Integrability and dark states in an anisotropic central spin model

Tamiro Villazon,Anushya Chandran,Pieter W Claeys

doi:10.1103/physrevresearch.2.032052

Tamiro Villazon, Anushya Chandran + Show 1 more

Open Access

https://doi.org/10.1103/physrevresearch.2.032052

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Abstract

Central spin models describe a variety of quantum systems in which a spin-1/2 qubit interacts with a bath of surrounding spins, as realized in quantum dots and defect centers in diamond. We show that the fully anisotropic central spin Hamiltonian with (XX) Heisenberg interactions is integrable. Building on the class of integrable Richardson-Gaudin models, we derive an extensive set of conserved quantities and obtain the exact eigenstates using the Bethe ansatz. These states divide into two exponentially large classes: bright states, where the qubit is entangled with the bath, and dark states, where it is not. We discuss how dark states limit qubit-assisted spin bath polarization and provide a robust long-lived quantum memory for qubit states.

Highlights

With the advent of new quantum technologies, there is increasing interest in using small quantum systems to control and coherently manipulate mesoscopic environments [1,2,3,4,5,6].In the simplest setting, a single spin-1 2 qubit controls a surrounding bath of spins, extending the available degrees of freedom and turning the detrimental effects of the bath into a useful resource
1 2 qubit interacts with a bath of surrounding spins, as realized in quantum dots and defect centers in diamond
These states divide into two exponentially large classes: bright states, where the qubit is entangled with the bath, and dark states, where it is not

Summary

Integrability and dark states in an anisotropic central spin model

Tamiro Villazon ,1 Anushya Chandran, and Pieter W. 1 2 qubit interacts with a bath of surrounding spins, as realized in quantum dots and defect centers in diamond. We show that the fully anisotropic central spin Hamiltonian with (XX) Heisenberg interactions is integrable. Richardson-Gaudin models, we derive an extensive set of conserved quantities and obtain the exact eigenstates using the Bethe ansatz. These states divide into two exponentially large classes: bright states, where the qubit is entangled with the bath, and dark states, where it is not. We discuss how dark states limit qubit-assisted spin bath polarization and provide a robust long-lived quantum memory for qubit states

Introduction

Hamiltonian describes a central

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Dark Bright

We established a family of integrable