Many-body quantum chaos of ultracold atoms in a quantum ratchet
There are now over 200 quantum simulators on at least 8 separate architectures with long coherence times and controlled dynamics. These experimental systems have generated tremendous excitement about driven interacting quantum systems resulting in physics ranging from time crystals to dynamical many-body localization. The quantum ratchet adds a new feature to periodic driving: a preferred direction in both time and space, i.e., parity and time-reversal symmetry-breaking. By studying weakly interacting ultracold bosons in a quantum ratchet on a ring in position, momentum, and Floquet representations, we demonstrate the limits of known measures of quantum chaos in a system with a clearly defined and rather famous semiclassical or mean-field limit, and moreover supporting experiments. We show that the usual Wigner-Dyson statistics used to identify chaos are smeared out as we couple non-resonant modes into the drive. In contrast, the entropy of entanglement, condensate depletion, and inverse participation ratio all serve as accurate alternate identifiers for the chaotic regime in which the current on the ring flip-flops with a positive Lyapunov exponent in the mean-field limit. The dimension of the strange attractor is found to depend on the local vs. global nature of the observables. Moreover, the growth of depletion indicates mean field theory breaks down at realistic experimental times scaling polynomially as N0.18±0.004 in the chaotic regime. This study opens the door to beyond single-frequency many-body Floquet physics showing many surprises and subtleties in both the quantum many-body dynamics and the mean-field limit (or lack thereof). Our prediction of a concrete time at which depletion grows is experimentally observable via an interference experiment. The dynamics and emergent structure of higher order correlators remains an especially intriguing avenue of exploration as we find that, contrary to oft-stated popular opinion, chaos, at least in the quantum ratchet, does not lead to high entanglement.
M. Heimsoth, C. E. Creffield, L. D. Carr, and F. Sols, "Orbital Josephson effect and interactions in driven atom condensates on a ring," New J. Phys., v. 14, p. 075023 (2012).
M. Heimsoth, D. Hochstuhl, C. E. Creffield, L. D. Carr, and F. Sols, "Effective Josephson dynamics in resonantly driven Bose-Einstein condensates," New J. Phys., New J. Phys. v. 15, p. 103006 (2013).
Marc Andrew Valdez, Gavriil Shchedrin, Martin Heimsoth, Charles E. Creffield, Fernando Sols, and Lincoln D. Carr, "Many-body Quantum Chaos and Entanglement in a Quantum Ratchet," Phys. Rev. Lett., under review (2016).
Marc Andrew Valdez, Gavriil Shchedrin, Fernando Sols, and Lincoln D. Carr, "Layered Chaos in Mean-field and Quantum Many-body Dynamics," to be submitted (2017).