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Soviet Journal of Quantum Electronics

Measurement of the emission and absorption spectra of strongly driven two-level atoms

Shaoul Ezekiel, F Y Wu

Published Aug 31, 1978• 5 citations
Publisher

Abstract

An investigation was made of the resonance fluorescence and absorption spectra of sodium atoms [corresponding to the 3 2 S 1/2 ( F =2)–3 2 P 3/2 ( F' =3) transition] excited by a strong monochromatic field, as well as by combinations of strong and tunable fields. The experimental results obtained were found to be in good agreement with the theoretical predictions.

DOI
10.1070/qe1978v008n08abeh010640

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Physical Review A•Dec 1, 1998•13 citations
An investigation was made of the resonance fluorescence and absorption spectra of sodium atoms [corresponding to the 3 2 S 1/2 ( F =2)–3 2 P 3/2 ( F' =3) transition] excited by a strong monochromatic field, as well as by combinations of strong and tunable fields. The experimental results obtained were found to be in good agreement with the theoretical predictions.
We have made measurements of the spectrum of resonance fluorescence emitted by sodium atoms in an intense, uniform, monochromatic field. The transition used in the experiment was between the 32S123^{2}S_{\frac{1}{2}}32S21​​ (F=2F=2F=2, mF=2{m}_{F}=2mF​=2) ground state and the 32P323^{2}P_{\frac{3}{2}}32P23​​ (${F}^{\ensuremath{'}}=3$, ${m}_{F}^{\ensuremath{'}}=3$) excited state. A separate light beam, circularly polarized and resonant with this transition, was used to prepare the sodium atoms in the F=2F=2F=2, mF=2{m}_{F}=2mF​=2 magnetic sublevel. This pumping scheme was used to obtain the spectrum for both on- and off-resonance excitations. The measurements are in good agreement with Mollow's calculation. In addition, we describe conditions under which we observed asymmetric spectra similar to those of earlier experiments.
We identify discrepancies between two published predictions of the resonance fluorescence from a two-level atom driven by a strong bichromatic field [J. Opt. Soc. Am. B 8,8,8, 1163 (1991) and Phys. Rev. A 48,48,48, 3092 (1993)]. These discrepancies are shown to arise from subtleties in extracting the time-averaged resonance fluorescence from the expansions used to solve the optical Bloch equations. We construct a solution to these equations that corrects the results of the latter reference and reconciles the two predictions.
We report the observation of optical amplification in a two-level atomic system driven by a strong, resonant field. By exciting an atomic beam of two-level sodium atoms simultaneously with a strong, fixed-frequency driving field and a weak, tunable, probe field, we have measured the absorption (amplification) line-shape function for several values of driving field strength. In addition, we have verified theoretical predictions that higher amplification is obtained when the strong field is detuned from exact resonance.
We examine the radiative properties of a two-level atom driven by a strong bichromatic field with frequencies ${\mathrm{\ensuremath{\omega}}}_{1}$=${\mathrm{\ensuremath{\omega}}}_{0}$-${\mathrm{\ensuremath{\delta}}}_{1}$ and ${\mathrm{\ensuremath{\omega}}}_{2}$=${\mathrm{\ensuremath{\omega}}}_{0}$+${\mathrm{\ensuremath{\delta}}}_{2}$, which can be asymmetrically placed about the atomic transition frequency ${\mathrm{\ensuremath{\omega}}}_{0}$ and can have different Rabi frequencies ${\mathrm{\ensuremath{\Omega}}}_{1}$ and ${\mathrm{\ensuremath{\Omega}}}_{2}$. Applying the optical Bloch equations for the bichromatic excitation, we derive an infinite set of equations of motion for the time evolution of the atomic variables. The equations are solved numerically by matrix inversion and Laplace transforms. Using the quantum regression theorem, we then solve for the steady-state total fluorescence intensity, and the resonance-fluorescence and absorption spectra. The spectra are found to depend on the frequency difference 2\ensuremath{\delta}=${\mathrm{\ensuremath{\delta}}}_{1}$+${\mathrm{\ensuremath{\delta}}}_{2}$, the average detuning \ensuremath{\Delta}=${\mathrm{\ensuremath{\omega}}}_{0}$-1/2(${\mathrm{\ensuremath{\omega}}}_{1}$+${\mathrm{\ensuremath{\omega}}}_{2}$), and the Rabi frequencies of the driving fields. For ${\mathrm{\ensuremath{\Omega}}}_{1}$=${\mathrm{\ensuremath{\Omega}}}_{2}$=\ensuremath{\Omega}, the total fluorescent intensity displays a series of maxima for \ensuremath{\Delta}=\ifmmode\pm\else\textpm\fi{}n\ensuremath{\delta}\ensuremath{\mp}${\mathrm{\ensuremath{\Omega}}}^{2}$/4\ensuremath{\delta}, where the n are the odd integers. The intensity-dependent shift from the resonances n\ensuremath{\delta} is explained as an analog of the generalized Bloch-Siegert shift. The resonance-fluorescence spectrum for \ensuremath{\Delta}\ensuremath{\ne}0 appears to contain more peaks than that for \ensuremath{\Delta}=0.This is due to the splitting of the central peak and the even sidebands into doublets. The absorption spectrum of a weak-probe beam for \ensuremath{\Delta}=0 and equal Rabi frequencies consists of a symmetric series of dispersionlike sidebands separated from ${\mathrm{\ensuremath{\omega}}}_{0}$ by integer multiples of \ensuremath{\delta}, together with a central absorption peak at ${\mathrm{\ensuremath{\omega}}}_{0}$, whose amplitude oscillates with \ensuremath{\Omega}. For \ensuremath{\Delta}\ensuremath{\ne}0 and/or ${\mathrm{\ensuremath{\Omega}}}_{1}$\ensuremath{\ne}${\mathrm{\ensuremath{\Omega}}}_{2}$, the odd sidebands remain dispersionlike, while the central peak and the even sidebands split into absorption-emission doublets. A simple physical interpretation of the spectral features is given in terms of the dressed-atom model.
The steady-state populations, the fluorescent intensity-intensity correlation function, and the resonance fluorescence and absorption spectra of a two-level atom bichromatically driven by a strong, coherent field and a weak, stochastic field with tunable carrier frequency and wide bandwidth are investigated analytically. Surprisingly, the population is inverted if the stochastic field is appropriately detuned from the coherent field, which is assumed resonant with the atomic transition. The resonance fluorescence spectrum still displays a three-peaked structure, but with linewidths and heights that depend upon the frequency and bandwidth of the stochastic field as well as the intensities of both fields. Asymmetric fluorescence spectra are found when the coherent field is detuned from the atomic resonance frequency. The intensity-intensity correlation function varies dramatically with the carrier frequency of the stochastic field. For appropriate choices of the parameters, the fluorescent emission of the atom is antibunched for all time. The absorption spectral features also deviate significantly from those of the monochromatically driven atom. By appropriately tuning the stochastic field, one finds that a sharp peak (absorption) or hole (gain) can occur at line center and the probe beam can be amplified at either the lower-frequency Rabi sideband or the higher-frequency sideband and the inversionless gain can be enhanced.