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International Journal of Theoretical Physics

Geometric Phase of Double Quantum Dot Qubits System with Coulomb Interaction

Bao Liu, Feng‐Yang Zhang, Zi-Hong Chen, He‐Shan Song

Published Aug 9, 2012• 1 citation
Publisher
DOI
10.1007/s10773-012-1296-2

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We propose a direct measurement scheme to read out the geometric phase of a coupled double quantum dot system via a quantum point contact(QPC) device. An effective expression of the geometric phase has been derived, which relates the geometric phase of the double quantum dot qubit to the current through QPC device. All the parameters in our expression are measurable or tunable in experiment. Moreover, since the measurement process affects the state of the qubit slightly, the geometric phase can be protected. The feasibility of the scheme has been analyzed. Further, as an example, we simulate the geometrical phase of a qubit when the QPC device is replaced by a single electron transistor(SET).
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.