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arXiv:quant-ph/0605128

Squeezing frequency combs

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

Published May 15, 2006• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.quant-ph/0605128

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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.
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.
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.
This Thesis studies, from a theoretical point of view, the dynamical and quantum properties of a type I degenerate optical parametric oscillator which is synchronously pumped by a mode-locked laser (SPOPO). In recent past, SPOPOs have been used for generating ultra-short optical pulses of tunable wavelength and their temporal properties have been investigated. Having a huge number of degrees of freedom, the output field of a SPOPO needs to be characterized via a multimodal quantum analysis. Then, we first develop a multimode model of the device, obtaining the quantum equations for the intra-cavity field operators. Afterwards, we study the steady state solutions of the average values of the generated fields that are the solutions of an eigenvalue equation. Its spectrum gives information about the “useful” number of modes in which are concentrated almost all the dynamical and quantum properties of the intra-cavity field and which we call “super-modes”.Indeed, we show that not only the super-mode of minimum threshold is (ideally) perfectly squeezed at threshold, but that all the other super-modes have an important non-classical character provided that their thresholds are close enough to the minimum one. This circumstance gives the clear image that a SPOPO is a highly quantum multi-mode system. Finally, the last part of this Thesis is focused on the study of the output of a SPOPO from the point of view of the generation of highly multi-mode entangled states and their optimization by means of specific experimental configurations.
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.
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.
We have constructed a mode-locked optical parametric oscillator (OPO), synchronously pumped by the second harmonic of a continuously mode-locked Nd:YAG laser and based on type II phase matching in a KTP crystal. The two subharmonics (signal and idler waves) are nearly degenerate in frequency but are distinct orthogonal polarization states, and the oscillator is thus a nondegenerate OPO. Above threshold, the intensities of the signal and idler output beams should be highly correlated, as recently demonstrated for a similar single-frequency OPO.1 Ideally, the quantum noise on the corresponding photocurrent difference signal is completely suppressed for frequencies that are small compared to the OPO cavity bandwidth. Since this configuration produces intense light beams with potentially very good noise suppression, it is an important prototype for possible applications, e.g., to spectroscopy. Initial results with our OPO show an excess uncorrelated polarization noise, possibly due to depolarized light scattering in the KTP crystal. When the OPO cavity is stabilized with the signal and idler degenerate in frequency, they can be mixed to form a superposition by manipulating their polarization. When the oscillator is pumped below threshold, a pulsed squeezed vacuum state is produced in two such mixtures.2 When the polarizations are mixed inside the OPO cavity by a Faraday rotator, the backaction evasion necessary for a quantum nondemolition (QND) measurement of one of the field quadratures of an externally injected beam is obtained.3 The pulsed local oscillator used in observing the squeezing or QND effects is derived from the fundamental output of the pump laser. Progress in implementing these experiments with our mode-locked OPO is described as well as possible applications to time-domain measurements with noise below the shot-noise limit.