The scrambling of quantum information describes the process by which information initially stored in local, accessible, degrees of freedom is rapidly spread out over many-body, inaccessible, degrees of freedom and is thus apparently lost. In combination with the intimately related concepts of entanglement and quantum chaos, scrambling has allowed us to better understand how isolated quantum many-body systems might thermalize, i.e. relax to states which are coarsely described by the framework of statistical thermal ensembles. Of particular recent interest has been the development of connections to high-energy physics, specifically the idea of identifying black holes as the fastest scramblers of information that exist in nature via the computation of `out-of-time-order correlators' (OTOCs). These chaotic systems show exponential growth of OTOCs, the rate of which is identified as a quantum Lyapunov exponent. Moreover, the inferred exponent is found to saturate a conjectured quantum bound on the largest possible Lyapunov exponent $\lambda_L\lambda_L \leq 2\pi T$. At the quantum scale, it has been argued that a many-body system that saturates this bound is related to a conformal field theory which is a holographic dual to a black hole via AdS-CFT.
AMO systems provide ideal experimental platforms to search for and investigate such fast-scrambling models due to their versatility as analog quantum simulators. Examples include Rydberg arrays, polar molecules, neutral atoms in optical lattices, cold atoms confined inside optical cavities and trapped ion arrays. The tunability and control over microscopic physics available in the latter, for example, has enabled the pioneering measurements of OTOCs using relatively straightforward schemes in which the sign of the Hamiltonian is reversed halfway through the dynamics, to realize the reversal of time and allow the effective measurement of observables at different times.
Some of the key questions we want to investigate are:
AMO systems provide ideal experimental platforms to search for and investigate such fast-scrambling models due to their versatility as analog quantum simulators. Examples include Rydberg arrays, polar molecules, neutral atoms in optical lattices, cold atoms confined inside optical cavities and trapped ion arrays. The tunability and control over microscopic physics available in the latter, for example, has enabled the pioneering measurements of OTOCs using relatively straightforward schemes in which the sign of the Hamiltonian is reversed halfway through the dynamics, to realize the reversal of time and allow the effective measurement of observables at different times.
Some of the key questions we want to investigate are:
- What are necessary ingredients for a many-body model to display exponentially rapid scrambling?
- For generic quantum states out-of-thermal-equilibrium what are the limits on information scrambling?
- How can OTOCs be used as probes of other non-equilibrium quantum phenomena, like dynamical phase transitions or many-body localization?