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arXiv:1212.1945 · Physical Review A

Cavity driven by a single photon: Conditional dynamics and nonlinear phase shift

Andre R. R. Carvalho, Michael Hush, M. R. James

Published Aug 3, 2012• 19 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.86.023806

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The cavity is a fundamental ingredient of quantum optical systems. This paper concerns the behavior of a quantum cavity driven by non-classical field in single-photon state. To this end, the number operator has been opted to reveal the number of photons inside the cavity. Then, the quantum filtering equations have been employed to derive a stochastic master equation for the cavity which is driven by single-photon and is observed by either Homodyne or photon-counting detector. Finally, the state of the cavity has been estimated by the derived equations, and the results have been compared with the conventional master equation.
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Abstract — The aim of this paper is to determine quantum master and filter equations for systems coupled to continuous-mode single photon fields. The system and field are de-scribed using a quantum stochastic unitary model, where the continuous-mode single photon state for the field is determined by a wavepacket pulse shape. The master equation is derived from this model and is given in terms of a system of coupled equations. The output field carries information about the system from the scattered photon, and is continuously monitored. The quantum filter is determined with the aid of an embedding of the system into a larger system, and is given by a system of coupled stochastic differential equations. An example is provided to illustrate the main results. I.
A major component of establishing quantum technologies in the quantum optic platform is the cavity. This paper concerns state estimation (filtering) of a quantum one-sided cavity driven by a vacuum field while the output field is monitored by either Homodyne or photodetector. The stochastic master equation in the schrödinger picture is presented for Homodyne and photon measurements. Then, the infinite state space of the cavity is truncated by considering some reasonable simplifying assumptions. Finally, the number of photons in the cavity is estimated using the derived equations. Simulation results are validated by demonstrating that the average of several paths of the derived filter matches the corresponding master equation.