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Schematic Representation of Spin Energy Levels and Spin-Phonon Coupling Processes. (A) The effect of the Zeeman and hyperfine interaction on the spin energy levels with an external field of ∼ 3 T. (B) An electronic spin-flip from an excited state to the ground state can be accompanied by the emission of a phonon with energy in resonance with the spin transition (one-phonon process) or the simultaneous absorption and emission of two high-energy phonons, whose energy difference is in resonance with the spin transition (two-phonon process).
Source publication
The development of spin qubits for quantum technologies requires their protection from the main source of finite-temperature decoherence: atomic vibrations. Here we eliminate one of the main barriers to the progress in this field by providing a complete first-principles picture of spin relaxation that includes up to two-phonon processes. Our method...
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Context 1
... the electronic (S=1/2) and nuclear (I=7/2) spins of 51 V interact with each other through the hyperfine tensor, A, and with the external magnetic field, B, through the electronic (nuclear) gyromagnetic tensor, β e g e (β n g n ). As schematically shown in Fig. 1A, the Zeeman and hyperfine interactions split the spin spectrum, ω, in the 10 −2 − 10 cm −1 range, depending on the size of the external field. For energies comparable to k B T , where k B is the Boltzman constant, only these states will be populated, as the first excited electronic state is more than 10,000 cm −1 higher in ...
Context 2
... of a single phonon from (to) the thermal bath. Figure 1B schematically describe the emission process. Twophonon contributions, instead, involve the simultaneous modulation of the spin Hamiltonian by two phonons and open up Raman relaxation pathways. The relaxation rate due to simultaneous absorption/emission of two phonons, also depicted in Fig. 1B, depends on secondorder spin-phonon coupling coefficients, i.e. V 2−ph = (∂ 2 A/∂Q αq ∂Q βq ) or V 2−ph = (∂ 2 g e /∂Q αq ∂Q βq ), and G 2−ph (ω, ω αq , ω βq ) ∝ δ(ω − ω αq + ω βq )¯ n αq (¯ n βq + ...
Context 3
... the electronic (S=1/2) and nuclear (I=7/2) spins of 51 V interact with each other through the hyperfine tensor, A, and with the external magnetic field, B, through the electronic (nuclear) gyromagnetic tensor, β e g e (β n g n ). As schematically shown in Fig. 1A, the Zeeman and hyperfine interactions split the spin spectrum, ω, in the 10 −2 − 10 cm −1 range, depending on the size of the external field. For energies comparable to k B T , where k B is the Boltzman constant, only these states will be populated, as the first excited electronic state is more than 10,000 cm −1 higher in ...
Context 4
... of a single phonon from (to) the thermal bath. Figure 1B schematically describe the emission process. Twophonon contributions, instead, involve the simultaneous modulation of the spin Hamiltonian by two phonons and open up Raman relaxation pathways. The relaxation rate due to simultaneous absorption/emission of two phonons, also depicted in Fig. 1B, depends on secondorder spin-phonon coupling coefficients, i.e. V 2−ph = (∂ 2 A/∂Q αq ∂Q βq ) or V 2−ph = (∂ 2 g e /∂Q αq ∂Q βq ), and G 2−ph (ω, ω αq , ω βq ) ∝ δ(ω − ω αq + ω βq )¯ n αq (¯ n βq + ...
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