We report our results on measurement of the total fluorescent power radiated by two-level atoms excited by a 100% amplitude modulated or bichromatic laser field. For the case of single-frequency excitation, it is well known that the total fluorescent power monotonically saturates as the intensity of the field is increased. This occurs because the inversion of the atoms approaches zero at high field strengths. In contrast, when the field is bichromatic the total fluorescent power displays resonant peaks as the strength of the driving field is increased. This occurs because there is enhanced absorption when the modulation frequency coincides with the Rabi freqeuncy or one of its subharmonics.
We report our results on measurement of the total fluorescent power radiated by two-level atoms excited by a 100% amplitude modulated or bichromatic laser field. For the case of single-frequency excitation, it is well known that the total fluorescent power monotonically saturates as the intensity of the field is increased. This occurs because the inversion of the atoms approaches zero at high field strengths. In contrast, when the field is bichromatic the total fluorescent power displays resonant peaks as the strength of the driving field is increased. This occurs because there is enhanced absorption when the modulation frequency coincides with the Rabi freqeuncy or one of its subharmonics.
For pt.I see ibid., vol.12, no.12, p.1939 (1979). The modulated fluorescence in an optical double resonance experiment, i.e. when an atom interacts with two intense monochromatic laser beams each of which is weakly modulated in amplitude at frequency Omega , is studied in detail. The modulation rate corresponding to the steady-state population of the highest atomic level exhibits resonant structures at the modulation frequencies Omega =0, +or- alpha 0 , +or-2 alpha 0 due to the dynamical Stark splitting of the various energy levels; alpha 0 being related to the Rabi frequencies alpha 1 and alpha 2 associated with the two lasers and the two atomic transitions, by alpha 0 2 = mod alpha 1 mod 2 + mod alpha 2 mod 2 . The peak at Omega =+or- alpha 0 is the most intense and exhibits splitting when the applied fields are detuned from exact resonance with the respective atomic frequencies. Resonances are observed in the modulation rate of the intermediate-level population at the modulation frequencies Omega =0, +or-2 alpha 0 . In the presence of detunings of the applied fields, additional resonant structures occur at Omega =+or- alpha 0 which increase in magnitude with higher detunings and split. Explicit expressions for the positions, widths and weights of these resonant components are obtained analytically for intense, resonant fields. Numerical results for general values of the laser field strengths and the detunings are given.
The interaction of a strong bichromatic field with a two-level atom has been the subject of numerous experimental and theoretical investigations. We performed an experimental study of the Interaction of an intense 100% amplitude-modulated (AM) field with an ensemble of homogeneously broadened two-level atoms. An optically pumped sodium atomic beam is used as the atomic medium. The field is created by interfering two intense frequency-stabilized laser fields. The frequency of one field is held fixed while another field of equal amplitude is scanned in frequency. The beat frequency produced by interfering the two laser fields is equal to twice the modulation frequency of a 100% AM field. We monitor the time-averaged fluorescent intensity of the atoms as the frequency separation between the two fields is varied. A similar experiment was done in the past in the rf regime.1 For the first time, we report the observation of multiple, well-resolved resonances in the absorption spectrum of the field in the optical regime. We present data and theory for several values of detuning between the fixed field and atomic resonance. The experimental results are in good agreement with theory.
We have investigated the interaction between
bichromatic optical fields and atomic transitions. We have
considered both the interaction of a saturating bichromatic field
in the form of a 100% amplitude-modulated field resonantly
interacting with a single atomic transition as well as the
interaction of a pair of 100% amplitude-modulated fields with two
coupled atomic transitions. In our studies of
a single atomic transition resonantly excited by a 100%
amplitude-modulated field we have used a fully
quantum-electrodynamical analysis to model the Autler-Townes effect
induced by a bichromatic optical field. We find that the effect
induced by a bichromatic field is markedly different from the
effect produced by a monochromatic exciting field. We have derived
analytic expressions for the bichromatic Autler-Townes absorption
spectrum. The absorption spectrum consists of equally spaced lines
spaced by the modulation frequency. The linewidths of neighboring
lines alternate as functions of the field strength. Experimentally,
we observed this spectrum for both resonant and detuned 100%
amplitude-modulated driving fields by monitoring the absorption of
a weak monochromatic field as it was tuned about the resonance
frequency of the 3²P₃/₂(F = 3,
mF = 3) ↔ 4²D₅/₂(F =
4, mF = 4) transition while driving the
3²S₁/₂(F = 2, mF = 2)
↔ 3²P₃/₂(F = 3, mF =
3) transition with a saturating 100% amplitude-modulated field. We
found excellent agreement between our predicted and measured
spectra. We then investigated the resonant
interaction between a pair of 100% amplitude-modulated fields and
two atomic transitions sharing a common atomic level. We considered
both a three-level atomic cascade system and a three-level atomic
lambda system. We examined the effect that the relative phase
between the two modulations has on the rate at which the modulated
fields are absorbed. We find that the saturated time-averaged field
absorption exhibits parametric resonances in both the cascade and
lambda systems. The time-averaged absorption is strongly dependent
upon the relative phase of modulation between the two fields and
for certain phase differences the time-averaged absorption can be
enhanced over the maximum saturated absorption experienced by cw
fields of the same time-averaged intensities. We also find that the
stationary atomic response exhibits periodic oscillations and for
the cascade system periodic two-photon inversions of up to 40% can
be achieved. We further find dark absorption resonances as a
function of phase in the lambda system. We analyze the results from
the point of view of semi-classical adiabatic dressed
states.
The phenomenon of resonance fluorescence provides an interesting manifestation of the quantum theory of light and is a “real world” application of the material of the Chapters 8 and 9. In this process, a two-level atom is typically driven by a resonant continuous-wave laser field and the spectral and quantum statistical properties of the fluorescent light emitted by the atom are measured. Experimentally this can be achieved by scattering a laser off a collimated atomic beam such that the directions of the laser beam, atomic beam, and detector axis are mutually perpendicular as shown in Fig. 10.1. If the driving field is monochromatic, then at low excitation intensity the atom absorbs a photon at the excitation frequency and reemits it at the same frequency as a consequence of conservation of energy. The spectral width of the fluorescent light is therefore very narrow. The situation, however, is considerably more complicated when the excitation intensity increases and the Rabi frequency associated with the driving field becomes comparable to, or larger than, the atomic linewidth. At such intensity levels, the Rabi oscillations show up as a modulation of the quantum dipole moment and sidebands start emerging in the spectrum of the emitted radiation. This so-called dynamic Stark splitting is an interesting feature of the atom–field interaction. In addition to that, the fluorescent light exhibits certain nonclassical properties including photon antibunching and squeezing. In this chapter, we develop a theory of resonance fluorescence to explain these phenomena.
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.
Resonance-fluorescence power spectrum of two-level atoms driven by a strong monochromatic laser field is discussed, taking into account effects due to the dipole-dipole interaction between the atoms. For two atoms confined to a region smaller than the wavelength of the driving field, we predict significant deviations of the power spectrum from the single-atom case. The two-atom spectrum is nonsymmetric, the wing peaks are shifted from their Rabi-frequency positions, and additional maxima may appear.