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arXiv:cond-mat/0701581 · Physical Review B

Non-Markovian dynamics of a double quantum dot charge qubit with static bias

Xiufeng Cao, Hang Zheng

Published Sep 4, 2007• 9 citations
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Abstract

We have studied the dynamics of charge qubit with the static bias by a perturbation treatment based on unitary transformations. The approach can be practiced for various forms of the spectral density and the usual Ohmic and piezoelectric spectra are used in our calculations. Analytical results of the quantum dynamics, described by the population inversion $P(t)$, are obtained together with the damping rate and the oscillation frequency. We find that a weak coupling of the qubit to the environment leads to a higher coherence oscillation frequency and a longer coherence time. For a fixed tunneling between the double quantum dots, the finite bias enhances the oscillation frequency effectively but its effect on the damping rate is relatively small. This is a possible way to maintain quantum coherence.

DOI
10.1103/physrevb.76.115301

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We have studied the dynamics of charge qubit with the static bias by a perturbation treatment based on unitary transformations. The approach can be practiced for various forms of the spectral density and the usual Ohmic and piezoelectric spectra are used in our calculations. Analytical results of the quantum dynamics, described by the population inversion P(t)P(t)P(t), are obtained together with the damping rate and the oscillation frequency. We find that a weak coupling of the qubit to the environment leads to a higher coherence oscillation frequency and a longer coherence time. For a fixed tunneling between the double quantum dots, the finite bias enhances the oscillation frequency effectively but its effect on the damping rate is relatively small. This is a possible way to maintain quantum coherence.
The dynamics of charge qubit in a double quantum dot coupled to phonons is investigated theoretically in terms of a perturbation treatment based on a unitary transformation. The dynamical tunneling current is obtained explicitly. The decoherence induced by acoustic phonons is analyzed in detail after a derivation of spectral density. It is shown that the contribution from deformation potential coupling is comparable to that from piezoelectric coupling in small dots and large tunneling rates. A possible decoupling mechanism is predicted.
In this paper, we develop a nonperturbation theory for describing decoherence dynamics of electron charges in a double quantum dot gated by electrodes. We extend the Feynman-Vernon influence functional theory to fermionic environments and derive an exact master equation for the reduced density matrix of electrons in the double dot for a general spectral density at arbitrary temperature and bias. We then investigate the decoherence dynamics of the double-dot charge qubit with backreaction of the reservoirs being fully taken into account. Time-dependent fluctuations and leakage effects induced from the dot-reservoir coupling are explicitly explored. The charge qubit dynamics from the Markovian to non-Markovian regime is systematically studied under various manipulating conditions. The decay behavior of charge qubit coherence and the corresponding relaxation time T1{T}_{1}T1​ and dephasing time T2{T}_{2}T2​ are analyzed in detail.
In this paper we investigate decoherence times of a double quantum dot (DQD) charge qubit due to it coupling with acoustic phonon baths. We individually consider the acoustic piezoelectric as well as deformation coupling phonon baths in the qubit environment. The decoherence times are calculated with two kinds of methods. One of them is based on the qusiadiabatic propagator path integral (QUAPI) and the other is based on Bloch equations, and two kinds of results are compared. It is shown that the theoretical decoherence times of the DQD charge qubit are shorter than the experimental reported results. It implies that the phonon couplings to the qubit play a subordinate role, resulting in the decoherence of the qubit.
We investigate the dynamics of a double quantum dot charge qubit which is coupled to piezoelectric acoustic phonons, appropriate for GaAs heterostructures. At low temperatures, the phonon bath induces the non-Markovian dynamical behavior of the oscillations between the two charge states of the double quantum dot. Upon applying the numerically exact quasiadiabatic propagator path-integral scheme, the reduced density matrix of the charge qubit is calculated, thereby avoiding the Born-Markov approximation. This allows a systematic study of the dependence of the QQQ factor on the lattice temperature, on the size of the quantum dots, as well as on the interdot coupling. We calculate the QQQ factor for a recently realized experimental setup and find that it is two orders of magnitudes larger than the measured value, indicating that the decoherence due to phonons is a subordinate mechanism.
The quantum dynamics of the dissipative two-level system with nonzero bias and sub-Ohmic bath is studied by means of the perturbation approach based on a unitary transformation. It has been shown that for the sub-Ohmic bath it is necessary to use the non-Markovian approach, especially for the short time behavior of the coupled system and environment. The nonequilibrium correlation P(t)P(t)P(t) has been calculated to show that a finite bias may favor the short time coherence. The spectrum of the susceptibility ${\ensuremath{\chi}}^{\ensuremath{''}}(\ensuremath{\omega})$ of the sub-Ohmic case may have a double peak structure in the range of $\ensuremath{\omega}>0$ when the coupling $\ensuremath{\alpha}$ is relatively strong. Besides, the coherence-decoherence transition point ${\ensuremath{\alpha}}_{c}$ is determined for different $0<s\ensuremath{\le}1$ by the condition of ${\ensuremath{\chi}}^{\ensuremath{''}}(\ensuremath{\omega}=0)=\ensuremath{\infty}$ when $\ensuremath{\alpha}={\ensuremath{\alpha}}_{c}$. Finally, we show that Shiba's relation is exactly satisfied in our results.
In this paper, we investigate the decoherence time of a double quantum dot (DQD) charge qubit in three kinds of baths through solving dynamics of the qubit. The dynamics of the qubit is investigated with Redfield master equation. It is shown that the decoherence time of the qubit in Ohmic bath has the same order of magnitude as the experiments reported. When the environment is modeled with the supra-Ohmic bath the decoherence time of the qubit is shorter than the experimental result. And when modeled with the sub-Ohmic bath the decoherence time of the qubit is longer than the experimental result.