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Physical Review A

Diode-laser-noise-based spectroscopy of allowed and crossover resonances

Kashyap V. Vasavada, Gautam Vemuri, G. S. Agarwal

Published Nov 1, 1995• 12 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.52.4159

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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.
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 have investigated theoretically the possibility of employing noisy laser fields for spectroscopic purposes. The basis for this spectroscopy is a modification of the statistic of the fluctuations caused by the nonlinear interaction. All atomic resonances within the range of several bandwidths can be observed in the power spectrum, even in case of large inhomogeneous broadening. We have derived analytical, nonperturbative results for a real Gaussian, a complex Gaussian, and a phase-diffusing field. The mean transmitted intensity and its variance as well as the power spectrum have been evaluated in the limit of weak absorption for two-level systems. Without modification, we can apply our results also to other transition schemes. As an example, the power spectrum of the D2{\mathit{D}}_{2}D2​ transition of 133Cs^{133}\mathrm{Cs}133Cs driven by a phase-diffusing field is calculated. For this four-level system we find qualitative agreement with experimental results by Yabuzaki et al. [Phys. Rev. Lett. 67, 2453 (1991)].
There has been much interest in the influence of the laser noise on the atomic system. So far theoretical works have been performed on calculation of the mean values and the variance of the fluctuated atomic populations, and verified through observation of the fluctuating resonance fluorescence from the atomic vapors. Yabuzaki et al. have observed the excess intensity noise of the resonant light from a diode laser propagated through alkali atomic vapor. They have measured the intensity power spectrum of the light when the laser was tuned near the D2 line of Cs and observed all corresponding hyperfine-splitting resonances in the excited state and Zeeman splitting resonances within a hyperfine level of the ground state. Walser et al. have theoretically studied the intensity fluctuation of laser light propagated through a weakly absorbing medium. The calculated power spectrum of a phase-diffusing field has been found qualitative agreement with the experimental results by Yabuzaki et al. on hyperfine-splitting resonances. Recently, Mitsui has reported a new type of noise spectroscopy with a highly stabilized diode laser. He has investigated the spontaneous noise appeared in optical detection of magnetic resonance of Rb atoms. In this note we report the first observation of hyperfine spectra in the ground state of K and K appearing as the intensity fluctuation at hyperfine splittings of 462MHz and 254MHz of circularly polarized light from a diode laser transmitted through a sample cell. We have also observed the Zeeman hyperfine spectra of K in a static magnetic field. We show that the spectra are strongly dependent of the direction of the static magnetic field. Their splittings as functions of the strength of static magnetic field are compared with the Breit–Rabi formula. The experimental apparatus is quite simple as shown in Fig. 1. The diode laser used was an ordinary Fabry–Perot type with output power of 5mW, operating near the D1 line (769.9 nm) of K atoms. The output of the laser was circularly polarized and applied to a cell containing K vapor at a temperature 90 C, corresponding atomic density to be about 1:15 10 cm 3. The transmitted light was detected by an avalanche photo-diode having frequency response up to 1GHz. The output of the photo-diode was applied to a rf frequency analyzer to obtain the power spectrum of the fluctuation of the transmitted light intensity. A static magnetic field is provided by two pairs of Helmholtz coils mutually perpendicular and about 90 cm in diameter. The strength of the magnetic field is calibrated by using magnetic resonance signals of optically pumped Rb atoms. Figure 2 shows the frequency spectrum of the intensity fluctuation of transmitted light observed when the laser was tuned to the transition from the state F 1⁄4 1 in the ground state to the state F0 1⁄4 1 in the excited state by adjusting the driving current of the laser diode. Sharp resonance signals can be seen at the hyperfine splittings of K and K, 462 and 254MHz, respectively, on the background of broad noise spectrum. When a weak static magnetic field H0 is applied to the K vapor, the hyperfine spectra of K splits into several lines (the effective gyro-magnetic ratio of K is known to be 1⁄4 2 700 kHz/G). Figures 3(a) and 3(b) show the observed Zeeman hyperfine spectra of K for
A three-level cascade system coupled to two pulsed, fluctuating multimode laser fields is studied with numerical Monte Carlo simulations. Laser noise is modeled by introducing abrupt, random variations into the field parameters. We show that both phase and amplitude fluctuations may increase the signal through the ac Stark effect, and we demonstrate how noise can change the whole spectral structure of the transitions. As a result that is conveniently produced with simulations but that is often difficult to attain analytically, we also present on- and off-resonance signal distributions at various saturation levels and in different noise scenarios.
We explore the use of degenerate four-wave-mixing (DFWM) intensity noise fluctuations as a spectroscopic tool for the study of atomic dynamics. Experimental results obtained from the spectral analysis of the intensity noise of the DFWM signal produced by a free running diode laser in a rubidium vapor cell are presented. For low exciting field intensities, the spectra are single peaked with a linewidth comparable to the atomic natural linewidth while at higher intensities a structure devleops revealing the existence of a dynamic Stark effect. The results are compared with numerical simulations of the power spectrum of the DFWM signal produced by a phase-diffusing field incident on two-level atoms.
We have investigated theoretically the applicability of phase-fluctuating laser fields in saturated absorption spectroscopy. The fluctuations of pump and probe fields are fully correlated if they are derived from the same laser source. Inside the saturable medium, phase fluctuations are converted into intensity noise. This nonlinear mixing modifies the statistics of the transmitted fields. By measuring higher-order correlations one can deduce additional spectroscopic information. Apart from the mean intensity, we have examined the intensity noise and intensity power spectrum of the weak probe field. The resonances of these correlation functions are also unaffected by large inhomogeneous broadening since they are inherently related to the usual saturated absorption dip. We find qualitative agreement with results of a recent experiment employing this technique [D. H. McIntyre et al., Opt. Lett. 18, 1816 (1993)], which demonstrates the advantages of noise spectroscopy using spectrum analyzers.