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arXiv:1911.09591 · Physical Review A

Fast route to equilibration

Roie Dann, Ander Tobalina, Ronnie Kosloff

Published May 4, 2020• 32 citations
arXivHTMLPDF

Abstract

We present a control scheme for quantum systems coupled to a thermal bath. We demonstrate state-to-state control between two Gibbs states. This scheme can be used to accelerate thermalization and cool the open system. Starting from a microscopic description, we derive the reduced system dynamics, leading to a nonadiabatic master equation. The equation contains nontrivial effects due to the nonadiabatic driving and bath interaction. These special features enable controlling the open system and accelerating the entropy changes. For a two-level system model, we obtain a general solution and introduce a reverse-engineering scheme for control. The control problem is analyzed in the context of the theory of quantum control and the accompanying thermodynamic cost.

DOI
10.1103/physreva.101.052102

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We present a control scheme for quantum systems coupled to a thermal bath. We demonstrate state-to-state control between two Gibbs states. This scheme can be used to accelerate thermalization and cool the open system. Starting from a microscopic description, we derive the reduced system dynamics, leading to a nonadiabatic master equation. The equation contains nontrivial effects due to the nonadiabatic driving and bath interaction. These special features enable controlling the open system and accelerating the entropy changes. For a two-level system model, we obtain a general solution and introduce a reverse-engineering scheme for control. The control problem is analyzed in the context of the theory of quantum control and the accompanying thermodynamic cost.
We present a procedure to accelerate the relaxation of an open quantum system towards its equilibrium state. The control protocol, termed the shortcut to equilibration, is obtained by reverse-engineering the nonadiabatic master equation. This is a nonunitary control task aimed at rapidly changing the entropy of the system. Such a protocol serves as a shortcut to an abrupt change in the Hamiltonian, i.e., a quench. As an example, we study the thermalization of a particle in a harmonic well. We observe that for short protocols the accuracy improves by 3 orders of magnitude.
We construct a quantum Markovian master equation for a driven system coupled to a thermal bath. The derivation utilizes an explicit solution of the propagator of the driven system. This enables the validity of the master equation to be extended beyond the adiabatic limit. The nonadiabatic master equation (NAME) is derived employing the weak system-bath coupling limit. The NAME is valid when a separation of timescales exists between the bath dynamics and the external driving. In contrast to the adiabatic master equation, the NAME leads to coupled equations of motion for the population and coherence. We employ the NAME to solve the example of an open driven time-dependent harmonic oscillator. For the harmonic oscillator the NAME predicts the emergence of coherence associated with the dissipation term. As a result of the nonadiabatic driving the thermalization rate is suppressed. The solution is compared with both numerical calculations and the adiabatic master equation.
We investigate the dynamic evolution and thermodynamic process of a driven quantum system immersed in a finite-temperature heat bath. A Born-Markovian quantum master equation is formally derived for the time-dependent system with discrete energy levels. This quantum master equation can be applied to situations with a broad range of driving speeds and bath temperatures and thus be used to study the finite-time quantum thermodynamics even when nonadiabatic transition and dissipation coexist. The dissipative Landau-Zener model is analyzed as an example. The population evolution and transition probability of the model reveal the importance of the competition between driving and dissipation beyond the adiabatic regime. Moreover, local maxima of irreversible entropy production occur at intermediate sweep velocity and finite temperature, which the low-dissipation model cannot describe.
We study deviations from thermal equilibrium between two-level systems (TLS) and a bath by frequent and brief quantum measurements of the TLS energy-states. The resulting entropy and temperature of both the system and the bath are found to be completely determined by the measurement rate, and unrelated to what is expected by standard thermodynamical rules that hold for Markovian baths. These anomalies allow for very fast control heating, cooling and state-purification (entropy reduction) of quantum systems much sooner than their thermal equilibration time.
Fast and reliable manipulation with qubits is fundamental for any quantum technology. The implementation of these manipulations in physical systems is the focus of studies involving optimal control theory. Realistic physical devices are open quantum systems. So far, studies in optimal control theory have primarily utilized the Redfield/Lindblad quantum master equation to simulate the dynamics of such systems. However, this Markov description is not always sufficient. Here, we present a study of qubit control utilizing the nonequilibrium Green's function method. We compare the traditional master equation with more general Green's function results and demonstrate that even in the parameter regime suitable for the application of the Redfield/Lindblad approach, the two methods yield drastically different results when addressing evolution involving mixed states. In particular, we find that, in addition to predicting different optimal driving profiles, a more accurate description of system evolution enables the system to reach the desired final state much more quickly. We argue that the primary reason for this is the significance of the non-Markov description of driven system dynamics due to the effect of time-dependent driving on dissipation.
Quantum control of an open system is demonstrated employing a thermodynamically consistent master equation. In this framework, the open system dynamics depend on the control protocol due to the dressing of the system by the drive. This interrelation serves as the key element for control. The influence of the external drive is incorporated within the dynamical equation, enabling an indirect control of the dissipation. The control paradigm is displayed by analyzing entropy changing state to state transformations, heating and cooling N-level systems. Following, we study the generation of quantum non-unitary maps via coherent control. These include both reset maps with complete memory loss and single-qubit unitary maps under dissipative conditions.