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Physical Review Letters

Two-Dimensional Spatial Solitary Waves from Traveling-Wave Parametric Amplification of the Quantum Noise

P. Di Trapani, Gintaras Valiulis, Walter Chinaglia, Alessandra Andreoni

Published Jan 12, 1998• 67 citations
Publisher

Abstract

In a single 15-mm lithium triborate crystal, operated at high gain and strong diffraction, we obtained the spatial mode locking of the quantum noise, its amplification up to the pump level, and quasisoliton propagation of the mutually trapped beams. Visible pulses of 1 $\ensuremath{\mu}\mathrm{J}$ 1.5 ps were converted, with $50%$ efficiency, into diffraction-limited superfluorescence, tunable in the range 0.67-- $2.5\ensuremath{\mu}\mathrm{m}$.

DOI
10.1103/physrevlett.80.265

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In a single 15-mm lithium triborate crystal, operated at high gain and strong diffraction, we obtained the spatial mode locking of the quantum noise, its amplification up to the pump level, and quasisoliton propagation of the mutually trapped beams. Visible pulses of 1 \ensuremathμJ\ensuremath{\mu}\mathrm{J}\ensuremathμJ 1.5 ps were converted, with 5050%50 efficiency, into diffraction-limited superfluorescence, tunable in the range 0.67-- 2.5\ensuremathμm2.5\ensuremath{\mu}\mathrm{m}2.5\ensuremathμm.
Summary form only given. Quadratic non-linear interaction is known to support the process of spatial soliton formation. A very simple set-up consists of a single pass, single crystal, quantum noise optical parametric amplifier (OPA) pumped by a focussed beam. The diffraction-free propagation achieved in the solitary-wave regime implies that the beam-waist plane of the pump beam can arbitrarily move inside the crystal without any relevant change in the size of the mutually trapped pump, signal and idler beams at the crystal output face. We present a very useful application of this property to the reconstruction of digital images. The experimental set-up is based on a 30 mm temperature tuned lithium triborate (LBO) crystal, operated in noncritical type I phase matching and pumped by a 15 ps, 527 nm pulse from an amplified frequency doubled Nd:glass laser. We set the crystal temperature to 107/spl deg/C to obtain generation at 1.8 /spl mu/m (idler) and 0.75 /spl mu/m (signal), ensuring minimum group velocity mismatch among interacting pulses.
Nonlinear optical waveguides hold promise as parametric amplifiers and as sources of quadrature-squeezed light. The confinement of the pump field drastically increases the efficiency of the nonlinear conversion. In addition, the control of the spatial mode profiles by the waveguide geometry should diminish the effect of gain-induced diffraction, which has been seen to limit the amount of attainable squeezing in bulk parametric crystals.1 Using subpicosecond laser pulses, we have observed parametric gain as well as quadrature squeezing in a quasi-phase matched KTP waveguide.
Although noiseless optical amplification has been demonstrated in bulk KTP crystals, and is well understood, there have been no observations of noiseless optical amplification in bulk quasi-phase-matched (QPM) systems. That such an amplifier is possible was predicted recently and indeed squeezing has already been observed in QPM waveguides (using KTP and LiNbO3). QPM materials are attractive for use in quantum-optical devices because they give access to certain (large) components of the nonlinear susceptibility tensor that cannot be used in conventional birefringent phase-matching schemes. They also extend the range of materials accessible for use in parametric amplifiers to include some low-birefringence crystals exhibiting large nonlinearities. Even with the technological advantages offered by certain QPM crystals, efforts to find practical applications for optical parametric amplifiers are hampered by the need for enormous pump-field strengths. The obvious solution to the problem of the pump-field requirement is to confine the incident energy to a narrow interaction region thereby increasing the energy density. However, this approach can only be realised at the expense of sacrificing the homogeneity of the parametric interaction between pump and signal waves. This in turn causes vacuum field fluctuations from parasitic modes to be mixed into the signal mode thereby degrading the signal to noise ratio and negating the advantage of using an optical parametric amplifier. In the experiments presented here, optical signals have been amplified with up to 9dB of gain, yet with a noise figure (NF) of only 1.09, as compared to the minimum possible NF of a classical amplifier with the same gain which would equal 1.86. Furthermore, the interaction is achieved with tightly focused incident fields in a sample of bulk QPM lithium niobate. The entire interaction region is only 200µm thick and 2.8mm long. This performance was achieved with the aid of a theoretical model m which the effect of wavefront curvature and mode distortion are treated within a quantised mode framework using a spatial mode basis. Such a simulation permits the fundamental origin of the excess quantum noise to be easily traced to zero-point fluctuations of high-order spatial modes which couple to the signal mode via the parametric interaction. Furthermore the simulation enabled an experimental geometry to be selected in which an optimal compromise is made between wavefront matching bump beam smaller than signal) and pump-homogeneity (pump larger than signal), so that the overall noise figure remains well into the quantum-performance region.
Measurements of quantum-noise reduction have been performed over a broad frequency range up to 0.5 GHz using pulses of squeezed light generated by parametric amplification in KTiOPO4{\mathrm{KTiOPO}}_{4}KTiOPO4​ crystals. Both balanced-homodyne and direct-difference photodetection schemes were employed, and 0.5 dB of noise reduction was routinely obtained. A continuous-mode traveling-wave theory including the effects of dispersion and loss has been employed to model the experimental results.
Recently, we have observed as much as 7 dB of quantum-noise reduction in the direct difference detection of twin-beam signal and idler outputs from a traveling-wave optical parametric amplifier (OPA).1 The OPA, which consists of a type-II phase-matched KTiOPO4 crystal, is pumped by the second harmonic of a mode-locked and Q-switched Nd:YAG laser. Here we describe an experiment in which we used these twin-beam pulses to improve on the optimal (shot-noise-limited) direct-detection signal-to-noise ratio (SNR) that can be achieved with coherent-state pulses of light of the same peak power.