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Physical Review A

Investigation of the dynamic Stark effect in aJ=0→1→0three-level system. III. The ‘‘strong-probe’’ case

Peter Fisk, Hans‐A. Bachor, R. J. Sandeman

Published Dec 1, 1986• 16 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.34.4762

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Investigation of the dynamic Stark effect in aJ=0→1→0three-level system. I. Experiment

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The dynamic Stark effect is investigated in a J=0\ensuremath{\rightarrow}1\ensuremath{\rightarrow}0 three-level ladder system in an atomic beam of natural barium. This system is free of hyperfine structure, which has complicated previous experiments of this type. An intense, actively stabilized cw dye laser was tuned to resonance with the transition between the upper two levels, and a similar, but much less intense, probe 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 allowed us to observe the effects of the strong laser on both the levels which it coupled. The smooth transition from an Autler-Townes doublet to a single light-shifted peak was observed, as well as effects related to coherent population trapping. The resulting profiles were found to be in excellent agreement with theoretical predictions. With a theoretical model extended to incorporate the contributions of the five most abundant isotopes of barium, and other nonideal features of the experiment, it was possible to account for every detail of the observed profiles. Comparing the experimental results with theory also yielded a measurement for the absorption f value for the 6s6p ${\mathrm{}}^{1}$${P}_{1}$\ensuremath{\rightarrow}6${p}^{2}$ $^{3}P_{0}$ (608.3 nm) transition in $^{138}\mathrm{Ba}$.

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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.

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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.

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Effects of Zeeman degeneracy on optical dynamic Stark splitting

Christian Delsart, J. Keller

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Observation of subnatural fluorescence linewidths due to coherent stabilization of quantum fluctuations

Daniel J. Gauthier, Yifu Zhu, THOMAS W. MOSSBERG

Recently, Narducci et al.1 studied V-configuration three-level atoms and predicted that quantum fluctuations associated with a "strong" optical transition driven by a coherent field can be stabilized through excitation of a coupled "weak" transition. This stabilization is manifest in a narrowing, to subnatural values, of the fluorescence linewidths associated with the strong transition as the weak transition is driven more and more strongly. We have experimentally investigated this problem and provide the first demonstration of the effect. In the experiment, a beam of Ba atoms was intercepted by two copropagating cw laser beams. One of the beams, of Rabi frequency Ω1, was tuned into resonance with the strong, 553.5 nm, 1S0→3P1 transition, while the other beam, of Rabi frequency Ω2, was tuned into resonance with the weak, 791.1 nm, 1S0→3P1 transition. The fluorescence spectrum of the strong transition was recorded for the case when Ω1≈35 MHz and Q2≈45 MHz and, it was found that the spectrum was three-peaked. Most interestingly, the measured linewidth (FWHM) for the central peak was 16 MHz, or 2 MHz less than the 18 MHz natural width of the strong transition even before the substantial instrumental broadening (≈8 MHz) of the peak was deconvolved.

Annual Meeting Optical Society of America•Jan 1, 1990•0 citations
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.
The dynamic Stark effect is investigated in a J=0\ensuremath{\rightarrow}1\ensuremath{\rightarrow}0 three-level ladder system in an atomic beam of natural barium. This system is free of hyperfine structure, which has complicated previous experiments of this type. An intense, actively stabilized cw dye laser was tuned to resonance with the transition between the upper two levels, and a similar, but much less intense, probe 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 allowed us to observe the effects of the strong laser on both the levels which it coupled. The smooth transition from an Autler-Townes doublet to a single light-shifted peak was observed, as well as effects related to coherent population trapping. The resulting profiles were found to be in excellent agreement with theoretical predictions. With a theoretical model extended to incorporate the contributions of the five most abundant isotopes of barium, and other nonideal features of the experiment, it was possible to account for every detail of the observed profiles. Comparing the experimental results with theory also yielded a measurement for the absorption f value for the 6s6p 1{\mathrm{}}^{1}1P1{P}_{1}P1​\ensuremath{\rightarrow}6p2{p}^{2}p2 3P0^{3}P_{0}3P0​ (608.3 nm) transition in 138Ba^{138}\mathrm{Ba}138Ba.
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 optical Hanle effect (light-shift-induced zero-field level crossing) has been investigated theoretically and experimentally. In the case of a $J=0\ensuremath{\rightarrow}1\ensuremath{\rightarrow}0$ three-level system and of a $J=0\ensuremath{\rightarrow}1$ two-level system, the resonance line shape has been obtained using a nonlinear-response-function method. Approximate expressions, valid under the conditions for the observation of light shifts, are obtained and compared with exact calculations as well as with the corresponding expression for the magnetic Hanle effect. As concerns the weak laser beam which produces the coherent excitation of atomic substates, we have calculated the linear response in the limiting case of monochromatic and of broad-band excitation. The experimental investigation has been performed for the Ba resonance line using two cw dye lasers at $\ensuremath{\lambda}=5535$ \AA{} and an atomic beam. The absorption- and dispersion-shaped level crossing resonances have been observed, for narrow- and broad-band excitation, by varying the power of the strong nonresonant laser beam. We have checked that the line shapes are only dependent upon the reduced variable $\frac{{P}_{L}}{\ensuremath{\delta}}$ (PL{P}_{L}PL​; beam power; $\ensuremath{\delta}$: frequency detuning). Using the theoretical expressions, we have tried to fit the experimental curves. Provided that the Gaussian distribution of the beams is taken into account, we have obtained a good agreement between theory and experiment for the whole set of experimental data.
In a double resonance experiment with a strong pump beam and a weak probe beam multiplet structures due to the AC Stark effect can be observed. The authors report the first observation of such a multiplet in a three-level experiment. The linearly polarised beams from a CW dye laser and a I 2 stabilised He-Ne laser were counter-propagating in the neon discharge cell and the saturating laser frequency was tuned across the resonances. The quadruplet structure was observed both for zero and for non-zero detuning delta 2 of the probe beam. The corresponding calculations for the three-level system with degenerate levels have been performed using the density matrix formalism with a tensorial expansion of the matrix elements. The theory includes the coupling of the various Zeeman sublevels by spontaneous emission and by the interaction with the two beams, and takes into account the finite value of the Doppler width.
Recently, Narducci et al.1 studied V-configuration three-level atoms and predicted that quantum fluctuations associated with a "strong" optical transition driven by a coherent field can be stabilized through excitation of a coupled "weak" transition. This stabilization is manifest in a narrowing, to subnatural values, of the fluorescence linewidths associated with the strong transition as the weak transition is driven more and more strongly. We have experimentally investigated this problem and provide the first demonstration of the effect. In the experiment, a beam of Ba atoms was intercepted by two copropagating cw laser beams. One of the beams, of Rabi frequency Ω1, was tuned into resonance with the strong, 553.5 nm, 1S0→3P1 transition, while the other beam, of Rabi frequency Ω2, was tuned into resonance with the weak, 791.1 nm, 1S0→3P1 transition. The fluorescence spectrum of the strong transition was recorded for the case when Ω1≈35 MHz and Q2≈45 MHz and, it was found that the spectrum was three-peaked. Most interestingly, the measured linewidth (FWHM) for the central peak was 16 MHz, or 2 MHz less than the 18 MHz natural width of the strong transition even before the substantial instrumental broadening (≈8 MHz) of the peak was deconvolved.