False signals of chaos from quantum probes
arXiv:2108.09391 · doi:10.1103/PhysRevA.104.043308
Abstract
We demonstrate that two-time correlation functions, which are generalizations of out-of-time-ordered correlators (OTOCs), can show 'false-flags' of chaos by exhibiting behaviour predicted by random matrix theory even in a system with classically regular dynamics. In particular, we analyze a system of bosons trapped in a double-well potential and probed by a quantum dot which is coupled to the bosons dispersively. This is an integrable system (considered both as separate parts and in total). Despite the continuous time evolution generated by the actual Hamiltonian, we find that the n-fold two-time correlation function for the probe describes an effective stroboscopic or Floquet dynamics whereby the bosons appear to be alternately driven by two different non-commuting Hamiltonians in a manner reminiscent of the Trotterized time evolution that occurs in digital quantum simulation. The classical limit of this effective dynamics can have a nonzero Lyapunov exponent, while the effective level statistics and return probability show traditional signatures of chaotic behaviour. In line with several other recent studies, this work highlights the fact that the behavior of OTOCs and their generalizations must be interpreted with some care.
14 pages, 7 figures
References in corpus (15)
- Localization of interacting fermions at high temperature
- A trapped single ion inside a Bose-Einstein condensate
- Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
- Ground-State Fidelity and Bipartite Entanglement in the Bose-Hubbard Model
- Measurement of many-body chaos using a quantum clock
- Dynamics of a tunable superfluid junction
- Fidelity and Quantum phase transition for the Heisenberg chain with the next-nearest-neighbor interaction
- Interferometric Approach to Probing Fast Scrambling
- Quantum dynamics of an atomic double-well system interacting with a trapped ion
- Inelastic collision dynamics of a single cold ion immersed in a Bose-Einstein condensate
- The two-site Bose--Hubbard model
- A Quantum Top Inside a Bose Josephson Junction
- Fingerprint of chaos and quantum scars in kicked Dicke model: An out-of-time-order correlator study
- Critical exponents for an impurity in a bosonic Josephson junction: Position measurement as a phase transition
- Ultra cold atoms and Bose-Einstein condensation for quantum metrology