Persistent nonlocality in an ultracold-atom environment

Bradley Longstaff and Jonatan Bohr Brask

Department of Physics, Technical University of Denmark, Fysikvej, 2800 Kgs. Lyngby, Denmark

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

We investigate nonlocal quantum correlations arising between multiple two-level impurity atoms coupled to an ultracold bosonic gas. We find that the environment-induced dynamics of the impurity subsystem can generate nonlocal states that are robust against noise and violate a multipartite Bell inequality when projective spin measurements are made. Genuine multipartite nonlocality is also observed in a system of three impurities. We show that non-Markovian effects, and the persistence of coherences in the impurity subsystem, are crucial for preventing complete loss of nonlocality and allow for nonlocal correlations to be generated and maintained for extended periods of time.

► BibTeX data

► References

[1] R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki. ``Quantum entanglement''. Rev. Mod. Phys. 81, 865–942 (2009).
https:/​/​doi.org/​10.1103/​RevModPhys.81.865

[2] R. Jozsa and N. Linden. ``On the role of entanglement in quantum-computational speed-up''. Proc. R. Soc. Lond. A 459, 2011–2032 (2003).
https:/​/​doi.org/​10.1098/​rspa.2002.1097

[3] V. Giovannetti, S. Lloyd, and L. Maccone. ``Quantum metrology''. Phys. Rev. Lett. 96, 010401 (2006).
https:/​/​doi.org/​10.1103/​PhysRevLett.96.010401

[4] A. Einstein, B. Podolsky, and N. Rosen. ``Can quantum-mechanical description of physical reality be considered complete?''. Phys. Rev. 47, 777–780 (1935).
https:/​/​doi.org/​10.1103/​PhysRev.47.777

[5] J. Bell. ``On the einstein podolsky rosen paradox''. Physics 1, 195–200 (1964).
https:/​/​doi.org/​10.1103/​PhysicsPhysiqueFizika.1.195

[6] N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner. ``Bell nonlocality''. Rev. Mod. Phys. 86, 419–478 (2014).
https:/​/​doi.org/​10.1103/​RevModPhys.86.419

[7] B. Hensen, H. Bernien, A. Dréau, et al. ``Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres''. Nature 526, 682–686 (2015).
https:/​/​doi.org/​10.1038/​nature15759

[8] L. K. Shalm et al. ``Strong loophole-free test of local realism''. Phys. Rev. Lett. 115, 250402 (2015).
https:/​/​doi.org/​10.1103/​PhysRevLett.115.250402

[9] M. Giustina et al. ``Significant-loophole-free test of bell’s theorem with entangled photons''. Phys. Rev. Lett. 115, 250401 (2015).
https:/​/​doi.org/​10.1103/​PhysRevLett.115.250401

[10] R. Colbeck. ``Quantum and relativistic protocols for secure multi-party computation''. Ph.D. Thesis, University of Cambridge (2009). arXiv:0911.3814 [quant-ph].
arXiv:0911.3814

[11] S. Pironio, A. Acín, S. Massar, A. Boyer de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe. ``Random numbers certified by bell's theorem''. Nature 464, 1021–1024 (2010).
https:/​/​doi.org/​10.1038/​nature09008

[12] S. Pironio, A. Acín, N. Brunner, N. Gisin, S. Massar, and V. Scarani. ``Device-independent quantum key distribution secure against collective attacks''. New J. Phys. 11, 045021 (2009).
https:/​/​doi.org/​10.1088/​1367-2630/​11/​4/​045021

[13] G. De Chiara and A. Sanpera. ``Genuine quantum correlations in quantum many-body systems: a review of recent progress''. Reports on Progress in Physics 81, 074002 (2018).
https:/​/​doi.org/​10.1088/​1361-6633/​aabf61

[14] R. F. Werner. ``Quantum states with einstein-podolsky-rosen correlations admitting a hidden-variable model''. Phys. Rev. A 40, 4277 (1989).
https:/​/​doi.org/​10.1103/​PhysRevA.40.4277

[15] J. Barrett. ``Nonsequential positive-operator-valued measurements on entangled mixed states do not always violate a bell inequality''. Phys. Rev. A 65, 042302 (2002).
https:/​/​doi.org/​10.1103/​PhysRevA.65.042302

[16] J. Tura, R. Augusiak, A. B. Sainz, T. Vértesi, M. Lewenstein, and A. Acín. ``Detecting nonlocality in many-body quantum states''. Science 344, 1256–1258 (2014).
https:/​/​doi.org/​10.1126/​science.1247715

