Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0610054 · Journal of Physics B Atomic Molecular and Optical Physics

The effect of atomic coherence on absorption in four-level atomic systems: an analytical study

S. N. Sandhya

Published Feb 12, 2007• 12 citations
arXivHTMLPDF

Abstract

The absorption profile of a four-level ladder atomic system interacting with three driving fields is studied perturbatively and analytical results are presented. Numerical results where the driving field strengths are treated up to all orders are presented. The absorption features are studied in two regimes—(i) the weak middle transition coupling, i.e. Ω 2 ≪ Ω 1,3 and (ii) the strong middle transition coupling Ω 2 ≫ Ω 1,3 . In case (i), it is shown that the ground-state absorption and the saturation characteristics of the population of level |2⟩ reveal deviation due to the presence of upper level couplings. In particular, the saturation curve for the population of level |2⟩ shows a dip for Ω 1 = Ω 3 . While the populations of levels |3⟩ and |4⟩ show a maxima when this resonance condition is satisfied. Thus the resonance condition provides a criterion for maximally populating the upper levels. A second-order perturbation calculation reveals the nature of these minima (maxima). In the second case, I report two important features: (a) filtering of the Aulter–Townes doublet in the three-peak absorption profile of the ground state, which is achieved by detuning only the uppermost coupling field and (b) control of line-width by controlling the strength of the upper coupling fields. This filtering technique coupled with the control of linewidth could prove to be very useful for high resolution studies.

DOI
10.1088/0953-4075/40/5/002

Related papers

Optical switching and bistability in four-level atomic systems

Pardeep Kumar, Shubhrangshu Dasgupta

We explore the coherent control of nonlinear absorption of intense laser fields in four-level atomic systems. For instance, in a four-level ladder system, a coupling field creates electromagnetically induced transparency (EIT) with an Aulter-Townes doublet for the probe field while the control field is absent. A large absorption peak appears at resonance as the control field is switched on. We show how such a large absorption leads to optical switching. Further, this large absorption diminishes and a transparency window appears due to the saturation effects as the strength of the probe field is increased. We further demonstrate that the threshold of the optical bistability can be modified by suitable choices of the coupling and the control fields. In a four-level $\mathsf{Y}$-type configuration, the effect of the control field on saturable absorption (SA) and reverse saturable absorption (RSA) is highlighted in the context of nonlinear absorption of the probe field. We achieve RSA and SA in a simple atomic system just by applying a control field.

arXiv:1602.07596•Physical Review A•Aug 30, 2016•34 citations

Spontaneous emission and absorption properties of a driven three-level system

Lorenzo M. Narducci, Marlan O. Scully, Gian‐Luca Oppo +2 more

We investigate the steady-state spontaneous emission spectrum of a three-level atom driven by two coherent fields and the absorption spectrum of a weak probe passing through a collection of such driven atoms. We find that the fluorescence spectrum is strongly affected by the decay rates of all the levels involved in the atomic evolution and not just by the decay parameters of the specific transition whose emission spectrum is being monitored. In particular, the spectral components can acquire very different widths and peak heights relative to the case of the standard resonance fluorescence in which a two-level system is driven by a single near-resonant field. An external probe signal passing through the gas of three-level atoms may be absorbed or amplified, as in the standard two-level case, but under specific operating conditions, amplification (or absorption) occurs over the entire range where the atomic response is appreciable. In this case the existence of amplification or absorption is controlled solely by the population difference between two dressed states of the system. We provide numerical results in support of our arguments for arbitrary values of the atomic and field parameters and also develop an analytic description in the limit of strong driving fields that leads to explicit line-shape and linewidth formulas.

