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Scientific Reports

Decoherence and control of a qubit in spin baths: an exact master equation study

Jun Jing, Lian-Ao Wu

Published Jan 18, 2018• 31 citations
Publisher

Abstract

In spin-based nanosystems for quantum information processing, electron spin qubits are subject to decoherence due to their interactions with nuclear spin environments. In this paper, we present an exact master equation for a central spin-1/2 system in time-dependent external fields and coupled to a spin-half bath in terms of hyperfine interaction. The master equation provides a unified description for free and controlled dynamics of the central spin and is formally independent of the details and size of spin environments. Different from the previous approaches, the master equation remains exact even in the presence of external control fields. Using the parameters for realistic nanosystems with nonzero nuclear spins, such as GaAs, we investigate the Overhauser's effect on the decoherence dynamics of the central spin under different distributions of bath-spin frequencies and system-bath coupling strengths. Furthermore, we apply the leakage elimination operator, in a nonperturbative manner, to this system to suppress the decoherence induced by hyperfine interaction.

DOI
10.1038/s41598-018-19977-9

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In spin-based nanosystems for quantum information processing, electron spin qubits are subject to decoherence due to their interactions with nuclear spin environments. In this paper, we present an exact master equation for a central spin-1/2 system in time-dependent external fields and coupled to a spin-half bath in terms of hyperfine interaction. The master equation provides a unified description for free and controlled dynamics of the central spin and is formally independent of the details and size of spin environments. Different from the previous approaches, the master equation remains exact even in the presence of external control fields. Using the parameters for realistic nanosystems with nonzero nuclear spins, such as GaAs, we investigate the Overhauser's effect on the decoherence dynamics of the central spin under different distributions of bath-spin frequencies and system-bath coupling strengths. Furthermore, we apply the leakage elimination operator, in a nonperturbative manner, to this system to suppress the decoherence induced by hyperfine interaction.
We present an exact master equation for a central spin-1/21/21/2 system coupled to a spin-1/21/21/2 bath in terms of hyperfine interaction, which provides a unified formalism for both free evolution and controlled dynamics of the central spin. The equation enables us to study controllability of dynamics processes with various degrees of non-Markovianity. We investigate the Overhauser's effect on decoherence dynamics of the central spin under different bath spectra and the system-bath coupling strengths. Nonperturbative leakage elimination approach is applied to the system to suppress decoherence in solid-state quantum information processing.
We solve the long-standing central spin problem for a general set of inhomogeneous bath couplings and a large class of initial bath states. We compute the time evolution of the coherence of a central spin coupled to a spin bath by resumming all orders of the time-convolutionless master equation, thus avoiding the need to assume weak coupling to the bath. The fully quantum, non-markovian solution is obtained in the large-bath limit and is valid up to a time scale set by the largest coupling constant. Our result captures the full decoherence of an electron spin qubit coupled to a nuclear spin bath in a GaAs quantum dot for experimentally relevant parameters. In addition, our solution is quite compact and can readily be used to make quantitative predictions for the decoherence process and to guide the design of nuclear state preparation protocols.
The dominant source of decoherence for an electron spin in a quantum dot is the hyperfine interaction with the surrounding bath of nuclear spins. The decoherence process may be slowed down by subjecting the electron spin to suitable sequences of external control pulses. We investigate the performance of a variety of dynamical decoupling protocols using exact numerical simulation. Emphasis is given to realistic pulse delays and the long-time limit, beyond the domain where available analytical approaches are guaranteed to work. Our results show that both deterministic and randomized protocols are capable to significantly prolong the electron coherence time, even when using control pulse separations substantially larger than what expected from the upper cutoff frequency of the coupling spectrum between the electron and the nuclear spins. In a realistic parameter range, the total width of such a coupling spectrum appears to be the physically relevant frequency scale affecting the overall quality of the decoupling.
The many-body dynamics of an electron spin−1/2 qubit coupled to a bath of nuclear spins by hyperfine interactions, as described by the central spin model in two kinds of external field, are studied in this paper. In a completely polarized bath, we use the state recurrence method to obtain the exact solution of the X X Z central spin model in a constant magnetic field and numerically analyze the influence of the disorder strength of the magnetic field on fidelity and entanglement entropy. For a constant magnetic field, the fidelity presents non-attenuating oscillations. The anisotropic parameter λ and the magnetic field strength B significantly affect the dynamic behaviour of the central spin. Unlike the periodic oscillation in the constant magnetic field, the decoherence dynamics of the central spin act like a damping oscillation in a disordered field, where the central spin undergoes a relaxation process and eventually reaches a stable state. The relaxation time of this process is affected by the disorder strength and the anisotropic parameter, where a larger anisotropic parameter or disorder strength can speed up the relaxation process. Compared with the constant magnetic field, the disordered field can regulate the decoherence over a large range, independent of the anisotropic parameter.
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.
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.