Dynamic Stark Splitting Research Articles

Erratum: Resonance fluorescence of a two-level atom in a strong bichromatic field

An experiment was performed recently [Y. Zhu, A. Lezama, Q. Wu, and T. W. Mossberg (unpublished)] in which a two-level atom of transition frequency \ensuremath{\Omega} was placed in a bichromatic laser field with frequencies \ensuremath{\Omega}\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta}, of sufficient intensity to produce dynamic Stark splitting. The observed fluorescence spectrum differed qualitatively in almost all its details from the well-known Mollow triplet [B. R. Mollow, Phys. Rev. 188, 1969 (1969)]. In this article, we use a dressed-atom model to explain the observed results.

Quantum trajectory simulations of two-state behavior in an optical cavity containing one atom.

Under conditions of strong dipole coupling an optical cavity containing one atom behaves as a two-state system when excited near one of the ``vacuum'' Rabi resonances. A coherent driving field induces a dynamic Stark splitting of the ``vacuum'' Rabi resonance. We demonstrate this two-state behavior in computer experiments based on quantum trajectory simulations.

Observation of dynamic Stark splitting in infrared-infrared double resonance in methyl fluoride

Dynamic Stark splitting has been observed by scanning the Q P(5, 3) transition in the 2 ν 3- ν 3 band in 13CH 3F with a CO 2-laser based infrared microwave sideband generator while pumping the Q R(4, 3) transition in the ν 3 band with a second CO 2 laser. Similar splitting has been observed in the Q Q(12, 9) and Q R(12, 9) transitions in the 2 ν 3- ν 3 band of 12CH 3F while pumping the Q R(11, 9) transition in the ν 3 band. The lineshapes of these and other double resonance effects have been fit to high accuracy by means of a computer program that computes the spectrum by solving the density matrix equations for a three-level system including summation over the spatially degenerate states and numerical integration over the velocity. The effects of contributions from collisional energy transfer, frequency modulation of the lasers, and misalignment of the laser beams have been calculated and are discussed. Difficulties that must be overcome in order to use these experiments for determination of energy transfer rates are described.

Squeezing-enhanced and -reduced atomic-level splitting in two-photon dynamics.

In this paper, the two-photon Bloch equations of a two-level atom in broadband squeezed light are derived. On this basis, we discuss two-photon dynamic Stark splitting of atomic levels and the time evolution of atomic variables. The phenomena of squeezing-induced enhancement and reduction of dynamic Stark splitting of the atomic levels and overdamping of atomic time evolution are obtained.

Resonance fluorescence of a two-level atom in a strong bichromatic field.

An experiment was performed recently [Y. Zhu, A. Lezama, Q. Wu, and T. W. Mossberg (unpublished)] in which a two-level atom of transition frequency \ensuremath{\Omega} was placed in a bichromatic laser field with frequencies \ensuremath{\Omega}\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta}, of sufficient intensity to produce dynamic Stark splitting. The observed fluorescence spectrum differed qualitatively in almost all its details from the well-known Mollow triplet [B. R. Mollow, Phys. Rev. 188, 1969 (1969)]. In this article, we use a dressed-atom model to explain the observed results.

Saturation behavior and dynamic Stark splitting of nearly-degenerate four-wave and multiwave mixing in a forward boxcar configuration

We analyze the saturation behavior of nearly degenerate forward four-wave mixing in a Doppler broadened vapor. Theoretical predictions as well as experiments on Cs vapor resonance line (λ=852 nm) reveal that the dynamic Stark splitting is directly observable in the case of a two-level system. Extensions to multiwave mixing are also discussed.

Molecular transition moment determination by Autler-Townes spectroscopy: D 1Π u-E,F 1Σ g+ bands of H 2

We investigate theoretically the determination of vibronic transition moments between two electronic states of a molecule by using the Autler-Townes effect (also known as ac, optical or dynamical Stark splitting) in a double optical resonance experiment. We calculate the Autler-Townes spectra of some representative bands of H 2(D 1Π u-E,F 1Σ g +) and examine their dependences on laser detuning, intensity, bandwidth, and the Doppler effect. As input to our calculation, the D-E,F electronic transition moment and the (ν′=0–15, ν=3, 6 and 7) vibronic transition moments have been computed. Our investigation shows that with moderate laser requirement, the Autler-Townes splitting of a large number of D-E,F vibronic transitions in H 2 should be observable so that their transition moments may be deduced experimentally.

Dynamic behavior of a two-level system in multimode squeezed light. I. Bloch equations and dynamic stark splitting

The optical Bloch equations of a two-level system with homogeneous broadening driven by multimode squeezed light are given. Its general solutions are analysed in terms of the mathematical technique of the Laplace transform. The results show that the quantum effect of the light field can result in the vanishing of the dynamic Stark splitting of atomic level.

Four-wave mixing in strongly driven four-level systems.

A nonperturbative theoretical study of four-wave-mixing processes in four-level systems is presented. Using the density-matrix formalism, numerical results are obtained for two arbitrarily intense pump fields with the third field a weak probe. The fourth wave, radiated by the system, is obtained analytically for some special cases. We find, for different frequency detunings, Rabi frequencies, and relaxation rates that the line shapes exhibit: (i) dynamic Stark splitting and shifting, and merging of resonances; (ii) power broadening with two-photon antiresonance behavior resulting from a destructive interference between different contributions to the optical polarization; and (iii) extra resonances induced by field intensities and saturation processes.

