Post-Ehrenfest many-body quantum interferences in ultracold atoms far out of equilibrium

Abstract

Far out-of-equilibrium many-body quantum dynamics in isolated systems necessarily generate interferences beyond an Ehrenfest time scale, where quantum and classical expectation values diverge. Of great recent interest is the role these interferences play in the spreading of quantum information across the many degrees of freedom, i.e. scrambling. Ultracold atomic gases provide a promising setting to explore these phenomena. Theoretically speaking, the heavily-relied-upon truncated Wigner approximation leaves out these interferences. We develop a semiclassical theory which bridges classical and quantum concepts in many-body bosonic systems and properly incorporates such missing quantum effects. For mesoscopically populated Bose-Hubbard systems, it is shown that this theory captures post-Ehrenfest quantum interference phenomena very accurately, and contains relevant phase information to perform many-body spectroscopy with high precision.

Many-Body Quantum Interference and the Saturation of Out-of-Time-Order Correlators

“…(91)For t > τ E , the sum of contributions from diagrams (c) and (d) produces the long-time saturation of OTOCs. As seen from Eqs (39,. 67), with their temporal behavior given in Eqs (49,.…”

“…(2). However, as originally developed for SP [26][27][28][29][30][31][32][33] and recently extended to MB systems [34][35][36][37][38][39], there exist semiclassical techniques that adequately describe post-Ehrenfest quantum phenomena. By extending these approaches to MB commutator norms, here we develop a unifying semiclassical theory for OTOCs which bridges classical mean-field and quantum MB concepts arXiv:1805.06377v2 [cond-mat.stat-mech] 24 Sep 2018 for bosonic large-N systems.…”

Reversible Quantum Information Spreading in Many-Body Systems near Criticality

“…Examples comprise systems with holographic duals to black holes [10,20], the SYK-model [11,[21][22][23], and condensed matter systems close to a quantum phase transition (QPT) [24][25][26][27] or exhibiting chaos in the classical limit of large particle number N . In such large-N systems, the exponential growth rate for OTOCs is given by the Lyapunov exponent of their classical counterpart [10,[27][28][29][30][31][32][33][34] and prevails up to the Ehrenfest log N time where MB quantum interference sets in [32,35]. Subsequent OTOC time evolution towards an ergodic limit is then often governed by slow classical modes [36].Here we show that exponentially fast scrambling need not necessarily lead to quantum information loss: There exist systems exhibiting initial growth of complexity without relaxation, i.e., after a quench to an interacting system close to criticality the OTOCs do not show monotonous saturation; instead the correlations imprinted initially can be periodically retrieved.Quantum critical large-N systems are particularly suited for considering the inter-relation between spreading of correlations, quantified through OTOCs, and corresponding nonlinear classical mean-field (MF) dynamics.…”

Semi-Classical Discretization and Long-Time Evolution of Variable Spin Systems

“…The sampling method is based on an algorithm [77] for numerical integration of multivariate functions and implemented by a modification of the routine cubature [78]. For r 2 = 81, g = 20, we take on average 7892 points inside S 3 sphere for each value of integer j ∈ [40,160]. The errors obtained in the estimation of the expectation values are lower than 0.0045% at t = 0.…”

“…Multiple attempts to improve the TWA [19,33,34] suggest that more sophisticated methods [35][36][37][38][39][40][41][42][43] should be applied in order to describe the quantum evolution in terms of continuously distributed classical phase-space trajectories. Alternatively, different types of discrete phase-space sampling were proposed [44][45][46][47][48][49][50] in order to emulate evolution of average values using the main idea of the TWA.…”