A transient two-photon process is observed in the infrared which exhibits all the co-operative properties associated with superradiant two-level systems. It arises when a cw laser beam excites a molecular sample whose level degeneracy is suddenly removed by a Stark field. The resulting emission, which heterodynes with the laser, gives precise ground- and excited-state Stark splittings, and decays with a homogeneous relaxation time since Doppler dephasing effects are absent in forward scattering.
A transient two-photon process is observed in the infrared which exhibits all the co-operative properties associated with superradiant two-level systems. It arises when a cw laser beam excites a molecular sample whose level degeneracy is suddenly removed by a Stark field. The resulting emission, which heterodynes with the laser, gives precise ground- and excited-state Stark splittings, and decays with a homogeneous relaxation time since Doppler dephasing effects are absent in forward scattering.
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.
A simple application of the Stark-pulse technique, developed by Brewer and Shoemaker, demonstrates optical free induction decay-the optical analog of free induction decay in NMR. A molecular sample which is coherently prepared by a cw laser beam exhibits such a decay when it is suddenly switched out of resonance by a Stark field. Observations are presented for a nondegenerate Doppler-broadened infrared transition of NH2D, where the sample is optically thin, and the decay behavior can be compared quantitatively with a solution of the Bloch equations. When the molecular sample is prepared under steady-state conditions, the solutions are analytic; for pulse excitation, a numerical solution is required. The treatment invokes a hard-collision relaxation model. Such characteristics as the abrupt termination of the decay and the related edge echo, which result from Doppler dephasing, can be examined for Stark pulses of finite extent.
A new method of observing two-photon optical transients is proposed, namely, by intensity switching of incident cw laser beams. This method, which is an alternative to the standard dc Stark or frequency-switching techniques, employs the second-order optical (ac) Stark effect to throw the two-photon active levels in or out of resonance by appropriately switching the intensities of the two laser beams. Theoretical treatment for the three basic transients optical nutation, free induction decay, and two-pulse echo in thin samples using intensity switching, is given for both the cases: co- and counter-propagating beams. The feasibility of the method for the $5{S}_{\frac{1}{2}}\ensuremath{-}3{S}_{\frac{1}{2}}$ transition in Na vapor is demonstrated. An important feature is the apearance of an intensity-dependent beat frequency in the optical FID signal.
Recent works have shown that collective single photon spontaneous emission from an ensemble of N resonant two-level atoms is a rich field of study. Superradiance describes emission from a completely symmetric state of N atoms, with a single excited atom prepared with a given phase, for instance imprinted by an external laser. Instead, subradiance is associated with the emission from the remaining N−1 asymmetric states, with a collective decay rate less than the single-atom value. Here, we discuss the properties of the orthonormal basis of symmetric and asymmetric states and the entanglement properties of superradiant and subradiant states.
The phenomenon of coherent Raman beats observed recently by Shoemaker and Brewer is analyzed through solutions of the coupled Maxwell-Schr\"odinger equations. The effect arises in coherently prepared molecular samples where the level degeneracy is suddenly removed by Stark-pulse switching. The problem divides into two parts: (a) a steady-state preparative regime whereby the initially degenerate quantum levels are placed in superposition by a resonant laser field, and (b) a transient regime in which coherent forward Raman scattering decays in the presence of the same laser field during a nonresonant condition. The laser and Raman light thus propagate together and produce at a detector a coherent beat with a frequency that corresponds to the level splitting between initial and final states. The beat signal possesses the remarkable property of being entirely independent of longitudinal molecular velocity in the case of a plane-wave laser beam and of being almost so for milliradian divergence. It follows that relaxation involving velocity-changing collisions and that Doppler dephasing effects are absent in coherent Raman beats, in agreement with experimental measurements of the decay rate. The effect of off-resonance excitation on the dephasing time and on the period of the beat signal is also discussed, and the possibility of a small rotation of the plane of polarization of the scattered light is included. The subject presents a new aspect of Raman scattering which can now yield precise radio-frequency splittings directly and offers a selective way of examining relaxation phenomena.
We develop for dipole-forbidden transition a dynamical theory of two-photon paired superradiance (PSR). This is a cooperative process characterized by two photons emitted back to back with equal energies. By irradiating the trigger laser from two target ends, with its frequency tuned at the half energy between two levels, a macroscopically coherent state of medium and fields dynamically emerges as time evolves, and a large signal of amplified output occurs with a time delay. The basic semiclassical equations in 1+1 space-time dimensions are derived for the field-plus-medium system to describe the space-time evolution of the entire system and are numerically solved to demonstrate the existence of both explosive and weak PSR phenomena in the presence of relaxation terms. The explosive PSR event terminates accompanying a sudden release of most of the energy stored in the target. Our numerical simulations are performed using the vibrational transition ${X}^{1}{\ensuremath{\Sigma}}_{g}^{+}v=1\ensuremath{\rightarrow}0$ of a para-H2 molecule and taking many different excited atom number densities and different initial coherences between the metastable and the ground states. In an example with a number density close to O(1021 cm${}^{\ensuremath{-}3}$) and a high initial coherence, the explosive event terminates several nanoseconds after the trigger irradiation, when the phase relaxation time larger than O(10 ns) is taken. After PSR events the system is expected to follow a steady-state solution which is obtained by analytic means and is made of many objects of field condensates endowed with a topological stability.