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Journal of the Optical Society of America B

Removing population trapping in a five-level system with fast decay

Xi‐Jing Ning

Published Nov 1, 2003• 2 citations
Publisher

Abstract

A five-level quantum system including two low-lying states and three excited states of the ladder type coupled with four laser fields is investigated as it relates to dressed-atom models, and a dressed state is found to be independent of the ionization decaying from the highest level. Under general conditions, half of the initial population of the two low-lying states is trapped in the dressed state, leading to a low probability of ionization. Based on the analytical results, two schemes are proposed for removing population trapping. For a five-level system with hyperfine structures, such as the system for ionizing 235U atoms, population trapping takes place when the laser fields are weak and can be gotten rid of by an increase in laser intensity.

DOI
10.1364/josab.20.002363

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A five-level quantum system including two low-lying states and three excited states of the ladder type coupled with four laser fields is investigated as it relates to dressed-atom models, and a dressed state is found to be independent of the ionization decaying from the highest level. Under general conditions, half of the initial population of the two low-lying states is trapped in the dressed state, leading to a low probability of ionization. Based on the analytical results, two schemes are proposed for removing population trapping. For a five-level system with hyperfine structures, such as the system for ionizing 235U atoms, population trapping takes place when the laser fields are weak and can be gotten rid of by an increase in laser intensity.
Abstract The coherence phenomenon of atomic population trapping in an excited state of a medium is interesting regarding the basic physics of laser-matter interaction and applications to the generation of pulsed lasers. Here, we propose N numbers of five-level atoms as a gain medium in a weak magnetic field with three excited closely-spaced Zeeman-hyperfine energy levels and two lower energy levels. The excited levels are strongly coupled with a lower level via a coherent-field and to the ground energy level via vacuum field modes. The spontaneous emission spectrum, in general, produces four spectral lines associated with the decaying four dressed states of the atom. Based on parallel dipole moments and radiative decay rates, we find the condition of double coherent population trapping (DCPT) originating from the non-decaying states of the excited dressed states. The decay from the states generates coherence among themselves to eliminate two distinct spectral lines from the spectrum using the trapping condition. In each of the two non-decaying dressed states, 23% of the total atom population traps.
A dressed-state study of lasing without population inversion from a three level atom interacting with a bi-chromatic laser field, in the ladder configuration, is formulated. We allow the atomic system to be dressed by both laser filed photons (double dressing). The evolution of the system under consideration is being explored both analytically and numerically, within the transient regime. Time dependent approximate analytic solutions for dressed-state populations and coherences are derived, within the so called “secular approximation,” under resonant conditions. We also present time dependent numerical solutions for population and coherences in the off-resonance regime. A spectral analysis is also performed revealing the structure of various dressed states transitions. These are shown to be composed of quintets centered about the frequencies of the coupling and probe laser fields and having sidebands located symmetrically at positions shifted from line center at the Rabi and double Rabi frequencies.
We study the effect of quantum interference on the population distribution and absorptive properties of a V-type three-level atom driven by two lasers of unequal intensities and different angular frequencies. Three coupling configurations of the lasers to the atom are analysed: (a) both lasers coupled to the same atomic transition, (b) each laser coupled to different atomic transition and (c) each laser coupled to both atomic transitions. Dressed states for the three coupling configurations are identified, and the population distribution and absorptive properties of the weaker field are interpreted in terms of transition dipole moments and transition frequencies among these dressed states. In particular, we find that in the first two cases there is no population inversion between the bare atomic states, but the population can be trapped in a superposition of the dressed states induced by quantum interference and the stronger field. We show, that the trapping of the population, which results from the cancellation of transition dipole moments, does not prevent the weaker field to be coupled to the cancelled (dark) transitions. As a result, the weaker field can be strongly amplified on transparent transitions. In the case of each laser coupled to both atomic transitions the population can be trapped in a linear superposition of the excited bare atomic states leaving the ground state unpopulated in the steady state. Moreover, we find that the absorption rate of the weaker field depends on the detuning of the strong field from the atomic resonances and the splitting between the atomic excited states. When the strong field is resonant to one of the atomic transitions a quasi-trapping effect appears in one of the dressed states. In the quasi-trapping situation all the transition dipole moments are different from zero, which allows the weaker field to be amplified on the inverted transitions. When the strong field is tuned halfway between the atomic excited states, the population is completely trapped in one of the dressed states and no amplification is found for the weaker field.
The finite bandwidth of a short laser pulse often overlaps several initially unpopulated low-lying excited states of an atom. We show that when such a pulse is used to photoionize an atom, the low-lying levels may be pumped into a coherent superposition that inhibits or prevents excitation of the atom, effectively trapping population in the initial state of the atom. The existence of the effect was first noted in a numerical study of short-pulse excitation of hydrogen. Here we explore the effect through a series of simple models that demonstrate the physics of the effect in the simplest possible situations.
We discuss the condition under which a pair of closely lying levels, when coupled to a fourth level via a single-laser field, exhibit population trapping without decay to a lower level. In the discussion, the decay between the pair and the fourth level is taken into account. When the fourth level is lower than the pair, the condition for population trapping in the pair can be satisfied under arbitrary laser intensity by adjusting the laser detuning. When the fourth level is above the pair, population trapping in the pair is impossible when the decay from the fourth level to the pair is included. The influence of the decay between the pair and the fourth level on the spontaneous spectrum from the pair to the lower level is also studied.
The effect of radiative decay and collisional damping on the delayed-field population transfer in the three-level system is investigated. The simple analytical steady-state solution of the three-level system, interacting with two intense delayed laser pulses in the dressed-state frame, is obtained and analyzed. The radiative relaxation transfers the system to the ``trapped state,'' which is shown to be stable relative to both radiative decay and collisional damping. The effect of an additional level \ensuremath{\Vert}m〉, situated close to the final level \ensuremath{\Vert}3〉, on the population-transfer process is considered. The field-induced relaxation rate from intermediate level \ensuremath{\Vert}2〉 to level \ensuremath{\Vert}3〉 is shown to be a very easily controllable parameter of the field intensities and their relative delay. This result leads to selective population transfer to the desired level and may prevent leaking out of the three-level system. Theoretical analysis corresponds entirely to recent experimental data [U. Gaubatz et al., J. Chem. Phys. 92, 1 (1990); 92, 5363 (1990)].