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arXiv:1011.6009 · Journal of the Optical Society of America B

Unconventional geometric phase gate with two nonidentical quantum dots trapped in a photonic crystal cavity

Jian‐Qi Zhang, Ya-Fei Yu, Zhi‐Ming Zhang

Published Jul 19, 2011• 6 citations
arXivHTMLPDF

Abstract

We propose a scheme for realizing a two-qubit controlled phase gate via an unconventional geometric phase with two nonidentical and spatially separated quantum dots (QDs) trapped in a photonic crystal cavity. In this system, the QDs simultaneously interact with a large detuned cavity mode and strong driving classical light fields. During the gate operation, the QDs undergo no transitions, while the cavity mode is displaced along a closed path in the phase space. In this way, the system can acquire different unconventional geometric phases conditional upon the states of the QDs, and a two-qubit entangling gate can be constructed.

DOI
10.1364/josab.28.001959

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We propose a scheme for realizing a two-qubit controlled phase gate via an unconventional geometric phase with two nonidentical and spatially separated quantum dots (QDs) trapped in a photonic crystal cavity. In this system, the QDs simultaneously interact with a large detuned cavity mode and strong driving classical light fields. During the gate operation, the QDs undergo no transitions, while the cavity mode is displaced along a closed path in the phase space. In this way, the system can acquire different unconventional geometric phases conditional upon the states of the QDs, and a two-qubit entangling gate can be constructed.
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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 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 propose a scheme to implement a three-qubit controlled phase gate with one control qubit and two target qubits using quantum dots (QDs) in two coupled photonic crystal (PC) cavities A and B. In the scheme, three QDs are embedded in two coupled photonic crystal cavities and the transitions between the levels are only coupled to the cavity modes without being driven by the classical laser fields. We investigate the dynamics of the system consisting of resonant and off-resonant couplings between the cavity modes and QDs and solve the time-dependent Schrodinger equation analytically. The results show that a three-qubit controlled phase gate can be directly implemented using one operational step, by exchanging a single photon between the PC cavities A and B. This scheme greatly simplifies the gate operation in experiments.