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Register a new userOut-of-time-ordered correlation functions in open systems: A Feynman-Vernon influence functional approach
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Authors
Jan Tuziemski
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Recent theoretical and experimental studies have shown significance of quantum information scrambling (i.e. a spread of quantum information over a system degrees of freedom) for problems encountered in high-energy physics, quantum information, and condensed matter. Due to complexity of quantum many-body systems it is plausible that new developments in this field will be achieved by experimental explorations. Since noise effects are inevitably present in experimental implementations, a better theoretical understanding of quantum information scrambling in systems affected by noise is needed. To address this problem we study indicators of quantum scrambling -- out-of-time-ordered correlation functions (OTOCs) in open quantum systems. As most experimental protocols for measuring OTOCs are based on backward time evolution we consider two possible scenarios of joint system-environment dynamics reversal: In the first one the evolution of the environment is reversed, whereas in the second it is not. We derive general formulas for OTOCs in those cases as well as study in detail the model of a spin chain coupled to the environment of harmonic oscillators. In the latter case we derive expressions for open systems OTOCs in terms of Feynman-Vernon influence functional. Subsequently, assuming that dephasing dominates over dissipation, we provide bounds on open system OTOCs and illustrate them for a spectral density known from the spin-boson problem. In addition to being significant for quantum information scrambling, our results also advance understating of decoherence in processes involving backward time evolution.
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Out-of-time-ordered correlation functions (OTOCs) play a crucial role in the study of thermalization, entanglement, and quantum chaos, as they quantify the scrambling of quantum information due to complex interactions. As a consequence of their out-of-time-ordered nature, OTOCs are difficult to measure experimentally. In this Letter we propose an OTOC measurement protocol that does not rely on the reversal of time evolution and is easy to implement in a range of experimental settings. We demonstrate application of our protocol by the characterization of quantum chaos in a periodically driven spin.
We derive an extension of the quantum regression theorem to calculate out-of-time-order correlation functions in Markovian open quantum systems. While so far mostly being applied in the analysis of many-body physics, we demonstrate that out-of-time-order correlation functions appear naturally in optical detection schemes with interferometric delay lines, and we apply our extended quantum regression theorem to calculate the non-trivial photon counting fluctuations in split and recombined signals from a quantum light source.
This letter reports the findings of the late time behavior of the out-of-time-ordered correlators (OTOCs) via a quantum kicked rotor model with $cal{PT}$-symmetric driving potential. An analytical expression of the OTOCs quadratic growth with time is yielded as $C(t)=G(K)t^2$. Interestingly, the growth rate $G$ features a quantized response to the increase of the kick strength $K$, which indicates the chaos-assisted quantization in the OTOCs dynamics. The physics behind this is the quantized absorption of energy from the non-Hermitian driving potential. This discovery and the ensuing establishment of the quantization mechanism in the dynamics of quantum chaos with non-Hermiticity will provide insights in chaotic dynamics, promising unprecedented observations in updated experiments.
We introduce a formalism for time-dependent correlation functions for systems whose evolutions are governed by non-Hermitian Hamiltonians of general type. It turns out that one can define two different types of time correlation functions. Both these definitions seem to be physically consistent while becoming equivalent only in certain cases. Moreover, when autocorrelation functions are considered, one can introduce another function defined as the relative difference between the two definitions. We conjecture that such a function can be used to assess the positive semi-definiteness of the density operator without computing its eigenvalues. We illustrate these points by studying analytically a number of models with two energy levels.
The out-of-time-ordered correlator (OTOC) is central to the understanding of information scrambling in quantum many-body systems. In this work, we show that the OTOC in a quantum many-body system close to its critical point obeys dynamical scaling laws which are specified by a few universal critical exponents of the quantum critical point. Such scaling laws of the OTOC imply a universal form for the butterfly velocity of a chaotic system in the quantum critical region and allow one to locate the quantum critical point and extract all universal critical exponents of the quantum phase transitions. We numerically confirm the universality of the butterfly velocity in a chaotic model, namely the transverse axial next-nearest-neighbor Ising model, and show the feasibility of extracting the critical properties of quantum phase transitions from OTOC using the Lipkin-Meshkov-Glick (LMG) model.
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