We have investigated the dynamic Stark effect in a J=0\ensuremath{\rightarrow}1\ensuremath{\rightarrow}0 three-level ladder system in an atomic beam of natural barium. An intense, actively stabilized cw dye laser was tuned to resonance between the upper two levels, and a similar laser was scanned through resonance with the transition connecting the lower two levels. Fluorescence arising from transitions out of the middle and upper levels was separately recorded as a function of probe laser frequency. This is the third and final paper in a series, of which the first two papers investigated theoretically and experimentally the ``weak-probe'' case, where the intensity of the probe laser was sufficiently low for the interaction between the atoms and the probe laser to be linear. In this paper we present an experimental investigation of the ``strong-probe'' case, where both lasers interact nonlinearly with the atoms, and we compare the results with the predictions of a theoretical model based on the optical Bloch equations.
We have calculated the steady-state intensity of fluorescence emitted from the middle and upper levels of a three-level (J=0\ensuremath{\rightarrow}1\ensuremath{\rightarrow}0) atomic ladder system subjected to a weak probe laser tuned to the transition between the lower two levels and a strong laser tuned to the transition between the upper two levels. This configuration of strong and probe lasers is the reverse of that used in previous experimental studies of three-level ladder systems. The configuration studied in this paper allowed the investigation of the population of both levels coupled by the strong laser. In order to predict in detail the results of a real, nonideal experiment carried out on a J=0\ensuremath{\rightarrow}1\ensuremath{\rightarrow}0 three-level system in a barium atomic beam, the theoretical model must include the effects of the experimental geometry, Zeeman degeneracy, hyperfine structure, and isotope structure. The experiment and the model were restricted to the case where both lasers have the same linear polarization. The method of Ben-Reuven and Klein was used to find an analytic solution to the Bloch equations for the three-level system. Without an analytic or semianalytic solution, the extension of the theory to describe a real experiment would have required a prohibitive amount of computer time.
The dynamic Stark effect (Autler-Townes splitting and radiative shift) of a J = 0 ↔ J = 1 optical transition have been investigated. The barium atomic beam is illuminated by a strong pump beam, resonant or slightly non-resonant with the BaI resonance line (λ = 5 535 Å) ; the fluorescence induced by a weak probe beam is detected versus the probe frequency. With linear polarizations for the two beams one deals either with a two-level (parallel polarizations) or with a three-level system (perpendicular polarizations). In the latter case and for small detunings of the pump beam, the Autler-Townes doublet has been observed. For large detunings of the pump beam a single, shifted resonance has been obtained with both polarization settings. In the three-level case the observation of the passage from the Autler-Townes situation to the light-shift situation, is reported. The corresponding calculations are presented; a particular attention is paid to the case of large detunings for the pump beam (light-shift situation). The evolution calculated for the resonance curve (position and relative intensities of the peaks) when the relative polarization directions are changed is consistent with the experimental data.
The Stark shift of the (6s
)2 1S0\ensuremath{\rightarrow}(6s6p
)1P1 transition in barium was measured using a laser to excite an atomic beam as it traversed a uniform electric field and a field-free region. The laser frequency was scanned across the transition while fluorescence produced by the radiative decay of the excited state was detected. The frequency scan was calibrated using an acousto-optic modulator which frequency shifted the laser by a specified amount. The Stark-shift rate was found to be -28.532\ifmmode\pm\else\textpm\fi{}0.060 kHz/(kV/cm
)2. The hyperfine splitting of the
135,137Ba F=1/2 level relative to
138Ba of the (6s6p
)1P1 state was determined to be -549.47\ifmmode\pm\else\textpm\fi{}0.12 MHz, where the minus sign indicates that the
138Ba transition is at a lower frequency.
A measurement of the Stark-induced amplitudes \ensuremath{\alpha} and \ensuremath{\beta} for the 6
P1/2\ensuremath{\rightarrow}7
P1/2 transition in atomic thallium is reported. Absorption of cw laser light tuned to this transition at 293 nm was compared to absorption of 378-nm cw laser light tuned to the allowed 6
P1/2\ensuremath{\rightarrow}7
S1/2 transition. The absorption sample was an intense atomic beam in the presence of a strong electric field. The measured values are \ensuremath{\alpha}=2.01(4)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$ ${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$/ (V/cm) and \ensuremath{\beta}=1.67(4)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$/ (V/cm), where ${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$ is the Bohr magneton. These results are in agreement with semiempirical theory, but disagree with previous measurements of these amplitudes in this laboratory. A critical analysis of the previous measurement is given to explain the discrepancy. The newly measured value of \ensuremath{\beta} makes it necessary to reinterpret previous measurements of parity nonconservation in the 6
P1/2\ensuremath{\rightarrow}7
P1/2 transition. In the course of the present experiment, Stark shifts of the 6
P1/2\ensuremath{\rightarrow}7
P1/2 and 6
P1/2\ensuremath{\rightarrow}7
S1/2 transitions were also measured: \ensuremath{\Delta}\ensuremath{\nu}(6
P1/2\ensuremath{\rightarrow}7
S1/2)=-112(6) kHz/(kV/cm
)2 and \ensuremath{\Delta}\ensuremath{\nu}(6
P1/2\ensuremath{\rightarrow}7
P1/2)=-618(31) kHz/(kV/cm
)2. These results are also in good agrement with semiempirical theory.
Autler-Townes (A-T) splitting, known as an AC Stark effect, shows a change of an absorption/emission spectral line of a probe beam when an oscillating field is tuned in resonance with the atomic or molecular transition. The A-T splitting is observed in different three-level atoms and widely investigated in a vapor cell and in a magneto-optical trap (MOT). The A-T splitting plays an important role in the atom-based microwave electric-field measurements where a cascade three-level system involving Rydberg state is adopted. In this work, an A-T splitting is observed in an ultracold cesium Rydberg gas, which is cooled down to about 100 pK and center density is about 1010 cm-3 in a conventional MOT by using the laser cooling technology. We present the A-T spectrum in a ladder three-level atomic system involving a 34D5/2 Rydberg state. The cesium ground state (6S1/2), excited state (6P3/2) and Rydberg state (34D5/2) constitute a Rydberg three-level system. A coupling laser, locked to the Rydberg transition by using a Rydberg electromagnetically induced transparency signal that is obtained from a cesium room-temperature vapor cell, couples 6P3/2 (F'=5) 34D5/2 Rydberg transition. A weak probe laser, stabilized to a ground-state transition by using a polarization spectroscopy, is swept, covering the transition 6S1/2 (F=4) 6P3/2 (F'=5) with a double-passed acousto-optic modulator. The probe and coupling lasers are counter-propagated through the MOT center. The power of probe light is 200 pW, corresponding Rabi frequency p=21.05 MHz. During the experiment, 50 s after turning off the trapping laser, both the coupling and probe beams are switched on and last 100 s. The A-T spectrum as a function of the probe detuning is detected with a single-photon counter module detector. We use Gaussian multiple peak fitting to obtain the positions of the A-T peaks and the A-T splitting. The measured A-T splitting is proportional to the Rabi frequency of the coupling light. We numerically solve the density matrix equations to obtain the A-T spectrum, and the calculations reproduce A-T spectra well. The measured A-T splitting shows good agreement with the theoretical calculation for Rabi frequency of the coupling light c29 MHz. The A-T splitting is less than the calculation for the case of c29 MHz, the deviation is mainly attributed to the increased dephasing rate induced by the strong interaction between Rydberg atoms, whose number increases with the coupling laser Rabi frequency. In this work, the adopted method for the cascade three-level system involving Rydberg state is also suitable for -and V-type cases.