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Annual Meeting Optical Society of America

Transient lineshapes in nonlinear mixing of pump and probe fields

Manoj Kumar, Joseph H. Eberly

Published Jan 1, 1990• 0 citations
Publisher

Abstract

We present results on transient lineshapes in signals generated coherently via the nonlinear mixing of pump and probe fields in a model two-level system. We confine ourselves to times short compared to atomic relaxation times and hence treat both fields nonperturbatively. However, the probe is assumed to be much weaker than the pump. Transient lineshapes have been studied earlier in the case of atomic relaxation times and hence treat both fields nonperturbatively. However, the probe is assumed to be much weaker than the pump. Transient lineshapes have been studies earlier in the case of atomic inversion. Here, we identify the lineshape with the intensity of the light scattered in a particular direction and around a particular central frequency. The lineshapes are found to exhibit, in the neighbourhood of subharmonic resonances, highly non-lorentzian profiles.

DOI
10.1364/oam.1990.mtt1

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The Journal of Physical Chemistry A•Nov 1, 1998•2 citations
We present results on transient lineshapes in signals generated coherently via the nonlinear mixing of pump and probe fields in a model two-level system. We confine ourselves to times short compared to atomic relaxation times and hence treat both fields nonperturbatively. However, the probe is assumed to be much weaker than the pump. Transient lineshapes have been studied earlier in the case of atomic relaxation times and hence treat both fields nonperturbatively. However, the probe is assumed to be much weaker than the pump. Transient lineshapes have been studies earlier in the case of atomic inversion. Here, we identify the lineshape with the intensity of the light scattered in a particular direction and around a particular central frequency. The lineshapes are found to exhibit, in the neighbourhood of subharmonic resonances, highly non-lorentzian profiles.
We present analytical and numerical results for the line shapes for a two-level atom interacting with pump and probe fields. We focus our attention on a time regime which is small enough that relaxation effects could be neglected, but sufficiently large that one could integrate the signal over a large number of population oscillations between the excited and ground states. As in our earlier work [J. H. Eberly and V. D. Popov, Phys. Rev. A 37, 2012 (1988)], we consider situations where the signal is determined by the atomic inversion, and identify the transient line shape with the time-averaged inversion considered as a function of the probe frequency. We present a formulation, based on the Floquet approach, that allows us to obtain formal expressions for the transient line shape in terms of infinite continued fractions, which can be evaluated numerically. We also present line shapes computed by directly solving the equations of motion numerically and integrating the inversion numerically over long times to compare with our continued-fraction results. We discuss the dependence on initial conditions, the relative pump-probe phase, and the non-Lorentzian character of these line shapes.
A very large number of physical phenomena in the resonant interaction of atomic-molecular systems with the radiation fields can be studied by treating the atomic system as a two level system and by examining its response to the applied fields. Various perturbative results are well known. A number of recent experimental works require the knowledge of the nonperturbative response functions, when both the applied fields are strong. These include a variety of experiments on instabilities(1) in lasers involving the switching from a single mode to for example two mode operation. Similarly recent nonlinear mixing experiments, where not only four wave mixing but also higher mixing in saturating fields has been studied. Pump probe experiments have also been repeated with probes whose intensity could be large. The purpose of this paper is to formulate the general theory and use it to understand the experiments. The formulation we present is also well suited for studying the effect of collisions. Details of various collisional induced coherences in fourwave and six wave mixing etc. can be studied.
Pump-probe interactions underlie the physics of four-wave and other wave-mixing effects. We present analytic formulas for probe response in a special category of pump-probe experiments. We consider a two-level system excited by two distinct fields, the stronger field with fixed frequency and the weaker with a tunable frequency. We focus attention on the spectral regions near the Rabi sidebands of the strong field and its various subharmonics. We consider times sufficiently short that relaxation effects can be ignored, but sufficiently long to encompass many cycles of population oscillation between the ground and excited states. Because there is no damping, both fields are in this sense strong, and we report here the time average of the response. Our results are obtained by making a suitable second-order rotating wave approximation and are shown to involve the initial phase relation between the two fields as well as the initial angles of orientation of the two-level system's Bloch vector. Depending on these initial phase and orientation angles, the absorption line shape may be either positive or negative and either symmetric or antisymmetric.
Summary form only given. It is well-known that the steady-state four-wave mixing (FWM) spectrum, obtained when a two-level atomic system interacts with a coherent pump of arbitrary intensity and a weak probe, is symmetrical and consists of three peaks: a central peak and two Rabi sidebands. Previously, we showed for temporally nonoverlapping pulses, that the spectrum becomes extremely asymmetrical and that only the Rabi sideband near the resonance frequency survives, in the case where the probe precedes the pump. For the opposite case, where the pump precedes the probe, no FWM spectrum is obtained at all. It should be noted that these results hold true provided the pump and probe pulses are much shorter than the transverse relaxation time T/sub 2/ and the pump-probe time delay /spl Delta/t/sub 0/ (/spl Delta/t/sub 0/<0 when the probe precedes the pump). We have also shown that T/sub 2/ can be determined from the slope of the semilog plot of the FWM intensity, near the resonance sideband, versus the pump-probe time delay /spl Delta/t/sub 0/ (for the case /spl Delta/t/sub 0/<0).
Measurements of the relaxation times T1 and T2 of a two-level system by nonlinear transient spectroscopic methods are discussed, where delayed incident pulses are assumed to have correlation times much shorter than T1 or T2 but varied widths. In particular, a delayed degenerate four-wave mixing (photon echoe) and apump-and-probe type transmission measurement with incoherent long pulses are considered in detail, and a principle of their use for ultrafast spectroscopy is clarified. If the field is steady and T1>>T2, the time resolutionof T2measurement by the delayed four-wave mixlng is determined by the field correlation, therefore by the spectral width of the incident light irrespective of the pulse width. The time resoution of the T1 measurement by the pump-and-probe method is determined by the intensity correlation of the incident light, whereasthe one by the delayed four-wave mixing by a higher order correlation.
We predict that the four-wave mixing (FWM) excitation spectrum for a two-level system becomes extremely asymmetrical when steady-state excitation is replaced by pulsed excitation, using temporally nonoverlapping probe and pump pulses. We also show that when a resonant probe pulse precedes the detuned pump pulse, the FWM signal may become more intense than when the pulses overlap. These effects are attributed to free-induction decay (FID): the coherence induced in the two-level system by a short resonant probe pulse survives the pulse (FID) and replaces it in producing a strong nonlinear signal on interaction with the strong pump pulse. Moreover, by plotting the FWM signal intensity as a function of the delay between the probe and pump pulses, an efficient method is proposed for determining short transverse relaxation times or fast chemical reaction rates.