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Physical Review A

Two-photon Rabi oscillations

A.F. Linskens, Iwan Holleman, N. Dam, J. Reuß

Published Dec 1, 1996• 48 citations
Publisher

Abstract

Rabi oscillations reflect the existence of a coherent superposition of two molecular eigenstates during the interaction of molecules with a strong, resonant electromagnetic field. This phenomenon is not restricted to two-level systems. We demonstrate its occurrence in a three-level system where the radiation induces a two-photon absorption. The intermediate level is (slightly) detuned from resonance. For a theoretical description the dressed-state picture is adopted. The two-photon excitation is performed either by using one laser, yielding a one-color two-photon process, or by using two counterpropagating, spatially overlapping laser beams, yielding a two-color two-photon process. Rabi oscillations are produced by varying the fluence, i.e., by changing either the laser power or the molecule-laser interaction time. For the one-color case the two-photon transition dipole moment for an ${\mathrm{SF}}_{6}$ transition has been determined from the relation between laser fluence and number of Rabi oscillations. For the two-color cases the detuning with the intermediate level is varied by tuning the respective laser frequencies while keeping the sum frequency constant. A dramatic change in the degree of excitation as a function of the intermediate detuning has been observed. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.4854

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Rabi oscillations reflect the existence of a coherent superposition of two molecular eigenstates during the interaction of molecules with a strong, resonant electromagnetic field. This phenomenon is not restricted to two-level systems. We demonstrate its occurrence in a three-level system where the radiation induces a two-photon absorption. The intermediate level is (slightly) detuned from resonance. For a theoretical description the dressed-state picture is adopted. The two-photon excitation is performed either by using one laser, yielding a one-color two-photon process, or by using two counterpropagating, spatially overlapping laser beams, yielding a two-color two-photon process. Rabi oscillations are produced by varying the fluence, i.e., by changing either the laser power or the molecule-laser interaction time. For the one-color case the two-photon transition dipole moment for an SF6{\mathrm{SF}}_{6}SF6​ transition has been determined from the relation between laser fluence and number of Rabi oscillations. For the two-color cases the detuning with the intermediate level is varied by tuning the respective laser frequencies while keeping the sum frequency constant. A dramatic change in the degree of excitation as a function of the intermediate detuning has been observed. \textcopyright{} 1996 The American Physical Society.
An optical analogue of two-photon Rabi oscillations, occurring in a three-level atomic or molecular system coherently driven by two detuned laser fields, is theoretically proposed and experimentally demonstrated using three evanescently coupled optical waveguides realized on an active glass substrate. The optical analogue stems from the formal analogy between spatial propagation of light waves in the three-waveguide structure and the coherent temporal evolution of populations in a three-level atomic medium driven by two laser fields under two-photon resonance. In our optical experiment, two-photon Rabi oscillations are thus visualized as a slow spatial oscillatory exchange of light power between the two outer waveguides of the structure with a small excitation of the central waveguide.
Rabi oscillations is a key phenomenon among the variety of quantum optical effects that manifests itself in the periodic oscillations of a two-level system between the ground and excited states when interacting with electromagnetic field. Commonly, the rate of these oscillations scales proportionally with the magnitude of the electric field probed by the two-level system. Here, we investigate the interaction of light with a two-level quantum emitter possessing permanent dipole moments. The semi-classical approach to this problem predicts slowing down and even full suppression of Rabi oscillations due to asymmetry in diagonal components of the dipole moment operator of the two-level system. We consider behavior of the system in the fully quantized picture and establish the analytical condition of Rabi oscillations collapse. These results for the first time emphasize the behavior of two-level systems with permanent dipole moments in the few photon regime, and suggest observation of novel quantum optical effects.