Physical Review A•Aug 1, 1990•284 citations

Two-photon Resonance Absorption in Four-level Systems

Tien D. Kieu, Bryan J. Dalton

An unconventional perturbation treatment of the theory of two-photon absorption in a four-level atomic system close to two-photon resonance is developed on the basis of the optical Bloch equations. The results for the longtime populations of the intermediate and upper states are valid in low- and medium-intensity regimes. In both regimes the upper state population shows a lorentzian resonance centred on zero two-photon detuning with a width equal to the natural linewidth of the upper state. The intermediate state population shows a similar behaviour in the intermediate regime only, with no significant dependence on two-photon detuning in the low-intensity regime. However, in both regimes the population of the virtual intermediate state is at least comparable to that of the resonant upper state. The perturbation theory results have been checked by direct numerical calculations based on the Bloch equations. Numerical calculations confirm the presence of a high-intensity regime characterized by power shifts, broadening and saturation effects.

Optica Acta International Journal of Optics•Nov 1, 1984•2 citations

Atomic coherence effects in four-level systems: Doppler-free absorption within an electromagnetically-induced-transparency window

S. N. Sandhya, K. K. Sharma

We report here an effect in a four-level ladderlike system, which is in contrast to the usual quantum interference effects such as electromagnetically induced transperency (EIT) or coherent population trapping: we predict the occurrence of a narrow absorption peak within the EIT window when an EIT atomic system interacts with an additional driving rf field. The Doppler-free-central absorption appears when the three-photon resonance condition is satisfied. In the limit of the rf field strength ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{rf}}$\ensuremath{\rightarrow}0, the usual EIT profile is recovered.

Physical Review A•Mar 1, 1997•49 citations

Study on probe field propagation in the presence of control and coupling fields through a four-level N-type atomic system

Khairul Islam, Dipankar Bhattacharyya, Arindam Ghosh +2 more

Abstract The absorption features of a probe field propagating through a four-level N-type atomic system in the presence of two coherent radiation fields is studied analytically by using a density matrix formulation. The system has two ground levels and two excited levels. A weak probe laser couples the upper ground level to the lower excited level whereas a strong control field connects the lower ground level to the lower excited level. The coupling field acts between the upper ground level and the upper excited level. The transition parameters of the 87 Rb D 1 line have been used to simulate the probe response. The simulated probe absorption shows a gain-like structure depending on the relative field intensities. The spectral features of the probe response exhibit substantial differences under thermal averaging as compared to a Doppler-free condition. The splitting of simulated probe absorption can be explained by the dressed state model. Electromagnetically induced absorption (EIA) is observed in the simulated probe response curve when the spontaneous decay of the population from the uppermost excited state to the lower ground state is absent.

Journal of Physics B Atomic Molecular and Optical Physics•Sep 8, 2017•8 citations

Nonlinear optical effects in a doubly driven four-level atom

Bibhas Kumar Dutta, P.K. Mahapatra

We have studied nonlinear quantum optical effects in a doubly driven four-level atomic system in a homogeneously broadened regime. On application of two strong fields the system can be made to display double electromagnetically induced transparency (EIT) because of constructive quantum interference giving rise to nonlinear absorption at three-photon resonance condition. This fact may be used to obtain other phenomena like the effect of photon switching in a pulsed regime and large cross phase modulation (XPM) effect. We also show that the behaviour of spatial modulation of transparency of the weak probe beam in a three-level system interacted with a strong standing wave pump field can be dramatically changed in our four-level ladder type system. Here, strong coupling field acting on the uppermost transition is represented by a standing wave whereas strong pump and weak probe fields acting successively on the lower transitions are represented by travelling waves. The effect of double EIT on nonlinear light generation based on the four-wave-mixing (FWM) technique is also investigated. We have examined that the four wave mixing efficiency can be effectively controlled by varying the strength of the pump field.

