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Electronics and Communications in Japan (Part I Communications)

Analysis on squeezing properties of degenerate parametric amplifier for quantum communication

Hidenori Koyano, Tomohiko Uyematsu, Norihiro Yoshida, Osamu Hirota

Published Jan 1, 1992• 1 citation
Publisher

Abstract

Abstract In this paper, characteristics of degenerate parametric amplifiers are analyzed and are expected to be useful as a generator of a squeezed state or a noiseless amplifier for an optical wave. Especially, when a degenerate parametric amplifier is used as a noiseless amplifier or a squeezed‐state generator (squeezer), the depletion of the pumping light which has been neglected affects the quantum noise characteristic of the squeezed light. This effect is analyzed in this paper. Further, when the incident light does not satisfy the phase matching condition, the effect of this phase shift on the gain and quantum noise characteristics of the degenerate parametric amplifier is studied. On the other hand, when a degenerate parametric amplifier is used as a preamplifier for the receiving side of the communication system, the phase noise of the pumping light can be a cause of degradation of the communication system performance. The phase noise of the pumping light is classified as the phase shift and the phase fluctuation caused by the quantum noise and then the effects of these phase noises on the quantum noise characteristics of the squeezed light are analyzed. Further, in the BPSK optical coherent communication system, the effect of the phase noise on the bit error rate is analyzed. A quantitative evaluation is made to determine how small the phase noise of the pumping light should be in order not to degrade the error rate.

DOI
10.1002/ecja.4410750107

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Abstract In this paper, characteristics of degenerate parametric amplifiers are analyzed and are expected to be useful as a generator of a squeezed state or a noiseless amplifier for an optical wave. Especially, when a degenerate parametric amplifier is used as a noiseless amplifier or a squeezed‐state generator (squeezer), the depletion of the pumping light which has been neglected affects the quantum noise characteristic of the squeezed light. This effect is analyzed in this paper. Further, when the incident light does not satisfy the phase matching condition, the effect of this phase shift on the gain and quantum noise characteristics of the degenerate parametric amplifier is studied. On the other hand, when a degenerate parametric amplifier is used as a preamplifier for the receiving side of the communication system, the phase noise of the pumping light can be a cause of degradation of the communication system performance. The phase noise of the pumping light is classified as the phase shift and the phase fluctuation caused by the quantum noise and then the effects of these phase noises on the quantum noise characteristics of the squeezed light are analyzed. Further, in the BPSK optical coherent communication system, the effect of the phase noise on the bit error rate is analyzed. A quantitative evaluation is made to determine how small the phase noise of the pumping light should be in order not to degrade the error rate.
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.
Abstract Phase-sensitive amplification of squeezed states is a technique to mitigate high detection loss, which is especially attractive at 2 µm wavelengths. We derived an analytical model proving that amplified squeezed states can mitigate phase noise significantly. Our model discloses two practical parameters: the effective measurable squeezing and the effective detection efficiency of amplified squeezed states. A realistic case study includes the dynamics of the gain-dependent impedance matching conditions of the amplifier. Our results recommend operating the optical parametric amplifier at high gains because of the signal-to-noise ratio’s robustness to phase noise. Amplified squeezed states are relevant in proposed gravitational wave detectors and interesting for applications in quantum systems degraded by the output coupling loss in optical waveguides.
We study the effect of non-coherent-state pumps on the behavior of the degenerate parametric amplifier. This is done both by developing some exact results and by extending the parametric approximation. Relations are found between the number fluctuations in the pump and those in the signal. The effect of initial phase uncertainty in the pump on the squeezing in the signal is also determined. In addition, we find that rotational symmetry in phase space of the signal-mode state is twice that of the pump-mode state. This implies, for example, that a pump in the squeezed vacuum state will produce a signal-mode state with a four-pronged structure. The effect of a squeezed pump with nonzero amplitude is studied by using a more general form of the parametric approximation. It is shown that in the time interval during which the parametric approximation is valid the effect of this pump is the same as one which is an incoherent superposition of coherent states. We find that while the squeezing of the pump degrades the squeezing of the signal it enhances its amplitude-squared squeezing.
We investigate the time evolution of squeezing in the signal mode of the undamped parametric amplifier. Both the degenerate and nondegenerate cases are considered. These are the simplest models that give limits to squeezing caused by both the intrinsic pump noise and pump depletion. Conflicting analytic expressions have been reported. We resolve this by the use of exact numerical methods, employing both number state and stochastic techniques. Our central result is that in both cases we find that the minimum in the squeezed quadrature variance scales as N${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}^{\mathrm{\ensuremath{-}}1/2}$, where N\ifmmode\bar\else\textasciimacron\fi{} is the initial coherent pump photon number. This bound on the amount of squeezing obtainable, coupled with the loss in energy due to the conversion efficiency, serves to limit the phase information in the squeezed channel to no more than that of the coherent pump. We believe this to be a fundamental limit for using the squeezed radiation generated in coherently driven parametric amplifiers.
Summary form only given. The generation of quantum states of light, such as squeezed states, often relies on degenerate optical parametric amplification. The input signal in a degenerate optical parametric amplifier (DOPA) may be amplified or deamplified depending on the phase of the signal field relative to that of the pump field (/spl Delta//spl phi/=/spl phi//sub pump/-2/spl phi//sub signal/). We present the results of an accurate numerical DOPA model for the generation of amplitude-squeezed light with Gaussian pump and signal beams. We find that the widely accepted 3-dB limit imposed by the Gaussian beam profiles can actually be exceeded in the tight focusing regime.
Optical parametric amplifiers (PAs) utilize highly efficient nonlinear effects in an optical fiber and they have the ability to operate in phase-sensitive mode. The inclusion of PAs in optical systems can give an ultimate limit for lumped amplified links in terms of achievable signal to noise ratio. The drawback is the complexity stemming from the requirement of phase matching a number of waves at each amplifier, phase lock, and the extra spectrum consumed by idler waves. In this chapter, the theories of a parametric amplifier, including the quantum-optical equations, are given. The properties of the gain saturation and the noise figure are presented. Practical amplifier systems and their applications in phase-sensitive amplification, all-optical signal regeneration, and squeeze state generation are outlined.