Abstract

We study theoretically the phonon-induced relaxation and decoherence of spin states of two electrons in a lateral double quantum dot in a SiGe/Si/SiGe heterostructure. We consider two types of singlet-triplet spin qubits and calculate their relaxation and decoherence times, in particular as a function of level hybridization, temperature, magnetic field, spin orbit interaction, and detuning between the quantum dots, using Bloch-Redfield theory. We show that the magnetic field gradient, which is usually applied to operate the spin qubit, may reduce the relaxation time by more than an order of magnitude. Using this insight, we identify an optimal regime where the magnetic field gradient does not affect the relaxation time significantly, and we propose regimes of longest decay times. We take into account the effects of one-phonon and two-phonon processes and suggest how our theory can be tested experimentally. The spin lifetimes we find here for Si-based quantum dots are significantly longer than the ones reported for their GaAs counterparts.

Highlights

  • Quantum dots (QDs) populated by electrons or holes are considered to be promising platforms for the physical realization of qubits for quantum computation [1,2,3]

  • Following the development in theory and experiment investigating the behavior of electron spin states in single and double quantum dots in spin qubits (Si) [44, 46,47,48,49,50,51,52,53, 56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73], we study a lateral double quantum dot (DQD) which is formed in a Si/SiGe heterostructure and occupied by two electrons

  • Our work focuses on singlet-triplet qubits which are based on the low-energy eigenstates of two electrons in a DQD with weakly coupled QDs (L > 2lc), such that the Hund-Mulliken approach is applicable [4, 87]

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Summary

Introduction

Quantum dots (QDs) populated by electrons or holes are considered to be promising platforms for the physical realization of qubits for quantum computation [1,2,3]. Much progress both in theory and experiment was made in studying GaAs-based QDs [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22].

Hamiltonian
Basis states and projected Hamiltonian
Bloch-Redfield theory
Corrections from valley degrees of freedom
Dependence on temperature
Dependence on the magnetic field gradient
Proposed experiments to confirm the theory
S-T0 qubit
Large detuning
Dependence on detuning
Dependence on tunnel coupling
Simple model for the S-T0 qubit at large detuning
Zero detuning
Comparison with other decay mechanisms
Conclusions
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