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Journal of Physics A Mathematical and Theoretical

The effect of the environment parameters on the geometric phase of a quantum dot system

Yin Sun, D. M. Tong

Published Jun 28, 2010• 3 citations
Publisher

Abstract

We investigate the effect of environment parameters on the geometric phase of a quantum dot (QD) system interacting with the environment. Specifically, we calculate the effect of two important parameters: the energy difference of the electron in QD and the backaction of the QD to the environment. Our result shows that the geometric phase values are obviously dependent on these parameters. The variance of the geometric phase as functions of the parameters is plotted. We further analyze the physical mechanism of the numerical result.

DOI
10.1088/1751-8113/43/30/305303

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We investigate the effect of environment parameters on the geometric phase of a quantum dot (QD) system interacting with the environment. Specifically, we calculate the effect of two important parameters: the energy difference of the electron in QD and the backaction of the QD to the environment. Our result shows that the geometric phase values are obviously dependent on these parameters. The variance of the geometric phase as functions of the parameters is plotted. We further analyze the physical mechanism of the numerical result.
Practical implementations of quantum computing are always done in the presence of decoherence. Geometric phase is useful in the context of quantum computing as a tool to achieve fault tolerance. Recent experimental progresses on coherent control of single electron have suggested that electron in quantum dot systems is a promising candidate of qubit in future quantum information processing devices. In this Brief Report, by considering a feasible quantum dot model, we calculate the geometric phase of the quantum dot system in nonunitary evolution and investigate the effect of environment parameters on the phase value.
We study theoretically the geometric phase of a double-quantum-dot (DQD) system measured by a quantum point contact (QPC) in the pure dephasing and dissipative environments, respectively. The results show that in these two environments, the coupling strength between the quantum dots has an enhanced impact on the geometric phase during a quasiperiod. This is due to the fact that the expansion of the width of the tunneling channel connecting the two quantum dots accelerates the oscillations of the electron between the quantum dots and makes the length of the evolution path longer. In addition, there is a notable near-zero region in the geometric phase because the stronger coupling between the system and the QPC freezes the electron in one quantum dot and the solid angle enclosed by the evolution path is approximately zero, which is associated with the quantum Zeno effect. For the pure dephasing environment, the geometric phase is suppressed as the dephasing rate increases which is caused only by the phase damping of the system. In the dissipative environment, the geometric phase is reduced with the increase of the relaxation rate which results from both the energy dissipation and phase damping of the system. Our results are helpful for using the geometric phase to construct the fault-tolerant quantum devices based on quantum dot systems in quantum information.
In the present report, the effects of decoherence in a two-electron quantum dot coupled with its environment are investigated. Environmental effects on the quantum dynamics of electrons are modeled by coupling the dot with a thermo-bath at fixed temperatures. In such an approach, the special emphasis is placed on the analysis of the entanglement degradation of electron orbital motion depending on the quantum dot parameters (the strength of electron interaction and quantum dot shapes) and on the temperature of environment.
Geometric phases and information flows of a two-level system coupled to its environment are calculated and analyzed. The information flow is defined as a cumulant of changes in trace distance between two quantum states, which is similar to the measure for non-Markovianity given by Breuer. We obtain an analytic relation between the geometric phase and the information flow for pure initial states, and a numerical result for mixed initial states. The geometric phase behaves differently depending on whether there are information flows back to the two-level system from its environment.
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We study quantum entanglement loss due to environmental interaction in a condensed matter system with a complex geometry relevant to recent proposals for computing with single electrons at the nanoscale. We consider a system consisting of two qubits, each realized by an electron in a double quantum dot, which are initially in an entangled Bell state. The qubits are widely separated and each interacts with its own environment. The environment for each is modeled by surrounding double quantum dots placed at random positions with random orientations. We calculate the unitary evolution of the joint system and environment. The global state remains pure throughout. We examine the time dependence of the expectation value of the bipartite Clauser-Horne-Shimony-Holt (CHSH) and Brukner-Paunković-Rudolph-Vedral (BPRV) Bell operators and explore the emergence of correlations consistent with local realism. Though the details of this transition depend on the specific environmental geometry, we show how the results can be mapped on to a universal behavior with appropriate scaling. We determine the relevant disentanglement times based on realistic physical parameters for molecular double-dots.