupling of a single nitrogen-vacancy center in diamond to a fiber-based microcavity,” Phys. Rev. Lett. 110, 243602 (2013).
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M. Steiner, H. M. Meyer, C. Deutsch, J. Reichel, and M. Köhl, “Single ion coupled to an optical fiber cavity,” Phys. Rev. Lett. 110, 043003 (2013).
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R. Gehr, J. Volz, G. Dubois, T. Steinmetz, Y. Colombe, B. L. Lev, R. Long, J. Estève, and J. Reichel, “Cavity-based single atom preparation and high-fidelity hyperfine state readout,” Phys. Rev. Lett. 104, 203602 (2010).
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Rev. Sci. Instrum. (3)

B. Brandstätter, A. McClung, K. Schüppert, B. Casabone, K. Friebe, A. Stute, P. O. Schmidt, C. Deutsch, J. Reichel, R. Blatt, and T. E. Northup, “Integrated fiber-mirror ion trap for strong ion-cavity coupling,” Rev. Sci. Instrum. 84, 123104 (2013).
[Crossref]

H. Zhong, G. Fläschner, A. Schwarz, R. Wiesendanger, P. Christoph, T. Wagner, A. Bick, C. Staarmann, B. Abeln, K. Sengstock, and C. Becker, “A millikelvin all-fiber cavity optomechanical apparatus for merging with ultra-cold atoms in a hybrid quantum system,” Rev. Sci. Instrum. 88, 023115 (2017).
[Crossref] [PubMed]

B. Petrak, K. Konthasinghe, S. Perez, and A. Muller, “Feedback-controlled laser fabrication of micromirror substrates,” Rev. Sci. Instrum. 82, 123112 (2011).
[Crossref]

Science (1)

G. Barontini, L. Hohmann, F. Haas, J. Esteve, and J. Reichel, “Deterministic generation of multiparticle entanglement by quantum Zeno dynamics,” Science 349, 1317–1321 (2015).
[Crossref] [PubMed]

Other (1)

J. R. Taylor, An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements, 2nd ed. (University Science Books, 1997).

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Figures (6)

Fig. 1
Fig. 1 (a): Scheme of a cavity with birefringent mirrors showing the mirrors and the intracavity eigenbases. θ is the angle between the fast axes of the two mirrors. Ψ is the angle between the fast eigenmode of the cavity and the fast axis of mirror 1. (b): The intracavity polarization eigenbasis is rotated by an angle Ψ relative to the first mirror’s birefringent basis and depends only on the relative rotation angle θ of the birefringent basis of the second mirror and on the ratio of the geometrical birefringences δ 1 δ 2.
Fig. 2
Fig. 2 Comparison of the spatial distributions of the intracavity mode when the two fast axes are parallel (left) or orthogonal (right). The birefringent cavity is formed by two identical elliptic paraboloidal mirrors with ROCs of 235 μm and 355 μm. We plot the mode size on the two mirrors along the two principal axes (a) and (c). We also plot the mode size on the two mirrors for a non-astigmatic 290 μm ROC circular cavity. (b) and (d): contour of equal intensity for a cavity length of 230 μm.
Fig. 3
Fig. 3 Realization of elliptic (left) and circular (right) fiber mirror shapes. (a,d): Shot patterns used to mill the fiber endfacet with CO2 laser pulses. The red dots indicate the relative position of the shots centered on the fiber core, and the numbers the corresponding number in the pulse series. The black curves mark the alignment ellipses. The dashed black circle on (d) is represented to emphasize the slight ellipticity of the shot pattern that optimizes the symmetry of the carved shape (cf. text). (b,e): Resulting profiles of the fiber shapes after laser ablation, showing large (b) and small (e) geometrical birefringences. In (b), a small 0.4-deg angle between the fiber facet and the profilometry plane is responsible for non-ideal elliptical contour lines. (c,f): Cuts of the fiber profile data and corresponding paraboloidal fits along the eigenaxes, x and y, of the shot patterns, centered on the minimum value to emphasize (a)symmetry. The fitted radii of curvature of these structures along their principal axes are 355 μm and 236 μm for the elliptic paraboloid mirror and 294 μm and 289 μm for the almost circular mirror.
Fig. 4
Fig. 4 Compensation of CO2 beam asymmetry with multi-shot technique. Each point is averaged over 3 shot fibers. (a) Principle of the compensation : an elliptical shooting pattern in the longitudinal direction compensates the vertically elongated single shot result. (b) Relative difference γ = R a R b R a of the produced mirrors (Eigenaxes ROCs Ra, Rb) as function of the shot pattern ellipticity se: ratio of major (Y) radius by minor (X) radius. Error bars represent the standard deviation of the dataset. Asymmetry is compensated down to 1.5%.
Fig. 5
Fig. 5 Finesse as a function of the length, measured for 780 nm (red) and 1559 nm (blue) on a PC-MM cavity. The solid line is a fit using the analytical model of Eq. (5), with only one free parameter that sets the effective size of the mirrors (see main text). The effective ROCs of the mirrors are slightly different for the two wavelengths: they are extracted from the profilometry data with a spherical fit on a region that corresponds to the mode diameter for the cavity length at which clipping losses start to dominate. The values of the ROCs are: R1x = 323 μm, R1y = 299 μm, R2x = 290 μm, R2y = 321 μm for 780 nm; R1x = 330 μm, R1y = 301 μm, R2x = 292 μm, R2y = 323 μm for 1559 nm. The dashed line is a best-fit curve obtained by considering symmetric mirrors, i.e. by neglecting the astigmatism of the cavity mode.
Fig. 6
Fig. 6 Geometrical birefringence retrieved from the birefringent frequency splitting shown in the inset after normalization by finesse and wavelength. Experimental error bars mainly come from cavity length uncertainty that implies finesse uncertainty. Full lines are fits with the geometrical birefringence of each mirror as parameters. Inset: Birefringent frequency splitting normalized by the cavity linewidth as function of the rotation angle of one fiber mirror obtained in a FFP cavity with asymmetric mirrors at 780 nm (red dots) and 1559 nm (blue squares).

Equations (6)

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ϕ m = λ 2 π δ m with δ m = 1 R a 1 R b = γ R b where γ = R a R b R a
( θ ) = Δ ν ( θ ) κ = λ 2 π 2 Δ c ( θ ) with Δ c ( θ ) = δ 1 2 + δ 2 2 + 2 δ 1 δ 2 cos ( 2 θ )
Δ ν ( θ ) = c λ 8 π 2 L Δ c ( θ ) ,
Ψ ( θ ) = arctan [ 1 sin ( 2 θ ) ( 1 + ( δ 1 δ 2 ) 2 + 2 δ 1 δ 2 cos ( 2 θ ) δ 1 δ 2 cos ( 2 θ ) ) ]
= π 𝒯 + A + S + ( C M 1 + C M 2 ) / 2
C M i ( w i , a , w i , b , a i , b i ) = 1 2 π w i , a w i , b E ( a i , b i ) exp ( 2 x 2 w i , a 2 2 y 2 w i , b 2 ) d x d y

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