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arXiv:quant-ph/0602027 · Physical Review A

Spin decoherence from Hamiltonian dynamics in quantum dots

D. D. Bhaktavatsala Rao, V. Ravishankar, V. Subrahmanyam

Published Aug 1, 2006• 16 citations
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Abstract

The dynamics of a spin-$1∕2$ particle coupled to a nuclear spin bath through an isotropic Heisenberg interaction is studied as a model for the spin decoherence in quantum dots. The time-dependent polarization of the central spin is calculated as a function of the bath-spin distribution and the polarizations of the initial bath state. For short times, the polarization of the central spin shows a Gaussian decay, and at later times it is revived displaying nonmonotonic time dependence. The decoherence time scale depends on moments of the bath-spin distribuition, and also on the polarization strengths in various bath-spin channels. The bath polarizations have a tendency to increase the decoherence time scale. The effective dynamics of the central spin polarization is shown to be described by a master equation with non-Markovian features.

DOI
10.1103/physreva.74.022301

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The decoherence of a spin‐1/2 particle (qubit) interacting with a nuclear spin bath in quantum dots has been studied using an isotropic Heisenberg model. An effective magnetic field (a feature of unitary evolution) and an effective temperature (a non‐unitary feature) describe the effective dynamics of the qubit. The decoherence time scale is calculated as a function of the nuclear bath spin distribution and the nuclear polarizations in various spin channels. The averaged auto correlation function of the qubit spin, averaged over all possible initial states of the qubit, depends on the nuclear spin distribution, but is insensitive to the nuclear polarizations.
The time evolution of spin states of two electrons interacting with a nuclear spin bath in a quantum dot system is studied. The hyperfine interaction between the electrons and the nuclear spins is modeled by an isotropic Heisenberg interaction, and the interaction between the electron spins by Heisenberg exchange. Depending on the extent of the overlap between the spatial wave functions of the electrons, there are two physically different cases, namely, the two qubits either interact with the same set of nuclear spins or they see different nuclear spin environments. In the two cases, the decoherence of the two-qubit state is studied analytically. We have identified a class of two-qubit states that have a rich dynamics when the exchange interaction between the qubits becomes large in comparison to the hyperfine interaction strengths. The decoherence time scale is determined as a function of the bath-spin distribution and the polarizations of the initial two-qubit state. States with large decoherence times are identified by performing a minimization over all the two-qubit pure states.
We investigate in detail, using both analytical and numerical tools, the decoherence of electron spins in quantum dots (QDs) coupled to a bath of nuclear spins in magnetic fields or with various initial bath polarizations, focusing on the longitudinal relaxation in low and moderate field and polarization regimes. An increase of the initial polarization of nuclear-spin bath has the same effect on the decoherence process as an increase of the external magnetic field, namely, the decoherence dynamics changes from smooth decay to damped oscillations. This change can be observed experimentally for a single QD and for a double-QD setup. Our results indicate that substantial increase of the decoherence time requires very large bath polarizations, and the use of other methods (dynamical decoupling or control of the nuclear spins distribution) may be more practical for suppressing decoherence of QD-based qubits.
The dynamics and decoherence of an electronic spin-1/2 qubit coupled to a bath of nuclear spins via hyperfine interactions in a quantum dot is studied. We show how exact results from the integrable solution can be used to understand the dynamic behavior of the qubit. It is possible to predict the main frequency contributions and their broadening for relatively general initial states analytically, leading to an estimate of the corresponding decay times, which are related to T1{T}_{1}T1​ of the electron. Furthermore, for a small bath polarization, a distinct low-frequency time scale is observed.
We study the influence of narrowed distributions of the nuclear Overhauser field on the decoherence of a central electron spin in quantum dots. We describe the spin dynamics in quantum dots by the central spin model. We use analytic solutions for uniform couplings and the time dependent density-matrix renormalization group (tDMRG) for nonuniform couplings. With these tools we calculate the dynamics of the central spin for large baths of nuclear spins with or without external magnetic field applied to the central spin. The focus of our study is the influence of initial mixtures with narrowed distributions of the Overhauser field and of applied magnetic fields on the decoherence of the central spin.
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.