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Journal of Experimental and Theoretical Physics Letters

Effective Group Velocity and Shape of Twin Beams

Pavel A. Prudkovskii

Published Apr 1, 2020• 1 citation
Publisher

Abstract

The shape and propagation velocities of pulsed twin beams generated in the process of parametric light down-conversion have been theoretically studied in the case where the delays caused by the dispersion of group velocities exceed the length of a pump pulse. It has been shown that the effective group velocity of the scattered pulse is determined by the arithmetic mean of the group velocities at the scattered radiation and pump frequencies. The scattering matrix elements for the large parametric gain have been numerically found. It has been shown that mixing of the spectral components of scattered radiation can cause a significant narrowing of the twin beam pulses. Finally, for the case of generation of broadband twin beams sequentially in two crystals with an aperiodic domain structure, it has been shown that the visibility of the three-frequency interference decreases as the pump pulse lags behind the scattered radiation pulses.

DOI
10.1134/s0021364020080081

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•Jan 1, 2017•0 citations
The shape and propagation velocities of pulsed twin beams generated in the process of parametric light down-conversion have been theoretically studied in the case where the delays caused by the dispersion of group velocities exceed the length of a pump pulse. It has been shown that the effective group velocity of the scattered pulse is determined by the arithmetic mean of the group velocities at the scattered radiation and pump frequencies. The scattering matrix elements for the large parametric gain have been numerically found. It has been shown that mixing of the spectral components of scattered radiation can cause a significant narrowing of the twin beam pulses. Finally, for the case of generation of broadband twin beams sequentially in two crystals with an aperiodic domain structure, it has been shown that the visibility of the three-frequency interference decreases as the pump pulse lags behind the scattered radiation pulses.
The effect of pump depletion on the spectrum of twin beams, which appear in the process of collinear parametric down-conversion in a nonlinear crystal with an aperiodic domain structure and have a high degree of simultaneity, has been described. A system of equations describing the interaction of pump with all modes of scattered light simultaneously has been derived. It has been shown that pump depletion results in a noticeable broadening of the spectrum of twin beams for a quadratic-hyperbolic law of variation of the reciprocal lattice vector of the domain structure. The effect of narrowing of the coherent peak in the sum-frequency generation signal from twin beams has been demonstrated. This effect increases as the pump is depleted.
Walk-off effects, originating from the difference between the group and phase velocities, limit the efficiency of nonlinear optical interactions. While transverse walk-off can be eliminated by proper medium engineering, longitudinal walk-off is harder to avoid. In particular, ultrafast twin-beam generation via pulsed parametric down-conversion and four-wave mixing is only possible in short crystals or fibres. Here we show that in high-gain parametric down-conversion, one can overcome the destructive role of both effects and even turn them into useful tools for shaping the emission. In our experiment, one of the twin beams is emitted along the pump Poynting vector or its group velocity matches that of the pump. The result is markedly enhanced generation of both twin beams, with the simultaneous narrowing of angular and frequency spectrum. The effect will enable efficient generation of ultrafast twin photons and beams in cavities, waveguides and whispering-gallery mode resonators.
Uniaxial anisotropy in nonlinear birefringent crystals limits the efficiency of nonlinear optical interactions and breaks the spatial symmetry of light generated in the parametric down-conversion (PDC) process. Therefore, this effect is usually undesirable and must be compensated for. However, high gain may be used to overcome the destructive role of anisotropy in order to generate bright two-mode correlated twin-beams. In this work, we provide a rigorous theoretical description of the spatial properties of bright squeezed light in the presence of strong anisotropy. We investigate a single crystal and a system of two crystals with an air gap (corresponding to a nonlinear SU(1,1) interferometer) and demonstrate the generation of bright correlated twin-beams in such configurations at high gain due to anisotropy. We explore the mode structure of the generated light and show how anisotropy, together with crystal spacing, can be used for radiation shaping.
We present an experimental implementation of spectral properties engineering on biphoton light, emitted via ultrafast type II spontaneous parametric down conversion (SPDC), based on the shaping of the pump pulse spectrum and propagation of the emitted correlated photons through dispersive media. Spectral properties of a biphoton state are fully characterized by the two-photon spectral amplitude (TPSA). Exploiting the group velocity dispersion (GVD) induced by the passage of optical fields through dispersive media, an energy to time two dimensional Fourier transform of the TPSA is operated: this returns a technique to reconstruct TPSA by means of a temporal measurement among the delay between the laser pulse emission (trigger) and the detection times of the two correlated photons. Exploiting this kind of measurement it is possible to deeply resolve the interference pattern in the shape of TPSA. In this research we report on the conditions under which subtle structure on TPSA spectra can be deliberately engineered via modulation of the pump beam spectrum.
