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arXiv:1803.02293 · Physical Review Letters

Pinning Transition of Bose-Einstein Condensates in Optical Ring Resonators

S. Schuster, P. Wolf, Dag Schmidt, Sebastian Slama, Claus Zimmermann

Published Nov 27, 2018• 18 citations
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Abstract

We experimentally investigate the dynamic instability of Bose-Einstein condensates in an optical ring resonator that is asymmetrically pumped in both directions. We find that, beyond a critical resonator-pump detuning, the system becomes stable regardless of the pump strength. Phase diagrams and quenching curves are presented and described by numerical simulations. We discuss a physical explanation based on a geometric interpretation of the underlying nonlinear equations of motion.

DOI
10.1103/physrevlett.121.223601

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We experimentally investigate the dynamical instability of a Bose Einstein condensate in an optical ring resonator for various cavity detuning and pump powers. The resulting phase diagram is asymmetric with respect to the cavity detuning and can be described by the coupling of two atomic modes with one optical mode. We compare the experimental data to a numerical simulation and to an analytic expression of the phase boundary. For positive and negative pump cavity detuning different coupling mechanisms are identified explaining the asymmetry of the phase diagram. We present a physical interpretation and discuss the connection to the Dicke quantum phase transition.
We investigate the dynamics of a Bose-Einstein condensate interacting with two noninterfering and counterpropagating modes of a ring resonator. Superfluid, supersolid, and dynamic phases are identified experimentally and theoretically. The supersolid phase is obtained for sufficiently equal pump strengths for the two modes. In this regime we observe the emergence of a steady state with crystalline order, which spontaneously breaks the continuous translational symmetry of the system. The supersolidity of this state is demonstrated by the conservation of global phase coherence at the superfluid to supersolid phase transition. Above a critical pump asymmetry the system evolves into a dynamic runaway instability commonly known as collective atomic recoil lasing. We present a phase diagram and characterize the individual phases by comparing theoretical predictions with experimental observations.
A periodically kicked ring of a Bose-Einstein condensate is considered as a nonlinear generalization of the quantum kicked rotor, where the nonlinearity stems from the mean-field interactions between the condensed atoms. For weak interactions, periodic motion (antiresonance) becomes quasiperiodic (quantum beating) but remains stable. There exists a critical strength of interactions beyond which quasiperiodic motion becomes chaotic, resulting in an instability of the condensate manifested by exponential growth in the number of noncondensed atoms. In the stable regime, the system remains predominantly in the two lowest energy states and may be mapped onto a spin model, from which we obtain an analytic expression for the beat frequency and discuss the route to instability. We numerically explore a parameter regime for the occurrence of instability and reveal the characteristic density profile for both condensed and noncondensed atoms. The Arnold diffusion to higher energy levels is found to be responsible for the transition to instability. Similar behavior is observed for dynamically localized states (essentially quasiperiodic motions), where stability remains for weak interactions but is destroyed by strong interactions.
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A periodically kicked ring of a Bose-Einstein condensate is considered as a nonlinear generalization of the quantum kicked rotor. For weak interactions between atoms, periodic motion (antiresonance) becomes quasiperiodic (quantum beating) but remains stable. There exists a critical strength of interactions beyond which quasiperiodic motion becomes chaotic, resulting in an instability of the condensate manifested by exponential growth in the number of noncondensed atoms. Similar behavior is observed for dynamically localized states (essentially quasiperiodic motions), where stability remains for weak interactions but is destroyed by strong interactions.