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Physica Scripta

Double coherent population trapping in a laser-driven atomic medium via spontaneous emission generated coherence

Shakir Ullah, Muhammad Kamil Abbasi, Haleema Sadia Qureshi, Fazal Ghafoor

Published May 8, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1402-4896/add62b

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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.
For a three-level atom in the ssV configuration (i.e., having two excited states each dipole-coupled to a common ground state), we have found a particular linear combination of bare-atom states in which Rabi oscillations and their associated collapses and revivals do not occur. Moving to a dressed-state picture, we discover that this particular linear combination state is just that dressed state which is decoupled from all the field modes. It is a dressed state for which the transition dipole moments with the other dressed states are zero. The existence of this decoupled dressed state depends on the tuning of the dressing laser field, which in turn depends on the bare-atom excited-state dipole moments and energy-level separation. When we include spontaneous emission, the population decays from the other dressed states into this decoupled state and remains coherently trapped there, producing a system that experiences no dynamical behavior. This is exact for \ensuremath{\delta}-function photon statistics (i.e., if there is no intensity uncertainty). The trapping becomes less perfect as the photon statistics are allowed to have a greater bandwidth. Also, if the applied field is tuned incorrectly, the spontaneous realignment of the atomic state amplitudes does not result in a totally decoupled dressed state, and the dynamics proceed normally.
We investigate the features of the spontaneous emission spectra in a coherently driven cold five-level atomic system by means of a radio frequency (rf) or microwave field driving a hyperfine transition within the ground state. It is shown that a few interesting phenomena such as spectral-line narrowing, spectral-line enhancement, spectral-line suppression, and spontaneous emission quenching can be realized by modulating the frequency and intensity of the rf-driving field in our system. In the dressed-state picture of the coupling and rf-driving fields, we find that this coherently driven atomic system has three close-lying levels so that multiple spontaneously generated coherence (SGC) arises. Our considered atomic model can be found in real atoms, such as rubidium or sodium, so a corresponding experiment can be done to observe the expected phenomena related to SGC reported by Fountoulakis et al. [Phys. Rev. A 73, 033811 (2006)], since no rigorous conditions are required.
The effect of spontaneously generated coherence (SGC) on spontaneous emission and dynamical evolution of a microwave-driven four-level atomic system is studied. Interesting phenomena due to SGC, such as spectral-line narrowing, spectra-line enhancement, spectral-line suppression, and fluorescence quenching, are shown in the spontaneous emission spectra, which can be effectively modulated by amplitude and phase of the microwave field. Due to SGC, the total populations are partly, even completely, trapped in upper levels in steady state, the decay time of which is sensitive to the phase of the microwave field. In the dressed state picture, multiple SGC arise during the process of three close-lying states decaying to the same state. The corresponding experiment to observe the expected phenomena related to SGC can be more conveniently realized in atoms, since no rigorous conditions are required and the amplitude and phase of the microwave field can be conveniently controlled.
In this paper we investigate the resonance fluorescence, the squeezing, and the absorption spectra of a laser-driven four-level atom consisting of three closely spaced upper levels decaying to a common lower level. The three upper levels are coupled by the same vacuum modes to the lower level leading to spontaneously generated coherence effects. High population inversion and extremely narrow emission lines are obtained with moderate Rabi frequencies, which are a direct consequence of decay-induced interferences. The fluorescent field is shown to exhibit two-mode squeezing in the in-phase quadrature. Squeezing in both quadratures simultaneously at different frequencies is greatly enhanced when quantum interference is accounted for. We also examine the absorption spectrum of a weak field and demonstrate that quantum interference can induce two prominent and nearly transparent holes where the slope of the refractive index is very steep. This special situation could allow the simultaneous propagation of two weak pulses with different frequencies, which could be feasibly exploited towards the realization of the entanglement of two photons.
Possibility of coherent control of spontaneous emission from four- and five-level systems in the laser radiation field is studied. The four-level system consists of two levels resonantly driven by laser radiation where either of levels may decay to a separate level. For such a system we show that the presence of the second decay channel may deteriorate the destructive interference occurring because of Autler-Townes effect in case of one decay channel. The five-level system represents two two-level resonantly driven systems with the upper levels decaying to a common level. For this case, the interference between the two decay channels is partially or completely destructive or constructive depending on the initial conditions and on the mutual orientation of the transition dipole moments. It is shown that population transfer takes place by the same quantum vacuum via spontaneous emission. The populations are shown to have damping oscillatory nature.
We investigate the spontaneous emission spectra of a coherently driven four-level cold atomic system. It is shown that a few interesting phenomena such as spectral-line narrowing, spectral-line enhancement, spectral-line suppression, and spontaneous emission quenching can be realized in our system. The spectral-line enhancement and suppression can be conveniently manipulated by appropriately modulating the frequency detuning of the probe driving field. In the dressed-state picture of the probe and coupling fields, we find that this coherently-driven atomic system has three close-lying levels so that multiple spontaneously-generated coherence (SGC) arises. Our considered atomic model can be found in real atoms, such as rubidium or sodium, so a corresponding experiment can be done to observe the expected phenomena related to SGC effect, since no rigorous conditions are required.