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arXiv:2012.04888 · Physical Review A

Self-trapped atomic matter wave in a ring cavity

Jieli Qin, Lu Zhou

Published Dec 7, 2020• 6 citations
arXivHTMLPDF

Abstract

We studied a system of atomic Bose-Einstein condensate coupled to a ring cavity within the mean-field theory. Due to the interaction between atoms and light field, the atoms can be self-trapped. This is verified with both variational and numerical methods. We examined the stability of these self-trapped states. For a weakly pumped cavity, they spread during the evolution; while at strong pumping, they can maintain the shape for a long time. We also studied the moving dynamics of these self-trapped waves, and found out that it can be strongly affected by the cavity decay rate. For a small cavity decay rate, the self-trapped waves undergo a damped oscillation. Increasing the cavity decay rate will lead to a deceleration of the self-trapped waves. We also compared the main results with the semiclassical theory in which atoms are treated as classical particles.

DOI
10.1103/physreva.102.063309

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We studied a system of atomic Bose-Einstein condensate coupled to a ring cavity within the mean-field theory. Due to the interaction between atoms and light field, the atoms can be self-trapped. This is verified with both variational and numerical methods. We examined the stability of these self-trapped states. For a weakly pumped cavity, they spread during the evolution; while at strong pumping, they can maintain the shape for a long time. We also studied the moving dynamics of these self-trapped waves, and found out that it can be strongly affected by the cavity decay rate. For a small cavity decay rate, the self-trapped waves undergo a damped oscillation. Increasing the cavity decay rate will lead to a deceleration of the self-trapped waves. We also compared the main results with the semiclassical theory in which atoms are treated as classical particles.
The interaction between atomic Bose-Einstein condensate (BEC) and light field in an optical ring cavity gives rise to many interesting phenomena such as supersolid and movable self-trapped matter wave packets. Here we examined the collision of two self-trapped atomic matter wave packets in an optical ring cavity, and abundant colliding phenomena have been found in the system. Depending on the magnitude of colliding velocity, the collision dynamics exhibit very different features compared with the cavity-free case. When the initial colliding velocities of the two wave packets are small, they correlatedly oscillate around their initial equilibrium positions with a small amplitude. Increasing the collision velocity leads to severe scattering of the BEC atoms; after the collision, the two self-trapped wave packets usually break into small pieces. Interestingly, we found that such a medium velocity collision is of great phase sensitivity, which may make the system useful in precision matter wave interferometry. When the colliding velocity is further increased, in the bad cavity limit, the two wave packets collide phenomenally similar to two classical particles-they first approach each other, then separate with their shape virtually maintained. However, beyond the bad cavity limit, they experience severe spatial spreading.
The system of a transversely pumped Bose-Einstein condensate (BEC) coupled to a lossy ring cavity can favor a supersolid steady state. Here we find the existence of supersolid gap soliton in such a driven-dissipative system. By numerically solving the mean-field atom-cavity field coupling equations, gap solitons of a few different families have been identified. Their dynamical properties, including stability, propagation, and soliton collision, are also studied. Due to the feedback atom-intracavity field interaction, these supersolid gap solitons show numerous new features compared with the usual BEC gap solitons in static optical lattices.
We present numerical simulations of the cavity optomechanical detection of persistent currents and bright solitons in an atomic Bose-Einstein condensate confined in a ring trap. This paper describes a technique that measures condensate rotation , in real time, and with minimal destruction, in contrast to currently used methods, all of which destroy the condensate completely. For weakly repulsive interatomic interactions, the analysis of persistent currents extends our previous few-mode treatment of the condensate [P. Kumar ] to a stochastic Gross-Pitaevskii simulation. For weakly attractive atomic interactions, we present the first analysis of optomechanical detection of matter-wave soliton motion. We provide optical cavity transmission spectra containing signatures of the condensate rotation, sensitivity as a function of the system response frequency, and atomic density profiles quantifying the effect of the measurement backaction on the condensate. We treat the atoms at a mean-field level and the optical field classically, account for damping and noise in both degrees of freedom, and investigate the linear as well as nonlinear response of the configuration. Our results are consequential for the characterization of rotating matter waves in studies of atomtronics, superfluid hydrodynamics, and matter-wave soliton interferometry. Published by the American Physical Society 2024
We investigated the optomechanical dynamics and explored the quantum phase of a Bose-Einstein condensate in a ring cavity. The interaction between the atoms and the cavity field in the running wave mode induces a semiquantized spin-orbit coupling (SOC) for the atoms. We found that the evolution of the magnetic excitations of the matter field resembles that of an optomechanical oscillator moving in a viscous optical medium, with very good integrability and traceability, regardless of the atomic interaction. Moreover, the light-atom coupling induces a sign-changeable long-range interatomic interaction, which reshapes the typical energy spectrum of the system in a drastic manner. As a result, a new quantum phase featuring a high quantum degeneracy was found in the transitional area for SOC. Our scheme is immediately realizable and the results are measurable in experiments.
We investigate the stability and dynamics of the orbital angular momentum modes of a repulsive Bose-Einstein condensate trapped in two tunnel-coupled rings in a stack configuration. Within mean-field theory, we derive a two-state model for the system in the case in which we populate both rings equally with a single orbital angular momentum mode and include small perturbations in other modes. Analyzing the fixed-point solutions of the model and the associated classical Hamiltonian, we characterize the destabilization of the stationary states and the subsequent dynamics. By populating a single orbital angular momentum mode with an arbitrary population imbalance between the rings, we derive analytically the boundary between the regimes of Josephson oscillations and macroscopic quantum self-trapping and study numerically the stability of these solutions.
We study ground-state properties and dynamics of a dilute ultracold atomic gas in a double-well potential. The Gaussian barrier separating the two wells derives from the interaction between the atoms and a quantized field of a driven Fabry-Perot cavity. Due to intrinsic atom-field nonlinearity, several interesting phenomena arise which are the focus of this work. For the ground state, there is a critical pumping amplitude in which the atoms self-organize and the intra-cavity-field amplitude drastically increases. In the dynamical analysis, we show that the Josephson oscillations depend strongly on the atomic density and may be greatly suppressed within certain regimes, reminiscent of self-trapping of Bose-Einstein condensates in double-well setups. This pseudo-self-trapping effect is studied within a mean-field treatment valid for large atom numbers. For small numbers of atoms, we consider the analogous many-body problem and demonstrate a collapse-revival structure in the Josephson oscillations.