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Exploring dynamical phase transitions with cold atoms in an optical  cavity

Nature volume 580, pages 602–607 (2020)Cite this article

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Abstract

Interactions between atoms and light in optical cavities provide a means of investigating collective (many-body) quantum physics in controlled environments. Such ensembles of atoms in cavities have been proposed for studying collective quantum spin models, where the atomic internal levels mimic a spin degree of freedom and interact through long-range interactions tunable by changing the cavity parameters1,2,3,4. Non-classical steady-state phases arising from the interplay between atom–light interactions and dissipation of light from the cavity have previously been investigated5,6,7,8,9,10,11. These systems also offer the opportunity to study dynamical phases of matter that are precluded from existence at equilibrium but can be stabilized by driving a system out of equilibrium12,13,14,15,16, as demonstrated by recent experiments17,18,19,20,21,22. These phases can also display universal behaviours akin to standard equilibrium phase transitions8,23,24. Here, we use an ensemble of about a million strontium-88 atoms in an optical cavity to simulate a collective Lipkin–Meshkov–Glick model25,26, an iconic model in quantum magnetism, and report the observation of distinct dynamical phases of matter in this system. Our system allows us to probe the dependence of dynamical phase transitions on system size, initial state and other parameters. These observations can be linked to similar dynamical phases in related systems, including the Josephson effect in superfluid helium27, or coupled atomic28 and solid-state polariton29 condensates. The system itself offers potential for generation of metrologically useful entangled states in optical transitions, which could permit quantum enhancement in state-of-the-art atomic clocks30,31.

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Fig. 1: System and dynamical phase diagram.
Fig. 2: Characteristic evolution of dynamical phases and scaling of DPT with atom number.
Fig. 3: Characterization of the DPT as a function of longitudinal field for two different transverse field values at fixed χN.
Fig. 4: Dependence of dynamical phases on initial conditions.

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Data availability

Data relevant to the figures and conclusions of this manuscript are available at https://doi.org/10.5061/dryad.mgqnk98w951.

Code availability

The codes used in the analysis of experimental data and to carry out associated theoretical calculations are available from the corresponding authors upon reasonable request.

References

  1. Leroux, I. D., Schleier-Smith, M. H. & Vuletić, V. Implementation of cavity squeezing of a collective atomic spin. Phys. Rev. Lett. 104, 073602 (2010).

    ADS  PubMed  Google Scholar 

  2. Norcia, M. A. et al. Cavity-mediated collective spin-exchange interactions in a strontium superradiant laser. Science 361, 259–262 (2018).

    ADS  CAS  PubMed  Google Scholar 

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

    ADS  CAS  PubMed  Google Scholar 

  4. Vaidya, V. D. et al. Tunable-range, photon-mediated atomic interactions in multimode cavity QED. Phys. Rev. X 8, 011002 (2018).

    CAS  Google Scholar 

  5. Baumann, K., Guerlin, C., Brennecke, F. & Esslinger, T. Dicke quantum phase transition with a superfluid gas in an optical cavity. Nature 464, 1301–1306 (2010).

    ADS  CAS  PubMed  Google Scholar 

  6. Klinder, J., Keßler, H., Wolke, M., Mathey, L. & Hemmerich, A. Dynamical phase transition in the open Dicke model. Proc. Natl Acad. Sci. USA 112, 3290–3295 (2015).

    ADS  CAS  PubMed  Google Scholar 

  7. Baden, M. P., Arnold, K. J., Grimsmo, A. L., Parkins, S. & Barrett, M. D. Realization of the Dicke model using cavity-assisted Raman transitions. Phys. Rev. Lett. 113, 020408 (2014).

    ADS  PubMed  Google Scholar 

  8. Ritsch, H., Domokos, P., Brennecke, F. & Esslinger, T. Cold atoms in cavity-generated dynamical optical potentials. Rev. Mod. Phys. 85, 553–601 (2013).

    ADS  CAS  Google Scholar 

  9. Landini, M. et al. Formation of a spin texture in a quantum gas coupled to a cavity. Phys. Rev. Lett. 120, 223602 (2018).

    ADS  CAS  PubMed  Google Scholar 

  10. Kroeze, R. M., Guo, Y., Vaidya, V. D., Keeling, J. & Lev, B. L. Spinor self-ordering of a quantum gas in a cavity. Phys. Rev. Lett. 121, 163601 (2018).

