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Journal of Fujian Normal University

Implement of Unconventional Geometric Quantum Phase Gate Via Cavity QED

LI Hong-cai

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

A scheme is proposed for realizing unconventional geometric quantum phase gate originated from high-dimensional squeezed operators,which can be easily generalized to the physical system of Cavity QED.In the scheme,two-qubit g unconventional geometric phase gate is carried out by threes level atoms in a cavity,strongly drive by a resonant classical field.Under ideal condition,the resonant interaction in our scheme results in a short gating time.

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A scheme is proposed for realizing unconventional geometric quantum phase gate originated from high-dimensional squeezed operators,which can be easily generalized to the physical system of Cavity QED.In the scheme,two-qubit g unconventional geometric phase gate is carried out by threes level atoms in a cavity,strongly drive by a resonant classical field.Under ideal condition,the resonant interaction in our scheme results in a short gating time.
We introduce the general definition of the unconventional geometric phase independent of the specific physical system and show how a highly squeezed operator can approximately induce the general unconventional geometric phase, which goes beyond the original unconventional one by displacement operators (Zhu and Wang 2003 Phys. Rev. Lett. 91 187902). By means of the squeezed operator concerning the cavity mode state along a closed path in the phase space, we discuss specifically how to implement approximately a two-qubit geometric phase gate in a cavity QED system with two-photon interaction between the atoms and the cavity mode, assisted by a classical field. Discussions regarding the implementation time of the gating, the possible decaying sources and the experimental feasibility are given in detail.
We propose a potential scheme for carrying out two-qubit unconventional geometric logic gates on two identical three-level atoms in a cavity, strongly driven by a resonant classical field. Compared to a previous scheme [S. B. Zheng, Phys. Rev. A 70, 052320 (2004)] based on the large-detuning interaction of the two identical three-level atoms with the cavity mode, our scheme can, in principle, achieve a faster gating because of the resonant coupling of the atoms to the classical field. We present the two-qubit unconventional geometric phase gates in both an ideal cavity and a real cavity with decay. Discussions about the fidelity and the success probability of the proposed scheme as well as the experimental feasibility are made in detail.
We propose a scheme for realizing two-qubit quantum phase gates via an unconventional geometric phase shift with atoms in a cavity. In the scheme the atoms interact simultaneously with a highly detuned cavity mode and a classical field. The atoms undergo no transitions during the gate operation, while the cavity mode is displaced along a circle in the phase space, aquiring a geometric phase conditional upon the atomic state. Under certain conditions, the atoms are disentangled with the cavity mode and thus the gate is insensitive to both the atomic spontaneous emission and the cavity decay.
In the system with superconducting quantum interference devices (SQUID) in cavity, a scheme for constructing two-qubit quantum phase gate via a conventional geometric phase-shift is proposed by using a quantized cavity field and classical microwave pulses. In this scheme, the gate operation is realized in the subspace spanned by the two lower flux states of the SQUID system and the population operator of the excited state has no effect on it. Thus the effect of decoherence caused from the levels of the SQUID system is possible to minimize. Under cavity decay, our strictly numerical simulation shows that it is also possible to realize the unconventional geometric phase gate. The experimental feasibility is discussed in detail.
In this paper, we present a scheme for implementing the unconventional geometric two-qubit phase gate with nonzero dynamical phase based on two-channel Raman interaction of two atoms in a cavity. We show that the dynamical phase and the total phase for a cyclic evolution are proportional to the geometric phase in the same cyclic evolution; hence they possess the same geometric features as does the geometric phase. In our scheme, the atomic excited state is adiabatically eliminated, and the operation of the proposed logic gate involves only the metastable states of the atoms; thus the effect of the atomic spontaneous emission can be neglected. The influence of the cavity decay on our scheme is examined. It is found that the relations regarding the dynamical phase, the total phase, and the geometric phase in the ideal situation are still valid in the case of weak cavity decay. Feasibility and the effect of the phase fluctuations of the driving laser fields are also discussed.