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arXiv:0706.4159 · Physical Review A

Multimode analysis of the light emitted from a pulsed optical parametric oscillator

Anne E. B. Nielsen, Klaus Mølmer

Published Sep 27, 2007• 13 citations
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Abstract

We present a multimode treatment of the optical parametric oscillator, which is valid for both pulsed and continuous-wave pump fields. The two-time correlation functions of the output field are derived, and we apply the theory to analyze a scheme for heralded production of nonclassical field states that may be subsequently stored in an atomic quantum memory.

DOI
10.1103/physreva.76.033832

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Multimode nonclassical states of light are an essential resource in quantum computation with continuous variables [1]. They can be generated either by mixing different squeezed light sources using linear optical operations [2], or directly in a multimode optical device [3, 4]. Synchronously Pumped Optical Parametric Oscillators (SPOPO) — which correspond to an OPO pumped by a train of ultrashort pulses that are synchronized with the cavity round-trip time — have been theoretically shown to be promising devices for the generation of multimode nonclassical frequency combs, since a SPOPO is a sole optical cavity acting as an assembly of independent squeezers in a particular basis called the supermodes basis [5]. The supermodes are optical frequency combs with specific spectrum and phase profiles that are determined by the length of the intracavity nonlinear crystal and the pulse shape of the pump.
We investigate semiclassical dynamics and quantum properties of light beams generated in time-modulated nondegenerate optical parametric oscillator (NOPO). Having in view production of continuous-variable (CV) entangled states of light beams we propose two experimentally feasible schemes of NOPO: (i) driven by continuously modulated pump field; (ii) under action of a periodic sequence of identical laser pulses. It is shown that the time modulation of pump field amplitude essentially improves the degree of CV entanglement in NOPO. On the whole the level of integral two-mode squeezing, which characterizes the degree of CV entanglement, goes below the standard limit established in an ordinary NOPO with monochromatic pumping. We develop semiclassical and quantum theories of these devices for both below- and above-threshold regimes of generation. Properties of CV entanglement for various operational regimes of the devices are discussed in the time domain in application to time-resolved quantum information technologies. Our analytical results are in well agreement with the results of numerical simulation and support a concept of CV entangled states of time-modulated light beams.
We perform the quantum analysis of the light emitted by a synchronously pumped optical parametric oscillator operating in the above threshold regime, i.e. when the peak power of pulsed pumping exceeds the threshold of continuous generation. We show that both regimes (below and above threshold) are realized at different times within each pulse of the signal field. We show that the quantum fluctuations of signal and pump pulses are correlated between nearby pulses at times that are placed in the same position relative to the center of the pulses, whereas fluctuations are totally not correlated at different times within the same pulse. The model also predicts the existence of cross-correlations between pump and signal pulses. It is shown theoretically that there is suppression of quantum noise at the frequencies multiple of the pulse repetition frequency in the spectra of phase quadratures of pump and signal fields measured by a balanced homodyne detection with a pulsed local oscillator.
In this paper, we examined a possibility of preservation of a substantially multimode radiation in a single cell of quantum memory. As a light source we considered a synchronously pumped optical parametric oscillator (SPOPO). As was shown in several studies, SPOPO radiation has a large number of the correlated modes making it attractive for the purposes of quantum communication and computing. We showed that these correlations can be mapped on the longitudinal spin waves of the memory cell and be restored later in the readout light. The efficiencies of the writing and readout depend on the mode structure of the memory determined by a mechanism of the light-matter interaction under consideration (the nonresonance Raman interaction) and by the profile of the driving light field. We showed that like the initial light pulse train, the restored one can be represented by a set of squeezed supermodes. The mapping of the quantum multimode correlations on the material medium offers opportunities to manipulate the quantum states within the memory cell followed by the reading of the transformed state.