    ADS  CAS  PubMed  Google Scholar 

  11. Kroeze, R. M., Guo, Y. & Lev, B. L. Dynamical spin–orbit coupling of a quantum gas. Phys. Rev. Lett. 123, 160404 (2019).

    ADS  CAS  PubMed  Google Scholar 

  12. Heyl, M., Polkovnikov, A. & Kehrein, S. Dynamical quantum phase transitions in the transverse-field Ising model. Phys. Rev. Lett. 110, 135704 (2013).

    ADS  CAS  PubMed  Google Scholar 

  13. Žunkovič, B., Heyl, M., Knap, M. & Silva, A. Dynamical quantum phase transitions in spin chains with long-range interactions: merging different concepts of nonequilibrium criticality. Phys. Rev. Lett. 120, 130601 (2018).

    ADS  PubMed  Google Scholar 

  14. Eckstein, M., Kollar, M. & Werner, P. Thermalization after an interaction quench in the Hubbard model. Phys. Rev. Lett. 103, 056403 (2009).

    ADS  PubMed  Google Scholar 

  15. Lamacraft, A. & Moore, J. in Ultracold Bosonic and Fermionic Gases (eds Levin, K. et al.) 177–202 (Elsevier, 2012).

  16. Nandkishore, R. & Huse, D. A. Many-body localization and thermalization in quantum statistical mechanics. Annu. Rev. Condens. Matter Phys. 6, 15–38 (2015).

    ADS  Google Scholar 

  17. Zhang, J. et al. Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator. Nature 551, 601–604 (2017).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  18. Fläschner, N. et al. Observation of dynamical vortices after quenches in a system with topology. Nat. Phys. 14, 265 (2018).

    Google Scholar 

  19. Jurcevic, P. et al. Direct observation of dynamical quantum phase transitions in an interacting many-body system. Phys. Rev. Lett. 119, 080501 (2017).

    ADS  CAS  PubMed  Google Scholar 

  20. Smale, S. et al. Observation of a transition between dynamical phases in a quantum degenerate Fermi gas. Sci. Adv. 5, eaax1568 (2019).

    ADS  PubMed  PubMed Central  Google Scholar 

  21. Zhang, J. et al. Observation of a discrete time crystal. Nature 543, 217–220 (2017).

    ADS  CAS  PubMed  Google Scholar 

  22. Choi, S. et al. Observation of discrete time-crystalline order in a disordered dipolar many-body system. Nature 543, 221–225 (2017).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  23. Prüfer, M. et al. Observation of universal dynamics in a spinor Bose gas far from equilibrium. Nature 563, 217–220 (2018).

    ADS  PubMed  Google Scholar 

  24. Erne, S., Bücker, R., Gasenzer, T., Berges, J. & Schmiedmayer, J. Universal dynamics in an isolated one-dimensional Bose gas far from equilibrium. Nature 563, 225–229 (2018).

    ADS  CAS  PubMed  Google Scholar 

  25. Lipkin, H., Meshkov, N. & Glick, A. Validity of many-body approximation methods for a solvable model: (I). Exact solutions and perturbation theory. Nucl. Phys. 62, 188–198 (1965).

    MathSciNet  CAS  Google Scholar 

  26. Ribeiro, P., Vidal, J. & Mosseri, R. Thermodynamical limit of the Lipkin–Meshkov–Glick model. Phys. Rev. Lett. 99, 050402 (2007).

    ADS  PubMed  Google Scholar 

  27. Backhaus, S. et al. Discovery of a metastable-state in a superfluid 3He weak link. Nature 392, 687–690 (1998).

    ADS  CAS  Google Scholar 

  28. Albiez, M. et al. Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction. Phys. Rev. Lett. 95, 010402 (2005).

    ADS  PubMed  Google Scholar 

  29. Abbarchi, M. et al. Macroscopic quantum self-trapping and Josephson oscillations of exciton polaritons. Nat. Phys. 9, 275–279 (2013).

    CAS  Google Scholar 

  30. Campbell, S. L. et al. A Fermi-degenerate three-dimensional optical lattice clock. Science 358, 90–94 (2017).

    ADS  CAS  PubMed  Google Scholar 

  31. Ludlow, A. D., Boyd, M. M., Ye, J., Peik, E. & Schmidt, P. O. Optical atomic clocks. Rev. Mod. Phys. 87, 637–701 (2015).

