Self-Polarization and Dynamical Cooling of Nuclear Spins in Double Quantum Dots

The spin-blockade regime of double quantum dots features coupled dynamics of electron and nuclear spins resulting from the hyperfine interaction. We explain observed nuclear self-polarization via a mechanism based on feedback of the Overhauser shift on electron energy levels, and propose to use the instability toward self-polarization as a vehicle for controlling the nuclear spin distribution. In the dynamics induced by a properly chosen time-dependent magnetic field, nuclear spin fluctuations can be suppressed significantly below the thermal level.

Figure 1

Spin-blockaded transport through the double quantum dot system. Initially the system is in the state (0, 1) with one electron on the right dot. Current flows as depicted by the arrows: an electron tunnels from the source into the left dot to form the state $(1,1{)}_{s/t}$ with singlet or triplet spin, respectively. The electron then must hop to the right dot to form $(0,2{)}_s$ before tunneling out and returning the system to the (0, 1) state. If $(1,1{)}_t$ is formed (bottom), the Pauli exclusion principle prohibits the second electron from tunneling into the right dot. The triplet can decay via hyperfine spin flip with rate $W_{\pm }^{\mathrm{HF}}$, Eq. (1), or by indirect tunneling with rate $W^{\mathrm{in}}$.

Figure 2

Electron energy levels in the arrangement appropriate for GaAs, where $g\mu \approx 26\mu \mathrm{eV}/\mathrm{T}$ and $E_{\mathrm{HF}}\approx -130\mu \mathrm{eV}$.

Figure 3

Squeezing of the nuclear spin distribution by periodic reversal of magnetic field. Numerical results for two initial values of polarization (red and blue) with $N={10}^6$ spins and reversal time ${\tau }_{\mathrm{rev}}=1\mu \mathrm{s}$ are shown. Inset: A zoom-in on the interval $45$ to $55\mu \mathrm{s}$. The size of fluctuations about the limiting orbit ${\sigma }_0$ is well below the size of fluctuations in the initial state ${\sigma }_{\mathrm{Th}}$.