[Paper Review] Phonon mediated spin relaxation in a moving quantum dot: Doppler shift, Cherenkov radiation, and spin relaxation boom

Xinyu Zhao, Peihao Huang+1 more|arXiv (Cornell University)|Feb 27, 2015

Quantum and electron transport phenomena40 references3 citations

TL;DR

This paper investigates phonon-mediated spin relaxation in a moving quantum dot, revealing that Doppler shifts and Cherenkov-like phonon emission emerge when the dot's velocity exceeds the speed of sound. A key finding is a peak in spin relaxation rate—termed 'spin relaxation boom'—near the speed of sound, with potential for reduced decoherence at supersonic speeds, suggesting a pathway for coherent spin qubit transport.

ABSTRACT

We study relaxation of a moving spin qubit caused by phonon noise. As we vary the speed of the qubit, we observe several interesting features in spin relaxation and the associated phonon emission, induced by Doppler effect. In particular, in the supersonic regime, the phonons emitted by the relaxing qubit is concentrated along certain directions, similar to the shock waves produced in classical Cherenkov effect. As the speed of the moving qubit increases from the subsonic regime to the supersonic regime, the qubit experiences a peak in the spin relaxation rate near the speed of sound, which we term a spin relaxation boom in analogy to the classical sonic boom. We also find that the moving spin qubit may have a lower relaxation rate than a static qubit, which hints at the possibility of coherence-preserving transportation for a spin qubit. While the physics we have studied here has strong classical analogies, we do find that quantum confinement for the spin qubit plays an important role in all the phenomena we observe. Specifically, it produces a correction on the Cherenkov angle, and removes the divergence in relaxation rate at the sonic barrier. It is our hope that our results would encourage further research into approaches for transferring and preserving quantum information in spin qubit architectures.

Motivation & Objective

• To understand how motion of a spin qubit in a quantum dot affects its spin relaxation via electron-phonon and spin-orbit interactions.
• To investigate the role of the Doppler effect in modifying phonon emission and relaxation dynamics in a moving qubit.
• To explore whether supersonic motion can reduce decoherence, enabling coherent transport of spin qubits.
• To examine the influence of quantum confinement on classical analogs like Cherenkov radiation and sonic booms in spin relaxation.
• To provide a theoretical framework for designing robust spin qubit architectures with controlled motion and reduced decoherence.

Proposed method

• Formulates a Hamiltonian for a single electron in a moving quantum dot, including orbital, Zeeman, spin-orbit, and electron-phonon interaction terms.
• Applies a Schrieffer-Wolff transformation to decouple spin and orbital dynamics, deriving an effective spin Hamiltonian with time-dependent terms due to motion.
• Uses Bloch-Redfield theory to compute the spin relaxation rate, incorporating Doppler-shifted phonon frequencies via the factor $(1 - ilde{ u}_j)$.
• Derives the relaxation rate as an integral over phonon modes, including angular and frequency-dependent terms modified by motion and quantum confinement.
• Introduces a correction to the Cherenkov angle due to quantum confinement, removing the divergence seen in classical models.
• Analyzes the relaxation rate across subsonic, sonic, and supersonic regimes to identify non-monotonic behavior and peak relaxation near the speed of sound.

Experimental results

Research questions

• RQ1 How does the motion of a quantum dot affect the angular distribution and emission pattern of phonons during spin relaxation?
• RQ2 What is the role of the Doppler effect in modifying the spin relaxation rate of a moving spin qubit?
• RQ3 Does the relaxation rate exhibit a peak near the speed of sound, analogous to a sonic boom, and what causes it?
• RQ4 How does quantum confinement alter classical analogs like Cherenkov radiation and the sonic boom in spin relaxation?
• RQ5 Can moving spin qubits achieve lower decoherence rates than static ones, and under what conditions?

Key findings

• A peak in the spin relaxation rate—termed 'spin relaxation boom'—occurs when the quantum dot's velocity approaches the speed of sound, analogous to a classical sonic boom.
• In the supersonic regime, phonons are emitted directionally along a Cherenkov-like cone, with the emission angle corrected by quantum confinement effects.
• The relaxation rate can be lower for a moving qubit than for a static one, particularly in the supersonic regime, indicating potential for coherence-preserving transport.
• Quantum confinement removes the divergence in the relaxation rate at the sonic barrier, which is present in classical models, due to the finite spatial extent of the wavefunction.
• The Cherenkov angle is corrected by quantum confinement, deviating from the classical prediction $\cos\phi_C = v_s / v_0$.
• The relaxation rate expression includes a Doppler-shifted phonon frequency factor $\omega_{qj}(1 - \xi_j)$, which arises from the time-dependent phase $e^{iq \cdot r_0(t)}$ in the moving frame.