Dynamic stark effect in the 4p2p-3s2s transition of sodium by intense two-photon pumping

Dynamic Stark shift and splitting in the u.v. transition 4p-3s of sodium has been studied under two-photon pumping of the 5s state. The influence of pump detuning, laser power and sodium pressure have been measured and compared with the theoretical model for three-level system

The Autler-Townes effect in hydrogen at low pressure

The author investigates the Autler-Townes effect (also known as AC, optical or dynamical Stark splitting) on the Balmer- alpha transition of hydrogen in 0.5-5 Torr of helium. In the double optical resonance scheme. H(3p) is excited by absorption of two 243 nm photons and a 656 nm photon via the 2s resonant intermediate level. Calculated results show that in a Doppler-free or a 'Doppler-reduced' beam configuration, the required intensity of the 656 nm laser (0.2 cm-1 bandwidth) for observation of the Autler-Townes doublet has to be greater than 2*104 and 2*105 W cm-2 for 243 nm laser bandwidths of 0.1 and 0.5 cm-1, respectively.

Dynamic stark splitting in a Morse oscillator

We have show that in the spirit of the Jaynes-Cummings model a Morse oscillator interacting with a single mode electromagnetic field can be solved within the rotating wave approximation. The model exhibits dynamic Stark splitting which is reminiscent of Rabi doublets in two-level atoms and Autler-Townes doublets in three-level systems.

Gain saturation in optically pumped standing-wave gas lasers

In an inhomogeneously Doppler broadened three-level system we analyze the gain lineshapes of a strong standing-wave generated field when a fixed frequency travelling-wave pumps a transition sharing the upper level with the lasing transition. Population pulsations and nonlinear coherent effects are included in our numerical solution. The physical processes determining the main features in the gain lineshapes have been identified. Comparison with solutions obtained neglecting the coupling between the travelling components of the generated field shows these effects to be significant at high intensities. Unexplored features such as the dynamic Stark splitting produced by the generated field on its own gain profile are presented and the conditions for their observation discussed.

Spectra of a linear molecule in a strong light field

Optical spectra of a linear molecule in a strong monochromatic field are considered within the framework of a numerically solvable quantum-mechanical model. Light field-molecule interaction causes the dynamic Stark splitting of molecular rotational levels. In the strong-field limit the orientational motion obtains a librational character. A new mechanism of the laser cooling of molecular rotation is discussed.

Frequency pulling in optically-pumped FIR methanol lasers

The frequency pulling of optically-pumped FIR methanol lasers was investigated experimentally and theoretically with the aid of a simple model with regard to the amplification. This model assumes Lorentzian lineshapes for the amplification and neglects the dynamical Stark splitting of the levels. The model was found to be adequate for a qualitative understanding of the measured behaviour of the laser.

Dynamic Stark splitting in two-photon resonance fluorescence

The excitation spectrum arising from resonant two-photon interaction between a strong pump field and a two-level model is investigated by means of the Green's function formalism. An atom-field interaction potential which is quadratic in photon creation and annihilation operators is used. The results, valid for high photon densities of the pump field, reveal a three-peak spectrum similar to the one-photon case. The energy shift is found to be linearly dependent on the intensity of the pump beam.

Application of a diagram technique to the problem of resonance fluorescence from strongly driven two level atoms

A Green's function formulation, valid for thermal as well as nonthermal equilibrium, is developed for the resonance fluorescence from strongly driven two level atoms. Translational motion and the Doppler broadening are also taken into account (collisions are considered in a second paper). The Feynman diagram technique is used to calculate the contribution of the physically important processes. The formulation is not based on the Markovian approximation or the quantum regression theorem. It takes full account of the dynamic Stark splitting and the saturation, and leads to a generalization of the "dressed atom" approach. Our "generalized dressed atom" (GDA) approach is valid for arbitrary values of the detuning and the pump field strength. The lowest order diagrams in the GDA picture give results equivalent to the existing theories. Some higher order diagrams are also considered. Although the resulting corrections are small, the physical processes involved are of some interest. These corrections include nonMarkovian effects.

Time-resolved laser saturation spectroscopy. Theory of the free induction decay of two-level saturation resonances

We give the theory of the free induction decay of two-level saturation resonances in the time-resolved laser saturation spectroscopy. The saturating and probe fields may be either co- or counter-propagating. The change-signal line-shape is analysed in detail in two cases of practical importance, namely when the saturating field is either strong or weak. The time evolution of the change-signal exhibits many interesting features which include Ramsey-type fringes, oscillatory decay, narrow resonances, line-narrowing etc. It is shown that by analysing the decay of the change-signal in time one can distinguish (i) various laser interaction processes such as population effects, coherence effects, three-photon Raman-type process, dynamic Stark splitting, power-broadening etc., and (ii) various relaxation mechanisms such as phase-changing collisions, etc.

AC Stark effect and fluorescence in modulated laser beams. II. Two-photon stepwise excitations

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 02= 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.

AC Stark effect and fluorescence using modulated laser beams. I. Effect of laser fluctuations and arbitrary relaxation parameters

The influence of relaxation parameters, as well as temporal fluctuations in the laser field on the modulation rate and phaseshift of the fluorescence from a two-level atom excited by a weakly modulated source is studied in detail. It is shown that, for intense resonant laser fields, the resonance in the modulation rate occurs at the modulation frequency Omega =2 due to the dynamical Stark splitting and has a width equal to 1/2(T1-1+T2-1). When temporal fluctuations of the exciting laser field are taken into account, the phaseshift of the scattered light is found to be strongly dependent on the bandwidth of the exciting source, as well as the frequency of modulation; hence experimental results on the determination of the lifetime by the phaseshift method have to be interpreted carefully. Numerical results for the modulation rates and phaseshift at different field strengths and various values of T1-1, T2-1, Delta laser bandwidth and Doppler broadening are presented.