[17] Z. Wang, S. Singh, and M. Navascués. ``Entanglement and nonlocality in infinite 1d systems''. Phys. Rev. Lett. 118, 230401 (2017).
https:/​/​doi.org/​10.1103/​PhysRevLett.118.230401

[18] D-L. Deng. ``Machine learning detection of bell nonlocality in quantum many-body systems''. Phys. Rev. Lett. 120, 240402 (2018).
https:/​/​doi.org/​10.1103/​PhysRevLett.120.240402

[19] E. Oudot, J-D. Bancal, P. Sekatski, and N. Sangouard. ``Bipartite nonlocality with a many-body system''. New Journal of Physics 21, 103043 (2019).
https:/​/​doi.org/​10.1088/​1367-2630/​ab4c7c

[20] T Wasak and J. Chwedeńczuk. ``Bell inequality, einstein-podolsky-rosen steering, and quantum metrology with spinor bose-einstein condensates''. Phys. Rev. Lett. 120, 140406 (2018).
https:/​/​doi.org/​10.1103/​PhysRevLett.120.140406

[21] M. Fadel and J. Tura. ``Bell correlations at finite temperature''. Quantum 2, 107 (2018).
https:/​/​doi.org/​10.22331/​q-2018-11-19-107

[22] A. Piga, A. Aloy, M. Lewenstein, and I. Frérot. ``Bell correlations at ising quantum critical points''. Phys. Rev. Lett. 123, 170604 (2019).
https:/​/​doi.org/​10.1103/​PhysRevLett.123.170604

[23] A. Bene Watts, N. Yunger Halpern, and A. Harrow. ``Nonlinear bell inequality for macroscopic measurements''. Phys. Rev. A 103, L010202 (2021).
https:/​/​doi.org/​10.1103/​PhysRevA.103.L010202

[24] I. Frérot and T. Roscilde. ``Detecting many-body bell nonlocality by solving ising models''. Phys. Rev. Lett. 126, 140504 (2021).
https:/​/​doi.org/​10.1103/​PhysRevLett.126.140504

[25] J. Kitzinger, X. Meng, M. Fadel, V. Ivannikov, K. Nemoto, W-J. Munro, and T. Byrnes. ``Bell correlations in a split two-mode-squeezed bose-einstein condensate''. Phys. Rev. A 104, 043323 (2021).
https:/​/​doi.org/​10.1103/​PhysRevA.104.043323

[26] C. H. S. Vieira, C. Duarte, R. C. Drumond, and M. Terra Cunha. ``Bell non-locality in many-body quantum systems with exponential decay of correlations''. Brazilian Journal of Physics 51, 1603–1616 (2021).
https:/​/​doi.org/​10.1007/​s13538-021-00998-1

[27] B. Kraus, H. P. Büchler, S. Diehl, A. Kantian, A. Micheli, and P. Zoller. ``Preparation of entangled states by quantum markov processes''. Phys. Rev. A 78, 042307 (2008).
https:/​/​doi.org/​10.1103/​PhysRevA.78.042307

[28] F. Verstraete, M. M. Wolf, and J. I. Cirac. ``Quantum computation and quantum-state engineering driven by dissipation''. Nature Physics 17, 633–636 (2009).
https:/​/​doi.org/​10.1038/​nphys1342

[29] G. Vacanti and A. Beige. ``Cooling atoms into entangled states''. New J. Phys. 11, 083008 (2009).
https:/​/​doi.org/​10.1088/​1367-2630/​11/​8/​083008

[30] C. Aron, M. Kulkarni, and H. E. Türeci. ``Steady-state entanglement of spatially separated qubits via quantum bath engineering''. Phys. Rev. A 90, 062305 (2014).
https:/​/​doi.org/​10.1103/​PhysRevA.90.062305

[31] S. Schneider and G. J. Milburn. ``Entanglement in the steady state of a collective-angular-momentum (dicke) model''. Phys. Rev. A 65, 042107 (2002).
https:/​/​doi.org/​10.1103/​PhysRevA.65.042107

[32] H. Y. Yuan, P. Yan, S. Zheng, Q. Y. He, K. Xia, and M. Yung. ``Steady bell state generation via magnon-photon coupling''. Phys. Rev. Lett. 124, 053602 (2020).
https:/​/​doi.org/​10.1103/​PhysRevLett.124.053602

[33] M. B. Plenio and S. F. Huelga. ``Entangled light from white noise''. Phys. Rev. Lett. 88, 197901 (2002).
https:/​/​doi.org/​10.1103/​PhysRevLett.88.197901

