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arXiv:2401.17066 · SciPost Physics Core

Markovian to non-Markovian phase transition in the operator dynamics of a mobile impurity

Dominic Gribben, Jamir Marino, Shane P. Kelly

Published Sep 9, 2024• 6 citations
arXivHTMLPDF

Abstract

We study a random unitary circuit model of an impurity moving through a chaotic medium. The exchange of information between the medium and impurity is controlled by varying the velocity of the impurity, v_d v d , relative to the speed of information propagation within the medium, v_B v B . Above supersonic velocities, v_d> v_B v d > v B , information cannot flow back to the impurity after it has moved into the medium, and the resulting dynamics are Markovian. Below supersonic velocities, v_d< v_B v d < v B , the dynamics of the impurity and medium are non-Markovian, and information is able to flow back onto the impurity. We show the two regimes are separated by a continuous phase transition with exponents directly related to the diffusive spreading of operators in the medium. This is demonstrated by monitoring an out-of-time-order correlator (OTOC) in a scenario where the impurity is substituted at an intermediate time. During the Markovian phase, information from the medium cannot transfer onto the replaced impurity, manifesting in no significant operator development. Conversely, in the non-Markovian phase, we observe that operators acquire support on the newly introduced impurity. We also characterize the dynamics using the coherent information and provide two decoders which can efficiently probe the transition between Markovian and non-Markovian information flow. Our work demonstrates that Markovian and non-Markovian dynamics can be separated by a phase transition, and we propose an efficient protocol for observing this transition.

