Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Investigation of the dynamic Stark effect in aJ=0→1→0three-level system. II. Theoretical description

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

Published Apr 1, 1986• 14 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.33.2424

Related papers

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

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.

Physical Review A•Dec 1, 1986•16 citations

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

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

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 $^{138}\mathrm{Ba}$.

Physical Review A•Apr 1, 1986•37 citations

Investigation of the dynamic Stark effect of a J = 0 ↔ J = 1 optical transition

Christian Delsart, J. Keller, V.Paul Kaftandjian

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.

Journal de physique•Jan 1, 1981•14 citations

Effects of Zeeman degeneracy on optical dynamic Stark splitting

Christian Delsart, J. Keller

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.

Journal of Physics B Atomic and Molecular Physics•Jan 28, 1980•22 citations

Fluorescence intensity and squeezing in a driven three-level atom: Ladder case

Z. Ficek, Bryan J. Dalton, P. L. Knight

A theoretical study is made of the steady-state intensity and squeezing properties of the fluorescent light from a three-level-atom system in a ladder configuration, which is subject to spontaneous-emission decay to the electromagnetic-field vacuum. Two cases are examined: in the equispaced (ES) level case, the two atomic transition frequencies are nearly equal and two photon absorption processes occur from a single coherent laser field that couples both transitions and has a small detuning from each; in the non- equispaced (NES) level case, the atomic transition frequencies are rather different and two photon absorption processes occur from two coherent laser fields, each coupled to a single transition and in near resonance with it. In both cases, a situation of small two-photon detuning occurs. Optical Bloch equations for the atomic density matrix in rotating frames are given and matrix expressions for determining the steady-state populations and coherences are obtained. Analytic expressions are also given for special cases. The fluorescent intensity is obtained from the populations of the intermediate and upper states, with the normally ordered variance (NOV) for quadrature components of the fluorescent field involving, in addition, the atomic coherences. The fluorescent intensities are shown graphically as a function of two-photon detuning for a variety of one-photon detunings and Rabi frequencies for the ES and NES cases.In both cases, the fluorescent intensities show the well known resonances from the upper state at zero two-photon detuning and from the intermediate state at zero one-photon detuning for the lower transition. However, further resonances are also found. The intermediate-state intensity displays a resonance at zero two-photon detuning. Also, the upper-state intensity shows a resonance at zero one-photon detuning for the upper transition, but only for the NES case; evidently, the transfer rate from upper to lower transition coherences destroys this resonance for the ES case. The time-averaged NOV is also shown graphically as a function of two-photon detuning for a variety of one-photon detunings and Rabi frequencies for the ES and NES cases. For the ES case, the quadrature frequency is chosen as the single laser frequency and for the NES case, it is chosen as either the average of the two laser frequencies or the lower transition laser frequency. Squeezing occurs near zero two-photon detuning for both ES and NES cases, though only for the quadrature frequency equal to the average laser frequency in the latter case. It also occurs near zero detuning for the lower transition for both cases, though only for the quadrature frequency equal to the lower transition laser frequency in the NES case. The squeezing minima show a splitting effect for large Rabi frequencies corresponding to two-photon or one-photon Rabi splitting of the dressed atom levels for the situation near two-photon or one-photon resonance, respectively. The large squeezing near two-photon resonance for moderate Rabi frequencies and large one-photon detuning corresponds to essentially pure three-level squeezing, while that near one-photon resonance for weak Rabi frequencies involves two-level squeezing.

Physical Review A•May 1, 1995•62 citations

ac Stark effect in a doubly driven three-level atom

Changjiang Wei, Dieter Suter, Andrew S. M. Windsor +1 more

In this paper we present a detailed treatment of the ac Stark effect of a three-level atom driven by two strong laser fields in a cascade scheme. We consider two situations where there is a weak laser field probing a new transition starting from one of the three levels to a fourth level. In one case the initial level of the probed transition is the ground state and in the other case the initial level is the intermediate state. For both situations we derive an analytical expression for the absorptive and dispersive responses of the weak probe field and present the spectrum obtained from numerical calculation. The general feature of the spectrum has a three-peak structure. The positions and relative intensities of the three spectral components are affected strongly by the driving field intensities and detunings. An account of the spectrum is given in terms of the dressed-state formalism.

Physical Review A•Sep 1, 1998•43 citations
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.
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.
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.
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.
A theoretical study is made of the steady-state intensity and squeezing properties of the fluorescent light from a three-level-atom system in a ladder configuration, which is subject to spontaneous-emission decay to the electromagnetic-field vacuum. Two cases are examined: in the equispaced (ES) level case, the two atomic transition frequencies are nearly equal and two photon absorption processes occur from a single coherent laser field that couples both transitions and has a small detuning from each; in the non- equispaced (NES) level case, the atomic transition frequencies are rather different and two photon absorption processes occur from two coherent laser fields, each coupled to a single transition and in near resonance with it. In both cases, a situation of small two-photon detuning occurs. Optical Bloch equations for the atomic density matrix in rotating frames are given and matrix expressions for determining the steady-state populations and coherences are obtained. Analytic expressions are also given for special cases. The fluorescent intensity is obtained from the populations of the intermediate and upper states, with the normally ordered variance (NOV) for quadrature components of the fluorescent field involving, in addition, the atomic coherences. The fluorescent intensities are shown graphically as a function of two-photon detuning for a variety of one-photon detunings and Rabi frequencies for the ES and NES cases.In both cases, the fluorescent intensities show the well known resonances from the upper state at zero two-photon detuning and from the intermediate state at zero one-photon detuning for the lower transition. However, further resonances are also found. The intermediate-state intensity displays a resonance at zero two-photon detuning. Also, the upper-state intensity shows a resonance at zero one-photon detuning for the upper transition, but only for the NES case; evidently, the transfer rate from upper to lower transition coherences destroys this resonance for the ES case. The time-averaged NOV is also shown graphically as a function of two-photon detuning for a variety of one-photon detunings and Rabi frequencies for the ES and NES cases. For the ES case, the quadrature frequency is chosen as the single laser frequency and for the NES case, it is chosen as either the average of the two laser frequencies or the lower transition laser frequency. Squeezing occurs near zero two-photon detuning for both ES and NES cases, though only for the quadrature frequency equal to the average laser frequency in the latter case. It also occurs near zero detuning for the lower transition for both cases, though only for the quadrature frequency equal to the lower transition laser frequency in the NES case. The squeezing minima show a splitting effect for large Rabi frequencies corresponding to two-photon or one-photon Rabi splitting of the dressed atom levels for the situation near two-photon or one-photon resonance, respectively. The large squeezing near two-photon resonance for moderate Rabi frequencies and large one-photon detuning corresponds to essentially pure three-level squeezing, while that near one-photon resonance for weak Rabi frequencies involves two-level squeezing.
In this paper we present a detailed treatment of the ac Stark effect of a three-level atom driven by two strong laser fields in a cascade scheme. We consider two situations where there is a weak laser field probing a new transition starting from one of the three levels to a fourth level. In one case the initial level of the probed transition is the ground state and in the other case the initial level is the intermediate state. For both situations we derive an analytical expression for the absorptive and dispersive responses of the weak probe field and present the spectrum obtained from numerical calculation. The general feature of the spectrum has a three-peak structure. The positions and relative intensities of the three spectral components are affected strongly by the driving field intensities and detunings. An account of the spectrum is given in terms of the dressed-state formalism.