[34] J. B. Brask, G. Haack, N. Brunner, and M. Huber. ``Autonomous quantum thermal machine for generating steady-state entanglement''. New J. Phys. 17, 113029 (2015).
https:/​/​doi.org/​10.1088/​1367-2630/​17/​11/​113029

[35] J. B. Brask, F. Clivaz, G. Haack, and A. Tavakoli. ``Operational nonclassicality in minimal autonomous thermal machines''. Quantum 6, 672 (2022).
https:/​/​doi.org/​10.22331/​q-2022-03-22-672

[36] J. Zou, S. Zhang, and Y. Tserkovnyak. ``Bell-state generation for spin qubits via dissipative coupling''. Phys. Rev. B 106, L180406 (2022).
https:/​/​doi.org/​10.1103/​PhysRevB.106.L180406

[37] D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller. ``Cold bosonic atoms in optical lattices''. Phys. Rev. Lett. 81, 3108 (1998).
https:/​/​doi.org/​10.1103/​PhysRevLett.81.3108

[38] F. Cosco, M. Borrelli, J. J. Mendoza-Arenas, F. Plastina, D. Jaksch, and S. Maniscalco. ``Bose-hubbard lattice as a controllable environment for open quantum systems''. Phys. Rev. A 97, 040101(R) (2018).
https:/​/​doi.org/​10.1103/​PhysRevA.97.040101

[39] F. Caleffi, M. Capone, I. de Vega, and A. Recati. ``Impurity dephasing in a bose–hubbard model''. New J. Phys 23, 033018 (2021).
https:/​/​doi.org/​10.1088/​1367-2630/​abe080

[40] P. Haikka, S. McEndoo, G. De Chiara, G. M. Palma, and S. Maniscalco. ``Quantifying, characterizing, and controlling information flow in ultracold atomic gases''. Phys. Rev. A 84, 031602(R) (2011).
https:/​/​doi.org/​10.1103/​PhysRevA.84.031602

[41] H.-P. Breuer, E.-M. Laine, and J. Piilo. ``Measure for the degree of non-markovian behavior of quantum processes in open systems''. Phys. Rev. Lett. 103, 210401 (2009).
https:/​/​doi.org/​10.1103/​PhysRevLett.103.210401

[42] S. McEndoo, P. Haikka, G. De Chiara, G. M. Palma, and S. Maniscalco. ``Entanglement control via reservoir engineering in ultracold atomic gases''. Europhys. Lett. 101, 60005 (2013).
https:/​/​doi.org/​10.1209/​0295-5075/​101/​60005

[43] J. I. Cirac and P. Zoller. ``Quantum computations with cold trapped ions''. Phys. Rev. Lett. 74, 4091 (1995).
https:/​/​doi.org/​10.1103/​PhysRevLett.74.4091

[44] K. Mølmer and A. Sørensen. ``Multiparticle entanglement of hot trapped ions''. Phys. Rev. Lett. 82, 1835 (1999).
https:/​/​doi.org/​10.1103/​PhysRevLett.82.1835

[45] A. Klein and M. Fleischhauer. ``Interaction of impurity atoms in bose-einstein condensates''. Phys. Rev. A 71, 033605 (2005).
https:/​/​doi.org/​10.1103/​PhysRevA.71.033605

[46] J. Catani, G. Lamporesi, D. Naik, M. Gring, M. Inguscio, F. Minardi, A. Kantian, and T. Giamarchi. ``Quantum dynamics of impurities in a one-dimensional bose gas''. Phys. Rev. A 85, 023623 (2012).
https:/​/​doi.org/​10.1103/​PhysRevA.85.023623

[47] N. Spethmann, F. Kindermann, S. John, C. Weber, D. Meschede, and A. Widera. ``Dynamics of single neutral impurity atoms immersed in an ultracold gas''. Phys. Rev. Lett. 109, 235301 (2012).
https:/​/​doi.org/​10.1103/​PhysRevLett.109.235301

[48] J. Catani, G. Barontini, G. Lamporesi, F. Rabatti, G. Thalhammer, F. Minardi, S. Stringari, and M. Inguscio. ``Entropy exchange in a mixture of ultracold atoms''. Phys. Rev. Lett. 103, 140401 (2009).
https:/​/​doi.org/​10.1103/​PhysRevLett.103.140401

[49] T. J. Elliott and T. H. Johnson. ``Nondestructive probing of means, variances, and correlations of ultracold-atomic-system densities via qubit impurities''. Phys. Rev. A 93, 043612 (2016).
https:/​/​doi.org/​10.1103/​PhysRevA.93.043612

