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Quantum-noise theory of atomic coherence phenomena

Klaus M. Gheri

Published May 8, 1994• 0 citations
OpenAlex

Abstract

The interaction of light with atomic media, i.e., media describable as an ensemble of free particles, can be used to alter the quantum statistics of the interacting light field. Nonlinear effects present in such an interaction are rather weak unless the light is tuned dose to resonance with a transition between two atomic energy eigenstates. Although semiclassical optical effects are now enhanced, the desired changes to the quantum statistics are normally washed out by atomic noise from absorption and spontaneous emission. Tuning away from resonance turns off nonlinearities faster than it turns off absorption.

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The interaction of light with atomic media, i.e., media describable as an ensemble of free particles, can be used to alter the quantum statistics of the interacting light field. Nonlinear effects present in such an interaction are rather weak unless the light is tuned dose to resonance with a transition between two atomic energy eigenstates. Although semiclassical optical effects are now enhanced, the desired changes to the quantum statistics are normally washed out by atomic noise from absorption and spontaneous emission. Tuning away from resonance turns off nonlinearities faster than it turns off absorption.
Enhanced nonlinear optical response of a coherent atomic medium is the basis for many atomic sensors, and their performance is ultimately limited by the quantum fluctuations of the optical readout. Here we demonstrate that the off-resonant interactions, with the aid of the near-resonant process, can significantly modify the quantum noise of a coherent light field, even when its effect on the mean signal is negligible. The altered quantum optical noise distribution results in excess noise in the measurement quantity. We illustrate this concept by using an atomic magnetometer based on the nonlinear Faraday effect. These results show the existence of previously unnoticed factors in fundamental limitations in atomic magnetometry and could have impact in a wide range of atom-light--based precision measurements.
The coherence and directional properties of stimulated and spontaneous emission can be understood without a knowledge of quantum electrodynamics. This paper presents a semiclassical description of the interaction between a free atom and a weak optical field under conditions of either a stimulated emission or a stimulated absorption resonance. It is shown that, under certain conditions, the stimulated or spontaneous radiation fields emitted from a sample of atoms will propagate in the same direction as the incident beam, will be coherent with the incident beam, and will have the correct phase to provide amplification or attenuation.
A quantum statistical theory of resonant optical phenomena is developed for the case when the fluctuations of the laser, used for exciting transitions, are important. The general equations describing the dynamics of a relaxing two-level atom (TLA) are solved exactly for different types of mean values and the two-time amplitude and intensity correlations. The phase-diffusion model is adopted for laser fluctuations. The exact results are used to analyze the effect of laser fluctuations on a number of optical effects-optical free-induction decay, adiabatic following, the spectrum of the scattered light from a relaxing TLA, the energy-absorption spectrum from a weak field, Hanle resonances, etc. In each case, the laser fluctuations are found to affect in an important way the characteristics of the above optical-resonance phenomena. For example, the spectrum of scattered radiation from a TLA has the usual three-peak structure for fields at resonance and with strengths $\ensuremath{\alpha}$ above the threshold and for $\ensuremath{\alpha}\ensuremath{\gg}{\ensuremath{\gamma}}_{c}$; however, now the peak heights (widths) are in the ratio 3x3x3x (23x\frac{2}{3x}3x2​), $x=\frac{[{\ensuremath{\gamma}}_{c}+\frac{({T}_{1}^{\ensuremath{-}1}+{T}_{2}^{\ensuremath{-}1})}{3}]}{[2{\ensuremath{\gamma}}_{c}+{T}_{2}^{\ensuremath{-}1}]}$, where ${\ensuremath{\gamma}}_{c}^{\ensuremath{-}1}$ is the correlation time for laser phase fluctuations. For ${\ensuremath{\gamma}}_{c}\ensuremath{\gg}\ensuremath{\alpha}$, one gets a single-peak spectrum. The laser field is treated as a second-quantized field with excitation in either a coherent state or a Fock state. The results, obtained by straightforward perturbation theory, but valid for arbitrary values of the relaxation parameters, detuning, and the laser correlation time, are also presented.
We show that \ensuremath{\Lambda} three-level atoms interacting with two coherent light fields tuned close to two-photon or dark resonance behave as a saturable dispersive nonlinearity. If one of the light fields is allowed to resonate within an optical cavity the quantum noise in a quadrature of the output light can be almost completely suppressed. As no dynamic retuning of the cavity is required to achieve noise reduction and cold atomic media are readily available in traps which conform in essence to the proposed configuration, an experimental realization would seem within reach.
Quantum interference and coherence lead to many interesting phenomenon and applications in quantum optics. In this dissertation, we study the quantum coherent properties in the following systems and aspects. We first investigate the optical bistability in a combined cavity-cold atoms system. In such a system the atom-photon interaction provides an optical lattice to the atoms and affects the mechanical motion of the atoms while atoms induce a position dependent phase shift on the cavity field. This highly nonlinearity induces optical bistability of intra-cavity photon number with respect to the pumping light added along the cavity axis. We show that the presence of this bistability can be controlled by a second pumping field added perpendicular to the cavity axis. It is also found that the critical input intensity of switching from one branch of bistability to the other depends on the the way of the field being added. This behavior is similar to the anomalous switching of the dispersive optical bistability of atomic media in the cavity. We also study the effect of counter-rotating terms in the control of spontaneous emission. We make use of a unitary transformation method and investigate the effect of dynamic energy shifts on the spontaneous emission modification via quantum interference in a four-level atomic system. We show that the counter-rotating terms, which are normally neglected in the usual investigation of atomic systems, do produce a significant influence on the evolution of the atomic amplitudes and the emission spectrum. This effect of counter-rotating terms can be observed in the time scale of the decay rate even when the dipole moments of the two upper levels are orthogonal to each other. The effect of counter-rotating terms on the spontaneous emission in a 3-D anisotropic photonic crystal is also discussed. It is shown that the behavior of the emission is similar to the case making rotating wave approximation, i.e., the localized and propagating fields are also separated by two characteristic atomic transition frequencies. However, the two characteristic frequencies are shifted due to the full Lamb shift which is obtained with counter-rotating terms being included in the Hamiltonian. We also utilize the unitary transformation method to show how the Lamb shift in a multi-level atom can be controlled by a driving field. Finally, we propose a subwavelength atom localization scheme for an atom located in a standing-wave field. The strategy is based on the observation that the photon statistics of resonance fluorescence depends on the position-dependent Rabi frequency.
The control of the optical properties of a medium by atomic coherence and quantum interference effects is an important area of research, not only for its fundamental aspects in the understanding of radiation and matter interaction, but also for its potential applications in the design of optical devices. Atomic coherence can emerge in a medium through the coupling of a strong coherent field to an atomic transition. This coupling affects the optical properties of the medium in a very interesting ways. For example, it may yield light amplification without population inversion. Also, it can modify the traditional dispersion of an optical medium in such a way that maximum variations of the refractive index occur around a spectral region of vanishing absorption. In the first part of this work we investigate some fundamental aspects of this coherent dynamics. We investigate how this non-inversion gain is affected by the presence of atomic motion. The coherent interaction between atom and radiation can lead to the interference between optical paths of decay. We report on an atomic setting where the interference structures depend upon the phase of the coherent field, an new effect which is absent in other resonance fluorescent phenomena. As a potential application, we investigate a novel approach for the modulation of optical signal. This approach consists of injecting atomic coherence in the medium in order to tailor its optical properties so it is a more suitable medium for modulation.