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Physical Review A

Effect of laser fluctuations on squeezed states in a degenerate parametric amplifier

K. Wódkiewicz, Muhammad Suhail Zubairy

Published Apr 1, 1983• 78 citations
Publisher

Abstract

The effect of phase and amplitude fluctuations of the pump mode on the quantum-statistical properties of the signal mode is considered. It is shown that these fluctuations in the laser field tend to decrease the squeezing of the signal field.
DOI
10.1103/physreva.27.2003

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Effect of the pump state on the behavior of the degenerate parametric amplifier

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We discuss the squeezing and statistical properties of the light produced by a coherently driven degenerate three-level laser with a parametric amplifier. We consider the case in which the atoms injected into the cavity are prepared in a coherent superposition of the top and bottom levels and with these levels coupled by the pump mode emerging from the parametric amplifier. It so happens that the presence of the parametric amplifier increases the squeezing and the mean photon number significantly. Furthermore, it is found that the maximum interacavity squeezing is 93% in the presence of the coupling and when the superposition has no contribution ( η = 0). On the other hand, the maximum interacavity squeezing turns out to be 94% in the absence of the coupling. This squeezing is due to the parametric amplifier and the superposition. In addition, our calculation shows that one effect of coupling the top and bottom levels is to decrease the mean and the normally-ordered variance of the photon number. PACS codes: 42.55.Ah, 42.50.Lc, 42.50.Ar

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Physical Review A•Feb 1, 1994•7 citations
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.
The parametric amplifier is usually studied under the assumption that the pump mode is in a large-amplitude coherent state. We consider what happens when this is no longer the case. We first derive some exact relations between the number fluctuations of the pump and signal, the pump and the idler, and also the signal and the idler. It is then determined how much phase noise can be tolerated in the initial pump state if two-mode squeezing is to be produced in the signal-idler field. The relation between the rotational symmetry in phase space of the initial pump state and that of the signal-idler subsystem is determined. We find that the sum phase distribution of the signal and idler has twice the rotational symmetry as that of the initial pump state. Finally, we generalize the parametric approximation to treat pump states which are not coherent states. We examine the effect of a phase-squeezed pump state and find that the pump squeezing can actually decrease the two-mode squeezing of the signal-idler field while enhancing a form of higher-order squeezing, sum squeezing, for these fields.
We study the effects of squeezed pump fluctuations in the degenerate parametric amplifier on signal squeezing. We find, both through semiclassical calculations and through several detailed analytic methods, that pump squeezing is responsible for two competing processes: Reduced pump phase fluctuations improve limitations to squeezing; at the same time, increased pump intensity fluctuations can lead to a ``spillover'' of pump fluctuations onto negative pump phases and a consequent reduction in signal squeezing.
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 discuss the squeezing and statistical properties of the light produced by a coherently driven degenerate three-level laser with a parametric amplifier. We consider the case in which the atoms injected into the cavity are prepared in a coherent superposition of the top and bottom levels and with these levels coupled by the pump mode emerging from the parametric amplifier. It so happens that the presence of the parametric amplifier increases the squeezing and the mean photon number significantly. Furthermore, it is found that the maximum interacavity squeezing is 93% in the presence of the coupling and when the superposition has no contribution ( η = 0). On the other hand, the maximum interacavity squeezing turns out to be 94% in the absence of the coupling. This squeezing is due to the parametric amplifier and the superposition. In addition, our calculation shows that one effect of coupling the top and bottom levels is to decrease the mean and the normally-ordered variance of the photon number. PACS codes: 42.55.Ah, 42.50.Lc, 42.50.Ar
Quantum fluctuations and squeezing of the signal field generated by a degenerate optical parametric oscillator are sensitive to the phase and amplitude fluctuations of the second-harmonic pump. The analysis reported here extends our previous calculations for a perfectly monochromatic noise-free pump to allow for finite pump amplitude and phase fluctuations. We treat the typically intense pump field with its fluctuations as a classical Gaussian stochastic process in two limits: first, when the pump has amplitude fluctuations but its phase is fixed and second, when its phase diffuses but its amplitude is fixed. Since pump amplitude noise affects the evolution of the signal field multiplicatively, it has a lesser impact on the quantum fluctuations of the signal than pump phase diffusion which compromises such fluctuations via the extreme phase sensitivity of the parametric amplification process. For the latter limit, our calculations extend the work of Gea-Banacloche and Zubairy [Phys. Rev. A 42, 1742 (1990)] to cavities with arbitrary transmission coefficients for the bounding mirrors.