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Fast quantum logic gates with trapped ions interacting with external laser and quantized cavity field beyond the Lamb-Dicke regime

Sharma, S S, Vidiella-Barranco, A

Published Oct 14, 2002• 6 citations
OpenAlex

Abstract

A scheme to implement quantum logic gates by manipulating trapped ions through interaction with monochromatic external laser field and quantized cavity field, beyond the Lamb-Dicke regime, is presented. Characteristic time, for implementing ionic state transitions using non-resont laser pulse or quantized cavity field, shows a sharp decline for large Lamb-Dicke parameter value of $\\eta_{L}=\\eta_{c}=0.2$, and is seen to decrease further with increase in number of initial state vibrational quanta $m$.

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A scheme to implement quantum logic gates by manipulating trapped ions through interaction with monochromatic external laser field and quantized cavity field, beyond the Lamb-Dicke regime, is presented. Characteristic time, for implementing ionic state transitions using non-resont laser pulse or quantized cavity field, shows a sharp decline for large Lamb-Dicke parameter value of etaL=etac=0.2\\eta_{L}=\\eta_{c}=0.2etaL​=etac​=0.2, and is seen to decrease further with increase in number of initial state vibrational quanta mmm.
The time evolution of ionic internal states for trapped cold ions interacting with external laser in a harmonic oscillator potential, and a potential with a small nonlinear component varying as x6, modeled through a q-deformed harmonic oscillator, is briefly discussed. The entanglement of ionic internal states and center of mass vibrational states results in collapse and revival of population inversion. For deformation parameter, τ = 0.004(q = eτ), the population inversion shows an extremely well behaved collapse and revival pattern. Next a simple application where entanglement is used for implementing quantum logic gates with ion trap placed inside an optical cavity, is presented. It is found that faster ionic state manipulation times can be obtained by working beyond the Lamb-Dicke regime.
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.
We present an alternative scheme to exactly implement one-qubit and two-qubit quantum gates with a single trapped cold ion driven by a travelling laser field. The internal degree of freedom of the ion acts as the target qubit and the control qubit is encoded by two Fock states of the external vibration of the ion. The conditions to realize these operations, including the duration of each applied laser pulse and Lamb-Dicke parameter, are derived. In our scheme neither the auxiliary atomic level nor the Lamb-Dicke approximation is required. The multiquantum transition between the internal and external degrees of freedom of the ion is considered.
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.
Quantum controlled-NOT (CNOT) gates with single trapped cold ions have been experimentally demonstrated [C. Monroe et al., Phys. Rev. Lett. 75, 4714 (1995)] by using auxiliary atomic levels (besides the qubit ones) and under the usual Lamb-Dicke (LD) limit (wherein the so-called LD parameter, which represents the interaction strength between the internal and external degrees of freedom of the driven ion, is required to be sufficiently small). It has been shown [C. Monroe et al., Phys. Rev. A 55, R2489 (1997); L. F. Wei et al., 65, 062316 (2002)] that, beyond the LD limit, these gates could also be implemented for certain specific LD parameters. Here, we further show that, without any auxiliary atomic level, the desirable quantum logic gates could still be realized with sufficiently high fidelities for arbitrary LD parameters, as long as the durations of the applied laser pulses are accurately set within the decoherence times of the ions.