Dynamics and thermodynamics of a central spin immersed in a spin bath

Abstract

An exact reduced dynamical map along with its operator sum representation is derived for a central spin interacting with a thermal spin environment. The dynamics of the central spin shows high sustainability of quantum traits such as coherence and entanglement in the low-temperature regime. However, for sufficiently high temperature and when the number of bath particles approaches the thermodynamic limit, this feature vanishes and the dynamics closely mimics Markovian evolution. The properties of the long-time-averaged state and the trapped information of the initial state for the central qubit are also investigated in detail, confirming that the nonergodicity of the dynamics can be attributed to the finite temperature and finite size of the bath. It is shown that if a certain stringent resonance condition is satisfied, the long-time-averaged state retains quantum coherence, which can have far reaching technological implications in engineering quantum devices. An exact time-local master equation of the canonical form is derived. With the help of this master equation, the nonequilibrium properties of the central spin system are studied by investigating the detailed balance condition and irreversible entropy production rate. The result reveals that the central qubit thermalizes only in the limit of very high temperature and large number of bath spins.Comment: Close to published versio

Coherence of an extended central spin model with a coupled spin bath

“…The central spin model, describing one central spin surrounded by a number of bath spins, was first introduced and solved by Gaudin in 1970s 1 . In the past decades, the study of central spin systems and the related generalizations has gained great attention because the model has appeared in a large variety of nanostructures, such as semiconductors [2][3][4] , quantum dots [5][6][7][8][9][10][11][12][13][14][15][16][17][18] , carbon nanotubes, and nitrogen vacancy centers in diamond 19,20 . This model is closely related to the spin qubit suitable for quantum information processing, quantum computation and quantum metrology devices.…”

Revisiting the Quantum Open System Dynamics of Central Spin Model

“…Both the qualitative and quantitative analysis of quantum non-Markovianity is of fundamental importance in the theory of open quantum dynamics. Over the past decade, there has been numerous proposals for quantifing non-Markovianity based on CP divisibility [36,44] and non-Markovianity witness [10,36,39,40,[44][45][46][47][48][49][50][51][52][53][54][55][56]. One of the prominent non-Markovianity measures based on the composition of the dynamical map was introduced in [36], the so called RHP measure.…”

“…In this work, we are going to review a method to derive the exact reduced dynamics [37][38][39][40] of a spin half system interacting with a special type of finite spin environment. One of the most significant aspects of this particular formalism is that, it is amongst the very few cases where the exact reduced dynamics can be derived without applying any major approximation technique.…”

Detecting non-Markovianity via uncertainty relations

“…(1) Spin bath model: Here we use the generalized non-Markovian evolution for a spin-bath model. This type of system has drawn significant interest in recent studies [71][72][73][74]. The model considered here in the present work consists of a central spin interacting uniformly with a collection of mutually uninteracting and completely unpolarized spins, considered as the environment.…”