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Physical Review A

Conditional phase gate using an optomechanical resonator

Julio R. Gea-Banacloche, Nikolett Német

Published May 27, 2014• 8 citations
Publisher

Abstract

We explore the possibility of using an optomechanical resonator to induce a conditional phase gate for single photons. The problem provides an illustration of the application to optomechanical systems of a recently developed input-output formalism for single- (or few-) photon states of the radiation field. At the two-photon level, we find significant departures from expectations based on a semiclassical treatment. We also find a tradeoff between the maximum achievable conditional phase and the fidelity of the final state, consistent with other multimode studies of conditional phases based on optical nonlinearities.1 MoreReceived 31 December 2013DOI:https://doi.org/10.1103/PhysRevA.89.052327©2014 American Physical Society

DOI
10.1103/physreva.89.052327

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We explore the possibility of using an optomechanical resonator to induce a conditional phase gate for single photons. The problem provides an illustration of the application to optomechanical systems of a recently developed input-output formalism for single- (or few-) photon states of the radiation field. At the two-photon level, we find significant departures from expectations based on a semiclassical treatment. We also find a tradeoff between the maximum achievable conditional phase and the fidelity of the final state, consistent with other multimode studies of conditional phases based on optical nonlinearities.1 MoreReceived 31 December 2013DOI:https://doi.org/10.1103/PhysRevA.89.052327©2014 American Physical Society
We analyze in detail the proposal for a two-qubit gate for travelling single-photon qubits recently presented by Ottaviani et al. [Phys. Rev. A 73, 010301(R) (2006)]. The scheme is based on an ensemble of five-level atoms coupled to two quantum and two classical light fields. The two quantum fields undergo cross-phase modulation induced by electromagnetically induced transparency. The performance of this two-qubit quantum phase gate for travelling single-photon qubits is thoroughly examined in the steady-state and transient regimes, by means of a full quantum treatment of the system dynamics. In the steady-state regime, we find a general trade-off between the size of the conditional phase shift and the fidelity of the gate operation. However, this trade-off can be bypassed in the transient regime, where a satisfactory gate operation is found to be possible, significantly reducing the gate operation time.
We present a full quantum treatment of a five-level atomic system coupled to two quantum and two classical light fields. The two quantum fields undergo a cross-phase-modulation induced by electromagnetically induced transparency. The performance of this configuration as a two-qubit quantum phase gate for traveling single photons is examined. A trade-off between the size of the conditional phase shift and the fidelity of the gate is found. Nonetheless, a satisfactory gate performance is still found to be possible in the transient regime, corresponding to a fast gate operation.
In this dissertation, we shall focus on theoretically studying quantum nonlinear optical schemes to construct a conditional phase gate at the single-photon level. With an aim to develop analytical models, we shall carry out a rigorous quantized multimode field analysis of some of these schemes involving only the interacting field operators. More specifically, we shall first study the three-wave mixing process involving two single-photons in a second-order nonlinear medium (x(2)) under two different cases viz. when the photons are traveling with equal velocities and when they are traveling with different velocities, and explore the possibility of using them for building a conditional phase phase gate. Finally, we shall study the interaction of single-photon wavepackets with a realistic atomic system viz. an ensemble of five-level atoms, to construct a phase gate. We will particularly look at the "giant Kerr" effect in electromagnetically induced transparency to explore the possibility of using this scheme for achieving a conditional phase shift and to understand how the bandwidth gets restricted naturally in such an atomic system.
A second-order nonlinearity has been proposed as a way to perform a conditional phase gate between two photons. The process involves combining the two photons into a single one (parametric up-conversion) and subsequently splitting that one into two photons identical to the original ones (parametric down-conversion), except for an overall phase shift. We show here that, when the multimode nature of the initial photon wave packets is considered, this approach suffers from the same difficulties as the third-order (Kerr-based) methods: specifically, the final state of the photons is inevitably spectrally distorted and entangled. The maximum fidelity appears to be limited to F<0.4F<0.4F<0.4 for a free-space configuration, but we find that this could theoretically be pushed to $F\ensuremath{\simeq}0.6$ if the nonlinear medium is placed in an optical cavity. We show analytically that this latter result is identical to what one would obtain from a third-order nonlinear medium in the same arrangement.
We propose a scheme for an optomechanical control phase-flip gate(CPFG) based on optomechanical equivalence Kerr nonlinearity. Analytical conditions for realization of CPFG is provided. By numerically solving the master equation of the system, we show that the fidelity of the two-qubit CPFG periodically achieves its maximum values under the condition of the appropriate rate of the coupling strengths. This scheme can break the limit of the Kerr effect at the single-photon level compared with the nature Kerr medium.