    ADS  CAS  Google Scholar 

  32. Cazalilla, M. A. & Rey, A. M. Ultracold Fermi gases with emergent SU(n) symmetry. Rep. Prog. Phys. 77, 124401 (2014).

    ADS  PubMed  Google Scholar 

  33. Daley, A. J. Quantum computing and quantum simulation with group-II atoms. Quantum Inform. Process. 10, 865 (2011).

    Google Scholar 

  34. Marino, J. & Diehl, S. Quantum dynamical field theory for nonequilibrium phase transitions in driven open systems. Phys. Rev. B 94, 085150 (2016).

    ADS  Google Scholar 

  35. Barberena, D., Lewis-Swan, R. J., Thompson, J. K. & Rey, A. M. Driven-dissipative quantum dynamics in ultra-long-lived dipoles in an optical cavity. Phys. Rev. A 99, 053411 (2019).

    ADS  CAS  Google Scholar 

  36. Mivehvar, F., Piazza, F. & Ritsch, H. Disorder-driven density and spin self-ordering of a Bose–Einstein condensate in a cavity. Phys. Rev. Lett. 119, 063602 (2017).

    ADS  PubMed  Google Scholar 

  37. Schiró, M. & Fabrizio, M. Time-dependent mean field theory for quench dynamics in correlated electron systems. Phys. Rev. Lett. 105, 076401 (2010).

    ADS  PubMed  Google Scholar 

  38. Sciolla, B. & Biroli, G. Quantum quenches and off-equilibrium dynamical transition in the infinite-dimensional Bose–Hubbard model. Phys. Rev. Lett. 105, 220401 (2010).

    ADS  PubMed  Google Scholar 

  39. Gambassi, A. & Calabrese, P. Quantum quenches as classical critical films. Europhys. Lett. 95, 66007 (2011).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  41. Smerzi, A., Fantoni, S., Giovanazzi, S. & Shenoy, S. R. Quantum coherent atomic tunneling between two trapped Bose–Einstein condensates. Phys. Rev. Lett. 79, 4950–4953 (1997).

    ADS  CAS  Google Scholar 

  42. Reinhard, A. et al. Self-trapping in an array of coupled 1D Bose gases. Phys. Rev. Lett. 110, 033001 (2013).

    ADS  PubMed  Google Scholar 

  43. Lerose, A., Žunkovič, B., Marino, J., Gambassi, A. & Silva, A. Impact of non-equilibrium fluctuations on pre-thermal dynamical phase transitions in long-range interacting spin chains. Phys. Rev. B 99, 045128 (2019).

    ADS  CAS  Google Scholar 

  44. Barankov, R. A., Levitov, L. S. & Spivak, B. Z. Collective Rabi oscillations and solitons in a time-dependent BCS pairing problem. Phys. Rev. Lett. 93, 160401 (2004).

    ADS  CAS  PubMed  Google Scholar 

  45. Yuzbashyan, E. A., Dzero, M., Gurarie, V. & Foster, M. S. Quantum quench phase diagrams of an s-wave BCS–BEC condensate. Phys. Rev. A 91, 033628 (2015).

    ADS  Google Scholar 

  46. Swingle, B., Bentsen, G., Schleier-Smith, M. & Hayden, P. Measuring the scrambling of quantum information. Phys. Rev. A 94, 040302 (2016).

    ADS  MathSciNet  Google Scholar 

  47. Swingle, B. Unscrambling the physics of out-of-time-order correlators. Nat. Phys. 14, 988–990 (2018).

    CAS  Google Scholar 

  48. Norcia, M. A. & Thompson, J. K. Strong coupling on a forbidden transition in strontium and nondestructive atom counting. Phys. Rev. A 93, 023804 (2016).

    ADS  Google Scholar 

  49. Norcia, M. A. et al. Frequency measurements of superradiance from the strontium clock transition. Phys. Rev. X 8, 021036 (2018).

    CAS  Google Scholar 

  50. Norcia, M. A., Winchester, M. N., Cline, J. R. K. & Thompson, J. K. Superradiance on the millihertz linewidth strontium clock transition. Sci. Adv. 2, e1601231 (2016).

    ADS  PubMed  PubMed Central  Google Scholar 

  51. Muniz Silva, J. A. et al. Exploring dynamical phase transitions with a cavity-QED platform, v2. Dryad dataset (2020); https://doi.org/10.5061/dryad.mgqnk98w9.

