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arXiv:quant-ph/0009110

Implementation of a quantum phase gate by the optical Kerr effect

Scott Glancy, John M. LoSecco, Carol E. Tanner

Published Sep 26, 2000• 0 citations
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Abstract

We show that the optical Kerr effect can be used to construct a quantum phase gate. It is well known from quantum nondemolition techniques that, as two photon field modes pass through a Kerr medium, the phase of each mode will be shifted, and the size of the phase shift will depend on the number of photons in both modes. We discuss the Hamiltonian responsible for this effect and show how this can produce an effective photon-photon interaction which corresponds to the quantum phase gate operating on two qubits each of which is represented by the elliptical polarization of one photon field. We discuss decoherence and losses and suggest some methods for dealing with them.

DOI
10.48550/arxiv.quant-ph/0009110

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We show that the optical Kerr effect can be used to construct a quantum phase gate. It is well known from quantum nondemolition techniques that, as two photon field modes pass through a Kerr medium, the phase of each mode will be shifted, and the size of the phase shift will depend on the number of photons in both modes. We discuss the Hamiltonian responsible for this effect and show how this can produce an effective photon-photon interaction which corresponds to the quantum phase gate operating on two qubits each of which is represented by the elliptical polarization of one photon field. We discuss decoherence and losses and suggest some methods for dealing with them.
We propose the use of magneto-optic Kerr effect (MOKE) to realize single-qubit quantum gates. We consider longitudinal and polar MOKE in reflection geometry in which the magnetic field is parallel to both the plane of incidence and surface of the film. MOKE couples incident TE and TM polarized photons and the Hamiltonian that represents this interaction is isomorphic to that of a canonical two-level quantum system. By varying the phase and amplitude of the magnetic field, we can realize Hadamard, NOT, and arbitrary phase-shift single-qubit quantum gates. The principal advantage is operation with magnetically non-transparent materials.
The self-Kerr interaction is an optical nonlinearity that produces a phase shift proportional to the square of the number of photons in the field. At present, many proposals use nonlinearities to generate photon-photon interactions. For propagating fields these interactions result in undesirable features such as spectral correlation between the photons. Here we engineer a discrete network composed of cross-Kerr interaction regions to simulate a self-Kerr medium. The medium has effective long-range interactions implemented in a physically local way. We compute the one- and two-photon SSS matrices for fields propagating in this medium. From these scattering matrices we show that our proposal leads to a high-fidelity photon-photon gate. In the limit where the number of nodes in the network tends to infinity, the medium approximates a perfect self-Kerr interaction in the one- and two-photon regime.
We describe a quantum phase gate in which the two qubits are represented by the photons in the two modes of the cavity field. The gate is implemented by passing a three-level atom in a cascade configuration through the cavity. The upper levels of the atom are resonant with one of the cavity modes whereas the lower levels are appropriately detuned from the other mode of the cavity. A $\ensuremath{\pi}$ phase shift is introduced when there is one photon each in the two modes and the atom is initially in the ground state. We also discuss the one-bit unitary gate in such a system and discuss potential applications.
A cross-Kerr interaction produces a phase shift on two modes of light proportional to the number of photons in both modes and is sometimes called cross-phase modulation. Cross-Kerr nonlinearities have many applications in classical and quantum nonlinear optics, including the possibility of a deterministic and all-optical controlled-phase gate. We calculate the one- and two-photon SSS matrices for fields propagating in a medium where the cross-Kerr interaction is spatially distributed at discrete interaction sites comprised of atoms. For the interactions considered, we analyze the cases where the photons copropagate and counterpropagate through the medium and give a physical interpretation to the differences between the two cases. Finally, we obtain the SSS matrix in the limit of infinitely long chains, showing that it corresponds to a perfect controlled-phase operation.