Cavity QED with quantum gases: new paradigms in many-body physics

Abstract

We review the recent developments and the current status in the field of quantum-gas cavity QED. Since the first experimental demonstration of atomic self-ordering in a system composed of a Bose–Einstein condensate coupled to a quantized electromagnetic mode of a high-Q optical cavity, the field has rapidly evolved over the past decade. The composite quantum-gas-cavity systems offer the opportunity to implement, simulate, and experimentally test fundamental solid-state Hamiltonians, as well as to realize non-equilibrium many-body phenomena beyond conventional condensed-matter scenarios. This hinges on the unique possibility to design and control in open quantum environments photon-induced tunable-range interaction potentials for the atoms using tailored pump lasers and dynamic cavity fields. Notable examples range from Hubbard-like models with long-range interactions exhibiting a lattice-supersolid phase, over emergent magnetic orderings and quasicrystalline symmetries, to the appearance of dynamic gauge potentials and non-equilibrium topological phases. Experiments have managed to load spin-polarized as well as spinful quantum gases into various cavity geometries and engineer versatile tunable-range atomic interactions. This led to the experimental observation of spontaneous discrete and continuous symmetry breaking with the appearance of soft-modes as well as supersolidity, density and spin self-ordering, dynamic spin-orbit coupling, and non-equilibrium dynamical self-ordered phases among others. In addition, quantum-gas-cavity setups offer new platforms for quantum-enhanced measurements. In this review, starting from an introduction to basic models, we pedagogically summarize a broad range of theoretical developments and put them in perspective with the current and near future state-of-art experiments.

Keywords:

• Cavity quantum electrodynamics (QED)
• ultracold quantum gases
• Bose–Einstein condensate (BEC)
• Fermi gases
• strong matter-field coupling
• Dicke superradiance
• self-organization
• cavity-enhanced metrology

Acknowledgments

The authors are grateful to Nishant Dogra, Peter Domokos, Francesco Ferri, Jürg Fröhlich, Yudan Gao, Sarang Gopalakrishnan, Andreas Hemmerich, Jonathan Keeling, Ronen Kroeze, Benjamin Lev, Brendan Marsh, Igor Mekhov, Heiko Rieger, and Claus Zimmermann, for critical reading and valuable feedback on our manuscript. The authors thank Jean-Philippe Brantut, R. Chitra, Tilman Esslinger, Petr Karpov, Corinna Kollath, Giovanna Morigi, and Oded Zilberberg for stimulating discussions. The authors also thank Elvia Colella for the assistance to create Figure 4.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Note that ${\delta }_c={\mathrm{\Delta }}_c-N{U}_0/2$ as defined here is intimately related to the dispersively shifted cavity detuning ${\delta }_c\equiv {\mathrm{\Delta }}_c-\int U\left(\mathbf{\text{r}}\right)\hat{n}\left(\mathbf{\text{r}}\right)d\mathbf{\text{r}}$ defined earlier in Section 2.1. Throughout this review paper, we will use ${\delta }_c$ in a rather liberal way, but all ultimately related to the dispersively shifted cavity detuning.

2 We will just use spin instead of pseudospin to refer to internal states and internal dynamics of the atom throughout this review paper.

3 Alternatively, the pump lasers ${\mathrm{\Omega }}_{1,2}\left(\mathbf{\text{r}}\right)$ can be aligned in the z direction with left/right circular polarizations, where now the physics in the x-z plane is identical to the one presented in the text for given choices.

Additional information

Funding

F. M. is supported by the Lise-Meitner Fellowship M2438-NBL of the Austrian Science Fund FWF. F. M. and H. R. acknowledge the International Joint Project No. I3964- N27 of the Austrian Science Fund FWF and the Agence Nationale de la Recherche ANR. T. D. acknowledges funding from the Swiss National Science Foundation SNF: NCCR QSIT and the project “Cavity-assisted pattern recognition” (Project No. IZBRZ2 186312). T. D. and H. R. acknowledge funding from EU Horizon 2020: ITN grant ColOpt (Project No. 721465).