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Europhysics Letters (EPL)

Emergence of prethermal states in a driven dissipative system through cross-correlated dissipation

Arnab Chakrabarti, Rangeet Bhattacharyya

Published May 12, 2023• 4 citations
Publisher

Abstract

Abstract Periodically driven closed quantum many-body systems are known to exhibit prethermal or quasi-steady-state dynamics. In this work, we theoretically show that such prethermal phases can appear in the dynamics of a dipolar two-spin-1/2 system coupled to a heat bath if the cross terms between the drive and dipolar interactions are taken into consideration. To this end, we use our recently reported fluctuation-regulated quantum master equation (Chakrabarti A. and Bhattacharyya R., Phys. Rev. A 97 (2018) 063837), to show that the predicted dynamics can successfully explain the experimentally observed features of the transient and prethermal regime.

DOI
10.1209/0295-5075/acd4e5

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Abstract Periodically driven closed quantum many-body systems are known to exhibit prethermal or quasi-steady-state dynamics. In this work, we theoretically show that such prethermal phases can appear in the dynamics of a dipolar two-spin-1/2 system coupled to a heat bath if the cross terms between the drive and dipolar interactions are taken into consideration. To this end, we use our recently reported fluctuation-regulated quantum master equation (Chakrabarti A. and Bhattacharyya R., Phys. Rev. A 97 (2018) 063837), to show that the predicted dynamics can successfully explain the experimentally observed features of the transient and prethermal regime.
We study the classic problem concerning the dissipative dynamics of a system of two interacting spin-1/21/21/2 particles, coupled to a thermal bath. In particular, we consider the case of a resonant excitation of the initial single-spin coherences and examine the consequences of the interplay between this excitation and the spin-spin dipolar coupling. Using a fluctuation-regulated Quantum Master Equation (frQME) [Phys. Rev. A 97, 063837 (2018)] we show that the relevant dissipator consists of cross-terms between the drive and the dipolar Hamiltonian, apart from regular self-terms responsible for ordinary relaxation effects. The drive-dipole cross-correlations provide for a novel second-order coupling of single and two-spin observables in the Zeeman basis, which cannot be classified as a dissipative effect. We show that the presence of these unique second-order non-dissipative terms lead to the well-known spin-locked steady-states in dipolar spin-ensembles. Importantly, the mathematical form of the steady-state magnetization in the spin-locked phase, obtained from our theory, matches with the prediction of the traditional spin-temperature based methods used to describe such phenomena.
Recent experiments show that periodic drives on dipolar systems lead to long-lived prethermal states. These systems are weakly coupled to the environment and reach prethermal states on a timescale much shorter than the timescale for thermalization. Such nearly closed systems have previously been analyzed using Floquet formalism, which shows the emergence of a prethermal plateau. We use a fluctuation-regulated quantum master equation (FRQME) to describe these systems. In addition to the system-environment coupling, FRQME successfully captures the dissipative effect from the various local interactions in the system. Our investigation reveals a cascaded journey of the system to a final steady state. The cascade involves a set of prethermal or arrested states characterized by a set of quasiconserved quantities. We show that these prethermal states emerge in a timescale much shorter than the relaxation timescale. We also find and report the existence of a critical limit beyond which the prethermal plateau ceases to exist.
Here we provide a theoretical framework to analyze discrete time-crystalline (DTC) phases in the dissipative dipolar systems subjected to a two-pulse excitation scheme. As a particular realization, we choose a quantum many-body system that exhibits prethermalization due to the presence of the quasiconserved quantities. The analysis uses a fluctuation-regulated quantum master equation, which captures the dissipative effects of the drive and dipolar coupling on the dynamics regularized by the thermal fluctuations. We find that the effects of such dissipation lend stability to the dynamics and are directly responsible for the robustness. Specifically, we find that longer fluctuation correlation time enhances the stability of DTC. We also obtain the lifetime of such a robust period-doubling response, a salient feature of the DTC phase, by varying several system parameters. Our results are in good agreement with the recent experimental findings in dipolar systems using nuclear magnetic resonance spectroscopy. Finally, we provide an estimate how the DTC performance degrades with temperature.
Here we provide a theoretical framework to analyze discrete time-crystalline phases (DTC) in open quantum many-body systems. As a particular realization, we choose a quantum many-body system that exhibits cascaded prethermalization . The analysis uses a fluctuation-regulated quantum master equation. The master equation captures the dissipative effects of the drive and dipolar coupling on the dynamics regularized by the thermal fluctuations. We find that the dissipators from the drive and the dipolar interactions lend stability to the dynamics and are directly responsible for the robustness. Specifically, we find that longer fluctuation correlation time enhances the stability of DTC. Our results are in good agreement with the experiments. Finally, we show and quantify how the DTC performance degrades with temperature.
We discuss the effect of dissipation on heating which occurs in periodically driven quantum many-body systems. We especially focus on a periodically driven Bose-Hubbard model coupled to an energy and particle reservoir. Without dissipation, this model is known to undergo parametric instabilities which can be considered as an initial stage of heating. By taking the weak on-site interaction limit as well as the weak system-reservoir coupling limit, we find that parametric instabilities are suppressed if the dissipation is stronger than the on-site interaction strength and stable steady states appear. Our results demonstrate that periodically driven systems can emit energy, which is absorbed from external drivings, to the reservoir so that they can avoid heating.
Periodically driven closed quantum systems are expected to eventually heat up to infinite temperature; reaching a steady state described by a circular orthogonal ensemble. However, such finite driven systems may exhibit sufficiently long prethermal regimes; their properties in these regimes are qualitatively different from that of their corresponding infinite temperature steady states. These, often experimentally relevant, prethermal regimes host a wide range of phenomena; they may exhibit dynamical localization and freezing, host Floquet scars, display signatures of Hilbert space fragmentation, and exhibit time crystalline phases. Such phenomena are often accompanied by emergent approximate dynamical symmetries which have no analogue in equilibrium systems. In this review, we provide a pedagogical introduction to the origin and nature of these symmetries and discuss their role in shaping the prethermal phases of a class of periodically driven closed quantum systems.