Phonon influence on the measurement of spin states in double quantum dots using the quantum point contact

Abstract

We study the influence of phonon scattering on the noise characteristics of a quantum point contact coupled to a two-electron system in a double quantum dot, as proposed for a singlet-triplet measurement scheme in a double-dot system. We point out that at low temperatures phonon-induced relaxation to the ground state suppresses transitions to doubly occupied singlet states which are the source of detectable current fluctuations in this measurement scheme. Thus, for a relatively strong electron-phonon interaction present in the system, the two configurations display the same noise characteristics. In this way, coupling to phonons reduces the distinguishability between the singlet and triplet configurations. Under such conditions, the proposed measurement scheme is no longer valid even though the times of the measurement-induced decoherence of an initial singlettriplet superposition and of the localization into the singlet or triplet subspace remain essentially unchanged.

Decoherence-enhanced quantum measurement of a quantum-dot spin qubit

“…As shown in Ref. [19], at very low temperatures which are characteristic for exper-iments performed on electron-spin states confined in QDs (strongly sub-Kelvin) [20][21][22][23][24][25][26] the electron-phonon interaction counteracts transitions to the high-energy doubly occupied states. This hinders the distinguishability of the measured states, which relies on charge fluctuations.…”

“…[7,11]) by defining its Hamiltonian and finding the equations of motion for its density matrix, which will then allow us to analyze the QPC current noise. None of the interactions taken into account can induce singlet-triplet transitions.…”

“…In Ref. [11] w e studied the phonon effects on the Q PC -based m easurem ent process. Phonons induce transitions betw een singly and doubly occupied QD states w hile they conserve tw o-electron spin sym m etry [12] (in fact, they cause exactly the sam e transitions as the D Q D -Q PC interaction [13]).…”

“…Let us first set the framework for the theoretical description of the system (following Refs. [13,19]) by defining its Hamiltonian and finding the equations of motion for its density matrix, which will then allow us to analyze the QPC current noise. We do not include any interactions that could induce singlet-triplet transitions.…”

“…Following Refs. [13,19], we find the quantum master equation in the Lindblad form for the DQD interacting with both environments (the bosonic phonon environment and the fermionic QPC environment) assuming that the environments are not correlated with each other,…”