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Physical Review Letters

Transient spectra of strong-field resonance fluorescence

J. E. Golub, THOMAS W. MOSSBERG

Published Nov 9, 1987• 28 citations
Publisher

Abstract

Working with a beam of two-level--atom--like $^{174}\mathrm{Yb}$, we have measured the temporal evolution of strong-field resonance fluorescence spectra during square-pulse excitation. In the case of resonant excitation, it is found that driving-field phase shifts transform the normal three-peaked Mollow spectrum into a transient doublet spectrum asymmetric with respect to the atomic transition frequency. This qualitatively new type of spectrum provides fundamental insight into the connection between atomic dynamics and spectra, and results from a nearly perfect polarization of the dressed atom-field states.

DOI
10.1103/physrevlett.59.2149

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Working with a beam of two-level--atom--like 174Yb^{174}\mathrm{Yb}174Yb, we have measured the temporal evolution of strong-field resonance fluorescence spectra during square-pulse excitation. In the case of resonant excitation, it is found that driving-field phase shifts transform the normal three-peaked Mollow spectrum into a transient doublet spectrum asymmetric with respect to the atomic transition frequency. This qualitatively new type of spectrum provides fundamental insight into the connection between atomic dynamics and spectra, and results from a nearly perfect polarization of the dressed atom-field states.
We study the transient fluorescence spectra of two-level atoms driven by a strong optical field when the atoms are initially prepared in pure dressed states of the atom-field Hamiltonian. Spectra obtained here differ qualitatively from those observed in the steady state. In the case of steady-state resonant excitation, a three-peaked spectrum symmetric about the laser frequency is obtained; with pure-dressed-state preparation, the symmetry of the spectrum about the driving field is broken---one side peak is initially enhanced and the other is initially suppressed. Furthermore, the temporal oscillations of fluorescence intensity observed in previous calculations of transient fluorescence spectra appropriate to atoms prepared in a superposition of dressed states [J. H. Eberly et al., J. Phys. B 13, 217 (1980)] are suppressed when pure-dressed-state preparation is considered.
Working with a beam of 174Yb^{174}\mathrm{Yb}174Yb, we have studied the temporal development of Autler-Townes spectra following switchon of a strong, resonant, driving field. The transient fluorescence spectra observed are dramatically different from those found in the steady state. We find that either member of the Autler-Townes doublet can be eliminated by an appropriate shift in the phase of the driving field, and that the spectral peaks can display interesting temporal oscillations. The observed behavior is interpreted in terms of atomic dynamics and a polarization of the dressed atom-field states.
We have measured the emission spectrum of two-level-like Ba atoms driven by a continuous-wave bichromatic field containing a strong resonant component and a weaker component detuned from atomic resonance by the strong-field Rabi frequency. With the specified detuning, the weak field resonantly drives a transition of the atom--strong-field dressed states. Observed spectra show that each peak of the normal (single-driving-field) resonance fluorescence triplet is split into three subpeaks separated by one-half the weak-field Rabi frequency. Also seen is another triplet of peaks displaced from the atomic resonance by twice the strong-field Rabi frequency. Splitting of the normal triplet peaks can be explained through weak-field dressing of the strong-field dressed states. The origin of the additional triplet is less transparent. Comparison with theory is made.
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.
Attention is focused on the dynamic evolution of the emission spectrum following abrupt excitation of a near-resonant two-level absorber by a strong laser field. The multiphoton character of the absorption-emission process is evident in the AC Stark splitting of the spectrum, which begins approximately half an atomic lifetime after excitation, if the laser field is strong enough. Analytic expressions for the spectra are given of arbitrary laser field strength, atomic lifetime, laser-atom detuning, and the bandwidth of the spectrometer used to analyse the spectrum. Selected graphs are included to illustrate various time-dependent features of the spectrum. The influence on the transient spectrum of three different states of atomic excitation prior to laser irradiation and the effect on the spectrum of irradiation by a phase-noisy laser are also considered. Comparison of the transient spectra from atoms initially prepared in ' pi /2' and '3 pi /2' states show clearly that phase relationships between the irradiating field and the emitting dipole are important even in fluorescence.
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.