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arXiv:2109.05775 · Quanta

Revisiting the Quantum Open System Dynamics of Central Spin Model

Samyadeb Bhattacharya, Subhashish Banerjee

Published Dec 12, 2021• 6 citations
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Abstract

In this work, we revisit the theory of open quantum systems from the perspective of fermionic baths. Specifically, we concentrate on the dynamics of a central spin half particle interacting with a spin bath. We have calculated the exact reduced dynamics of the central spin and constructed the Kraus operators in relation to that. Further, the exact Lindblad type canonical master equation corresponding to the reduced dynamics is constructed. We have also briefly touched upon the aspect of non-Markovianity from the backdrop of the reduced dynamics of the central spin. Quanta 2021; 10: 55–64.

DOI
10.12743/quanta.v10i1.162

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Data of the numerical solution of the time-dependent Schrödinger equation of a system containing one spin-1/2 particle interacting with a bath of up to 32 spin-1/2 particles is used to construct a Markovian quantum master equation describing the dynamics of the system spin. The procedure of obtaining this quantum master equation, which takes the form of a Bloch equation with time-independent coefficients, accounts for all non-Markovian effects inasmuch the general structure of the quantum master equation allows. Our simulation results show that, with a few rather exotic exceptions, the Bloch-type equation with time-independent coefficients provides a simple and accurate description of the dynamics of a spin-1/2 particle in contact with a thermal bath. A calculation of the coefficients that appear in the Redfield master equation in the Markovian limit shows that this perturbatively derived equation quantitatively differs from the numerically estimated Markovian master equation, the results of which agree very well with the solution of the time-dependent Schrödinger equation.
In this article we derive the exact dynamics of a two-qubit (spin 1/21/21/2) system interacting centrally with separate spin baths composed of qubits in a thermal state. Furthermore, each spin of the bath is coupled to every other spin of the same bath. The corresponding dynamical map is constructed. It is used to analyze the non-Markovian nature of the two qubit central spin dynamics. We further observe the evolution of quantum correlations like entanglement and discord under the influence of the environmental interaction. Moreover, we demonstrate the comparison between this exact two-qubit dynamics and the locally acting central spin model in a spin bath. This work is a stepping stone towards the realization of non-Markovian heat engines and other quantum thermal devices.
A model of an arbitrary spin coupled to a bath of spins 12\frac{1}{2}21​ in a star configuration is considered. The exact reduced dynamics of the central spin is found for the case of noncorrelated initial conditions of the system and the bath. The exact solution is used to test two approximation techniques, namely, the Nakajima-Zwanzig projection operator technique and the time-convolutionless projection operator technique corresponding to the second order of the coupling constant. Two types of projection operators are used for deriving the master equations, and the results are compared with the exact solution for a central spin equal to one. It is shown that the approximate master equations reproduce the exact dynamics on time scales 1/(AN)1/(A\sqrt{N})1/(AN​), where AAA is the coupling constant and NNN is the number of spins in the bath.
We present an exact master equation for a central spin-1/21/21/2 system coupled to a spin-1/21/21/2 bath in terms of hyperfine interaction, which provides a unified formalism for both free evolution and controlled dynamics of the central spin. The equation enables us to study controllability of dynamics processes with various degrees of non-Markovianity. We investigate the Overhauser's effect on decoherence dynamics of the central spin under different bath spectra and the system-bath coupling strengths. Nonperturbative leakage elimination approach is applied to the system to suppress decoherence in solid-state quantum information processing.
An exact canonical master equation of the Lindblad form is derived for a central spin interacting uniformly with a sea of completely unpolarized spins. The Kraus operators for the dynamical map are also derived. The non-Markovianity of the dynamics in terms of the divisibility breaking of the dynamical map and the increase of the trace distance fidelity between quantum states is shown. Moreover, it is observed that the irreversible entropy production rate is always negative (for a fixed initial state) whenever the dynamics exhibits non-Markovian behavior. In continuation with the study of witnessing non-Markovianity, it is shown that the positive rate of change of the purity of the central qubit is a faithful indicator of the non-Markovian information backflow. Given the experimental feasibility of measuring the purity of a quantum state, a possibility of experimental demonstration of non-Markovianity and the negative irreversible entropy production rate is addressed. This gives the present work considerable practical importance for detecting the non-Markovianity and the negative irreversible entropy production rate.
In this work, we introduce a method for deriving exact master equations from the dynamical map for finite open quantum systems coupled to (in)finite reservoirs, using the principle of minimal dissipation. The exact dynamics of the central spin model, which models a finite-bath open quantum system, is developed for two interaction types: Heisenberg and stochastic pure-dephasing interactions. The Heisenberg interaction yields a novel phase-covariant quantum channel in the strong-coupling regime, offering a new platform for studying a range of quantum information protocols. The stochastic pure-dephasing interaction provides the microscopic derivation of the paradigmatic non-Markovian random telegraph noise (RTN) channel, establishing its quantum foundation and offering insight into stochastic couplings. We derive the closed-form master equations for both models. As a demonstration, we explore the thermodynamic performance of these systems as quantum batteries. A direct relationship between quantum heat current and charging power is revealed, and RTN quantum batteries are shown to have advantages in charge storage.