It is shown that the collision-induced four-wave mixing signal in two-photon quasi-resonant excitation has the property of frequency non-mutuality, i.e. when the probe field frequency omega s is replaced by the signal frequency omega out the four-wave mixing coherent signal does not arise. The reason for such frequency non-mutuality lies in the nature of the collision-induced coherent scattering. It is shown that this scattering occurs because of double non-adiabatic transitions (as affected by collisions) between the states of a dressed atom without changing the environment (buffer) state during the four-photon-scattering elementary process; this scattering will be referred to as coherent collisionally double induced scattering (CCDIS).
It is shown that the collision-induced four-wave mixing signal in two-photon quasi-resonant excitation has the property of frequency non-mutuality, i.e. when the probe field frequency omega s is replaced by the signal frequency omega out the four-wave mixing coherent signal does not arise. The reason for such frequency non-mutuality lies in the nature of the collision-induced coherent scattering. It is shown that this scattering occurs because of double non-adiabatic transitions (as affected by collisions) between the states of a dressed atom without changing the environment (buffer) state during the four-photon-scattering elementary process; this scattering will be referred to as coherent collisionally double induced scattering (CCDIS).
In recent years, the collisional redistribution of radiation and collision-induced broadening of Rydberg atomic spectral lines by buffer gas perturbation have aroused the renewed interest. Rydberg atoms having a large dipole moment and long lifetime can interact with each other coherently for relatively long time, which makes them a potential candidate for quantum information processing. Besides, collisional redistribution has an important potential application in laser cooling and trapping. Based on previous experimental data, in this paper, two-nondegenerate four-wave mixing (NFWM) for studying atom collision, composed of two-photon resonant NFWM and collisional redistribution NFWM, is reported. The spectrum variation of the two-NFWM affected by the pressure, temperature, detuning and collision-broadening rate coefficient is analyzed. The principle of two-NFWM involving three incident beams is explained as follows. Consider two-NFWM in a |0-|1-|2 cascade three-level system, where states between |0 and |1 and between |1 and |2 ightangle are coupled by resonant frequencies 1 and 2 , respectively. Beam 1 with frequency 1 propagates along the direction opposite to the direction of beam 2, beams 2 and 2' have the same frequency 2, and between their directions there exists a small angle. Assuming that 1 1 and 2 2 so that 1 drives the transition from |0 to |1 while 2 drives the transition from |1 to |2, the simultaneous interactions of atoms with beams 1 and 2 will induce atomic coherence between |0 and |2 through two-photon excitation. This coherence is probed by beam 2', and as a result a two-photon resonant NFWM signal of frequency 1 is generated in the direction almost opposite to the direction of beam 2'. To avoid strong absorption at the resonant frequency of transition from |0 to |1, here the wavelength of beam1 is detuned from the exact resonance. An atom population of level |1 caused by collisional redistribution can be induced when a certain buffer gas pressure is imposed. The collisional redistribution NFWM process also exists in this case. Beam 2 drives the transition from |1 to |2 to induce an atomic coherence which is probed by beam 2' for giving rise to an atomic population grating. A collisional redistribution NFWM signal propagating along the same direction as the two-photon resonant NFWM signal is generated when beam 1 is scattered by the grating. Much information about atomic collisions can be obtained by analyzing the two NFWM signals. In a cascade three-level system composed of ground state, intermediate state and Rydberg state, and the two-NFWM can be used to investigate not only the broadening and shifting of the Rydberg level but also the collisional redistribution of the intermediate state. Unlike other experiments studying the pressure dependence of the longitudinal relaxation rate of atom states, this technique is a purely optical coherent means, and can measure the transverse relaxation rate 20 between Rydberg state and ground state as well as the pressure dependence of the transverse relaxation rate 21 between Rydberg state and intermediate state.
