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Physical Review A

Multimode squeezing of frequency combs

Germán J. de Valcárcel, Giuseppe Patera, Nicolas Treps, Claude Fabre

Published Dec 8, 2006• 90 citations
Publisher

Abstract

We have developed a full multimode theory of a synchronously pumped type-I optical parametric oscillator. We calculate the output quantum fluctuations of the device and find that, in the degenerate case (coincident signal and idler set of frequencies), significant squeezing is obtained when one approaches threshold from below for a set of well-defined ``supermodes,'' or frequency combs, consisting of a coherent linear superposition of signal modes of different frequencies which are resonant in the cavity.

DOI
10.1103/physreva.74.061801

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We have developed a full multimode theory of a synchronously pumped type-I optical parametric oscillator. We calculate the output quantum fluctuations of the device and find that, in the degenerate case (coincident signal and idler set of frequencies), significant squeezing is obtained when one approaches threshold from below for a set of well-defined ``supermodes,'' or frequency combs, consisting of a coherent linear superposition of signal modes of different frequencies which are resonant in the cavity.
We have developed the full theory of a synchronously pumped type I optical parametric oscillator (SPOPO). We derive expressions for the oscillation threshold and the characteristics of the generated mode-locked signal beam. We calculate the output quantum fluctuations of the device, and find that, in the degenerate case (coincident signal and idler set of frequencies), perfect squeezing is obtained when one approaches threshold from below for a well defined "super-mode', or frequency comb, consisting of a coherent linear superposition of signal modes of different frequencies which are resonant in the cavity.
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 show that synchronously pumped Optical Parametric Oscillators are able to generate strongly squeezed trains of femtosecond pulses in “supermodes”, which are well defined superpositions of many modes of different frequencies. In some conditions, several supermodes can be simultaneously squeezed. In addition, we show that the use of such squeezed trains of pulses can improve time transfer between remote clocks and ranging techniques beyond the standard quantum limit provided they have an optimized temporal shape.
The multimode operation of an optical parametric oscillator (OPO) operating below threshold is calculated. We predict that squeezing can be generated in a comb that is limited only by the phase matching bandwidth of the OPO. Effects of technical noise on the squeezing spectrum are investigated. It is shown that maximal squeezing can be obtained at high frequency even in the presence of seed laser noise and cavity length fluctuations. Furthermore the spectrum obtained by detuning the laser frequency off OPO cavity resonance is calculated.
The novel aspect of this study is grounded on the fact that squeezing spectrum of a finite set of super-modes operators can be below the standard quantum limit, giving a clear image that the system is a highly quantum multi-mode system. In fact, not only the super-mode of minimum threshold is perfectly squeezed at threshold but, further, all the other super-modes have nonclassical character and are significantly squeezed provided that their threshold is sufficiently close to the minimum one. It is concluded that synchronously pumped OPOs reveal to be very interesting devices for studying frequency combs at the quantum level. Their quantum multi-modal behavior could be exploited for generation of nonclassical states of the light used for implement optical time measurement of great sensitivity or quantum information protocols.
A full quantum treatment about the process of parametric down-conversion with frequency degenerate but polarization non-degenerate in an optical parametric oscillator (OPO) cavity is presented. Using the linearized Langevin equations and spectral matrix, we calculated the squeezing spectra of the coupled mode in the output field. The squeezing as a function of driving field and detection frequency is obtained. The results obtained, which are compared with those found semiclassically by Reynaud et al. , indicate that it is possible to generate a two-mode coherent squeezed state with large amplitude. The quantum correlation between the signal and the idler modes is also discussed. It is shown that there is an inseparable relationship between the two-mode squeezing and the intermode quantum correlation.