We report on the observation of broadband (40 THz) bright twin beams through high-gain parametric downconversion in an aperiodically poled lithium niobate crystal. The output photon number is shown to scale exponentially with the pump power and not with the pump amplitude, as in homogeneous crystals. Photon number correlations and the number of frequency/temporal modes are assessed by spectral covariance measurements. By using sum-frequency generation on the surface of a non-phase-matched crystal, we measure a cross-correlation peak with the temporal width of 90 fs. (C) 2018 Optical Society of America
Twin photon pairs generated through parametric downconversion (PDC) in a χ 2 medium is one of the most widely used source of entanglement. We focus here on a non-conventional geometry in which one of the twin photons propagates in the opposite direction with respect to the pump beam, exploiting quasi-phase-matching in a periodically poled crystal. Through predicted almost 50 years ago, this new PDC configuration has been realized experimentally only recently [1] thanks to new fabrication techniques achieving the required sub-micrometer poling period. Because of the presence of distributed feedback, the optical system has been shown to behave as a Mirrorless Optical Parametric Oscillator (MOPO) and exhibits peculiar spectral properties which strongly differ from those found in more common geometries involving co-propagating beams. In this work we provide a detailed analysis of the correlation and coherence properties of counter-propagating twin beams both in the purely spontaneous regime and in the neighborhood of the MOPO threshold. We consider on the on side the regime of spontaneous pair production where the characteristic narrow band of the counter-propagating twin beams offers the unique opportunity of generating heralded single photon states with a high degree of purity, a relevant property for applications in quantum communication. In this context, we investigate how the degree of separability of the twin photon state varies with the pump pulse duration τp. We find that two well separated time scales characterize the system dynamics: a short time scale τgvm, in the picoseconds range, corresponding to the typical temporal delay of co-propagating waves due to group-velocity mismatch, and a much longer time scale τgvs associated with the temporal separation of counter-propagating waves. Such a difference of time scales occurs naturally in the counterpropagating configuration, for basically any kind of material and tuning condition. Because of this same feature, counter-propagating twin photons in a pure state can in principle be heralded at any wavelength by choosing the appropriate poling period. We show that a high degree of separability can be achieved when the pump pulse duration satisfy the condition τgvm ≪ τp ≪ τgvs, as put in evidence from the evaluation of Schmidt number as a function of the pump pulse duration which reaches a minimum close to unity in this region. The separability is lost in the nearly monochromatic limit ( τp ≫ τgvs ) as well as for ultra-short pulses ( τp ≪ τgvm ), where the entanglement between the signal and idler frequencies can be inferred by the non factorable shape of the spectral biphoton amplitude. We offer a physical interpretation of such a behaviour, and a detailed analysis of the Schmidt number characterizing the entanglement of the state. We also considered a completely different regime of operation, close to the MOPO threshold, where the combined effect of stimulated PDC and distributed feedback affects dramatically the property of coherence of the field. Our analysis put in evidence a progressive narrowing of both the spectral twin beam correlation and the intensity spectra as the pump field intensity approaches its threshold value. This translates into a drastic increase of the correlation and coherence times in the temporal domain, a feature which can be attributed to the critical slowing down of the fluctuation dynamics characterizing the transition toward coherent emission occurring at the MOPO threshold. Furthermore, we investigate the potentiality of the source to generate squeezing and EPR type correlations in the threshold vicinity. In this regards, the obtained results shows that the system displays a behaviour which is very similar to that found in standard optical parametric oscillators enclosed in a resonant cavity. In the last part of the work, we present some preliminary results from numerical simulations illustrating the transition above the MOPO thresholds. We also take into account non collinear PDC emission, showing explicitely that the spatial and the temporal degrees of freedoms of the emitted twin photons are almost uncoupled. This feature strongly distinguish the counter-propagating configuration from standard co-propagating geometries where the phase-matching mechanism usually leads to strong angular dispersion.