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Register a new userAnalytical results for a conditional phase shift between single-photon pulses in a nonlocal nonlinear medium
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Added by
Julio Gea-Banacloche
Publication date
2017
fields
Physics
and research's language is
English
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It has been suggested that second-order nonlinearities could be used for quantum logic at the single-photon level. Specifically, successive two-photon processes in principle could accomplish the phase shift (conditioned on the presence of two photons in the low frequency modes) $ |011 rangle longrightarrow i|100 rangle longrightarrow -|011 rangle $. We have analyzed a recent scheme proposed by Xia et al. to induce such a conditional phase shift between two single-photon pulses propagating at different speeds through a nonlinear medium with a nonlocal response. We present here an analytical solution for the most general case, i.e. for an arbitrary response function, initial state, and pulse velocity, which supports their numerical observation that a $pi$ phase shift with unit fidelity is possible, in principle, in an appropriate limit. We also discuss why this is possible in this system, despite the theoretical objections to the possibility of conditional phase shifts on single photons that were raised some time ago by Shapiro and by one of us.
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We apply the stochastic master equations (quantum filter) derived by Gough et al. (Proc. 50th IEEE Conference on Decision and Control, 2011) to a system consisting of a cavity driven by a multimode single photon field. In particular, we analyse the conditional dynamics for the problem of cross phase modulation in a doubly resonant cavity. Through the exact integration of the stochastic equations, our results reveal features of the problem unavailable from previous models.
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Large conditional phase shifts from coupled atom-cavity systems are a key requirement for building a spin photon interface. This in turn would allow the realisation of hybrid quantum information schemes using spin and photonic qubits. Here we perform high resolution reflection spectroscopy of a quantum dot resonantly coupled to a pillar microcavity. We show both the change in reflectivity as the quantum dot is tuned through the cavity resonance, and measure the conditional phase shift induced by the quantum dot using an ultra stable interferometer. These techniques could be extended to the study of charged quantum dots, where it would be possible to realise a spin photon interface.
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