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arXiv:quant-ph/0611268 · Physical Review A

Single-photon-state generation from a continuous-wave nondegenerate optical parametric oscillator

Anne E. B. Nielsen, Klaus Mølmer

Published Feb 6, 2007• 30 citations
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Abstract

We present a theoretical treatment of conditional preparation of one-photon states from a continuous-wave nondegenerate optical parametric oscillator. We obtain an analytical expression for the output state Wigner function, and we maximize the one-photon state fidelity by varying the temporal mode function of the output state. We show that a higher production rate of high fidelity Fock states is obtained if we condition the outcome on dark intervals around trigger photo detection events.

DOI
10.1103/physreva.75.023806

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Conditional preparation of photon number states from a continuous-wave nondegenerate optical parametric oscillator is investigated. We derive the phase space Wigner function for the output state conditioned on photodetection events that are not necessarily simultaneous, and we maximize its overlap with the desired photon number state by choosing the optimal temporal output state mode function. We present a detailed numerical analysis for the case of two-photon state generation from a parametric oscillator driven with an arbitrary intensity below threshold, and in the low-intensity limit we present a formalism that yields the optimal output state mode function and fidelity for higher-photon-number states.
We study the characteristics of the quantum state of light produced by a conditional preparation protocol totally performed in the continuous-variable regime. It relies on conditional measurements on quantum intensity correlated bright twin beams emitted by a nondegenerate optical parametric oscillator above threshold. Analytical expressions as well as computer simulations of the selected state properties and preparation efficiency are developed and show that a sub-Poissonian state can be produced by this technique. Projection onto a given trigger value is studied and then extended to a finite band. The continuous-variable regime offers the unique possibility to improve dramatically the preparation efficiency by choosing multiple selection bands and thus to generate a great number of sub-Poissonian states in parallel.
Engineering non-classical states of the electromagnetic field is a central quest for quantum optics(1,2). Beyond their fundamental significance, such states are indeed the resources for implementing various protocols, ranging from enhanced metrology to quantum communication and computing. A variety of devices can be used to generate non-classical states, such as single emitters, light-matter interfaces or non-linear systems(3). We focus here on the use of a continuous-wave optical parametric oscillator(3,4). This system is based on a non-linear χ(2) crystal inserted inside an optical cavity and it is now well-known as a very efficient source of non-classical light, such as single-mode or two-mode squeezed vacuum depending on the crystal phase matching. Squeezed vacuum is a Gaussian state as its quadrature distributions follow a Gaussian statistics. However, it has been shown that number of protocols require non-Gaussian states(5). Generating directly such states is a difficult task and would require strong χ(3) non-linearities. Another procedure, probabilistic but heralded, consists in using a measurement-induced non-linearity via a conditional preparation technique operated on Gaussian states. Here, we detail this generation protocol for two non-Gaussian states, the single-photon state and a superposition of coherent states, using two differently phase-matched parametric oscillators as primary resources. This technique enables achievement of a high fidelity with the targeted state and generation of the state in a well-controlled spatiotemporal mode.