Decoherence of an electrically driven spin qubit

We study decoherence of a field-driven qubit in the presence of environmental noises. For a general qubit, we find that driving, whether on-resonance or off-resonance, alters the qubit decoherence rates (including dissipation and pure dephasing), allowing both blue and red sideband contributions from the reservoir. Depending on the noise spectral density, driving field detuning, and driving field phase shift, the qubit decoherence rates could be either accelerated or reduced. We apply our general theory to the system of an electron spin qubit that is confined in a quantum dot and driven by an in-plane electric field. We analyze how spin relaxation induced by the electrical noise due to electron-phonon interaction varies as a function of driving frequency, driving magnitude, driving field phase shift, and spin-orbit coupling strengths.

Figure 1

Dimensionless [without multiplying the common prefactor in the expressions of decoherence times in Eqs. (25) and (26)] rotating-frame decoherence rates $1/T_1^{\prime }$, $1/T_{\varphi }^{\prime }$, and $1/T_2^{\prime }$ as functions of $\delta$, with different combinations of $\varphi$ and $r$. Note that when $r=0$, none of these rates depend on $\varphi$.

Figure 2

The ratio of on-resonance relaxation rate $(1/T_1){|}_{\mathrm{res}}$ to nondriven relaxation rate $(1/T_1){|}_{\mathrm{nondriven}}$ of electron spin as a function of ${\Omega }_S$, the ratio of driving electrical field strength to Zeeman frequency, with different angles of driving electrical field. We choose (a) $r=0.05$ and (b) $r=0.8$. Here $B_z$, $\hslash {\omega }_d$, $|E_x|$, and $|E_y|$ are to be tuned such that ${\Omega }_S$ is in the range of $[{10}^{-3},{10}^{-1}]$.

Figure 3

On-resonance relaxation rate $1/T_1$ (solid lines with symbols) of electron spin as a function of the ratio $r$ and the angle (phase shift) $\varphi$ of driving electrical field in GaAs QDs, where we suppose $\beta =1000$ m/s. The curves depicted only by symbols imply $(1/T_1){|}_{\mathrm{sideband}}$. We choose $B_z=1$ T, $\hslash {\omega }_d=1$ meV, and $|E_x|=4000$ V/m.

Figure 4

Modification of the piezoelectric electron-phonon spectrums for GaAs QD in units of driven strength $\Omega$ in Rabi oscillation. We choose driving field along the angle (a) $\varphi =0$ and (b) $\varphi =\pi /2$.

Figure 5

On-resonance pure dephasing rate $1/T_{\varphi }$ of electron spin as a function of driving field amplitude ${\Omega }_S$ at a few different ratios $r$ in GaAs QDs, where we have taken $\varphi =0$ and $\beta =1000$ m/s. $B_z$, $\hslash {\omega }_d$, $|E_x|$, and $|E_y|$ are tuned such that ${\Omega }_S$ is in the range of $[{10}^{-3},{10}^{-1}]$.

Figure 6

Off-resonance relaxation rate $1/T_1$ of electron spin as a function of dimensionless frequency detuning $\delta$ in the presence of electrical noise for GaAs QD under the conditions (a) different $r$ with $\varphi =0$ and (b) different $\varphi$ with $r=0.9$. We choose $\beta =1000$ m/s, $B_z=1$ T, $\hslash {\omega }_d=1$ meV, and $|E_x|=4000$ V/m. Insets: The ratio $(1/T_1){{|}_{\mathrm{driven}}/(1/T_1)|}_{\mathrm{nondriven}}$ vs $\delta$.

Figure 7

Off-resonance pure dephasing rate $1/T_{\varphi }$ of electron spin as a function of dimensionless frequency detuning $\delta$ in the presence of electrical noise for GaAs QD under the conditions with different $r$ with $\varphi =0$.