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Journal of Modern Optics

Quantum interference in a Λ system with a close lying excited level: probe absorption versus amplification

Niharika Singh, Richard D’Souza, Q. V. Lawande, B. N. Jagatap

Published Jun 4, 2018• 2 citations
Publisher

Abstract

Pump–probe spectroscopy of a four-level system (FLS) consisting of a Λ system with an additional close lying excited level is investigated. The level configuration gives rise to two simultaneously excited Λ resonances driven by the same pump and probe laser beams. Two such four-level configurations, 5s1/2F=1,2→5p1/2F′=1,2 (FLS1) and 5s1/2F=1,2→5p3/2F′=1,2 (FLS2) respectively in the D1 and D2 transitions of 87Rb, are used as model systems to study theoretically the probe absorption spectrum. It is observed that the signature of the quantum interference is dependent on the nature of the FLS; FLS1 exhibits probe amplification as against probe absorption in FLS2. This contrasting behaviour is further corroborated by analytical results, which highlight the importance of transition dipole moments, atom–field interaction parameters and incoherent decays associated with the FLS. The discussion is further augmented using quantum jump formalism, which provides useful insight into the underlying mechanism responsible for probe amplification versus absorption.

DOI
10.1080/09500340.2018.1480067

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arXiv:quant-ph/0005118•Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Oct 21, 1998•7 citations
Pump–probe spectroscopy of a four-level system (FLS) consisting of a Λ system with an additional close lying excited level is investigated. The level configuration gives rise to two simultaneously excited Λ resonances driven by the same pump and probe laser beams. Two such four-level configurations, 5s1/2F=1,2→5p1/2F′=1,2 (FLS1) and 5s1/2F=1,2→5p3/2F′=1,2 (FLS2) respectively in the D1 and D2 transitions of 87Rb, are used as model systems to study theoretically the probe absorption spectrum. It is observed that the signature of the quantum interference is dependent on the nature of the FLS; FLS1 exhibits probe amplification as against probe absorption in FLS2. This contrasting behaviour is further corroborated by analytical results, which highlight the importance of transition dipole moments, atom–field interaction parameters and incoherent decays associated with the FLS. The discussion is further augmented using quantum jump formalism, which provides useful insight into the underlying mechanism responsible for probe amplification versus absorption.
We investigate coherent pump–probe spectroscopy of a medium of atoms in Λ configuration with a closely placed adjacent excited level. The presence of the additional level results in two simultaneous Λ resonances excited by the same pair of pump and probe fields. A master equation framework is used to discuss the probe absorption spectrum and dispersion in the absence/presence of inhomogeneous broadening, and the results are illustrated by using a model four-level system in the D2 transition of 85Rb. The system is observed to exhibit additional interference effects arising from two competing Λ resonances. These effects manifest in terms of linewidths of the triplet dressed state spectrum and suppression of the subnatural peak for the stationary atoms. The effect on electromagnetically induced transparency is discussed in the light of its shape, position and linewidth. The discussion is further augmented by the study of a six-level model as applicable to the D2 transition of 85Rb. The analysis presented here provides a realistic theoretical description of the pump–probe spectroscopy of hyperfine transitions of alkali atoms.
We examine the absorption of a weak probe beam by a laser driven V-type atom with a pair of closely lying excited levels, where both the driving and probe lasers interact simultaneously with the two transitions. The effects of quantum interference among decay channels on the absorption spectra are also investigated. We introduce dipole moments in the dressed-state representation and the Hamiltonian in terms of the dressed states describing the interaction between the probe and the atom. In the degenerate case, features similar to that of a driven two-level atomic system are found due to some dark transitions in the spontaneous emission and the fact that the probe beam only detects certain transitions. In the nondegenerate case, the absorption spectrum is strongly influenced by the degree of quantum interference, resulting in different line shapes for emission peaks, absorption peaks, and dispersionlike profiles. The effect of probe polarization on the absorption spectrum is also investigated.
The response of a coherently prepared four-level λ-type system, interacting with two electromagnetic fields in a Doppler-free pump–probe configuration is analytically formulated. Under density matrix formalism the probe coherence (field-dependent phase) and atomic coherence (field-independent phase) are introduced through the off-diagonal matrix elements. The coherent effects on probe response is investigated for probe coherence, as well as for the driving contribution (coherence) of the pump field. We show how probe coherence can modify the Rabi splitting and two-photon absorption, through shifting and broadening of spectral lines for on- and off-resonance pumping, respectively. In addition, we report on the enhancement of absorptionless dispersion (i.e. refractive index for on and around probe resonance) and two-photon absorption, via coherent control of the driving contribution of the pump field.
We have analyzed the properties of weak probe absorption in a closed four-level Y -type system driven by a coherent driving field. The system with two nearly degenerate uppermost levels interacting with the same modes of the vacuum radiation field exhibits the interference effect between the spontaneous decay channels. The phenomenon of this quantum interference can significantly change the absorptive response of the weak probe field. On varying the amplitude of the resonant driving field, in the absence of incoherent pumping in the upper transitions the system can display probe transparency as well as enhanced absorption peak under the condition of resonant detuning of the probe field. With the application of incoherent pumping to the system the phenomenon of symmetric light amplification with two distinct gain peaks one each at the positions of Autler–Townes resonances can be achieved in the presence of the decay-interference effect. We have also shown that the unidirectional incoherent pumping mode is necessary for the evolution of probe gain.
We calculate the absorption spectrum of a weak probe interacting with a \ensuremath{\Lambda}-shaped three-level system driven by a single pump. We find that there are four types of terms that contribute to the probe absorption: population-difference and two-photon coherence terms which derive solely from interaction with the pump (dc terms) and population-difference and two-photon coherence terms that pulsate at the pump-probe frequency offset. We find that the main features of the probe spectrum derive from the pulsating terms whereas the dc terms either interfere destructively with each other or with the pulsating terms. This is a clear extension to the three-level system of the concept of light amplification by coherence. We calculate the spectrum for three cases: (i) a degenerate population-trapped system, (ii) a degenerate system in which both transitions are population inverted, and (iii) a nondegenerate population-trapped system. The results of case (i) are similar to those for the two-level system but the population-trapped system has the advantage of avoiding pump absorption. We show that the Rabi frequency of the nonabsorbed pump can be found by determining the probe frequencies at which probe nonabsorption occurs. In (ii), the results are compared with the case where two pumps interact resonantly with a nondegenerate system. In (iii), we find that the populations in the lower states behave dispersively as a function of the pump detuning. For Rabi frequencies that are small compared to the separation between the lower levels, the lower level nearer to resonance is less populated than the other level. However, at higher Rabi frequencies, the situation is reversed. The probe spectrum contains two absorption peaks when the pump Rabi frequency is small and two emission peaks when it is large.
An influence of nonlinear interference processes at quantum transitions in strong resonance electromagnetic fields on absorption, amplification and refractive indices as well as on four-wave mixing processes is investigated. Doppler broadening of the coupled transitions, incoherent excitation, relaxation processes, as well as power saturation processes associated with the coupled levels are taken into account. Both closed (ground state is involved) and open (only excited states are involved) energy level configurations are considered. Common expressions are obtained which allow to analyze the optical characteristics (including gain without inversion and enhanced refractive index at vanishing absorption) for various V, (Lambda) and H configurations of interfering transitions by a simple substitution of parameters. Similar expressions for resonant four-wave mixing (FWM) in Raman configurations are derived too. Crucial role of Doppler broadening is shown. Theory is applied for numerical analysis of some recent and potential experiments.