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arXiv:cond-mat/0508566 · Physical Review B

Nonequilibrium electron spin polarization in a double quantum dot: Lande mechanism

Yuri A. Serebrennikov

Published Jul 20, 2006• 3 citations
arXivHTMLPDF

Abstract

In moderately strong magnetic fields, the difference in Land\'e $g$ factors in each of the dots of a two-electron double quantum dot (DQD) may induce oscillations between singlet and triplet states of an entangled pair and lead to a nonequilibrium electron spin polarization in the system. The calculated bipolar polarization reflects the strong spin correlation in the spatially separated pair of electrons that occupy almost degenerate states in a coupled DQD. We will show that this polarization may partially survive the rapid inhomogeneous decoherence caused by random nuclear magnetic fields.

DOI
10.1103/physrevb.74.035325

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In moderately strong magnetic fields, the difference in Land'e ggg factors in each of the dots of a two-electron double quantum dot (DQD) may induce oscillations between singlet and triplet states of an entangled pair and lead to a nonequilibrium electron spin polarization in the system. The calculated bipolar polarization reflects the strong spin correlation in the spatially separated pair of electrons that occupy almost degenerate states in a coupled DQD. We will show that this polarization may partially survive the rapid inhomogeneous decoherence caused by random nuclear magnetic fields.
We have evaluated hyperfine-induced electron spin dynamics for two electrons confined to a double quantum dot. Our quantum solution accounts for decay of a singlet-triplet correlator even in the presence of a fully static nuclear spin system, with no ensemble averaging over initial conditions. In contrast to an earlier semiclassical calculation, which neglects the exchange interaction, we find that the singlet-triplet correlator shows a long-time saturation value that differs from 12\frac{1}{2}21​, even in the presence of a strong magnetic field. Furthermore, we find that the form of the long-time decay undergoes a transition from a rapid Gaussian to a slow power law $(\ensuremath{\sim}1∕{t}^{3∕2})$ when the exchange interaction becomes nonzero and the singlet-triplet correlator acquires a phase shift given by a universal (parameter independent) value of $3\ensuremath{\pi}∕4$ at long times. The oscillation frequency and time-dependent phase shift of the singlet-triplet correlator can be used to perform a precision measurement of the exchange interaction and Overhauser field fluctuations in an experimentally accessible system. We also address the effect of orbital dephasing on singlet-triplet decoherence and find that there is an optimal operating point where orbital dephasing becomes negligible.
We consider a system of two strongly coupled electron spins in zero magnetic field, each of which is interacting with an individual bath of nuclear spins via the hyperfine interaction. Applying the long-spin approximation that we introduced in a previous paper [Europhys. Lett. 95, 47009 (2011)] (here each bath is replaced by a single long spin), we numerically study the electron spin and entanglement dynamics. We demonstrate that the decoherence time is scaling with the bath size according to a power law. As expected, the decaying part of the dynamics decreases with increasing bath polarization. However, surprisingly it turns out that, under certain circumstances, combining quantum dots of different geometry to the double dot setup has a very similar effect on the magnitude of the spin decay. Finally, we show that even for a comparatively weak exchange coupling the electron spins can be fully entangled.
In double quantum dots, the exchange interaction between two electron spins renormalizes the excitation energy of pair flips in the nuclear spin bath, which in turn modifies the non-Markovian bath dynamics. As the energy renormalization varies with the static Overhauser field mismatch between the quantum dots, the electron singlet-triplet decoherence resulting from the bath dynamics depends on sampling of nuclear spin states from an ensemble, leading to the transition from superexponential decoherence in single-sample dynamics to power-law decay under ensemble averaging. In contrast, the decoherence of a single electron spin in one dot is essentially the same for different choices of the nuclear spin configuration.
A global quantitative picture of the phonon-induced two-electron spin relaxation in GaAs double quantum dots is presented using highly accurate numerics. Wide regimes of interdot coupling, magnetic field magnitude and orientation, and detuning are explored in the presence of a nuclear bath. Most important, the giant magnetic anisotropy of the singlet-triplet relaxation can be controlled by detuning switching the principal anisotropy axes: a protected state becomes unprotected upon detuning and vice versa. It is also established that nuclear spins can dominate spin relaxation for unpolarized triplets even at high magnetic fields, contrary to common belief.
We investigate theoretically the hyperfine-induced dephasing of two-electron-spin states in a double quantum dot with a finite singlet-triplet splitting JJJ. In particular, we derive an effective pure dephasing Hamiltonian, which is valid when the hyperfine-induced mixing is suppressed due to the relatively large JJJ and the external magnetic field. Using both a quantum theory based on resummation of ring diagrams and semiclassical methods, we identify the dominant dephasing processes in regimes defined by values of the external magnetic field, the singlet-triplet splitting, and inhomogeneity in the total effective magnetic field. We address both free induction and Hahn echo decay of superposition of singlet and unpolarized triplet states (both cases are relevant for singlet-triplet qubits realized in double quantum dots). We also study hyperfine-induced exchange gate errors for two single-spin qubits. Results for III-V semiconductors as well as silicon-based quantum dots are presented.
We study the pumping of spin-polarized electrons in a double quantum dot system with up to two electrons per dot, via an applied AC field and a constant magnetic field. The behaviour of the current through the double-dot system is studied as a function of the AC field and coupling to the leads, using a Markov master equation approach for the time evolution of the reduced density matrix. For up to two electrons in the system, we find that the formation of a spin-triplet state blocks the current through the device, and analyse possible solutions. When we incorporate three-and four-particle states, with up to two opposite spin electrons per dot, we find a regime where the pumping of spin-polarized electrons is realized through double occupancy states in each dot. This property is robust against spin-relaxation and decoherence processes which are taken into account phenomenologically. Finally we study the effects of applying a pulsed AC field and the possibility of the resolution of Rabi oscillations.