Cavity-enhanced metrology in an atomic spin-1 Bose−Einstein condensate

Abstract

Atom interferometer has been proven to be a powerful tool for precision metrology. Here we propose a cavity-aided nonlinear atom interferometer, based on the quasi-periodic spin mixing dynamics of an atomic spin-1 Bose−Einstein condensate trapped in an optical cavity. We unravel that the phase sensitivity can be greatly enhanced with the cavity-mediated nonlinear interaction. The influence of encoding phase, splitting time and recombining time on phase sensitivity are carefully studied. In addition, we demonstrate a dynamical phase transition in the system. Around the criticality, a small cavity light field variation can arouse a strong response of the atomic condensate, which can serve as a new resource for enhanced sensing. This work provides a robust protocol for cavity-enhanced metrology.

Graphical abstract

Keywords

nonlinear atom interferometer / spin-1 Bose−Einstein condensate / spin-mixing dynamics / quantum Fisher information / parameter estimation

References

[1] A. D. Cronin, J. Schmiedmayer, D. E. Pritchard. Optics and interferometry with atoms and molecules. Rev. Mod. Phys., 2009, 81(3): 1051

[2] J. B. Fixler, G. Foster, J. McGuirk, M. Kasevich. Atom interferometer measurement of the Newtonian constant of gravity. Science, 2007, 315(5808): 74

[3] G. Lamporesi, A. Bertoldi, L. Cacciapuoti, M. Prevedelli, G. M. Tino. Determination of the Newtonian gravitational constant using atom interferometry. Phys. Rev. Lett., 2008, 100(5): 050801

[4] P. W. Graham, J. M. Hogan, M. A. Kasevich, S. Rajendran. New method for gravitational wave detection with atomic sensors. Phys. Rev. Lett., 2013, 110(17): 171102

[5] G. Rosi, F. Sorrentino, L. Cacciapuoti, M. Prevedelli, G. Tino. Precision measurement of the Newtonian gravitational constant using cold atoms. Nature, 2014, 510(7506): 518

[6] W. Chaibi, R. Geiger, B. Canuel, A. Bertoldi, A. Landragin, P. Bouyer. Low frequency gravitational wave detection with ground-based atom interferometer arrays. Phys. Rev. D, 2016, 93(2): 021101

[7] R. H. Parker, C. Yu, W. Zhong, B. Estey, H. Müller. Measurement of the fine-structure constant as a test of the standard model. Science, 2018, 360(6385): 191

[8] K. Bongs, M. Holynski, J. Vovrosh, P. Bouyer, G. Condon, E. Rasel, C. Schubert, W. P. Schleich, A. Roura. Taking atom interferometric quantum sensors from the laboratory to real-world applications. Nat. Rev. Phys., 2019, 1(12): 731

[9] A. Peters, K. Y. Chung, S. Chu. Measurement of gravitational acceleration by dropping atom. Nature, 1999, 400(6747): 849

[10] P. Altin, M. Johnsson, V. Negnevitsky, G. Dennis, R. P. Anderson, J. Debs, S. Szigeti, K. Hardman, S. Bennetts, G. McDonald, L. D. Turner, J. D. Close, N. P. Robins. Precision atomic gravimeter based on Bragg diffraction. New J. Phys., 2013, 15(2): 023009

[11] M. Snadden, J. McGuirk, P. Bouyer, K. Haritos, M. Kasevich. Measurement of the earth’s gravity gradient with an atom interferometer-based gravity gradiometer. Phys. Rev. Lett., 1998, 81(5): 971

[12] A. Trimeche, B. Battelier, D. Becker, A. Bertoldi, P. Bouyer, C. Braxmaier, E. Charron, R. Corgier, M. Cornelius, K. Douch, N. Gaaloul, S. Herrmann, J. Müller, E. Rasel, C. Schubert, H. Wu, F. Pereira dos Santos. Concept study and preliminary design of a cold atom interferometer for space gravity gradiometry. Class. Quantum Gravity, 2019, 36(21): 215004

[13] F. Riehle, T. Kisters, A. Witte, J. Helmcke, C. J. Bordé. Optical Ramsey spectroscopy in a rotating frame: Sagnac effect in a matter-wave interferometer. Phys. Rev. Lett., 1991, 67(2): 177

[14] T. Gustavson, P. Bouyer, M. Kasevich. Precision rotation measurements with an atom interferometer gyroscope. Phys. Rev. Lett., 1997, 78(11): 2046

[15] J. Stockton, K. Takase, M. Kasevich. Absolute geodetic rotation measurement using atom interferometry. Phys. Rev. Lett., 2011, 107(13): 133001

