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Nonlinear Optics

Excess Noise Introduced by Beam Propagation Through an Atomic Vapor

Martti Olavi Kauranen, Alexander L. Gaeta, William V. Davis, Robert W. Boyd

Published Jan 1, 1992• 0 citations
Publisher

Abstract

We propose and show experimental evidence of a mechanism that is important in reducing the amount of noise reduction that can be achieved at low (<100 MHz) frequencies utilizing atomic vapors as the nonlinear medium.1 The mechanism is based on the two-beam-coupling gain2 experienced by the vacuum sidebands of a weak probe wave as it interacts with a strong degenerate pump wave in an atomic vapor. The mechanism leads to the amplification of intensity fluctuations of an initially shot-noise-limited probe field.

DOI
10.1364/nlo.1992.pd10

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•Jan 1, 1989•0 citations
We propose and show experimental evidence of a mechanism that is important in reducing the amount of noise reduction that can be achieved at low (<100 MHz) frequencies utilizing atomic vapors as the nonlinear medium.1 The mechanism is based on the two-beam-coupling gain2 experienced by the vacuum sidebands of a weak probe wave as it interacts with a strong degenerate pump wave in an atomic vapor. The mechanism leads to the amplification of intensity fluctuations of an initially shot-noise-limited probe field.
We show both theoretically and experimentally that fluctuations of a weak probe beam are increased above the coherent-state shot-noise level as the beam interacts with a strong degenerate pump beam in an atomic vapor. The origin of this noise amplification process is the two-beam-coupling process between the pump beam and the vacuum sidebands of the probe beam. The major contribution to this excess noise arises from the quantum fluctuations of the atomic medium that are induced by the pump beam. We believe that this mechanism can be important in preventing the reduction of noise below the quantum-noise limit in experiments that utilize atomic vapors.
We have observed that a single laser beam that has propagated through an atomic potassium vapor can acquire excess noise. In particular, we find that even if the incident laser beam is shot noise limited, the transmitted laser beam contains noise in excess of its shot noise limit. We interpret this observation in terms of the amplification of vacuum sidemodes of the incident laser beam through forward four-wave mixing processes. These amplified sidebands then beat with the incident laser beam at the photodetector to create excess noise. The excess noise is maximum when the laser frequency is detuned from the potassium resonance by approximately one linewidth on either side of the resonance. We are presently developing a quantitative theoretical model to describe the process that produces this excess noise. We believe that this excess noise can degrade the noise properties of any nonlinear optical interaction that utilizes atomic vapors.
We have found that an intense shot-noise-limited laser beam tuned near the 4 2^{2}2S1/2{\mathit{S}}_{1/2}S1/2​\ensuremath{\leftrightarrows}4 2^{2}2P3/2{\mathit{P}}_{3/2}P3/2​ potassium resonance transition acquires excess noise after passing through an atomic-potassium vapor cell. The noise is maximum for laser detunings of approximately \ifmmode\pm\else\textpm\fi{}1 GHz and falls to nearly the shot-noise limit for detunings greater than \ifmmode\pm\else\textpm\fi{}3 GHz. We describe the production of this noise in terms of a forward four-wave mixing process involving the laser field and its side modes, which are initially in the vacuum state. We present a fully quantum-mechanical theory of forward four-wave mixing in a system of two-level atoms and use it to predict the noise properties of the transmitted laser beam. The predictions of this theory are in good agreement with the experimental data.
We investigate theoretically the noise properties of the amplification of a weak probe beam in an atomic vapor pumped by an intense nearly resonant pump field. For the case of gain via the three-photon effect, we find that only in the limit in which collisional broadening is absent can the system operate as an ideal quantum-noise limited optical amplifier for the probe wave. For the case of gain via stimulated Rayleight scattering, we find that the minimum noise figure is four times that of an ideal optical amplifier, and that it occurs when the atomic system is predominantly collisionally broadened.
We present the results of an experimental and theoretical study of the gain experienced by a weak probe beam propagating through a sodium vapor in the presence of an intense pump field that is nearly resonant with the 3s→3p atomic transition. This interaction provides a means by which the outputs of two lasers can be combined coherently. The probe transmission spectrum is comprised of three distinct features, two of which result in amplification of the probe wave. The origin of these features can be traced to the modification of the atomic level structure by the ac Stark effect. The experimentally measured spectra are in good agreement with the predictions of a theoretical model based on the solution of the density-matrix equations of motion for a two-level atom and including the effects of Doppler broadening. The dependence of the induced gain on the pressure of a helium buffer gas has been measured and is in good agreement with the predictions of theory. The maximum gain observed in these experiments occurs at one of the Rabi sidebands and leads to a 38-fold increase in the intensity of the probe wave.
Two spectral regions of gain exist for a weak probe beam propagating through a medium of two-level-atoms pumped by a strong near-resonance field. Experimentally a cw ring-dye laser is used to explore this gain at the Na D₂ resonance in a vapor. Plane-wave calculations of probe-gain spectra which include the Doppler broadening inherent in a vapor agree well with experimental spectra obtained with a Fabry-Perot interferometer. Such two-beam-coupling gain might have applications as optical pre- or power amplifiers. The gain is also the primary step in four-wave-mixing. Mixing of the pump and sideband which experiences gain produces the medium polarization from which the fourth-wave arises. For phase-matched propagation the fourth-wave, which is at a frequency that experiences little or negative probe-gain (i.e., absorption), grows at nearly the same rate as the primary sideband. Together the two sidebands extract far more than twice as much energy from the pump than does the primary sideband acting alone. Experimentally four-wave-mixing which arises from noise at the gain-sideband-frequency is sometimes accompanied by conical emission at the fourth-wave sideband. Since this sideband is also seen on axis the explanation cannot be simply phase-matching. Simulations which include the full transverse nature of the experiment are currently running on a CRAY supercomputer. These simulations indicate that the radial variation of the medium index of refraction is responsible for conical emission.