Early experiments on spin-blockaded double quantum dots revealed surprising robust, large-amplitude current oscillations in the presence of a static (dc) source-drain bias [see e.g. K. Ono, S. Tarucha, Phys. Rev. Lett. 92, 256803 (2004)]. Experimenta
l evidence strongly indicates that dynamical nuclear polarization plays a central role, but the mechanism has remained a mystery. Here we introduce a minimal albeit realistic model of coupled electron and nuclear spin dynamics which supports robust self-sustained oscillations. Our mechanism relies on a nuclear-spin analog of the tunneling magnetoresistance phenomenon (spin-dependent tunneling rates in the presence of an inhomogeneous Overhauser field) and nuclear spin diffusion, which governs dynamics of the spatial profile of nuclear polarization. The extremely long oscillation periods (up to hundreds of seconds) observed in experiments as well as the differences in phenomenology between vertical and lateral quantum dot structures are naturally explained in the proposed framework.
Entanglement generation and detection are two of the most sought-after goals in the field of quantum control. Besides offering a means to probe some of the most peculiar and fundamental aspects of quantum mechanics, entanglement in many-body systems
can be used as a tool to reduce fluctuations below the standard quantum limit. For spins, or spin-like systems, such a reduction of fluctuations can be realized with so-called squeezed states. Here we present a scheme for achieving coherent spin squeezing of nuclear spin states in few-electron quantum dots. This work represents a major shift from earlier studies in quantum dots, which have explored classical narrowing of the nuclear polarization distribution through feedback involving stochastic spin flips. In contrast, we use the nuclear-polarization-dependence of the electron spin resonance (ESR) to provide a non-linearity which generates a non-trivial, area-preserving, twisting dynamics that squeezes and stretches the nuclear spin Wigner distribution without the need for nuclear spin flips.
Topological phase transitions can occur in the dissipative dynamics of a quantum system when the ratio of matrix elements for competing transport channels is varied. Here we establish a relation between such behavior in a class of non-Hermitian quant
um walk problems [M. S. Rudner and L. S. Levitov, Phys. Rev. Lett. 102, 065703 (2009)] and nuclear spin pumping in double quantum dots, which is mediated by the decay of a spin-blockaded electron triplet state in the presence of spin-orbit and hyperfine interactions. The transition occurs when the strength of spin-orbit coupling exceeds the strength of the net hyperfine coupling, and results in the complete suppression of nuclear spin pumping. Below the transition point, nuclear pumping is accompanied by a strong reduction in current due to the presence of non-decaying dark states in this regime. Due to its topological character, the transition is expected to be robust against dephasing of the electronic degrees of freedom.
Transport through spin-blockaded quantum dots provides a means for electrical control and detection of nuclear spin dynamics in the host material. Although such experiments have become increasingly popular in recent years, interpretation of their res
ults in terms of the underlying nuclear spin dynamics remains challenging. Here we point out a fundamental process in which nuclear spin dynamics can be driven by electron shot noise; fast electric current fluctuations generate much slower nuclear polarization dynamics, which in turn affect electron dynamics via the Overhauser field. The resulting extremely slow intermittent current fluctuations account for a variety of observed phenomena that were not previously understood.
Spin-blockaded quantum dots provide a unique setting for studying nuclear-spin dynamics in a nanoscale system. Despite recent experimental progress, observing phase-sensitive phenomena in nuclear spin dynamics remains challenging. Here we point out t
hat such a possibility opens up in the regime where hyperfine exchange directly competes with a purely electronic spin-flip mechanism such as the spin-orbital interaction. Interference between the two spin-flip processes, resulting from long-lived coherence of the nuclear-spin bath, modulates the electron-spin-flip rate, making it sensitive to the transverse component of nuclear polarization. In a system repeatedly swept through a singlet-triplet avoided crossing, nuclear precession is manifested in oscillations and sign reversal of the nuclear-spin pumping rate as a function of the waiting time between sweeps. This constitutes a purely electrical method for the detection of coherent nuclear-spin dynamics.
