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Physical Review A

Field-induced resonances in four-wave mixing

Nadav Horesh, Yehiam Prior

Published Jul 1, 1993• 7 citations
Publisher

Abstract

An experimental observation of field-induced resonances in four-wave mixing is reported. In experiments on Na vapor near the D lines, when the input fields are strong, new resonances appear, confirming recent theoretical predictions based on a nonperturbative approach to wave-mixing processes. The analogy to and differences from the pressure-induced extra resonances are discussed.

DOI
10.1103/physreva.48.r38

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Annual Meeting Optical Society of America•Jan 1, 1991•0 citations
An experimental observation of field-induced resonances in four-wave mixing is reported. In experiments on Na vapor near the D lines, when the input fields are strong, new resonances appear, confirming recent theoretical predictions based on a nonperturbative approach to wave-mixing processes. The analogy to and differences from the pressure-induced extra resonances are discussed.
Four wave mixing experiments are normally performed near atomic (molecular) resonances, when some of the input frequencies or their combinations are at resonance with the atomic transitions. If dephasing process are present, several new resonances appear, that may be traced directly to the influence of the dephasing processes. The origin of the ‘‘dephasing’’ may vary from collisions and other material relaxation processes, to field fluctuations, to higher order interactions in the wave mixing process. The source of these extra resonances is discussed, and specific results are shown for the various cases.
A nonperturbative semiclassical theory is presented for the treatment of four-wave mixing (FWM) in a four-level system. This treatment is based on a transformation to a generalized rotating frame followed by a numerical diagonalization of the resulting time-independent Hamiltonian. For strong fields, all resonant frequencies are shifted from the atomic (molecular) frequencies. Lines are split up in a way similar to the ac Stark effect for a two-level system, and for even stronger fields, the effect of stirring is observed for the first time in four-wave mixing. In addition, a new extra resonance appears which is induced by the saturating field. This field-induced resonance is the new member in the family of extra resonances (pressure induced, or stochastic fluctuation induced), and it should be observed whenever saturating fields interact with a multilevel atomic or molecular system.
A nonperturbative density-matrix formalism is used for the analysis of strong-field four-wave mixing, allowing the treatment of relaxation processes, including lifetime as well as dephasing. The combined role of proper dephasing and level saturation in the generation of extra resonances is studied. It is shown that, whereas in the absence of proper dephasing there is no pressure-induced resonance, there is always a nonzero contribution to the field-induced resonance. For increasing field intensity, a characteristic double saturation is predicted as a function of the field strength. The dependence on the various parameters is investigated, and the conditions under which these effects should be observable are identified.
Experiments on pressure-induced extra resonances in degenerate four-wave mixing involving Zeeman coherence have been performed on Ba atoms in an argon atmosphere under conditions of large detunings from the Ba resonance line. The dependence on the detuning gives evidence for a breakdown of the impact approximation, when the laser is detuned by more than 5\ifmmode\times\else\texttimes\fi{}1011{10}^{11}1011 rad ${\mathrm{sec}}^{\ensuremath{-}1}$; the behavior can be interpreted semiquantitatively by a model based on optical collisions.
A recently presented treatment of four-wave mixing for fields of arbitrary strength1 is applied to the 3S–3P transitions of sodium. The line shapes associated with ordinary resonances, and with both pressure-induced and field-induced extra resonances are investigated. In sodium, the two lower levels (g,t) are very close, i.e., their separation is 0.059 cm-1. Thus decays from the upper (k,j) levels to each of the lower levels are expected to contribute significantly. Also, contributions associated with (g,t) population exchange because of the close proximity of these states are incorporated. The influence of the decay pattern and of the respective values of the decay constants is studied, especially as compared to the line shapes that would result if all decays were dominantly to the ground state. Regions of enhancement for the more complex decay pattern are found for field-induced extra resonances. The relative effects of spontaneous decay (T1) and proper dephasing (T2) on the line shapes is examined. It is found that (T2) dominates for weak field conditions but that both contribute significantly for strong field situations.