Motivated by experimental advances that the collective excitation of two Rydberg atoms was observed, we provide an elaborate theoretical study for the dynamical behavior of two-atom Rabi oscillations. In the large-intermediate-detuning case, the two-photon Rabi oscillation is found to be significantly affected by the strength of the interatomic van der Waals interaction. With a careful comparison of the exact numbers and values of the oscillation frequency, we propose a new way to determine the strength of excitation blockade, agreeing well with the previous universal criterion for full, partial, and no blockade regions. In the small-intermediate-detuning case, we find a blockade-like effect, but the collective enhancement factor is smaller than 2 due to the quantum interference of double optical transitions involving the intermediate state. Moreover, a fast two-photon Rabi oscillation in ns timescale is manifested by employing intense lasers with an intensity of ∼ MW/cm 2 , offering a possibility of ultrafast control of quantum dynamics with Rydberg atoms.
A class of molecular two-photon processes, occurring under transient or steady-state conditions, is analyzed exactly for certain cases using a density-matrix formalism. Our results are relevant to the recently observed phenomena of transient coherent Raman beats and steady-state two-photon absorption of oppositely directed laser beams. Lowest-order perturbation theories have shown that these processes are insensitive to the Doppler effect, and consequently the linewidth is unaffected by Doppler broadening and by elastic collisions that change molecular velocity. The solutions presented here are of the same form for the Raman and two-photon problems and reveal significant power-dependent frequency shifts and line broadening that correct the ideal Doppler-free solutions. For the transient case, we assume a molecular three-level quantum structure that can be switched in or out of optical resonance with cw laser radiation by means of a pulsed dc Stark field, but the solutions also apply when resonant optical pulses are introduced. During the resonant condition when the Stark pulse is on, the three levels are prepared in coherent superposition, and during the nonresonant condition following the Stark pulse, the laser field(s) stimulates the coherently prepared sample in a transient two-photon process. One of these processes, the Ramanbeat effect, has been observed in forward scattering, but the second one, transient two-photon emission, should be observable in backward scattering. Bloch-like equations are derived for this three-level problem that facilitate an exact pulse solution for state preparation. Following the pulse, transient decay is well-approximated by a perturbation calculation. For the steady-state case, an exact solution is also obtained and is of interest for continuous-wave spectroscopy or for transient experiments requiring an initial preparation of quantum states, prior to Stark switching. These solutions exhibit a power-dependent line broadening and a frequency shift of magnitude $\ensuremath{\sim}\frac{\ensuremath{\Delta}({\ensuremath{\alpha}}^{2}\ensuremath{-}{\ensuremath{\beta}}^{2})}{({\ensuremath{\Delta}}^{2}+\frac{1}{{T}_{2}^{2}})}$, in agreement with our earlier estimate, where $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ are the Rabi flopping frequencies for the two intermediate transitions and $\ensuremath{\Delta}$ is the off-resonance tuning behavior for one of them.
This investigation describes the interaction of a three level atom with two laser fields. One of the transitions from the ground state is in resonance with twice the frequency of the first laser and the other transition from the ground state is in resonance with the second laser. The Green's function formalism is used to derive expressions from which the induced two photon and one photon excitation spectra are computed. Also, approximate expressions are derived for the excitation spectra in the appropriate frequency regions. These results agree well with the numerical computations based upon the precise expressions. The interference between the two transitions produce some splittings; these splittings depend upon the Rabi frequency of the one photon transition. The intensities of the weak peaks depend upon the ratio of the Rabi frequency of the two photon transition to the frequency of the first laser. Some features of the excitation spectra are interpreted in terms of previous knowledge about the behavior of two level atoms in strong laser fields.
The two-photon transitions of a system of two dissimilar molecules are studied in the dipole approximation. Special attention is paid to transitions in which both molecules participate simultaneously. By use of a reduced Hamiltonian the influence of long-range intermolecular forces is also studied. The three main transitions considered occur when: (i) no molecular level is in resonance with a primary photon, (ii) one primary photon excites a molecular level, and (iii) two primary photons excite a molecular level. It is shown that in no case can the mixing of excited states by intermolecular forces be represented as a change to an effective transition dipole moment for one of the molecules. The one-photon decay of a state in which both molecules are excited is also treated.