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arXiv:0909.4952 · Physical Review B

Decoherence of charge qubit coupled to interacting background charges

I. V. Yurkevich, Jim Baldwin, Igor V. Lerner, B. L. Altshuler

Published Mar 15, 2010• 23 citations
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Abstract

The major contribution to decoherence of a double quantum dot or a Josephson-junction charge qubit comes from the electrostatic coupling to fluctuating background charges hybridized with the conduction electrons in the reservoir. However, estimations according to previously developed theories show that finding a sufficient number of effective fluctuators in a realistic experimental layout is quite improbable. We show that this paradox is resolved by allowing for a short-range Coulomb interaction of the fluctuators with the electrons in the reservoir. This dramatically enhances both the number of effective fluctuators and their contribution to decoherence, resulting in the most dangerous decoherence mechanism for charge qubits.

DOI
10.1103/physrevb.81.121305

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The major contribution to decoherence of a double quantum dot or a Josephson-junction charge qubit comes from the electrostatic coupling to fluctuating background charges hybridized with the conduction electrons in the reservoir. However, estimations according to previously developed theories show that finding a sufficient number of effective fluctuators in a realistic experimental layout is quite improbable. We show that this paradox is resolved by allowing for a short-range Coulomb interaction of the fluctuators with the electrons in the reservoir. This dramatically enhances both the number of effective fluctuators and their contribution to decoherence, resulting in the most dangerous decoherence mechanism for charge qubits.
Lateral semiconductor quantum dot structures have been proposed as an effective quantum bit (qubit) for quantum computation. A single excess electron with the freedom to move between two capacitively coupled quantum dots creates a `pseudo'-spin system with the same qubit behavior as the more natural two level system of a single electron spin. The excess electron in the double dot system is restricted to one of the two dots, thereby creating two separate and distinct states (usually referred to as |L> and |R>). The benefit of these charge qubits lie in the relative ease with which they can be manipulated and created. Experiments have been performed in this area and have shown controllable coherent oscillations and thus efficient single-qubit operations. However, the decoherence rates observed in the experiments is still quite high, making double dot charge qubits not very appealing for large-scale implementations. The following work describes the effect of the electromagnetic (EM) environment of the double quantum dot system on the decoherence of the charge state. Sources of decoherence in similar systems have been extensively investigated before and this paper follows a close theoretical framework to previous work done in the area. The effect of the EM environment can been seen in the calculations discussed below, although it is clear that the decoherence seen in experiments cannot be fully explained by the voltage fluctuations as they are investigated here. The limitations of the calculations are discussed and improvements are suggested.
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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.
We have found an exact expression for the decoherence rate of a Josephson charge qubit coupled to fluctuating background charges. At low temperatures TTT the decoherence rate $\ensuremath{\Gamma}$ is linear in TTT while at high temperatures it saturates in agreement with a known classical solution which, however, reached at surprisingly high TTT. In contrast to the classical picture, impurity states spread in a wide interval of energies (⪢T)(⪢T)(⪢T) may essentially contribute to $\ensuremath{\Gamma}$.
In this lectures, we have described some essential features of loss of coherence by a qubit coupled to the environment. We have first presented well known semiclassical arguments that relate both decoherence and relaxation to the environmental noise. Then we have shown that models with pure decoherence (but no relaxation in qubit states) can be exactly solvable. As an example, we have treated in detail the model of fluctuating background charges which is believed to describe one of the most important channels for decoherence for the charge Josephson junction qubit. We have shown that the decoherence rate saturates at `high' temperatures while becoming linear in T at low temperatures and showing in all regimes a non-monotonic behaviour as a function of the coupling of the qubit to the fluctuating background charges. We have also considered, albeit only perturbatively, the qubit relaxation by the background charges and demonstrated that a quasi-linear behaviour of the spectral density of noise deduced from the measurements of the relaxation rate can be qualitatively explained.