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Chinese Physics B

Generation of unconventional geometric phase gates in ion trap-optical cavity system by squeezed operators

Ying-Qiao Zhang, Jin Xing-Ri, Zhang Shou

Published Feb 1, 2008• 4 citations
Publisher

Abstract

Based on squeezed operators this paper has implemented an ideal unconventional geometric quantum gate (GQG) in ion trap-optical cavity system by radiating the trapped ions with the cavity field of frequency ω c and an external laser field of frequency ωL. It can ensure that the gate time is shorter than the coherence time for qubits and the decay time of the optical cavity by appropriately tuning the ionic transition frequency ω 0 , the frequencies of the cavity mode ω c and the vibrational mode ν. It has also realized the unconventional GQG under the influence of the cavity decay based on the squeezed-like operators and found that the present scheme works well for the smaller cavity decay by investigating the corresponding fidelity and success probability.

DOI
10.1088/1674-1056/17/2/013

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Based on squeezed operators this paper has implemented an ideal unconventional geometric quantum gate (GQG) in ion trap-optical cavity system by radiating the trapped ions with the cavity field of frequency ω c and an external laser field of frequency ωL. It can ensure that the gate time is shorter than the coherence time for qubits and the decay time of the optical cavity by appropriately tuning the ionic transition frequency ω 0 , the frequencies of the cavity mode ω c and the vibrational mode ν. It has also realized the unconventional GQG under the influence of the cavity decay based on the squeezed-like operators and found that the present scheme works well for the smaller cavity decay by investigating the corresponding fidelity and success probability.
We propose a scheme to generate a quantum phase gate via an unconventional geometric phase shift in an ion-trap system.Since the gate time is only related to the frequency of the vibrational mode, the present scheme, based on the resonant interaction of the trapped ions with a standing-wave laser beam, requires a much shorter gate time than the scheme based on the resonant interaction of the atoms and the cavity.Also the heating effect of the vibrational mode is negligible under certain conditions.
We propose a scheme for the realization of unconventional geometric two-qubit phase gates with two identical two-level ions. In the present scheme, the two ions are simultaneously illuminated by a standing-wave laser pulse with its pulse frequency being tuned to the ionic transition. The gate operation time can be much shorter, making the system robust against decoherence. In addition, we choose the appropriate experimental parameters to construct the geometric phase gate in one step, and thus avoid implementing the pure geometric single qubit operation.
In this paper, we propose a scheme for implementing an unconventional two-qubit geometric phase gate for two distant atoms trapped in cavities connected by an optical fiber. During the gate operation, the atoms are still in the ground states, while the cavity modes and fiber mode are displaced along a circle in the phase space. In this way, the system can acquire different geometric phases conditional upon the atomic states. We find that the operation of the geometric phase gate can be speeded up as the detuning between the cavity field and light fields decreases. Moreover, it is observed that the fidelity for the geometric phase gate is remarkably insensitive to the fluctuation of the detuning parameter. The effects of cavity decay and fiber loss on the gate have also been checked.
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.