[16] H. Strobel, W. Muessel, D. Linnemann, T. Zibold, D. B. Hume, L. Pezzè, A. Smerzi, M. K. Oberthaler. Fisher information and entanglement of non-Gaussian spin states. Science, 2014, 345(6195): 424

[17] J. Estève, C. Gross, A. Weller, S. Giovanazzi, M. K. Oberthaler. Squeezing and entanglement in a Bose–Einstein condensate. Nature, 2008, 455(7217): 1216

[18] B. Lücke, M. Scherer, J. Kruse, L. Pezzé, F. Deuretzbacher, P. Hyllus, O. Topic, J. Peise, W. Ertmer, J. Arlt, L. Santos, A. Smerzi, C. Klempt. Twin matter waves for interferometry beyond the classical limit. Science, 2011, 334(6057): 773

[19] C. Gross, T. Zibold, E. Nicklas, J. Esteve, M. K. Oberthaler. Nonlinear atom interferometer surpasses classical precision limit. Nature, 2010, 464(7292): 1165

[20] Y. Zeng, P. Xu, X. He, Y. Liu, M. Liu, J. Wang, D. Papoular, G. Shlyapnikov, M. Zhan. Entangling two individual atoms of different isotopes via Rydberg blockade. Phys. Rev. Lett., 2017, 119(16): 160502

[21] E. Pedrozo-Peñafiel, S. Colombo, C. Shu, A. F. Adiyatullin, Z. Li, E. Mendez, B. Braverman, A. Kawasaki, D. Akamatsu, Y. Xiao, V. Vuletić. Entanglement on an optical atomic-clock transition. Nature, 2020, 588(7838): 414

[22] L. Pezzè, A. Smerzi, M. K. Oberthaler, R. Schmied, P. Treutlein. Quantum metrology with nonclassical states of atomic ensembles. Rev. Mod. Phys., 2018, 90(3): 035005

[23] G. Jin, Y. Liu, L. You. Optimal phase sensitivity of atomic Ramsey interferometers with coherent spin states. Front. Phys., 2011, 6(3): 251

[24] J. Wrubel, A. Schwettmann, D. P. Fahey, Z. Glassman, H. Pechkis, P. Griffin, R. Barnett, E. Tiesinga, P. Lett. Spinor Bose–Einstein-condensate phase-sensitive amplifier for SU(1, 1) interferometry. Phys. Rev. A, 2018, 98(2): 023620

[25] T. W. Mao, Q. Liu, X. W. Li, J. H. Cao, F. Chen, W. X. Xu, M. K. Tey, Y. X. Huang, L. You. Quantum enhanced sensing by echoing spin-nematic squeezing in atomic Bose–Einstein condensate. Nat. Phys., 2023, 19(11): 1585

[26] X. Y. Luo, Y. Q. Zou, L. N. Wu, Q. Liu, M. F. Han, M. K. Tey, L. You. Deterministic entanglement generation from driving through quantum phase transitions. Science, 2017, 355(6325): 620

[27] P. Feldmann, M. Gessner, M. Gabbrielli, C. Klempt, L. Santos, L. Pezzè, A. Smerzi. Interferometric sensitivity and entanglement by scanning through quantum phase transitions in spinor Bose–Einstein condensates. Phys. Rev. A, 2018, 97(3): 032339

[28] Y. Q. Zou, L. N. Wu, Q. Liu, X. Y. Luo, S. F. Guo, J. H. Cao, M. K. Tey, L. You. Beating the classical precision limit with spin-1 Dicke states of more than 10 000 atoms. Proc. Natl. Acad. Sci. USA, 2018, 115(25): 6381

[29] E. Davis, G. Bentsen, M. Schleier-Smith. Approaching the Heisenberg limit without single-particle detection. Phys. Rev. Lett., 2016, 116(5): 053601

[30] F. Fröwis, P. Sekatski, W. Dür. Detecting large quantum Fisher information with finite measurement precision. Phys. Rev. Lett., 2016, 116(9): 090801

[31] T. Macrì, A. Smerzi, L. Pezzè. Loschmidt echo for quantum metrology. Phys. Rev. A, 2016, 94(1): 010102

[32] D. Linnemann, H. Strobel, W. Muessel, J. Schulz, R. J. Lewis-Swan, K. V. Kheruntsyan, M. K. Oberthaler. Quantum-enhanced sensing based on time reversal of nonlinear dynamics. Phys. Rev. Lett., 2016, 117(1): 013001

[33] M. Gabbrielli, L. Pezzè, A. Smerzi. Spin-mixing interferometry with Bose–Einstein condensates. Phys. Rev. Lett., 2015, 115(16): 163002

[34] Q. Liu, L. N. Wu, J. H. Cao, T. W. Mao, X. W. Li, S. F. Guo, M. K. Tey, L. You. Nonlinear interferometry beyond classical limit enabled by cyclic dynamics. Nat. Phys., 2022, 18(2): 167