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Acknowledgements

We acknowledge discussions with I. Spielman, M. Holland and A. Shankar. This work is supported by the Air Force Office of Scientific Research (AFOSR) grant FA9550-18-1-0319, by the Defense Advanced Research Projects Agency (DARPA) Extreme Sensing and ARO grant W911NF-16-1-0576, the ARO single investigator award W911NF-19-1-0210, the US National Science Foundation (NSF) PHY1820885, NSF JILA-PFC PHY-1734006 grants, and by the National Institute of Standards and Technology (NIST). J.R.K.C. acknowledges financial support from NSF GRFP.

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Author notes

  1. These authors contributed equally: Juan A. Muniz, Diego Barberena, Robert J. Lewis-Swan

Authors and Affiliations

  1. JILA, NIST and Department of Physics, University of Colorado, Boulder, CO, USA

    Juan A. Muniz, Diego Barberena, Robert J. Lewis-Swan, Dylan J. Young, Julia R. K. Cline, Ana Maria Rey & James K. Thompson

  2. Center for Theory of Quantum Matter, University of Colorado, Boulder, CO, USA

    Diego Barberena, Robert J. Lewis-Swan & Ana Maria Rey

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Contributions

J.A.M., D.J.Y., J.R.K.C. and J.K.T. collected and analysed the experimental data. R.J.L.-S., D.B. and A.M.R. developed the theoretical model. All authors discussed the results and contributed to the preparation of the manuscript.

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Correspondence to Ana Maria Rey or James K. Thompson.

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The authors declare no competing interests.

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Peer review information Nature thanks Murray Barrett, Maria Luisa Chiofalo and Farokh Mivehvar for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Fig. 1 Experimental platform.

a, An optical cavity is driven by a 689-nm coherent field that establishes an intra-cavity field \({\varOmega }_{{\rm{p}}}{{\rm{e}}}^{{\rm{i}}{\omega }_{{\rm{p}}}t}\), which is near resonance with the 1S0 to 3P1 transition in 88Sr. Inside the cavity, an ensemble of atoms is confined in a 1D optical lattice at 813 nm. Different lasers are applied for shelving excited-state atoms into long-lived metastable excited states, for freezing the system dynamics, for applying a radiation pressure force that pushes ground states in a direction transverse to the cavity axis, for optically pumping atoms from long lived metastable excited states back to the ground state, and for fluorescence imaging of atoms in the ground state. b, A typical fluorescence image captured on a CCD, showing the state-resolved imaging technique. The Ne excited state atoms that were shelved into 3P0,2 while the freeze/push beam was applied remain near the trapping region. The Ng ground-state atoms are pushed away from the trapping region. Based on their spatial location, the atoms assigned to be in the excited (ground) state are shown in false colour blue (orange). c, The relevant energy levels for 88Sr, the laser wavelengths and their functions. d, Experimental timing sequence and typical timescales.

Extended Data Fig. 2 Probing many-body dynamics and mapping the phase boundary.

a, Oscillation period as function of the cavity detuning Δ for 2Ωp/(Ng) = 0.104(4), δ = 0 and atoms starting in \(|\downarrow \,\rangle \). Blue points are experimental values, solid red line represents the mean-field prediction for the same drive and atom number, and the shaded red area represents typical experimental fluctuations on 2Ωp/(Ng). The period is extracted from sinusoidal fits to data as in Fig. 2a, after removing a linear term caused by the single-particle dephasing effects. The mean-field value (red solid line) is Tosc = 2π/(Nχ) with the effective replacements due to inhomogeneous coupling as discussed in Methods. Measurements are taken in the dispersive limit where \(\varDelta \gg \sqrt{N}g\). b, Critical detuning δc as function of the drive Δ for Δ/(2π) = ±50 MHz (red and blue points, respectively). We also plot the theoretical prediction for the phase boundary (equation (11)) with rescaled parameters, and predictions of the numerical model (solid lines) including uncertainty based on the typical fluctuations in Ω/(χN). Error bars are statistical (1σ).

Supplementary information

Supplementary Information

This Supplementary Information file contains the following sections: I, Effective spin model; II, Axial motion; III, Anomalous decoherence due to residual motion and technical noise; IV, Dynamical phase diagram; and V, Mapping between spin model and macroscopic self-trapping.

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Muniz, J.A., Barberena, D., Lewis-Swan, R.J. et al. Exploring dynamical phase transitions with cold atoms in an optical  cavity. Nature 580, 602–607 (2020). https://doi.org/10.1038/s41586-020-2224-x

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