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Physical Review A

Use of cavities in squeezed-state generation

Bernard Yurke

Published Jan 1, 1984• 269 citations
Publisher

Abstract

Cavity degenerate-parametric-amplifier and cavity four-wave-mixing configurations capable of producing a large amount of squeezing near the threshold of oscillation are discussed. Cavities allow one to reduce the pump power delivered to the gain medium, or to select a gain medium which has less gain per unit length, but may be better suited for squeezed-state production in other respects.

DOI
10.1103/physreva.29.408

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Cavity degenerate-parametric-amplifier and cavity four-wave-mixing configurations capable of producing a large amount of squeezing near the threshold of oscillation are discussed. Cavities allow one to reduce the pump power delivered to the gain medium, or to select a gain medium which has less gain per unit length, but may be better suited for squeezed-state production in other respects.
Phase dependent nonlinear optical processes can make large fractional changes in the phase and amplitude of an optical field. An example is the prediction(1) that four-wave-mixing can generate squeezed states of an optical field where the variance in the two quadratures of the field are unequal. In order to observe squeezed states and utilize them in interferometric measurements this inequality in variances must be large (e.g. ≳ 50%). The large phase shifts required to achieve this regime of squeezing can be obtained near the threshold for oscillation of four-wave-mixing in an optical cavity. (2) This paper describes an experimental study(3) of four-wave-mixing in a cavity near threshold using the nonlinear index of the Na atomic resonance.
A squeezed state of the electromagnetic field has less noise in one of its two amplitude components than that of a coherent state. This property makes squeezed states potentially useful in low noise and precision measurement. Squeezed states may be generated by, among other things, degenerate parametric amplifiers and four-wave mixers. The reduced noise in one of the amplitude components is most easily observed via a homodyne detector. A number of experimental efforts to generate and detect squeezed states are under way. Here, in describing experimental techniques, the experiments' carried out by Slusher et al. are emphasized. A number of techniques were employed to successfully generate squeezed light. An atomic beam of sodium provided the optical nonlinearity in a cavity-backward four-wave mixer. By employing pairs of Fabry-Perot modes spaced symmetrically about the pump frequency, squeezed light was generated in nondegenerate conditions where Rayleigh scattering of pump light could be avoided. To observe squeezing, a number of nonidealities such as phase jitter and detector inefficiencies also had to be overcome.
Squeezed states of light have been predicted to be generated by four-wave mixing in cavity configurations. Any noise fields in the cavity can degrade or modify these squeezed states. An experiment using a Na atomic beam as the nonlinear mixing medium shows that spontaneous emission from the excited atoms results in a broadband frequency spectrum of noise in the cavity used for squeezing. The limits this noise places on the observed amount of squeezing and possible techniques for avoiding this noise source are discussed.
High-Q cavities play a central role in quantum optics for the generation and study of novel quantum mechanical states of light like squeezed states. It is however not widely recognized that even low-Q cavities can produce such states. For example, a degenerate optical parametric oscillator (DOPO) with one nearly perfect mirror can produce perfectly squeezed output light regardless of the second mirror transmission, provided the DOPO is at oscillation threshold. Moreover, the squeezing bandwidth increases with increasing transmission of the second mirror.
The authors present a quantum analysis of four-wave mixing in a non-resonant nonlinear medium inside a cavity which is driven by two driving fields. In this process a nonlinear medium couples two pump modes with a signal mode of the frequency equal to the half-sum of the two pump field frequencies. Three types of stable steady-state solutions of the deterministic problem, describing three regimes of oscillation, are found: one below threshold and two different above-threshold regimes. The spectra of fluctuations of the quadrature-phase amplitudes for all three modes are calculated. It is found that in the above-threshold regime each of three modes may display a squeezed noise reduction. Below threshold a squeezing is realized for the central mode.