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arXiv:1104.1648

Quantum correlated pulses from a synchronously pumped optical parametric oscillator operating above threshold

Valentin Averchenko, Yu. M. Golubev, Claude Fabre, Nicolas Treps

Published Apr 8, 2011• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.1104.1648

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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.
The quantum analysis of radiation from a degenerate optical parametric oscillator synchronously pumped above its oscillation threshold is presented. It is shown that pulses of signal and pump fields at the output of the oscillator have the following properties: quantum fluctuations of the fields are independent in each individual pulse, but correlated in pulses of the pulse train with a temporal step multiple of the pulse period. The number of essentially correlated pulses is on the order of the oscillator cavity finesse. Cross-correlations between the pump and signal pulses are established above the oscillation threshold. These correlations lead to a significant quantum effect in the integral characteristics of the fields. A theoretical analysis revealed that the spectrum of field fluctuations measured using a balanced homodyne detection technique of phase quadratures of the fields with a pulsed local oscillator reveals quantum noise suppression in the vicinity of frequencies that are multiples of the pulse repetition rate.
We present in this paper a general model for determining the quantum properties of the light generated by a synchronously pumped optical parametric oscillator (SPOPO) operating below threshold. This model considers time and frequency on an equal footing, which allows us to find new quantum properties, related for example to the carrier envelope offset (CEO) phase, and to consider situations that are close to real experiments. We show that, in addition to multimode squeezing in the so-called ‘supermodes’, the system exhibits quadrature entanglement between frequency combs of opposite CEO phases. We have also determined the quantum properties of the individual pulses and their quantum correlations with the neighboring pulses. Finally, we determine the quantum Cramer–Rao limit for an ultra-short time delay measurement using a given number of pulses generated by the SPOPO.
SUMMARY Parametric processes in the interaction of electromagnetic field with a medium in an optical cavity are well known to produce states of light with nonclassical properties. The quantum correlations between these states can be employed for a realization of an EinsteinPodolsky-Rosen (EPR) paradox [l], in the original formulation using continuous variables, as proposed [2] and experimentally demonstrated [3] in the case of Nondegenerate Parametric Amplification below threshold. In this paper we study EPR-like behaviour between the signal and idler fields emitted by a degenerate optical parametric oscillator (OPO) above threshold; these fields, generated by conversion of a pump photon of frequency 2w0 in two photons of frequency w. , are spatially separated in the far field, showing non-local quantum correlations. The system is described by the full Hamiltonian for the operators associated with the pump and signal fields; the optical cavity introduces proper damping constants and corresponding vacuum field operators [4,5]. Above the threshold for the generation of the signal field, we consider the fluctuations in the intensity difference and in the phase sum of the signal beams, which are related to their degree of mutual correlation. By linearizing around the stationary state, we calculate the spectral variances of these quantities (i.e. the Fourier transform of the two time correlation functions). The Heisenberg uncertainty principle sets a lower limit to the product of the spectral variances for the fluctuations in the intensity and in the phase of each individual signal field; by using the idler beam to infer results of measurements on the correlated signal beam, we have an EPR paradox if the product of the spectral variances for the fluctuations in the intensity difference and phase sum of the fields, is below the uncertainty limit. This feature is apparent for a wide interval around zero frequency in the far field of the active OPO system, depending on the parameter space; in particular there is maximum correlation between signal beams, and therefore maximum breaking of the uncertainty limit, if the damping constant of the signal field is larger than that of the pump field.
Noise plays a very important role in synchronously pumped optical parametric oscillators (SPOPOs). For example, these devices have been suggested as tunable source of short pulses. However, it was shown that in the pulse compression regime the signal pulses may suffer from considerable noise-induced jitter. In the context of quantum optics, optical parametric oscillators have been suggested as a tool to amplify and detect quantum fluctuations. However, this requires very large amplification factors.
Abstract Parametric down-conversion in a nonlinear crystal is a widely employed technique for generating quadrature squeezed light with multiple modes, which finds applications in quantum metrology, quantum information and communication. Here we study the generation of temporally multimode femtosecond pulsed squeezed light in a synchronously pumped optical parametric oscillator (SPOPO) operating below the oscillation threshold, while considering the presence of non-compensated intracavity group-velocity dispersion. Based on the developed time-domain model of the system, we show that the dispersion results in mode-dependent detuning of the broadband supermodes of the pulsed parametric process from the cavity resonance due to temporal Gouy phase, as well as linear coupling between these supermodes. With perturbation theory up to the second order in the coupling coefficients between modes, we obtained a solution for the amplitudes of multiple supermodes given an arbitrary sub-threshold pump level. The dispersion affects the quantum state of the supermodes by influencing their squeezing level and the rotation of the squeezing ellipse. It also affects the entanglement among the supermodes, leading to reduced suppression of shot noise level as measured in the balanced homodyne detection scheme. Furthermore, our study highlights the potential of SPOPO with group-velocity dispersion as a testbench for experimental investigations of multimode effects in linearly evanescent coupled parametric oscillators.
The dependence of quantum correlations of twin beams on the pump finesse of an optical parametric oscillator is studied via a semi-classical analysis. It is found that the phase-sum correlation of the output signal and idler beams from an optical parametric oscillator operating above threshold depends on the finesse of the pump field when the spurious pump phase noise generated inside the optical cavity and the excess noise of the input pump field are involved in the Langevin equations. The theoretical calculations can explain the previously experimental results quantitatively.