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Journal of the Optical Society of America B

Squeezed-state generation in optical bistability

Luis A. Orozco, Mark G. Raizen, Min Xiao, Robert J. Brecha, Harry J. Kimble

Published Oct 1, 1987• 86 citations
Publisher

Abstract

Experiments to generate squeezed states of light are described for a collection of two-level atoms within a high-finesse cavity. The investigation is conducted in a regime for which the weak-field coupling of atoms to the cavity mode produces a splitting in the normal mode structure of the atom–field system that is large compared with the atomic linewidth. Reductions in photocurrent noise of 30% (−1.55 dB) below the noise level set by the vacuum state of the field are observed in a balanced homodyne detector. A degree of squeezing of approximately 50% is inferred for the field state in the absence of propagation and detection losses. The observed spectrum of squeezing extends over a very broad range of frequencies (~±75 MHz), with the frequency of best squeezing corresponding to an offset from the optical carrier given by the normal mode splitting.

DOI
10.1364/josab.4.001490

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Annual Meeting Optical Society of America•Jan 1, 1988•0 citations
Experiments to generate squeezed states of light are described for a collection of two-level atoms within a high-finesse cavity. The investigation is conducted in a regime for which the weak-field coupling of atoms to the cavity mode produces a splitting in the normal mode structure of the atom–field system that is large compared with the atomic linewidth. Reductions in photocurrent noise of 30% (−1.55 dB) below the noise level set by the vacuum state of the field are observed in a balanced homodyne detector. A degree of squeezing of approximately 50% is inferred for the field state in the absence of propagation and detection losses. The observed spectrum of squeezing extends over a very broad range of frequencies (~±75 MHz), with the frequency of best squeezing corresponding to an offset from the optical carrier given by the normal mode splitting.
A theoretical and experimental investigation of the generation of squeezed states of light has been carried out for a system of two-level atoms inside a high-finesse cavity. The regime that we consider is such that the coupling of atoms to the cavity mode produces a splitting in the normal mode structure of the atom-field system (the so-called vacuum-field Rabi splitting). We have employed this splitting to generate squeezing with observed reductions in photocurrent noise of 30 % below the shot-noise level. A degree of squeezing of ~50% is inferred for the field state in the absence of propagation and detection losses. Squeezing has been observed in two different cavity geometries with quite different coupling coefficients. In each case, the frequency of best squeezing corresponds to that of the normal mode splitting g N (g= single atom coupling coefficent and N = number of atoms) in good agreement with our theoretical predictions. Regions of parameter space with very large degrees of squeezing (>20×) are identified. Preliminary extensions of the theory into a transient regime with (cavity lifetime) ≪ (interaction time) ≪ (atomic lifetime) are described.
A new regime for the generation of squeezed states of the electromagnetic field is described for a collection of atoms within a high-finesse cavity. The process responsible for squeezing is a coupling-induced splitting in the normal-mode structure of the atom-field system. A theoretical analysis is presented that predicts large degrees of squeezing for modest operating conditions. An experimental investigation of this regime has produced noise reductions of 30% relative to the vacuum noise level.
Optical bistability is reexamined as a candidate system for the generation of squeezed states of light. Previous analyses have concluded that significant squeezing can be achieved only in a rather extreme range of parameter space relative to current experimental capabilities and only over a restricted range of frequencies near the carrier.1 By contrast we have identified a new regime in which appreciable squeezing should be obtainable for rather modest operating conditions and without excessive demands on the stability of external control parameters. Following the treatment by Carmichael,2 we have conducted a theoretical search for optimal squeezing in optical bistability in the general case without adiabatic elimination of atomic or cavity variables. Our analysis is based on a linearization of the generalized Fokker-Planck equation for a system of N atoms coupled to a single mode of a high finesse cavity. For comparable atomic and cavity decay rates, there is a mode splitting in the eigenvalue structure of the system which is responsible for the vacuum field Rabi splitting. It is near the spectral features associated with these vacuum field Rabi sidebands that we find significant squeezing. The concepts of optimum squeezing as indicated by Mandel's Q parameter and by the spectrum of squeezing are discussed with reference to the various operating regimes in optical bistability.
Squeezed states of the electromagnetic field are generated by degenerate parametric downconversion in a sub-threshold optical parametric oscillator. Reductions in photocurrent noise greater than 60% (−4 dB) below the limit set by the vacuum fluctuations of the field are observed in a balanced homodyne detector. A quantitative comparison with theory suggests that the observed noise reductions result from a field that in the absence of avoidable linear attenuation would be squeezed more than tenfold. A degree of squeezing of approximately fivefold is inferred for the actual field emitted through one mirror of the optical parametric oscillator. An explicit demonstration of the Heisenberg uncertainty principle for the electromagnetic field is made from the measurements, which show that the field state produced by the downconversion process is a state of minimum uncertainty.
We have generated squeezed states of light by the process of second harmonic conversion within an optical cavity resonant at both fundamental and harmonic frequencies. The experiment consists of a standing-wave cavity containing a crystal of lithium niobate doped with magnesium oxide and driven by the field from a frequency-stabilized Nd:YAG laser (incident power, ~10 mW). The total field reflected from the cavity illuminates a pair of high quantum efficiency photodiodes, whose individual photocurrents are summed. Observations of squeezing are made by analyzing the spectral density of fluctuations for this sum photo-current while the cavity detuning is scanned through resonance. An intensity regulator holds the reflected light intensity constant during the scan by control of the incident light level. Reductions in photocurrent fluctuations of 12% relative to the vacuum-state or shot-noise level are achieved for frequency offsets near 4 MHz. Since significantly higher degrees of squeezing are predicted by our theoretical analysis, we discuss those processes that currently limit the observed noise reduction, including phase noise produced by the intracavity crystal in the absence of nonlinear conversion.