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Physical Review A

Nondecaying state in a three-level system driven by a single field:mEffect of relaxations

Hu Huang, Shi-Yao Zhu, Muhammad Suhail Zubairy

Published Jan 1, 1997• 47 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.55.744

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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 authors consider population trapping in a three-level system which is driven by two applied fields of arbitrary intensity, frequency and bandwidth. An irreversible loss of population is allowed to take place from the common level. The conditions are investigated under which population trapping can occur when spontaneous emission and finite radiation bandwidths are allowed. For the lambda configuration with monochromatic lasers the authors find that increasing the spontaneous emission rate can increase the amount of population trapped in the system, whereas spontaneous emission destroys trapping in the ladder configuration. For the case of uncorrelated lasers, finite laser bandwidths destroy trapping for either configuration.
We derive equations that describe the dynamics of three-level atoms with a cascade system of levels interacting with two resonant coherent fields in conditions where cooperative relaxation dominates over incoherent spontaneous emission. We calculate the temporal dynamics of the values of the atomic populations. The possibility of coherent population trapping in the presence of the cooperative decay is established. Finally, we calculate the averaged population of the intermediate level as a function of detuning for different values of the coupling constant.
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)].
The collective spontaneous emission of a pair of two coupled three-level radiators in vacuum is investigated in the presence of a possibly intense laser field. The parameters describing the collective interaction along with the population and decay rates of all involved dressed states are shown to be controllable by the applied laser field. In particular, all populations of the collective system may be transferred at will in a reversible way into a subradiant state, allowing effective storage and manipulation of the quantum system.
We show that an arbitrary system described by two dipole moments exhibits coherent superpositions of internal states that can be completely decoupled from the dissipative interactions (responsible for decoherence) and an external driving laser field. These superpositions, known as dark or trapping states, can be completely stable or can coherently interact with the remaining states. We examine the master equation describing the dissipative evolution of the system and identify conditions for population trapping and also classify processes that can transfer the population to these undriven and nondecaying states. It is shown that coherent transfers are possible only if the two systems are nonidentical, that is the transitions have different frequencies and/or decay rates. In particular, we find that the trapping conditions can involve both coherent and dissipative interactions, and depending on the energy level structure of the system, the population can be trapped in a linear superposition of two or more bare states, a dressed state corresponding to an eigenstate of the system plus external fields or, in some cases, in one of the excited states of the system. A comprehensive analysis is presented of the different processes that are responsible for population trapping, and we illustrate these ideas with three examples of two coupled systems: single V- and $\ensuremath{\Lambda}$-type three-level atoms and two nonidentical two-level atoms, which are known to exhibit dark states. We show that the effect of population trapping does not necessarily require decoupling of the antisymmetric superposition from the dissipative interactions. We also find that the vacuum-induced coherent coupling between the systems could be easily observed in $\ensuremath{\Lambda}$-type atoms. Our analysis of the population trapping in two nonidentical atoms shows that the atoms can be driven into a maximally entangled state which is completely decoupled from the dissipative interaction.
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.