Cavity QED with ultracold atomic ensembles in the sub-recoil regime

Following Franck Wilczek’s proposal of a new dynamical phase dubbed time crystal, discrete or Floquet time crystals have been observed in periodically driven closed and open quantum systems. However, in all of these experiments, the continuous time translation symmetry is already broken by a time-periodic drive. The challenge remains, to realize a system, which breaks spontaneously a continuous time translation symmetry. This was proposed for a driven open quantum system, where in contrast to closed system time crystals, the dissipation has a positive role, since it actually stabilizes the oscillation rather than melts the time crystal.

We report the observation of spontaneous breaking of a continuous time translation symmetry in a dissipative atom-cavity system. Using an atomic Bose-Einstein condensate inside a high-finesse optical cavity, with a time-independent pump, we observe a limit cycle phase, which is characterized by periodic oscillation of the intracavity photon number accompanied by the atomic density cycling through recurring patterns. We show that the time phase of the oscillation can take any value between 0 and 2π, as it is expected for a spontaneously broken continuous symmetry.  Furthermore, we demonstrate the robustness of the dynamical phase by first, identifying its stability area in the relevant parameter space and, second, showing the persistence of the limit cycle oscillations in the presence of strong temporal perturbations. Hence, we demonstrate, for the first time, the realization of a continuous time crystal.

Observation of a continuous time crystal
Phatthmon Kongkhambut, Jim Skulte, Ludwig Mathey, Jayson G. Cosme, Andreas Hemmerich, and Hans Keßler, First Release in Science, 377, 6606, pp. 670-673 (2022)

arXiv:2202.06980

Similarly, as the spontaneous breaking of translation symmetry can lead to crystallisation in space, a related phenomenon can occur with respect to time. Inspired by Franck Wilczek’s original proposal, discrete or Floquet time crystals have been observed in periodically driven closed many-body quantum systems. In these experiments, undesired residual coupling to the environment acts to limit the lifetimes of the time crystals due to unwanted dissipation and decoherence. In this work, we present the first realisation of a time crystal stabilised by tailored dissipation and fluctuations, induced via controlled coupling to a suitable environment.

Observation of a dissipative time crystal

Hans Keßler, Phatthamon Kongkhambut, Christoph Georges, Ludwig Mathey, Jayson G. Cosme, and Andreas Hemmerich

 Phys. Rev. Lett. 127, 043602 (2021)

Highlighted as Editors' Suggestion, Featured in Physics Viewpoint, in a News & Views article by Philip Ball in Nature Materials, Ingrid Fadelli in Phys.org, by Robert Gast in ZeitOnline, and by Claudia Krapp in Forschung & Lehre

arXiv:2012.08885

It is shown experimentally that a Bose-Einstein condensate inside an optical cavity, operating in the regime of strong cooperative coupling, responds to an external force by an optomechanical Bloch oscillation, which can be directly observed in the light leaking out of the cavity. Previous theoretical work predicts that the frequency of this oscillation matches with that of conventional Bloch oscillations such that its in-situ monitoring may help to increase the data acquisition speed in precision force measurements.

New Journal of Physics 18, 102001 (2016)

https://arxiv.org/abs/1606.08386

It is well known that the bosonic Hubbard model possesses a Mott insulator phase. Likewise, it is known that the Dicke model exhibits a self-organized superradiant phase. By implementing an optical lattice inside of a high finesse optical cavity both models are merged such that an extended Hubbard model with cavity-mediated infinite range interactions arises. In addition to a normal superfluid phase, two superradiant phases are found, one of them coherent and hence superfluid and one incoherent Mott insulating.

Physical Review Letters, 115, 230403 (2015)

http://arxiv.org/abs/1511.00850

The Dicke model with a weak dissipation channel is realized by coupling a Bose-Einstein condensate to an optical cavity with ultra-narrow bandwidth. We explore the dynamical critical properties of the Hepp-Lieb-Dicke phase transition by performing quenches across the phase boundary. We observe hysteresis in the transition between a normal phase and a self-organized collective phase with an enclosed loop area showing power law scaling with respect to the quench time, which suggests an interpretation within a general framework introduced by Kibble and Zurek.

PNAS 112, 3290 (2015)

https://arxiv.org/abs/1409.1945

This article  provides  a brief synopsis of our recent work  on  the  interaction of  Bose-Einstein condensates with the light field inside an optical cavity exhibiting a bandwidth on the order of the recoil frequency. Three different coupling scenarios are discussed giving rise to different physical phenomena at the borderline between the fields of quantum optics and many-body physics. This includes sub-recoil opto-mechanical cooling, cavity-controlled matter wave superradiance and  the emergence of a superradiant superfluid or a superradiant Mott insulating many-body phase in a self-organized  intra-cavity optical lattice with retarded infinite range interactions.

This article is part of the topical collection “Enlightening the World with the Laser” - Honoring T. W. Hänsch guest edited by Tilman Esslinger, Nathalie Picqué, and Thomas Udem.

Applied Physics B 122, 299 (2016)

The coherent scattering of radiation by matter, commonly referred to as Rayleigh scattering, is an ubiquitous phenomenon in nature with basic consequences such as the blue color of the sky. In ultracold gases superradiant Rayleigh scattering can be studied in the ultimate quantum mechanical limit when the atomic momentum is quantized in units of the single photon recoil momentum, a regime that has been termed matter wave superradiance. In a recent work - Phys. Rev. Lett. 113, 070404 (2014) - we show that by surrounding the cold gas with an optical high finesse cavity with very low bandwidth, the scattering channels of matter wave superradiance can be precisely controlled with possible applications as efficient matter wave beam splitters or multiple path matter wave interferometers. This work has been spotlighted in a synopsis in "APS Physics".