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The Journal of Chemical Physics

Noise spectroscopy of randomly modulated atoms

Gautam Vemuri

Published Dec 1, 2001• 2 citations
Publisher

Abstract

The coupling between a chromophore and its surroundings can, in the event of environmental perturbations, result in a stochastic modulation of the chromophore’s transition frequency, which in turn can cause fluctuations in the population of the excited state. We demonstrate that by using these fluctuations in population inversion as the spectroscopic variable, one can extract information on whether the random modulation of the chromophore follows a diffusion process or a jump process. The population fluctuations also discriminate between Markov and non-Markov fluctuations of the atomic frequency. In addition, we show that this observable allows, in certain regimes, to unambiguously determine whether the population fluctuations are due to atomic frequency noise, or due to noise in the irradiating laser field. Finally, through a dressed state analysis, we demonstrate that the response of a randomly modulated atom is similar to that of an unmodulated atom driven by a noisy field that has amplitude fluctuations in only one quadrature.

DOI
10.1063/1.1416869

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The coupling between a chromophore and its surroundings can, in the event of environmental perturbations, result in a stochastic modulation of the chromophore’s transition frequency, which in turn can cause fluctuations in the population of the excited state. We demonstrate that by using these fluctuations in population inversion as the spectroscopic variable, one can extract information on whether the random modulation of the chromophore follows a diffusion process or a jump process. The population fluctuations also discriminate between Markov and non-Markov fluctuations of the atomic frequency. In addition, we show that this observable allows, in certain regimes, to unambiguously determine whether the population fluctuations are due to atomic frequency noise, or due to noise in the irradiating laser field. Finally, through a dressed state analysis, we demonstrate that the response of a randomly modulated atom is similar to that of an unmodulated atom driven by a noisy field that has amplitude fluctuations in only one quadrature.
The effect of environmental perturbations on a system of two-level atoms is to alter the coupling between the atoms and their surroundings, which manifests itself as a change in the relaxation rates of the atoms. One of the ways in which environmental fluctuations can affect an atom is to modulate its transition frequency in a stochastic manner. We study the response of such two-level atoms to irradiation by a monochromatic laser, and report the results of numerical experiments on the spectrum of scattered light. It is observed that this spectrum is a sensitive indicator of the parameters that describe the stochastic modulation. In addition, the spectra exhibit substantially different features depending on whether the stochastic process follows a diffusion or a jump mechanism. The numerical results are based on a Monte Carlo procedure, which can be applied to stochastic processes in a wide variety of biological, chemical, and physical processes.
We investigate nonlinear wave mixing in two-level atoms wherein, using a dressed state formalism, it is shown that the signal arises as a consequence of quantum interference between relevant probability amplitudes for photon emission. We then report a theoretical study of the modifications that are induced in the four-wave mixing signals when the transition frequency of the atoms is stochastically modulated. Such modulations, which arise from perturbations in the immediate environment of the atoms, are shown to cause significant alterations in the nonlinear response of the atoms. We also describe how one can, via an investigation of the four-wave mixing signal, differentiate between Markov and non-Markov fluctuations in the transition frequency of the two-level system. The calculations rely on a recently developed Monte Carlo procedure that can be used to obtain exact solutions to a wide variety of spectroscopic problems, with minimal restrictions on atom, field, and noise parameters.
Significant fluctuations, above the shot-noise limit, have been observed in the intensity of fluorescent light scattered from atoms excited by an intense noisy laser, where a central role is played by the nonlinearity of the atom-field interaction. By considering the variance of the atomic populations, we show that ``noise spectroscopy'' is sensitive to the field statistics of the laser. We specifically consider the cases of resonance fluorescence (analogous in the weak-field limit to analysis by a Fabry-P\'erot interferometer), two-photon excitation, and double optical resonance for variable laser intensity and bandwidth. We show that large differences in the ``noise'' spectra can occur between lasers characterized by a phase-diffusion or a phase-jump model, although these models would give the same values for the mean atomic populations. We believe that observation of population fluctuations can become a useful method for characterizing laser noise.
We present a continuation of a general theoretical approach to noisy laser-atom interactions based on a special Markov-chain description of external fluctuations. This chain, composed of n independent two-state jump processes, forms a non-Gaussian stochastic process from which a detailed discussion of the atomic response can be given. We show that the n-component Markov chain also has the property of pre-Gaussian noise, because in the limit of n → ∞ it converges to a Gaussian stochastic process. We exhibit solutions for the field spectrum and the atomic-fluorescence spectrum for phase, frequency, and amplitude pre-Gaussian fluctuations of the driving-laser light.
It is well known that a field's quantum noise can have a profound effect on the fluctuations of laser-induced fluorescence (LIF). However, though previous studies have led to a good understanding of this process in the case of stationary fields, many of the important applications of LIF employ some form of laser modulation, yielding a field of nonstationary stochastic character. Here, we discuss the results from numerical experiments that examine the influence of a nonstationary field on the LIF noise. Specifically, we consider a phase-diffusion field and LIF from a beam of alkali-metal-like atoms with ground and excited-state Zeeman splitting when the field undergoes deterministic frequency modulation. Our computational results show that deterministic modulation at high Fourier frequencies (i.e., 10 MHz) can significantly increase the LIF noise at low Fourier frequencies (e.g., 1 Hz), and that the amount of LIF noise amplification depends on a complicated interplay among the laser's linewidth, the modulation frequency, the modulation index, and the multilevel atomic system's energy-level spacing. Interestingly, we find that certain values of the atom's Zeeman splitting significantly decrease the magnitude of LIF noise.
This paper analyses the extraction of spectroscopic information on an atom via use of field fluctuations in a diode laser, wherein the statistics of diode-laser radiation are modeled by a phase-diffusion process. Using Monte Carlo methods, we solve density-matrix equations for a three-level V system, driven by this fluctuating field, tuned approximately to the two allowed transitions. The model is very general and allows us to incorporate arbitrary field strengths and bandwidths. We suggest two different signal detection schemes, each of which provides insight into different aspects of the energy-level structure in an atomic sample. Specifically, if intensity fluctuations in the field radiated from the sample are spectrally analyzed, via a homodyne technique, one can isolate contributions that are linear and quadratic in the radiated field, and these reveal resonances at the allowed transition frequencies of the atom. If we employ direct detection instead of the homodyne method, then the crossover transition is also revealed in the signal. The strengths of these resonances are very sensitive to the bandwidth of the field fluctuations, as well as the details of the field statistics. We also discuss the role of Stark shifts at higher intensities.