The four-wave mixing susceptibility χ(3)(ω1, ω1, -ω2) of a system of two-level atoms driven by weak external fields of frequencies ω1 and ω2 in a high-Q cavity is evaluated in the presence of atomic collisions. That susceptibility exhibits resonances corresponding to dipole-allowed transitions between the first two excited manifolds of the dressed states and the ground state and also the collision-induced Bloembergen resonances. The resonances corresponding to transitions between the first two manifolds of excited states that characterize the quantum and nonlinear nature of the atom–field interaction are, however, flattened in the absence of collisions. The collisions thus induce the quantum effects in four-wave mixing in a high-Q cavity.
It is demonstrated that, in the presence of collisions and for nonresonant lasers, it is energetically possible to access resonantly excited states and induce a coherence between the states. This situation cannot arise in the absence of collisions if the starting state does not decay. This explains why, when collisions are introduced, a new signal can be generated in a wave-mixing type of experiment. The collisionally induced generation of a coherent signal is intimately related to the process of collisional redistribution. It is shown that all the collisionally induced coherent signals that have been reported up to now involve putting real populations in the excited states. This fact has not always been fully appreciated. No resonance between unpopulated states can exist. The time dependence of these new coherent signals is briefly discussed. In the case of a Raman resonance between equally populated states, it is pointed out that new coherent pathways of equal importance should be considered for explaining the experimental results. A new pressure-induced signal in four-wave mixing is also discussed. It is called "collisionally triggered two-photon quasiresonant coherent signal."
We study two-photon resonant nondegenerate four-wave mixing (NFWM) in a dressed cascade four-level system. In the presence of a strong coupling field, the two-photon resonant NFWM spectrum exhibits Autler-Townes splitting, accompanied by either suppression or enhancement of the NFWM signal. Such phenomena are demonstrated in Ba through inducing of atomic coherence between the ground state 6s2 and the doubly excited autoionizing Rydberg state 6pnd. This technique provides a spectroscopic tool for measuring not only the resonant frequency and dephasing rate but also the transition dipole moment between two highly excited atomic states.
We present a theoretical analysis of high-frequency optical heterodyne saturation spectroscopy in Doppler-broadened coupled three-level systems. The saturating beam, which is assumed to be amplitude modulated at frequency δ (double-sideband suppressed carrier amplitude modulation) is resonant for one of the transitions. Through non-degenerate four-wave mixing processes, this modulation is transferred to a probe beam, resonant for the coupled transition. Saturating and probe fields may be either co-propagating or counter-propagating. The lineshape of the probe modulation is analysed via a third-order perturbation expansion of the atomic density matrix with respect to the incident field amplitudes. The resulting signal is integrated over velocities, in the Doppler limit approximation. Both population saturation effects and coherent (Raman-type, or two-photon) processes contribute to the signal. The various contributions appear as Lorentzian-type resonance doublets. We show that, in the absence of relaxation processes (collisional dephasing, or radiative cascades), destructive interferences between population saturation and coherent two-photon processes are responsible for the disappearance of one resonance doublet. Phase-interrupting collisions are thus predicted to lead to the existence of a « pressure-induced extra-resonance » (PIER) doublet, which could yield information on collisional processes in the impact regime. The properties of the predicted PIER doublets are analysed in relation with other types of PIER signals studied in four-wave mixing, and in time-resolved saturation spectroscopy.
Resonances of the six-wave mixing susceptibility χ(5)(ω1, ω1, ω1,-ω2,-ω2) at frequency 3ω1-2ω2 of a system of two-level atoms dissipating through the spontaneous emission and collisions and driven by a weak bichromatic external field of frequencies ω1 and ω2 in a finite Q cavity are analyzed. It is shown that the atomic collisions not only induce the usual Bloembergen resonances but that they also play a major role in enhancing the transitions among the higher-order dressed states, thereby bringing out some of the quantum resonances that are suppressed in the absence of collisions. The important contribution of collisions in this higher-order nonlinear process is the generation of the subharmonic resonances at ±1/2 times the hyperfine splitting of the first and the second excited manifolds.