[35] W. T. He, C. W. Lu, Y. X. Yao, H. Y. Zhu, Q. Ai. Criticality-based quantum metrology in the presence of decoherence. Front. Phys., 2023, 18(3): 31304

[36] A. W. Chin, S. F. Huelga, M. B. Plenio. Quantum metrology in non-Markovian environments. Phys. Rev. Lett., 2012, 109(23): 233601

[37] M. Jarzyna, R. Demkowicz-Dobrzański. True precision limits in quantum metrology. New J. Phys., 2015, 17(1): 013010

[38] L. Zhou, H. Pu, H. Y. Ling, W. Zhang. Cavity-mediated strong matter wave bistability in a spin-1 condensate. Phys. Rev. Lett., 2009, 103(16): 160403

[39] L. Zhou, H. Pu, H. Y. Ling, K. Zhang, W. Zhang. Spin dynamics and domain formation of a spinor Bose–Einstein condensate in an optical cavity. Phys. Rev. A, 2010, 81(6): 063641

[40] A. Kuzmich, L. Mandel, N. P. Bigelow. Generation of spin squeezing via continuous quantum nondemolition measurement. Phys. Rev. Lett., 2000, 85(8): 1594

[41] A. Kuzmich, L. Mandel, J. Janis, Y. Young, R. Ejnisman, N. Bigelow. Quantum nondemolition measurements of collective atomic spin. Phys. Rev. A, 1999, 60(3): 2346

[42] A.KuzmichE. S. Polzik, Atomic continuous variable processing and light-atoms quantum interface, in: Quantum Information with Continuous Variables, Springer, pp 231–265, 2003

[43] R. Miller, T. Northup, K. Birnbaum, A. Boca, A. Boozer, H. Kimble. Trapped atoms in cavity QED: Coupling quantized light and matter. J. Phys. At. Mol. Opt. Phys., 2005, 38(9): S551

[44] H. Ritsch, P. Domokos, F. Brennecke, T. Esslinger. Cold atoms in cavity-generated dynamical optical potentials. Rev. Mod. Phys., 2013, 85(2): 553

[45] H.Tanji-SuzukiI.D. LerouxM.H. Schleier-SmithM.CetinaA.T. GrierJ.Simon V.Vuletić, Interaction between atomic ensembles and optical resonators: Classical description, in: Advances in Atomic, Molecular, and Optical Physics, Vol. 60, Elsevier, pp 201–237, 2011

[46] M. Eckstein, M. Kollar, P. Werner. Thermalization after an interaction quench in the Hubbard model. Phys. Rev. Lett., 2009, 103(5): 056403

[47] A. Gambassi, P. Calabrese. Quantum quenches as classical critical films. Europhys. Lett., 2011, 95(6): 66007

[48] P. Smacchia, M. Knap, E. Demler, A. Silva. Exploring dynamical phase transitions and prethermalization with quantum noise of excitations. Phys. Rev. B, 2015, 91(20): 205136

[49] J. Lang, B. Frank, J. C. Halimeh. Concurrence of dynamical phase transitions at finite temperature in the fully connected transverse-field Ising model. Phys. Rev. B, 2018, 97(17): 174401

[50] S. S. Mirkhalaf, E. Witkowska, L. Lepori. Supersensitive quantum sensor based on criticality in an antiferromagnetic spinor condensate. Phys. Rev. A, 2020, 101(4): 043609

[51] S. S. Mirkhalaf, D. B. Orenes, M. W. Mitchell, E. Witkowska. Criticality-enhanced quantum sensing in ferromagnetic Bose–Einstein condensates: Role of readout measurement and detection noise. Phys. Rev. Lett., 2021, 103(2): 023317

[52] Q. Guan, R. J. Lewis-Swan. Identifying and harnessing dynamical phase transitions for quantum-enhanced sensing. Phys. Rev. Res., 2021, 3(3): 033199

[53] L. Zhou, J. Kong, Z. Lan, W. Zhang. Dynamical quantum phase transitions in a spinor Bose–Einstein condensate and criticality enhanced quantum sensing. Phys. Rev. Res., 2023, 5(1): 013087

[54] C. Law, H. Pu, N. Bigelow. Quantum spins mixing in spinor Bose–Einstein condensates. Phys. Rev. Lett., 1998, 81(24): 5257

[55] B. Megyeri, G. Harvie, A. Lampis, J. Goldwin. Directional bistability and nonreciprocal lasing with cold atoms in a ring cavity. Phys. Rev. Lett., 2018, 121(16): 163603

[56] S. C. Schuster, P. Wolf, D. Schmidt, S. Slama, C. Zimmermann. Pinning transition of Bose–Einstein condensates in optical ring resonators. Phys. Rev. Lett., 2018, 121(22): 223601

