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arXiv:quant-ph/0701104

Graph states and carrier-envelope phase squeezing

Olivier Pfister

Published Jan 16, 2007• 4 citations
arXivHTMLPDF

Abstract

We outline a new class of continuous-variable graph states that can be useful to describe entangle- ment, and also multimode squeezing, in an optical frequency comb. We show that a particular case of such states coincides with the squeezing of the carrier-envelope phase, or of the total intensity, of a mode-locked laser. We then discuss the experimental issues related to measuring the quantum noise of the carrier-envelope phase of a frequency comb and show that this can be carried out by use of quantum heterodyne multiplexing, a technique that may be useful to measure multipartite entanglement as well.

DOI
10.48550/arxiv.quant-ph/0701104

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We outline a new class of continuous-variable graph states that can be useful to describe entangle- ment, and also multimode squeezing, in an optical frequency comb. We show that a particular case of such states coincides with the squeezing of the carrier-envelope phase, or of the total intensity, of a mode-locked laser. We then discuss the experimental issues related to measuring the quantum noise of the carrier-envelope phase of a frequency comb and show that this can be carried out by use of quantum heterodyne multiplexing, a technique that may be useful to measure multipartite entanglement as well.
The frequency comb of an optical resonator is a naturally large set of exquisitely well defined quantum systems, such as in the broadband mode-locked lasers which have redefined time/frequency metrology and ultraprecise measurements in recent years. High coherence can therefore be expected in the quantum version of the frequency comb, in which nonlinear interactions couple different cavity modes, as can be modeled by different forms of graph states. We show that is possible to thereby generate states of interest to quantum metrology and computing, such as multipartite entangled cluster and Greenberger-Horne-Zeilinger states.
The dynamical behavior of Kerr optical frequency combs is very well understood today from the perspective of the semi-classical approximation. In this article, we provide a theoretical understanding of the phenomena of quantum correlations, multimode entanglement and squeezed states of light that can occur in these frequency combs when quantum noise is accounted for. We prove that for all stationary spatio-temporal patterns, the side-modes that are symmetrical relatively to the central (pumped) mode in the frequency domain display quantum correlations that can lead to squeezed states of light under some optimal conditions that are analytically determined. We show that these quantum correlations can persist regardless the dynamical state of the system (rolls or solitons), regardless of the spectral extension of the comb (number sidemodes), and regardless of the dispersion regime (normal or anomalous). We study with particular emphasis the two principal architectures for Kerr comb generation, namely the add-through and add-drop configurations. We show that in both cases, the ratio between out-coupling and total losses plays a key role as it directly determines the efficiency of the squeezing. We also explicitly determine the phase quadratures leading to photon entanglement, and analytically calculate their quantum noise spectra. The relevance of Kerr combs for quantum information systems at optical telecommunication wavelengths is also discussed.
In this paper, we investigate the generation of multimode entanglement and squeezing of an optical field via coupled four-wave mixing interactions in a Kerr nonlinear medium pumped at multiple well-separated frequencies. We show that genuine multimode entanglement can be obtained and this entanglement can be verified with the measurable multimode squeezing present in the system. This scheme may be used to achieve entangled frequency combs which are useful in continuous-variable quantum communication networks.