[50] M. Streif, A. Buchleitner, D. Jaksch, and J. Mur-Petit. ``Measuring correlations of cold-atom systems using multiple quantum probes''. Phys. Rev. A 94, 053634 (2016).
https:/​/​doi.org/​10.1103/​PhysRevA.94.053634

[51] D. van Oosten, P. van der Straten, and H. T. C. Stoof. ``Quantum phases in an optical lattice''. Phys. Rev. A 63, 053601 (2001).
https:/​/​doi.org/​10.1103/​PhysRevA.63.053601

[52] R. F. Werner and M. M. Wolf. ``All-multipartite bell-correlation inequalities for two dichotomic observables per site''. Phys. Rev. A 64, 032112 (2001).
https:/​/​doi.org/​10.1103/​PhysRevA.64.032112

[53] M. Żukowski and C. Brukner. ``Bell’s theorem for general n-qubit states''. Phys. Rev. Lett. 88, 210401 (2002).
https:/​/​doi.org/​10.1103/​PhysRevLett.88.210401

[54] G. Svetlichny. ``Distinguishing three-body from two-body nonseparability by a bell-type inequality''. Phys. Rev. D 35, 3066 (1987).
https:/​/​doi.org/​10.1103/​PhysRevD.35.3066

[55] J.-D. Bancal, J. Barrett, N. Gisin, and S. Pironio. ``Definitions of multipartite nonlocality''. Phys. Rev. A 88, 014102 (2013).
https:/​/​doi.org/​10.1103/​PhysRevA.88.014102

[56] M. L. Almeida, S. Pironio, J. Barrett, G. Tóth, and A. Acín. ``Noise robustness of the nonlocality of entangled quantum states''. Phys. Rev. Lett. 99, 040403 (2007).
https:/​/​doi.org/​10.1103/​PhysRevLett.99.040403

[57] S. Sarkar, S. McEndoo, D. Schneble, and A. J. Daley. ``Interspecies entanglement with impurity atoms in a lattice gas''. New J. Phys. 22, 083017 (2020).
https:/​/​doi.org/​10.1088/​1367-2630/​ab9fc1

[58] R. Horodecki, P. Horodecki, and M. Horodecki. ``Violating bell inequality by mixed spin-12 states: necessary and sufficient condition''. Phys. Lett. A 200, 340 (1995).
https:/​/​doi.org/​10.1016/​0375-9601(95)00214-N

[59] A. Miranowicz. ``Violation of bell inequality and entanglement of decaying werner states''. Phys. Lett. A 327, 272 (2004).
https:/​/​doi.org/​10.1016/​j.physleta.2004.05.001

[60] G. M. Palma, K-A. Suominen, and A. K. Ekert. ``Quantum computers and dissipation''. Proc. R. Soc. Lond. A 452, 567–584 (1996).
https:/​/​doi.org/​10.1098/​rspa.1996.0029

[61] M. A. Cirone, G. De Chiara, G. M. Palma, and A. Recati. ``Collective decoherence of cold atoms coupled to a bose–einstein condensate''. New J. Phys. 11, 103055 (2009).
https:/​/​doi.org/​10.1088/​1367-2630/​11/​10/​103055

[62] M. Bruderer and D. Jaksch. ``Probing bec phase fluctuations with atomic quantum dots''. New J. Phys 8, 87 (2006).
https:/​/​doi.org/​10.1088/​1367-2630/​8/​6/​087

[63] K. V. Hovhannisyan, M. R. Jørgensen, G. T. Landi, A. M. Alhambra, J. B. Brask, and M. Perarnau-Llobet. ``Optimal quantum thermometry with coarse-grained measurements''. PRX Quantum 2, 020322 (2021).
https:/​/​doi.org/​10.1103/​PRXQuantum.2.020322

[64] W. Magnus. ``On the exponential solution of differential equations for a linear operator''. Comm. Pure and Appl. Math. 7, 649 (1954).
https:/​/​doi.org/​10.1002/​cpa.3160070404

[65] J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt. ``Proposed experiment to test local hidden-variable theories''. Phys. Rev. Lett. 23, 880 (1969).
https:/​/​doi.org/​10.1103/​PhysRevLett.23.880

Cited by

On Crossref's cited-by service no data on citing works was found (last attempt 2023-11-29 19:03:44). On SAO/NASA ADS no data on citing works was found (last attempt 2023-11-29 19:03:45).