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arXiv:quant-ph/9909061 · Physical Review A

Coherent properties of a tripod system coupled via a continuum

Razmik G. Unanyan, Nikolay V. Vitanov, Bruce W. Shore, Klaas Bergmann

Published Mar 9, 2000• 30 citations
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Abstract

We present results from a study of the coherence properties of a system involving three discrete states coupled to each other by two-photon processes via a common continuum. This tripod linkage is an extension of the standard laser-induced continuum structure (LICS), which involves two discrete states and two lasers. We show that in the tripod scheme, there exist two population trapping conditions; in some cases these conditions are easier to satisfy than the single trapping condition in a two-state LICS. Depending on the pulse timing, various effects can be observed. We derive some basic properties of the tripod scheme, such as the solution for coincident pulses, the behavior of the system in the adiabatic limit for delayed pulses, the conditions for no ionization and for maximal ionization, and the optimal conditions for population transfer between the discrete states via the continuum. In the case when one of the discrete states is strongly coupled to the continuum, the population dynamics reduces to a standard two-state LICS problem (involving the other two states) with modified parameters; this provides the opportunity to customize the parameters of a given two-state LICS system.

DOI
10.1103/physreva.61.043408

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We present results from a study of the coherence properties of a system involving three discrete states coupled to each other by two-photon processes via a common continuum. This tripod linkage is an extension of the standard laser-induced continuum structure (LICS), which involves two discrete states and two lasers. We show that in the tripod scheme, there exist two population trapping conditions; in some cases these conditions are easier to satisfy than the single trapping condition in a two-state LICS. Depending on the pulse timing, various effects can be observed. We derive some basic properties of the tripod scheme, such as the solution for coincident pulses, the behavior of the system in the adiabatic limit for delayed pulses, the conditions for no ionization and for maximal ionization, and the optimal conditions for population transfer between the discrete states via the continuum. In the case when one of the discrete states is strongly coupled to the continuum, the population dynamics reduces to a standard two-state LICS problem (involving the other two states) with modified parameters; this provides the opportunity to customize the parameters of a given two-state LICS system.
Laser-induced-continuum-structure (LICS) allows for coherent control techniques to be applied in a Raman type system with an intermediate continuum state. The standard LICS problem involves two bound states coupled to one or more continua. In this paper, we discuss the simplest non-trivial multistate generalization of LICS which couples two bound levels, each composed of two degenerate states through a common continuum state. We reduce the complexity of the system by switching to a rotated basis of the bound states, in which different sub-systems of lower dimension evolve independently. We derive the trapping condition and explore the dynamics of the sub-systems under different initial conditions.
Summary form only given. We study two fundamental systems that involve continua: a system with a single autoionizing state and the laser induced continuum structure scheme (LICS), both shown. We pay special attention to the response of these systems to time-dependent pulse interactions, which we find to differ from that of square pulse interactions. Such a study is particularly useful from the point of view of the many applications associated with these systems. For the theoretical analysis we perform appropriate transformations that allow us to study both systems simultaneously. From an analysis of the resulting Hamiltonian of these systems, we determine the important conditions for efficient population trapping.
We present experimental and theoretical results of a detailed study of laser-induced continuum structures (LICS's) in the photoionization continuum of helium out of the metastable state 2s1S0.2s{}^{1}{S}_{0}.2s1S0​. The continuum dressing, with a 1064-nm laser, couples the same region of the continuum to the 4s1S04s{}^{1}{S}_{0}4s1S0​ state. The experimental data, presented for a range of intensities, show pronounced ionization suppression (by as much as 70% with respect to the far-from-resonance value) as well as enhancement, in a Beutler-Fano resonance profile. This ionization suppression is a clear indication of population trapping mediated by coupling to a continuum. We present experimental results demonstrating the effect of pulse delay upon the LICS's, and for the behavior of LICS's for both weak and strong probe pulses. Simulations based upon numerical solution of the Schr\"odinger equation model the experimental results. The atomic parameters (Rabi frequencies and Stark shifts) are calculated using a simple model-potential method for the computation of the needed wave functions. The simulations of the LICS profiles are in excellent agreement with experiment. We also present an analytic formulation of pulsed LICS's. We show that in the case of a probe pulse shorter than the dressing one, the LICS profile is the convolution of the power spectra of the probe pulse with the usual Fano profile of stationary LICS's. We discuss some consequences of deviation from steady-state theory.
In recent years our understanding of how laser fields interact with a continuum of levels has progressed substantially. No longer is the continuum viewed as a dissipative environment, best described by a set of kinetic equations. Recent theoretical* and experimental work has shown that strong laser fields involving a continuum of levels may often maintain perfeet coherence. One of the m ore interesting colterent phenomena involving the continuum is the dressing of a continuum by a bound state, termed laser-induced continuum structure (LICS). In the LICS phenomenon, a strong laser field, connecting an unpopulated bound state to the continuum mixes some bound- state character into the continuum. This optically induced resonance can be detected by a second (weaker) laser field, which induces a transition from a populated bound state to the structured continuum.
Laser induced continuum structures (LICS) can be produced by a strong laser embedding an excited atomic bound state into a flat atomic continuum, leading to a tunable resonance of adjustable width that can be probed by a second laser. If this second laser is of similar intensity to the embedding laser then the distinction between the two becomes artificial and saturation effects become important. In this paper the effect on LICS of transitions caused by both lasers between the original atomic continuum and a second atomic continuum are studied in the Markoff approximation by means of Laplace transform methods and allowing for the ionization of each atomic state by both laser fields. Formal results correct to all orders are also given in terms of a T-matrix approach. Numerical calculations are presented showing the effects on the LICS resonant structures of continuum-continuum coupling processes. Significant changes to the Fano profiles (second laser weak) and to coherence holes (second laser strong) occur. Analytical results are also given.
We have developed a theory of three-pulse coherent control of photochemical processes. It is based on adiabatic passage and quantum coherence and interference attributed to the lower-lying dissociation continuum and excited upper discrete states, which are otherwise not connected to the ground state by one-photon transitions. Opportunities offered by the proposed scheme are demonstrated through extensive numerical simulations with the aid of a model relevant to typical experiments. The opportunities for manipulating the distribution of the population among discrete and continuous states with any necessary ratio by the end of the pulses are demonstrated.