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Physical Review A

Time-dependent spectrum of resonance fluorescence for atoms prepared in pure dressed states

Ning Lü, P. R. Berman, Yue Bai, J. E. Golub, THOMAS W. MOSSBERG

Published Jul 1, 1986• 22 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.34.319

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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.
Time-dependent features of the fluorescence radiation from a strongly driven three-level atom in a Raman configuration are studied applying the Eberly-W\'odkiewicz counting-rate definition of the spectrum. Using our earlier formalism, where we assume that one or both of the driving fields are intense, we obtain analytical expressions for the time-dependent fluorescence spectra. We have also studied the influence on the transient spectrum of the initial preparation of the atom in three different dressed states.
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.
A study is presented for the time-dependent resonance-fluorescence spectrum of two-level atoms irradiated by hyperbolic-secant pulsed lasers, allowing for an arbitrary spontaneous-emission rate from the excited level to the ground level. Novel features of the temporally transient spectrum have been observed. The spectrum is dominated by a central peak which oscillates in time and is accompanied by multiple side peaks. Asymptotically (i.e., after the pulse has passed) the side peaks disappear, leaving a tail at the line center which displays a Lorentzian shape of width equal to the sum of the spontaneous-emission rate and the width of the spectrometer considered and of magnitude proportional to the instantaneous intensity of the pulse. The exact behavior of the spectrum is dictated by the area of the engaged pulse and by how the atom is prepared initially. In particular, it is found that the spectrum can be asymmetric even when the laser is tuned to exact resonance if the atoms are initially prepared in a certain class of proper coherent states, irrespective of how the field amplitude may vary in time. An analysis of the spectral symmetry without resorting to any explicit evaluation of the spectrum itself is also presented. Furthermore, the associated optical Bloch equations are solved analytically in terms of hypergeometric functions in a similar manner to that done previously for the undamped two-level Schr\"odinger equation. Specific numerical results are presented for pulses of area equal to \ensuremath{\pi}, 2\ensuremath{\pi}, 3\ensuremath{\pi}, 4\ensuremath{\pi}, and 5\ensuremath{\pi} for both symmetric and asymmetric cases.
We analyze the transient probe spectra that arise when a three-level atom is strongly driven by an optical field nearly resonant with one transition and is probed by a step-function weak field on a coupled transition. We pay particular attention to the effect of imbalances in the initial dressed-state populations on the observed spectra. As recently pointed out, such imbalances may be induced by sudden changes in the phase of the driving field. We find that transient probe spectra may differ dramatically for different initial atomic conditions. We follow the temporal relaxation of these novel probe spectra to their steady-state form. Our calculations do not include the effect of inhomogeneous broadening and are hence appropriate to studies of collimated atomic beams.
We compute the time-dependent spectrum of fluorescence by two-level atoms after a strong resonant exciting laser pulse is turned off abruptly. The behavior of the "delayed" three-peaked spectrum is shown to be dependent on the natural lifetime of the upper state and on the bandwidth of the interferometer used in the measurement. A prompt increase in the central-peak intensity and an oscillating decay in the two side peaks are predicted to occur immediately after the laser is turned off. These are manifestations of the "undressing" of the atomic states. Our calculation permits consideration of the question of the speed of the undressing and its observation.
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.