We analyze the efficiency of coherent population trapping (CPT) in a superposition of the ground states of three-level atoms under the influence of the decoherence process induced by a broadband thermal field. We show that in a single atom there is no perfect CPT when the atomic transitions are affected by the thermal field. The perfect CPT may occur when only one of the two atomic transitions is affected by the thermal field. In the case when both atomic transitions are affected by the thermal field, we demonstrate that regardless of the intensity of the thermal field the destructive effect on the CPT can be circumvented by the collective behavior of the atoms. An analytic expression was obtained for the populations of the upper atomic levels which can be considered as a measure of the level of thermal decoherence. The results show that the collective interaction between the atoms can significantly enhance the population trapping in that the population of the upper state decreases with an increased number of atoms. The physical origin of this feature is explained by the semiclassical dressed-atom model of the system. We introduce the concept of multiatom collective coherent population trapping by demonstrating the existence of collective (entangled) states whose storage capacity is larger than that of the equivalent states of independent atoms.
We analyze the efficiency of coherent population trapping (CPT) in a superposition of the ground states of three-level atoms under the influence of the decoherence process induced by a broadband thermal field. We show that in a single atom there is no perfect CPT when the atomic transitions are affected by the thermal field. The perfect CPT may occur when only one of the two atomic transitions is affected by the thermal field. In the case when both atomic transitions are affected by the thermal field, we demonstrate that regardless of the intensity of the thermal field the destructive effect on the CPT can be circumvented by the collective behavior of the atoms. An analytic expression was obtained for the populations of the upper atomic levels which can be considered as a measure of the level of thermal decoherence. The results show that the collective interaction between the atoms can significantly enhance the population trapping in that the population of the upper state decreases with an increased number of atoms. The physical origin of this feature is explained by the semiclassical dressed-atom model of the system. We introduce the concept of multiatom collective coherent population trapping by demonstrating the existence of collective (entangled) states whose storage capacity is larger than that of the equivalent states of independent atoms.
ABSTRACT We investigate the steady-state properties and dynamics of a three-level cascade atom interacting with a thermal light field, focusing on how ther mal photon occupation affects population distributions, coherence decay, and fluorescence spectra. Using a rate-equation model and analytical ex pressions for the steady-state populations, we examine the time evolution of the atomic populations under low, intermediate, and high thermal pho ton numbers ¯n. At intermediate ¯n, a balance between spontaneous emis sion and thermal absorption emerges, yielding nonzero stable populations at all levels; conversely, for low ¯n, spontaneous emission dominates, and the system rapidly decays to the ground state. We also investigate the degradation of coherence |ρfe(t)| between the upper and intermediate lev els. At high thermal photon numbers, thermalization drives the system toward equipartition, such that the populations of all levels become nearly equal. We show that increasing thermal occupation shortens the life time of quantum superpositions and accelerates decoherence, as evidenced by the loss of |ρfe(t)|. In the steady-state fluorescence spectrum of the |e〉 → |g〉 transition, Lorentzian broadening, proportional to the effective decoherence rate, highlights the influence of thermal photons on phase co herence and spectral features. These findings have direct implications for quantum information processing: they demonstrate how thermal noise markedly degrades coherence, gate fidelity, and photon emission quality. Keywords: population distribution; three-level cascade atom; thermal light field; steady state population; rate-equation model; coherence decay. vii
We explore the quantum entanglement between two collective fields via atomic coherence effects. For three-level atoms in V configuration driven by two applied fields on two-photon resonance, one coherent superposition of the excited states is not excited, which is the counterpart of coherent population trapping. The coherence-induced depopulation makes two cavity fields in each collection combine into a quantum-beat, i.e., equivalently, the difference mode of the two components decouples from the driven atoms. The two sum modes, when they are arranged in the four-wave mixinglike interactions, can be prepared in Einstein-Podolsky-Rosen entangled state. Correspondingly, any two individual fields from different collective modes are entangled with each other. Furthermore, the effects of thermal reservoir and laser linewidths are discussed, and a generalization is given to the case in which each quantum beat involves more than two modes.
ABSTRACT We investigate the steady-state properties and dynamics of a three-level cascade atom interacting with a thermal light field, focusing on how ther mal photon occupation affects population distributions, coherence decay, and fluorescence spectra. Using a rate-equation model and analytical ex pressions for the steady-state populations, we examine the time evolution of the atomic populations under low, intermediate, and high thermal pho ton numbers ¯n. At intermediate ¯n, a balance between spontaneous emis sion and thermal absorption emerges, yielding nonzero stable populations at all levels; conversely, for low ¯n, spontaneous emission dominates, and the system rapidly decays to the ground state. We also investigate the degradation of coherence |ρfe(t)| between the upper and intermediate lev els. At high thermal photon numbers, thermalization drives the system toward equipartition, such that the populations of all levels become nearly equal. We show that increasing thermal occupation shortens the life time of quantum superpositions and accelerates decoherence, as evidenced by the loss of |ρfe(t)|. In the steady-state fluorescence spectrum of the |e〉 → |g〉 transition, Lorentzian broadening, proportional to the effective decoherence rate, highlights the influence of thermal photons on phase co herence and spectral features. These findings have direct implications for quantum information processing: they demonstrate how thermal noise markedly degrades coherence, gate fidelity, and photon emission quality. Keywords: population distribution; three-level cascade atom; thermal light field; steady state population; rate-equation model; coherence decay. vii
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.
Master equation methods are used to investigate the effects of a broad-band squeezed vacuum on a three-level atom of the lambda configuration. The two-mode squeezed vacuum is treated as a Markovian reservoir in a non-stationary phase-dependent state. In addition to the squeezed vacuum the atom is driven by two coherent laser fields each of which, depending on the polarization, can couple to one or both of the atomic transitions. We show that in general the optical Bloch equations for the atomic density matrix elements have oscillatory coefficients, thereby necessitating the use of Floquet methods. For the case of equal laser frequencies, which are also equal to the carrier frequency of the squeezed vacuum, the coefficients of the Bloch equations become time independent and stationary solutions for the populations and coherences are obtained by standard matrix methods. For the ordinary vacuum the usual coherent population trapping effect at two-photon resonance is obtained, with the upper state population being zero. An unsqueezed thermal field partially destroys the trapping effect as the upper state population is no longer zero at two-photon resonance. The squeezed vacuum has the effect of improving the trapping in that the coherence hole becomes more pronounced for some values of the relative phase between the squeezed vacuum and the driving fields. The additional effects of a coherence transfer rate between the two optical coherences, which occurs for special choices of angular momentum quantum numbers are also studied. For the case of equal laser frequencies, the inclusion of this coherence transfer process destroys population trapping and reduces the lambda system to a two-level system. However, for the case of unequal laser frequencies, the coherence transfer process in combination with the squeezed vacuum can restore to some extent the population trapping. We show that other features that do not occur for two-level atoms, such as stationary population inversions between pairs of the atomic levels, also depend on the relative phase and can be enhanced in the squeezed vacuum. In the case of unequal frequencies of the driving fields the population in the upper state depends on the relative phase only when the carrier frequency of the squeezed vacuum is equal to one of the two frequencies of the driving fields. When the carrier frequency of the squeezed vacuum is slightly detuned from both frequencies of the driving fields, the population in the upper state is insensitive to the relative phase but is dependent on the degree of squeezing. For large detunings, the population does not show any dependence on the degree of squeezing and its distribution in function of the two-photon detuning is similar to that in the thermal vacuum field.