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International Journal of Modern Physics A

Quantum Logic Gates with Ion Trap in an Optical Cavity

S. Shelly Sharma

Published May 10, 2003• 4 citations
Publisher

Abstract

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.

DOI
10.1142/s0217751x03015684

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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.
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.
We examine the time evolution of a two-level ion interacting with a light field in a harmonic oscillator trap and in a trap with anharmonicities. The anharmonicities of the trap are quantified in terms of the deformation parameter τ characterizing the q -analogue of the harmonic oscillator trap. Initially the ion is prepared in a Schrödinger cat state. The entanglement of the centre-of-mass motional states and the internal degrees of freedom of the ion results in a characteristic collapse and revival pattern. We numerically calculate the population inversion I ( t ), quasi-probabilities Q ( t ) and partial mutual quantum entropy S ( P ) for the system as a function of time. Interestingly, small deformations of the trap enhance the contrast between population inversion collapse and revival peaks as compared to the zero-deformation case. For β = 3 and 4 (β determines the average number of trap quanta linked to centre-of-mass motion) the best collapse and revival sequence is obtained for τ = 0.0047 and 0.004, respectively. For large values of τ, decoherence sets are accompanied by loss of amplitude of population inversion, and for τ ~0.1 the collapse and revival phenomenon disappear. Each collapse or revival of population inversion is characterized by a peak in the S ( P ) versus t plot. During the transition from collapse to revival and vice-versa, we have a minimum mutual entropy value that is S ( P ) = 0. Successive revival peaks show a lowering of the local maximum point indicating a dissipative irreversible change in the ionic state. An improved definition of the collapse and revival pattern as the anharmonicity of the trapping potential increases is also reflected in the quasi-probability versus t plots.
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 propose the efficient combinations of laser pulses for constructing a multiqubit gate with cold trapped ions in order to implement maximally entangled states with quantum logic. Within the ion-trap quantum computation using the center of mass as the data bus, we can minimize the number of laser pulses as well as their operation time, which can improve the fidelity. We also present some numerical results of the operation time for different numbers of qubits and values of the Lamb-Dicke parameter.
A trapped ion in a cavity can simultaneously interact with a laser field as well as the cavity field. Based on the point, we propose a new scheme to implement quantum logic gates such as single qubit rotation gate, two qubit controlled-phase gate and controlled-NOT gate. and scheme employs the model used in literature [10-12] and is different from these works because computation basis is composed by the internal ionic state and motional state. We also discussed the experimental requirement for our 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.