Nuclear Tuning and Detuning of the Electron Spin Resonance in a Quantum Dot: Theoretical Consideration

We study nuclear spin dynamics in a quantum dot close to the conditions of electron spin resonance. We show that at a small frequency mismatch, the nuclear field detunes the resonance. Remarkably, at larger frequency mismatch, its effect is opposite: The nuclear system is bistable, and in one of the stable states, the field accurately tunes the electron spin splitting to resonance. In this state, the nuclear field fluctuations are strongly suppressed, and nuclear spin relaxation is accelerated.

Figure 1

A quantum dot under ESR conditions. Left: The spin-split levels $|+⟩$ and $|-⟩$ in the rotating wave approximation. The arrows show the first-order transitions with a dissipative electron spin-flip (thick) and second-order transitions with a nuclear spin-flip (thin). Right: The initial and final states of the transitions for the case when dissipation is dominated by cotunneling to the leads.

Figure 2

Two plots of $dP/dt$ normalized by the maximum ESR pumping rate ${\dot{P}}_{\max }=2{\Gamma }_p(0)/N$, versus the nuclear polarization $P$. The circles indicate the stable configurations. (a) Detuning at small frequency mismatch ($\Delta f=0$). (b) Bistability and tuning at large frequency mismatch ($\Delta f=100{\tilde{B}}_1$). For both plots $\alpha ={10}^{-3}$.

Figure 3

Stability diagram in the ($\omega$, $B_0$)-plane for ESR induced DNSP. Bistability and tuning to the resonance occur in the gray-shaded region. The arrows show an adiabatic frequency sweep leading to the tuned state. The dashed lines present the separate contributions of mechanism (i) and (ii). This diagram qualitatively agrees with 15, Fig. 2C.