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Journal of Optics B Quantum and Semiclassical Optics

Quantum logic operation with a single trapped ion using the nonlinear interaction beyond the Lamb-Dicke limit

L X Li, Guan-Can Guo

Published Feb 1, 2000• 3 citations
Publisher

Abstract

Using the nonlinear interaction between internal and external degrees of a trapped ion assisted by a laser beam, we present simplified methods for two-qubit quantum logic operation. The nonlinear interaction arises when the Lamb-Dicke parameter is not small enough. Two special cases, one with the laser tuned to the first red sideband and the other tuned to the carrier, are discussed in detail.

DOI
10.1088/1464-4266/2/1/310

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Using the nonlinear interaction between internal and external degrees of a trapped ion assisted by a laser beam, we present simplified methods for two-qubit quantum logic operation. The nonlinear interaction arises when the Lamb-Dicke parameter is not small enough. Two special cases, one with the laser tuned to the first red sideband and the other tuned to the carrier, are discussed in detail.
We suggest a scheme for realizing a universal two-quantum-bit (qubit) operation. The scheme uses two laser beams with different intensities to illuminate two different ions in a harmonic trap. Both beams are tuned to the red motional sideband. We find that, under certain conditions, the interaction will realize a universal two-qubit operation, the controlled-rotation operation, which is to rotate the phase of the state by $\ensuremath{\pi}$ only when the two states are both in the ∣1〉|1〉∣1〉 state. The scheme requires careful control of laser intensity and Lamb-Dicke parameters. But after we reach the required parameters, the logic operation is very simple.
We propose a simple scheme for implementing quantum logic gates with a string of two-level trapped cold ions outside the Lamb-Dicke limit. Two internal states of each ion are used as one computational qubit (CQ) and the collective vibration of ions acts as the information bus, i.e., the bus qubit (BQ). Using the quantum dynamics for the laser-ion interaction as described by a generalized Jaynes-Cummings model, we show that quantum entanglement between any one CQ and the BQ can be coherently manipulated by applying classical laser beams. As a result, universal quantum gates, i.e., the one-qubit rotation and two-qubit controlled gates, can be implemented exactly. The required experimental parameters for the implementation, including the Lamb-Dicke (LD) parameter and the durations of the applied laser pulses, are derived. Neither the LD approximation for the laser-ion interaction nor the auxiliary atomic level is needed in the present scheme.
In the system with two two-level ions confined in a linear trap, this paper presents a simple scheme to realize the quantum phase gate (QPG) and the swap gate beyond the Lamb–Dicke (LD) limit. These two-qubit quantum logic gates only involve the internal states of two trapped ions. The scheme does not use the vibrational mode as the data bus and only requires a single resonant interaction of the ions with the lasers. Neither the LD approximation nor the auxiliary atomic level is needed in the proposed scheme. Thus the scheme is simple and the interaction time is very short, which is important in view of decoherence. The experimental feasibility for achieving this scheme is also discussed.