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Bulletin of the American Physical Society

Single Photon Nonlinearity in Cold Polar Molecular Arrays: Controlled Phase Operation

T. Bragdon, R.M.G. Rajapakse, Ana María Rey, Susanne F. Yelin

Published May 30, 2008• 0 citations
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We model single-photon nonlinearities resulting from the dipole-dipole interactions of cold polar molecules. We propose utilizing ``dark state polaritons'' to effectively couple photon and molecular states; through this framework, coherent control of the nonlinearity can be expressed and potentially used in an optical quantum computation architecture. Due to the dipole-dipole interaction the photons pick up a measurable nonlinear phase even in the single-photon regime. A manifold of protected symmetric eigenstates is used as basis. Depending on the implementation, major sources of decoherence result from nonsymmetric interactions and phonon dispersion. We discuss the strength of the nonlinearity per photon and the feasibility of this system.
Integrating the modules of the controlled phase-flip gate, the distributed entanglement gate, and the simplified entanglement gate, we propose schemes for preparing, linking, and unlinking standard cluster-type polarization-entangled states, which are achieved by performing different operations for cluster-type states consisting of even and odd photons, in company with Hadamard gate operations and other single-photon operations.Mediated by weak cross-Kerr nonlinear interactions, two individual photons interact with each other depending on the assistance of the coherent state in Kerr media.Exploiting homodyne measurement and polarization beam splitters, the photon paths take on a certain ambiguity and photons entangle together in the polarization mode.Assisted by a classical feed-forward, these aforementioned modules can be realized with an efficiency approaching unity.Employing the module of the controlled phase-flip gate, standard even-and odd-photon cluster-type states can be prepared, which are distinguished by the different photons performed by Hadamard gate operations.Linking two or more standard cluster-type states, a new standard cluster-type state can be produced after combination of the module of the controlled phase-flip gate and Hadamard gate operations.Dividing, truncating, or pinching a multi-photon cluster-type state can be accomplished by applying the module of the controlled phase-flip gate and single-photon operations including Hadamard gate operations.. . . . . . .
We propose a linear optical scheme for direct realization of a nondestructive NNN-qubit controlled phase gate without resorting to a sequence of single- and two-qubit gates. The proposed setup involves linear optical elements, nonmaximally entangled pairs of photons, and multiphoton coincidence detection. To implement the scheme, physical qubits represented by the polarization states of single photons are probabilistically encoded into the two-photon states. Based on such encoding operation, a nondestructive NNN-qubit phase gate can be directly achieved by NNN-photon interference on an array of polarization beam splitters and NNN-photon coincidence detection.