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Optics Letters

Limits to wideband pulsed squeezing in a traveling-wave parametric amplifier with group-velocity dispersion

M. G. Raymer, P. D. Drummond, S. J. Carter

Published Aug 1, 1991• 43 citations
Publisher

Abstract

A theoretical method is developed to treat wideband pulsed squeezing in a traveling-wave parametric amplifier with group-velocity dispersion. Classical stochastic wave equations that are fully equivalent to operator equations of motion are developed and solved numerically. It is found that squeezing occurs over the entire phase-matching bandwidth, although the degree of squeezing decreases when the pump-pulse duration is shorter than the inverse of this bandwidth.

DOI
10.1364/ol.16.001189

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A theoretical method is developed to treat wideband pulsed squeezing in a traveling-wave parametric amplifier with group-velocity dispersion. Classical stochastic wave equations that are fully equivalent to operator equations of motion are developed and solved numerically. It is found that squeezing occurs over the entire phase-matching bandwidth, although the degree of squeezing decreases when the pump-pulse duration is shorter than the inverse of this bandwidth.
We investigate temporal effects in pulsed squeezing by parametric amplification, including effects of group-velocity dispersion. Our calculations show that the local oscillator pulse used to detect the squeezed field cannot be made shorter than the inverse phase-matching bandwidth of the generation process without degrading the amount of squeezing detected. This result generalizes an earlier result that showed that in the absence of dispersion, the local oscillator pulse duration should approach zero for optimum squeezing detection. We further show that by using local oscillator amplitude and phase pulse shaping it should be possible to achieve more than 40 dB of detectable quadrature squeezing. This is applicable where it is possible to neglect transverse spatial dimensions and diffraction, such as in a waveguide. We derive the s-parametrized quasiprobability evolution equation for the traveling-wave parametric amplifier. As the Wigner representation results in third-order derivatives, we also use the positive-P representation as an exact representation with equivalent Ito stochastic differential equations. This allows us to compare approximate --- but easily simulated --- Wigner representation results with those using the positive-P representation.
This thesis is primarily a theoretical study of degenerate parametric amplification as a means of generating squeezed-state light. i) A wideband traveling-wave formalism is developed for analyzing quantum mechanically a degenerate parametric amplifier. The formalism is based on spatial differential equations — spatial Langevin equations — that propagate temporal Fourier components of the field through the nonlinear medium. In addition to the parametric nonlinearity, the Langevin equations include absorption and associated fluctuations, dispersion, and pump quantum fluctuations. The dominant effects of dispersion and pump quantum fluctuations on the squeezing produced by a degenerate parametric amplifier are analyzed. ii) The wideband formalism of i) is used to carry out a more detailed analysis of the effects of phase mismatching. With the assumption of a lossless medium and a classical pump, we find that parametric amplification is capable of generating squeezed-state light over a wide band if materials with large χ(2) nonlinearities can be found, and that the squeezing bandwidth can be enhanced by phase mismatching away from degeneracy. iii) We consider again the effect of pump quantum fluctuations on the squeezing produced by parametric amplification. We perform discrete-mode calculations for a parametric amplifier with a quantum pump, and discuss some of the limitations of calculations of this sort in quantum optics. We derive stochastic differential equations (SDEs) for one- and two-mode parametric amplifiers, and from them obtain an iterative solution showing that pump quantum fluctuations impose a limitation on the degree of squeezing obtainable from a parametric amplifier. iv) A possible application of squeezing is considered; in particular, we study the effects of squeezing the intracavity noise in a laser oscillator. We solve the classical noise problem of a realistic laser model by making a bold — and possibly unrealizable — assumption, that the in-phase and quadrature Langevin sources which are responsible for the "noisiness" of the laser can be squeezed. We show that the effect of squeezing the in-phase quadrature is to reduce the phase noise, including the linewidth, of the laser but, due to amplitude-phase coupling, not to eliminate them altogether.
We develop a wideband traveling-wave formalism for analyzing quantum mechanically a degenerate parametric amplifier. The formalism is based on spatial differential equations—spatial Langevin equations—that propagate temporal Fourier components of the field operators through the nonlinear medium. In addition to the parametric nonlinearity, the Langevin equations include absorption and associated fluctuations, dispersion (phase mismatching), and pump quantum fluctuations. We analyze the dominant effects of phase mismatching and pump quantum fluctuations on the squeezing produced by a degenerate parametric amplifier.
We demonstrate broadband phase-sensitive amplification (PSA) measurement of squeezed light generated by a waveguide optical parametric amplifier (OPA) with external dispersion compensation. In broadband systems, group velocity dispersion (GVD) induces a frequency-dependent rotation of the squeezing axis, which limits the observable bandwidth in PSA measurements. To overcome this limitation, we introduce external dispersion compensation between two OPAs and suppress the quadrature rotation over a wide frequency range. As a result, we observe a maximum squeezing of 5.9 dB near the carrier frequency and more than 5 dB of squeezing up to a frequency offset of 4.5 THz from the carrier. Furthermore, squeezing below the shot-noise level is confirmed up to a frequency offset of 6 THz from the carrier, corresponding to the accessible phase-matching bandwidth of the waveguide OPA. Our results establish a practical method for broadband characterization of squeezed light and provide a key step toward ultrafast continuous-variable quantum information processing.
We present analytical solutions to nonlinear coupling equations for parametric down-conversion of a broadband pump at large gain. The feasibility of analytical expressions is demonstrated for the case of a collinear type II parametric interaction in beta-barium borate crystal and group-velocity matching of signal and pump waves. The correlation function of amplified signal wave is obtained, and it is revealed that the bandwidth of a noise-seeded optical parametric amplifier increases with a decrease in pump pulse duration, especially for femtosecond pump pulses.
Superconducting traveling-wave parametric amplifiers (TWPA) have emerged as highly versatile devices, offering broadband amplification with quantum-limited noise performance. They hold significant potential for addressing the readout bottleneck in prototype quantum computers, enabling scalability. Key challenges with this technology include achieving sufficient gain with minimal gain ripple while maintaining low noise performance. Efficient phase matching between a weak signal and a strong pump over the entire length of the TWPA is critical to overcoming these challenges. We present an experimental demonstration of the inverse Kerr phase matching technique in a TWPA, first proposed in Ref. Phys. Rev. Appl. 4, 024014. This method addresses several limitations of conventional dispersion engineering approaches of phase matching in the four-wave mixing parametric process in TWPAs. Most notably the existence of an unusable region of gain near the pump frequency which typically corresponds to the region of most optimal phase matching and maximum gain. The inverse Kerr phase matching approach, allows for greater frequency separation between the region of optimal gain and pump, \textit{in situ} tunability of the pump, minimal gain ripple, and a compact footprint which reduces losses. A TWPA employing the inverse Kerr phase matching technique experimentally demonstrated 20 dB of gain over a 3 GHz instantaneous bandwidth, with a tunable bandwidth of 8 GHz, minimal gain ripple, and near quantum-limited noise performance, with 1.5 photons of added noise.