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arXiv:1205.4093

Decoherence in an infinite range Heisenberg model

Amit Dey, Muzaffar Qadir Lone, Sreenija Yarlagadda

Published May 18, 2012• 0 citations
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Abstract

We study decoherence in an infinite range Heisenberg model (IRHM) in the two situations where the system is coupled to a bath of either local optical phonons or global optical phonons. Using a non-perturbative treatment, we derive an effective Hamiltonian that is valid in the regime of strong spin-phonon coupling under non-adiabatic conditions. It is shown that the effective Hamiltonian commutes with the IRHM and thus has the same eigenstates as the IRHM. By analyzing the dynamics of the system using a quantum master equation approach, we show that the quantum states of the IRHM system do not decohere under Markovian dynamics when the spins interact with local phonons. For interactions with global phonons, the off-diagonal matrix elements of the system's reduced density matrix, obtained for non-Markovian dynamics, do not indicate decoherence only when states with the same $S^z_T$ (i.e., eigenvalue for the z-component of the total spin) are considered.

DOI
10.48550/arxiv.1205.4093

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We study decoherence in an interacting qubit system described by infinite range Heisenberg model (IRHM) in a situation where the system is coupled to a bath of local optical phonons. Using perturbation theory in polaron frame of reference, we derive an effective Hamiltonian that is valid in the regime of strong spin-phonon coupling under nonadiabatic conditions. It is shown that the effective Hamiltonian commutes with the IRHM upto leading orders of perturbation and thus has the same eigenstates as the IRHM. Using a quantum master equation with Markovian approximation of dynamical evolution, we show that the off-diagonal elements of the density matrix do not decay in the energy eigen basis of IRHM.
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We study two anisotropically interacting spins coupled to optical phonons; we restrict our analysis to the regime of strong coupling to the environment, to the antiadiabatic region, and to the subspace with zero value for STz{S}_{T}^{z}STz​ (the zzz component of the total spin). In the case where each spin is coupled to a different phonon bath, we assume that the system and the environment are initially uncorrelated (and form a simply separable state) in the polaronic frame of reference. By analyzing the polaron dynamics through a non-Markovian quantum master equation, we find that the system manifests a small amount of decoherence that decreases both with increasing nonadiabaticity and with enhancing strength of coupling; whereas, under the Markovian approximation, the polaronic system exhibits a decoherence-free behavior. For the situation where both spins are coupled to the same phonon bath, we also show that the system is decoherence-free in the subspace where STz{S}_{T}^{z}STz​ is fixed. To suppress decoherence through quantum control, we employ a train of $\ensuremath{\pi}$ pulses and demonstrate that unitary evolution of the system can be retained. We propose realization of a weakly decohering charge qubit from an electron in an oxide-based (tunnel-coupled) double-quantum-dot system.
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We investigate the dynamics of a central spin that is coupled to a bath of spins through a non-uniform distribution of coupling constants. Simple analytical arguments based on master equation techniques as well as numerical simulations of the full von Neumann equation of the total system show that the short-time damping and decoherence behaviour of the central spin can be modelled accurately through an effective Hamiltonian involving a single effective coupling constant. The reduced short-time dynamics of the central spin is thus reproduced by an analytically solvable effective Hamiltonian model.
The dynamics of a spin-1∕21∕21∕2 particle coupled to a nuclear spin bath through an isotropic Heisenberg interaction is studied as a model for the spin decoherence in quantum dots. The time-dependent polarization of the central spin is calculated as a function of the bath-spin distribution and the polarizations of the initial bath state. For short times, the polarization of the central spin shows a Gaussian decay, and at later times it is revived displaying nonmonotonic time dependence. The decoherence time scale depends on moments of the bath-spin distribuition, and also on the polarization strengths in various bath-spin channels. The bath polarizations have a tendency to increase the decoherence time scale. The effective dynamics of the central spin polarization is shown to be described by a master equation with non-Markovian features.