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Physical Review A

Gating of population flow in resonant multiphoton excitation

Bruce W. Shore

Published Mar 1, 1984• 9 citations
Publisher

Abstract

I discuss the flow of excitation probability along a multistate chain of resonant excitations as driven by coherent photoexcitation, in particular the gated interruption of this probability flow caused by a strongly coupled side branch. If the side branch is itself a chain, not a single transition, then flow inhibition occurs if the number of branch transitions is odd, but no inhibition occurs if the number is even. The inhibition provides a limiting bound on the intensity of amplified stimulated emission.

DOI
10.1103/physreva.29.1578

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I discuss the flow of excitation probability along a multistate chain of resonant excitations as driven by coherent photoexcitation, in particular the gated interruption of this probability flow caused by a strongly coupled side branch. If the side branch is itself a chain, not a single transition, then flow inhibition occurs if the number of branch transitions is odd, but no inhibition occurs if the number is even. The inhibition provides a limiting bound on the intensity of amplified stimulated emission.
Laser isotope separation schemes which require resonant photoexcitation of atoms or molecules with complex spectra will in general involve processes more complicated than a simple chain of transitions between successive pairs of energy levels. In the rotating-wave approximation these situations can be described by excitation graphs with side branches and cycles. For many cases a simple change of basis removes the time dependence of the interaction Hamiltonian and reduces the calculation of level populations and interlevel flows to an eigenvalue problem. By this method it is shown that a side branch with a large matrix element strongly inhibits the flow of population along the path to which it is attached. When several phase-locked lasers are employed, the populations and flows depend on certain linear combinations of the phases, one for each independent cycle in the excitation graph. In the simplest one-cycle example this phase dependence allows a continuous change from no population inversion to complete inversion.
We have calculated the excitation spectra of a single electron in the excited state of a four-level atom interacting with three laser fields at low intensities, where two of them are on two-photon resonance with the three levels of the atom, while the third laser is a weak one operating between the fourth and excited level of the atom. It is shown that light is switched off at certain frequency due to the coherent population trapping while light is turned on at another frequency, where stimulated emission occurs leading to light amplification without population inversion.
We present a detailed theory of a technique for the adiabatic control of the population flow through a preselected decaying excited level in a three-level ladder quantum system, as was experimentally demonstrated recently by Garcia-Fernandez et al. [Phys. Rev. Lett. 95, 043001 (2005)]. Specifically, we consider a three-state excitation chain of bound states, 1-2-3, of successively increasing excitation energy, in which probability loss via fluorescence occurs from states 2 and 3. We describe a laser excitation scheme that can, by adjustment of laser parameters, alter at will the relative fraction of population that, starting from state 1, is ultimately lost through states 2 and 3. We present analytical results for the conditions under which quasiadiabatic passage can take place.
When exposed to intense light of \ensuremath{\sim}580 nm, the ground state of K shifts up in energy, passing through two-photon resonances with Rydberg states and finally crossing the two-photon ionization limit. Using laser pulses of 0.5 to 13 ps duration, we have shown experimentally that ionization occurs for short pulses, but for long pulses the population is diverted into the Rydberg states where some population survives the peak intensity of the pulse, in excellent agreement with a dynamic Floquet model.
The propagation of a strong coherent "pump" wave traveling through a resonant medium is discussed. The medium is assumed to consist of identical stationary atoms, and the pump-wave frequency is assumed to coincide exactly with the resonance frequency for transitions between a particular pair of atomic states. A previously developed theory of the response of a strongly driven atom to a weak nearly resonant "signal" field is used to deduce the existence of a coupling between any two waves travelling parallel to the pump wave whose (nearly equal) frequencies sum to twice the pump-wave frequency. In the limit of very intense (highly saturating) pump fields, the coupling between the two waves of nearby frequencies leads to amplification of both waves if their frequencies lie within an interval about the pump-wave frequency equal to the Rabi frequency of population inversion. The basic process, which is roughly described by travelling-wave parametric-amplifier equations of motion, consists of the absorption of two pump-field photons followed by their emission at different nearby frequencies, and thus implies a frequency instability of the initially coherent pump wave.