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arXiv:1102.3405 · Physical Review A

Hybrid squeezing of solitonic resonant radiation in photonic crystal fibers

Truong X. Tran, K. N. Cassemiro, Christoph Söller, K. J. Blow, Fabio Biancalana

Published Jul 21, 2011• 11 citations
arXivHTMLPDF

Abstract

We report the existence of a kind of squeezing in photonic crystal fibers which is conceptually intermediate between four-wave-mixing-induced squeezing in which all the participant waves are monochromatic waves, and self-phase-modulation-induced squeezing for a single pulse in a coherent state. This hybrid squeezing occurs when an arbitrary short soliton emits quasimonochromatic resonant radiation near a zero-group-velocity-dispersion point of the fiber. Photons around the resonant frequency become strongly correlated due to the presence of the classical soliton, and a reduction of the quantum noise below the shot-noise level is predicted.

DOI
10.1103/physreva.84.013824

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We report the existence of a kind of squeezing in photonic crystal fibers which is conceptually intermediate between four-wave-mixing-induced squeezing in which all the participant waves are monochromatic waves, and self-phase-modulation-induced squeezing for a single pulse in a coherent state. This hybrid squeezing occurs when an arbitrary short soliton emits quasimonochromatic resonant radiation near a zero-group-velocity-dispersion point of the fiber. Photons around the resonant frequency become strongly correlated due to the presence of the classical soliton, and a reduction of the quantum noise below the shot-noise level is predicted.
Squeezing is a fundamental quantum optical phenomenon - induced by various nonlinear optical processes - in which a special state of the electromagnetic field is generated, for which quantum noise fluctuations are reduced below the shot noise level for certain frequency ranges. Two qualitatively different kinds of squeezing are currently known to take place in optical fibers. The first is the four-wave mixing (FWM) induced quadrature squeezing, in which an intense continuous wave (CW) pump initiates a spontaneous emission of signal and idler waves from vacuum fluctuations at symmetric detunings from the pump. The noise components at the signal and idler frequencies become correlated via the fiber nonlinearity, leading to a reduction of the noise power spectrum below the shot noise level. All the waves participating to the FWM-induced squeezing are monochromatic waves. The second kind of squeezing is the so called self-phase modulation (SPM) induced squeezing, in which the spectral components of an intense short pulse in a coherent state become correlated via the SPM during propagation. We demonstrate theoretically that a third kind of squeezing is possible in optical fibers, in which the noise spectrum of the quasi-monochromatic resonant radiation (RR) emitted by optical solitons when subject to perturbations shows evidence of photon correlation and a reduction of noise below the shot-noise level.
Optical solitons are pulses that propagate in optical fibers without temporal or spectral distortion, owing to balancing of the second-order dispersion of the refractive index by nonlinear self-phase modulation induced by the intensity-dependent refractive index. Classically, this stationary, distortion-free propagation requires only the proper choice of pulse width and shape for a given pulse energy. However, quantum mechanical zero-point fluctuations of the amplitude and phase of the optical pulse limit the precision with which this pulse shape can be produced. These quantum fluctuations do not undergo stationary propagation but, rather, evolve because of dispersion and self-phase modulation, As a soliton pulse propagates, this zero-point or vacuum noise associated with the pulse evolves into squeezed noise owing to self-phase modulation in the fiber.1,2
Optical solitons are pulses that propagate in optical fibers without temporal or spectral distortion, owing to balancing of the second-order dispersion of the refractive index by nonlinear self-phase modulation induced by the intensity-dependent refractive index. Classically, this stationary distortion-free propagation only requires the proper choice of pulse width and shape for a given pulse energy. However, quantum fluctuations do not undergo stationary propagation but rather evolve due to dispersion and self-phase modulation. As a soliton pulse propagates, zero-point or vacuum noise associated with the pulse evolves into squeezed noise. Vacuum fluctuations are responsible for the fundamental detector noise floor known as the shot noise limit. Reduction of the noise in the detection of squeezed soliton pulses has achieved a noise level 34% below this limit. In optical fibers, thermal fluctuation of the refractive index limit the noise reduction that can be achieved by adding phase fluctuations in excess of the vacuum noise. At low frequencies thermal noise originates from local structural dynamics of fused silica which produces a 1/f power spectrum and from guided acoustic wage Brillouin scattering which modulates the refractive index at frequencies characteristic of the fiber structure. The bandwidth of these fluctuations is ~2 GHz; and for soliton pulses with spectral bandwidth much >2 GHz, we have shown that this noise can be made insignificant. For very short pulses, however, noise from Raman scattering must be considered. Recent calculations incorporating this noise mechanism are compared with experiment.
Parametric interactions such as four wave mixing have been predicted to produce states of the radiation field where the quantum fluctuations in one phase quadrature are less than those of a coherent state.1 These “squeezed states” have proved remarkably difficult to generate and detect, not least because of the presence of additional classical noise in many laser sources and parametric devices. We have now demonstrated the reduction of classical fluctuations by means of four wave mixing in an optical fiber under conditions very similar to those needed to demonstrate squeezed state generation. This success reinforces the plausibility of related quantum noise experiments, and has implications for fiber optic communications.
We present new results on photon number squeezing of spectrally filtered solitons in fibers. The impact of frequency low-, high-, and bandpass filtering on noise reduction has been measured as a function of fiber length for 130-fs pulses close to the soliton energy. For short fibers our results agree qualitatively with theoretical predictions. For longer fibers, however, the measured squeezing increases to an unexpectedly large value. Filtering out the long-wavelength components of strongly Raman-shifted, higher energy pulses squeezed the directly detected photocurrent fluctuations down to 3.8+/-0,2 dB (59%) below the shot noise level. The measured noise reductions are broadband from 5 to 90 MHz.
There is great interest in photonic crystal fibers (PCFs) because of their potential for hosting highly nonlinear material. Already with material of low nonlinearity such as silica for solid core PCFs, the nonlinear properties can be utilized since high intensities of light are guided within the core. To create squeezed states, we plan to exploit the high nonlinearity of resonant Rb vapor filled in the hollow fiber core and to use self-induced transparency (SIT) solitons to avoid resonant loss. High nonlinearity is induced from the self-phase modulation of a detuned 2pi soliton. Photon-phonon interactions, which cause a significant amount of excess noise in solid core fibers, will be highly reduced in our system.