DOI
10.21468/scipostphyscore.7.3.060

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We study a random unitary circuit model of an impurity moving through a chaotic medium. The exchange of information between the medium and impurity is controlled by varying the velocity of the impurity, v_d v d , relative to the speed of information propagation within the medium, v_B v B . Above supersonic velocities, v_d> v_B v d > v B , information cannot flow back to the impurity after it has moved into the medium, and the resulting dynamics are Markovian. Below supersonic velocities, v_d< v_B v d < v B , the dynamics of the impurity and medium are non-Markovian, and information is able to flow back onto the impurity. We show the two regimes are separated by a continuous phase transition with exponents directly related to the diffusive spreading of operators in the medium. This is demonstrated by monitoring an out-of-time-order correlator (OTOC) in a scenario where the impurity is substituted at an intermediate time. During the Markovian phase, information from the medium cannot transfer onto the replaced impurity, manifesting in no significant operator development. Conversely, in the non-Markovian phase, we observe that operators acquire support on the newly introduced impurity. We also characterize the dynamics using the coherent information and provide two decoders which can efficiently probe the transition between Markovian and non-Markovian information flow. Our work demonstrates that Markovian and non-Markovian dynamics can be separated by a phase transition, and we propose an efficient protocol for observing this transition.
We study quantum information scrambling in a random unitary circuit that exchanges qubits with an environment at a rate p. As a result, initially localized quantum information not only spreads within the system, but also spills into the environment. Using the out-of-time-order correlator (OTOC) to characterize scrambling, we find a nonequilibrium phase transition in the directed percolation universality class at a critical swap rate p_{c}: for p<p_{c} the ensemble-averaged OTOC exhibits ballistic growth with a tunable light cone velocity, while for p>p_{c} the OTOC fails to percolate within the system and vanishes uniformly within a finite timescale, indicating that all local operators are rapidly swapped into the environment. To elucidate its information-theoretic consequences, we demonstrate that the transition in operator spreading coincides with a transition in an observer's ability to decode the system's initial quantum information from the swapped-out, or "radiated," qubits. We present a simple decoding scheme which recovers the system's initial information with perfect fidelity in the nonpercolating phase, and with continuously decreasing fidelity with decreasing swap rate in the percolating phase. Depending on the initial state of the swapped-in qubits, we further observe a corresponding entanglement transition in the coherent information from the system into the radiated qubits.
We study quantum information flow in a model comprised of a trapped impurity qubit immersed in a Bose-Einstein-condensed reservoir. We demonstrate how information flux between the qubit and the condensate can be manipulated by engineering the ultracold reservoir within experimentally realistic limits. We show that this system undergoes a transition from Markovian to non-Markovian dynamics, which can be controlled by changing key parameters such as the condensate scattering length. In this way, one can realize a quantum simulator of both Markovian and non-Markovian open quantum systems, the latter ones being characterized by a reverse flow of information from the background gas (reservoir) to the impurity (system).
We investigate the dynamics of quantum information flow in one and two impurity qubits trapped in a double-well potential and interacting with a one-dimensional ultracold Bose-Bose mixture reservoir. For a single qubit immersed in a binary Bose mixture, we show that the system maintains coherence over finite timescales and exhibits non-Markovian dynamics, particularly in the upper branch of the environment. We explore the transition from Markovian to non-Markovian dephasing through the Ohmicity of the spectral density functions, which are significantly influenced by interspecies interactions. In the case of two spatially separated qubits coupled to the Bose-Bose mixture reservoir, we demonstrate that collective decoherence affects the system dynamics, leading to prolonged coherence survival in both branches of the mixture. The intricate evolution of the decoherence factors is reflected in the density spectral functions and their Ohmicity characteristics. We find that the decoherence functions and spectra oscillate with increasing distance between the qubits, modifying the information flow dynamics. Additionally, we conduct a thorough investigation of the entanglement dynamics between the two qubits induced by the binary Bose mixture reservoir in both branches, underscoring the critical role of interspecies interactions.
Abstract In a fully-controllable experiment platform for studying non-Markovian open quantum dynamics, we show that the non-Markovianity could be investigated from the global and local aspects. By mixing random unitary dynamics, we demonstrate non-Markovian and Markovian open quantum dynamics. From the global point of view, by tuning the base frequency we demonstrate the transition from the Markovianity to the non-Markovianity as measured by the quantum mutual information (QMI). In a Markovian open quantum process, the QMI decays monotonically, while it may rise temporarily in a non-Markovian process. However, under some circumstances, it is not sufficient to globally investigate the non-Markovianity of the open quantum dynamics. As an essential supplement, we further utilize the quantum Fisher information (QFI) flow to locally characterize the non-Markovianity in different channels. We demonstrate that the QMI in combination with the QFI flow are capable of measuring the non-Markovianity for a multi-channel open quantum dynamics.
We study the scrambling of local quantum information in chaotic many-body systems in the presence of a locally conserved quantity like charge or energy that moves diffusively.The interplay between conservation laws and scrambling sheds light on the mechanism by which unitary quantum dynamics, which is reversible, gives rise to diffusive hydrodynamics, which is a slow dissipative process.We obtain our results in a random quantum circuit model that is constrained to have a conservation law.We find that a generic spreading operator consists of two parts: (i) a conserved part which comprises the weight of the spreading operator on the local conserved densities, whose dynamics is described by diffusive charge spreading; this conserved part also acts as a source that steadily emits a flux of (ii) nonconserved operators.This emission leads to dissipation in the operator hydrodynamics, with the dissipative process being the slow conversion of operator weight from local conserved operators to nonconserved, at a rate set by the local diffusion current.The emitted nonconserved parts then spread ballistically at a butterfly speed, thus becoming highly nonlocal and, hence, essentially nonobservable, thereby acting as the "reservoir" that facilitates the dissipation.In addition, we find that the nonconserved component develops a power-law tail behind its leading ballistic front due to the slow dynamics of the conserved components.This implies that the out-of-time-order commutator between two initially separated operators grows sharply upon the arrival of the ballistic front, but, in contrast to systems with no conservation laws, it develops a diffusive tail and approaches its asymptotic late-time value only as a power of time instead of exponentially.We also derive these results within an effective hydrodynamic description which contains multiple coupled diffusion equations.
Collision models provide a flexible framework for studying open quantum systems and introducing non-Markovianity. We present a novel class of collision models, which we term Markovian impurity models, motivated by physical scenarios in which information backflow is periodically blocked. Using the Breuer-Laine-Piilo (BLP) measure of non-Markovianity, we show that if a ppp-impurity model is non-Markovian, then the corresponding (p+1)(p+1)(p+1)-impurity model is also non-Markovian, implying the existence of a critical ppp at which the process transitions from Markovian to non-Markovian. Numerical simulations are used to investigate how this critical parameter depends on the system-ancilla and ancilla-ancilla interaction strengths. We find that, altough exceptions exist, increasing either interaction strength generally lowers the critical ppp, while sufficiently weak ancilla-ancilla interactions lead to a regime in which the dynamics remain Markovian even in the absence of impurities. Finally, we briefly introduce the complementary non-Markovian impurity model.