[57] S. Yi, Ö. Müstecaplıoğlu, C. P. Sun, L. You. Single mode approximation in a spinor-1 atomic condensate. Phys. Rev. A, 2002, 66(1): 011601

[58] W. Zhang, D. Zhou, M. S. Chang, M. Chapman, L. You. Coherent spin mixing dynamics in a spin-1 atomic condensate. Phys. Rev. A, 2005, 72(1): 013602

[59] C. Gerving, T. Hoang, B. Land, M. Anquez, C. Hamley, M. Chapman. Non-equilibrium dynamics of an unstable quantum pendulum explored in a spin-1 Bose–Einstein condensate. Nat. Commun., 2012, 3(1): 1169

[60] M. S. Chang, Q. Qin, W. Zhang, L. You, M. S. Chapman. Coherent spinor dynamics in a spin-1 Bose condensate. Nat. Phys., 2005, 1(2): 111

[61] P. B. Blakie, A. Bradley, M. Davis, R. Ballagh, C. Gardiner. Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques. Adv. Phys., 2008, 57(5): 363

[62] C. W. Helstrom. Minimum mean-squared error of estimates in quantum statistics. Phys. Lett. A, 1967, 25(2): 101

[63] S. L. Braunstein, C. M. Caves. Statistical distance and the geometry of quantum states. Phys. Rev. Lett., 1994, 72(22): 3439

[64] A.S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory, Vol. 1, Springer Science & Business Media, 2011

[65] W. M. Zhang, D. H. Feng, R. Gilmore. Coherent states: Theory and some applications. Rev. Mod. Phys., 1990, 62(4): 867

[66] E. Yukawa, M. Ueda, K. Nemoto. Classification of spin-nematic squeezing in spin-1 collective atomic systems. Phys. Rev. A, 2013, 88(3): 033629

[67] C. D. Hamley, C. Gerving, T. Hoang, E. Bookjans, M. S. Chapman. Spin-nematic squeezed vacuum in a quantum gas. Nat. Phys., 2012, 8(4): 305

[68] S. Pang, T. A. Brun. Quantum metrology for a general Hamiltonian parameter. Phys. Rev. A, 2014, 90(2): 022117

[69] A. Goussev, R. A. Jalabert, H. M. Pastawski, D. A. Wisniacki. Loschmidt echo and time reversal in complex systems. Philos. Trans. R. Soc. A, 2016, 374(2069): 20150383

[70] T. Gorin, T. Prosen, T. H. Seligman, M. Žnidarič. Dynamics of Loschmidt echoes and fidelity decay. Phys. Rep., 2006, 435(2-5): 33

[71] F. Gerbier, A. Widera, S. Fölling, O. Mandel, I. Bloch. Resonant control of spin dynamics in ultracold quantum gases by microwave dressing. Phys. Rev. A, 2006, 73(4): 041602

[72] S. Leslie, J. Guzman, M. Vengalattore, J. D. Sau, M. L. Cohen, D. Stamper-Kurn. Amplification of fluctuations in a spinor Bose–Einstein condensate. Phys. Rev. A, 2009, 79(4): 043631

[73] P. Kunkel, M. Prüfer, H. Strobel, D. Linnemann, A. Frölian, T. Gasenzer, M. Gärttner, M. K. Oberthaler. Spatially distributed multipartite entanglement enables EPR steering of atomic clouds. Science, 2018, 360(6387): 413

[74] E. J. Davis, G. Bentsen, L. Homeier, T. Li, M. H. Schleier-Smith. Photon-mediated spin-exchange dynamics of spin-1 atoms. Phys. Rev. Lett., 2019, 122(1): 010405

[75] M. A. Norcia, R. J. Lewis-Swan, J. R. Cline, B. Zhu, A. M. Rey, J. K. Thompson. Cavity-mediated collective spin exchange interactions in a strontium superradiant laser. Science, 2018, 361(6399): 259

[76] S. J. Masson, M. Barrett, S. Parkins. Cavity QED engineering of spin dynamics and squeezing in a spinor gas. Phys. Rev. Lett., 2017, 119(21): 213601

[77] D. S. Ding, Z. K. Liu, B. S. Shi, G. C. Guo, K. Mølmer, C. S. Adams. Enhanced metrology at the critical point of a many-body Rydberg atomic system. Nat. Phys., 2022, 18(12): 1447

[78] M. Olsen, A. Bradley. Numerical representation of quantum states in the positive-P and Wigner representations. Opt. Commun., 2009, 282(19): 3924

Declarations

The authors declare that they have no competing interests and there are no conflicts.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12074120 and 11904063) and the Key Scientific Research Project of Colleges and Universities in Henan Province (No. 23A140001).

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