1. www.buffalo.edu Phonon mediated spin relaxation in a moving quantum dot: Doppler shift, Cherenkov radiation, and spin relaxation boom Xinyu Zhao 1, Peihao Huang 1,2, and Xuedong Hu 1 1 Department of Physics, University at Buffalo, SUNY, Buffalo, New York 14260, USA and 2 Department of Physics, California State University Northridge, Northridge, California 91330, USA Abstract What we study: Spin relaxation of a moving quantum dot (QD) Results: 1. Doppler effect on emitted phonons. 2. Phonons making dominant contribution to spin relaxation is concentrated in two particular directions, which is similar to the classical Cherenkov radiation. 3. There is a peak in the relaxation curve near the sound barrier, we term this as “spin relaxation boom” in analogy to the classical sonic boom. Introduction In a large-scale electron-spin-based quantum information processor, it is inevitable that information is transferred over finite distances frequently. One straightforward way to achieve such communication is to move the electron spin qubits themselves directly. For example, the qubits can be carried by a surface acoustic wave (SAW). However, a moving spin qubit may suffer decoherence due to the spin-orbit interaction. In this work, we investigate the influences of motion on spin relaxation. In particular, we show that the Doppler effect is integral to the spin relaxation process, and leads to interesting features similar to the classical Cherenkov radiation and the sonic boom. Model and solution Directional phonon emission: Cherenkov radiation The overall behavior of the angular distribution for the phonon emission is shown in Fig. 2. (A). In the subsonic regime, the frequency of the phonon is shifted. But no directional emission is observed. The extra energy of the phonon with shifted frequency is provided by the classical force maintaining the linear motion of the electron. Fig. 1 A schematic diagram of a moving spin qubit interacting with phonon reservoir and the resulting Doppler effect. Fig. 2 The Cherenkov radiation of phonons Transition from subsonic regime to supersonic regime Quantum correction on Cherenkov angle induced by confinement effect Spin relaxation boom Classically, the drag force on an aircraft increases sharply when the aircraft velocity approaches the sound barrier. This is the so-called sonic boom. We find a similar behavior in the relaxation rate for a moving spin qubit. In Fig. 4, the total spin relaxation rate (black, dot- dashed) peaks at the two sound barriers due to TA and LA phonons. Each peak for a single type of phonon is similar to the Prandtl-Glauert singularity for the classical “sonic boom”. Accordingly, we name these peaks “spin-relaxation boom”. Conclusion and discussion In this work, we have studied decoherence of a moving spin qubit caused by phonon noise through spin-orbit interaction. We find that the QD motion leads to Doppler shifts in the emitted/absorbed phonons. When the moving velocity is larger than the sound velocity, spin relaxation is dominated by phonon emission/absorption in certain directions, which is similar to the classical Cherenkov radiation. We derive an explicit formula for the quantum confinement correction to the Cherenkov angle. We also find a “spin-relaxation boom” when the moving QD break the sound barriers, in analogy to the classical sonic boom. The current experimental technology using the interference of two orthogonal SAWs could allow direct observation of the TA boom, since it happens at a lower moving speed. Our results may be used in various potential applications. For example, the narrowly directional phonon emission from the moving spin qubit may also be used as a source of phonons, even stimulated emission or lasing of phonons. Besides, knowing the phonon emission angle may allow better continuous monitoring of the phonon environment, which could in turn provide more accurate information to possible feedback operations. Acknowledgements – We acknowledge financial support by US ARO (W911NF0910393) and NSF PIF (PHY-1104672). References: [1] V. N. Golovach, A. Khaetskii, and D. Loss, Phys. Rev. Lett. 93, 016601 (2004). [2] P. Huang and X. Hu, Phys. Rev. B 88, 075301 (2013). [3] X. Zhao, P. Huang, X. Hu, arXiv:1503.00014. Fig. 3 Fig.4