1 Department of Physics ， University at Buffalo, SUNY APS March Meeting 2015 Phonon mediated spin relaxation in a moving quantum dot: Doppler shift, Cherenkov radiation, and spin relaxation boom Xinyu Zhao 1 Peihao Huang 1,2 Xuedong Hu 1 For details, see arXiv: Department of Physics ， California State University, Northridge Supported by NSA/LPS through ARO

Moving spin qubit R. P. G. McNeil et al., Nature 477, 439 (2011). Experimental realization of moving spin qubit – playing pingpong between two quantum dots. P. Huang and X. Hu, PRB 88, (2013) Spin qubit relaxation in a moving quantum dot Spin qubits in double quantum dots. Figure is from Wiki In this work, we study the spin relaxation caused by the phonon environment

Moving QD, Doppler effect Subsonic regime, Doppler shiftBreaking the sound barrier, shock wave Can we observe these phenomenon in spin relaxation? Figure is from Internet

Model For details, see arXiv:

Subsonic to supersonic regime

Supersonic regime: Cherenkov effect Only the phonon from certain directions make obvious contribution to the relaxation. This is a characteristic feature of Cherenkov radiation.

Quantum confinement Cherenkov angle is the same as the classical case Without quantum confinement With quantum confinement The Cherenkov angle is slightly shifted Quantum correction on Cherenkov angle Confinement causes phonon bottleneck effect

Spin relaxation boom Sonic boom vs. Spin relaxation boom 1.For a single type of phonon, the relaxation curve is quite similar to the Prandtl-Glauert singularity. 2.The total relaxation (black, dash-dotted) is the combination of all types of phonon. 3.The position where the peak occurs is slightly shifted due to the quantum confinement effect. Figure is from Wiki

Spin relaxation for moving QD

Summary In this work, we study the spin relaxation in a moving quantum dot. Several interesting features caused by Doppler effect are observed.  Subsonic regime: Frequency shift, Doppler effect.  Transonic regime: Breaking the sonic barrier, formation of the shock wave, spin relaxation boom vs. sonic boom.  Supersonic regime: Cherenkov radiation of the phonons, A quantum correction on Cherenkov angle is given explicitly. arXiv:

Cherenkov radiation

Applications Feedback control operation Phonon Detector click e Fluctuation of the Cherenkov angle reflects the fluctuation of the moving velocity.  Direct detection of the decoherence rate !!! Measuring environment is important in many quantum error correction schemes. Our results: 1.Phonon is concentrated in certain directions 2.Small correction of Cherenkov angle These results are quite useful in measuring the environment.

Schrieffer-Wolff transformation

Eular rotation

Static QD Consistent with the results presented in Phys. Rev. Lett. 93, (2004).

Quantum confinement Without considering cutoff function (quantum confinement), the kernel function is This is just the angular relation in the Cherenkov radiation in optics While considering cutoff function (quantum confinement) in x-y plane, the kernel function is Without quantum confinement With quantum confinement 1.There is no singularity 2.The Cherenkov angle is slightly shifted The Cherenkov angle is slightly shifted due to the quantum confinement effect.

My point: The spin relaxation depends on THREE major factors: 1.Moving velocity, reflected by Doppler effect 2.Magnetic field, determining the original Zeeman splitting 3.Quantum confinement, causing the phonon bottleneck effect

Quantum confinement will affect the spin relaxation

The position of spin relaxation boom depends on the B field There is a long tail for the LA phonon, it is better to plot the 3-D relaxation figure for single type of phonon separately.

Quantum confinement will affect the spin relaxation boom (where the peak appears)

My point: The spin relaxation depends on THREE major factors: 1.Moving velocity, reflected by Doppler effect 2.Magnetic field, determining the original Zeeman splitting 3.Quantum confinement, causing the phonon bottleneck effect

Uncertainty relation Phonon frequency Strong QD confinement Weak QD confinement Interacting with a wide range of phonon Interacting with a small range of phonon, Decoherence is suppressed. high low

Uncertainty relation Electron-phonon interaction Electron part Phonon part Momentum conservation Strong confinement Weak confinement Interacting with a wide range of phonon Interacting with a small range of phonon, Decoherence is suppressed. Phonon frequency high low Spin relaxation rate as a function of the size of the quantum dot in z direction.