Physica Scripta•Feb 8, 2007•40 citations
The absorption profile of a four-level ladder atomic system interacting with three driving fields is studied perturbatively and analytical results are presented. Numerical results where the driving field strengths are treated up to all orders are presented. The absorption features are studied in two regimes—(i) the weak middle transition coupling, i.e. Ω 2 ≪ Ω 1,3 and (ii) the strong middle transition coupling Ω 2 ≫ Ω 1,3 . In case (i), it is shown that the ground-state absorption and the saturation characteristics of the population of level |2⟩ reveal deviation due to the presence of upper level couplings. In particular, the saturation curve for the population of level |2⟩ shows a dip for Ω 1 = Ω 3 . While the populations of levels |3⟩ and |4⟩ show a maxima when this resonance condition is satisfied. Thus the resonance condition provides a criterion for maximally populating the upper levels. A second-order perturbation calculation reveals the nature of these minima (maxima). In the second case, I report two important features: (a) filtering of the Aulter–Townes doublet in the three-peak absorption profile of the ground state, which is achieved by detuning only the uppermost coupling field and (b) control of line-width by controlling the strength of the upper coupling fields. This filtering technique coupled with the control of linewidth could prove to be very useful for high resolution studies.
We explore the coherent control of nonlinear absorption of intense laser fields in four-level atomic systems. For instance, in a four-level ladder system, a coupling field creates electromagnetically induced transparency (EIT) with an Aulter-Townes doublet for the probe field while the control field is absent. A large absorption peak appears at resonance as the control field is switched on. We show how such a large absorption leads to optical switching. Further, this large absorption diminishes and a transparency window appears due to the saturation effects as the strength of the probe field is increased. We further demonstrate that the threshold of the optical bistability can be modified by suitable choices of the coupling and the control fields. In a four-level Y\mathsf{Y}Y-type configuration, the effect of the control field on saturable absorption (SA) and reverse saturable absorption (RSA) is highlighted in the context of nonlinear absorption of the probe field. We achieve RSA and SA in a simple atomic system just by applying a control field.
We investigate the steady-state spontaneous emission spectrum of a three-level atom driven by two coherent fields and the absorption spectrum of a weak probe passing through a collection of such driven atoms. We find that the fluorescence spectrum is strongly affected by the decay rates of all the levels involved in the atomic evolution and not just by the decay parameters of the specific transition whose emission spectrum is being monitored. In particular, the spectral components can acquire very different widths and peak heights relative to the case of the standard resonance fluorescence in which a two-level system is driven by a single near-resonant field. An external probe signal passing through the gas of three-level atoms may be absorbed or amplified, as in the standard two-level case, but under specific operating conditions, amplification (or absorption) occurs over the entire range where the atomic response is appreciable. In this case the existence of amplification or absorption is controlled solely by the population difference between two dressed states of the system. We provide numerical results in support of our arguments for arbitrary values of the atomic and field parameters and also develop an analytic description in the limit of strong driving fields that leads to explicit line-shape and linewidth formulas.
An unconventional perturbation treatment of the theory of two-photon absorption in a four-level atomic system close to two-photon resonance is developed on the basis of the optical Bloch equations. The results for the longtime populations of the intermediate and upper states are valid in low- and medium-intensity regimes. In both regimes the upper state population shows a lorentzian resonance centred on zero two-photon detuning with a width equal to the natural linewidth of the upper state. The intermediate state population shows a similar behaviour in the intermediate regime only, with no significant dependence on two-photon detuning in the low-intensity regime. However, in both regimes the population of the virtual intermediate state is at least comparable to that of the resonant upper state. The perturbation theory results have been checked by direct numerical calculations based on the Bloch equations. Numerical calculations confirm the presence of a high-intensity regime characterized by power shifts, broadening and saturation effects.
We report here an effect in a four-level ladderlike system, which is in contrast to the usual quantum interference effects such as electromagnetically induced transperency (EIT) or coherent population trapping: we predict the occurrence of a narrow absorption peak within the EIT window when an EIT atomic system interacts with an additional driving rf field. The Doppler-free-central absorption appears when the three-photon resonance condition is satisfied. In the limit of the rf field strength ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{rf}}$\ensuremath{\rightarrow}0, the usual EIT profile is recovered.
Abstract The absorption features of a probe field propagating through a four-level N-type atomic system in the presence of two coherent radiation fields is studied analytically by using a density matrix formulation. The system has two ground levels and two excited levels. A weak probe laser couples the upper ground level to the lower excited level whereas a strong control field connects the lower ground level to the lower excited level. The coupling field acts between the upper ground level and the upper excited level. The transition parameters of the 87 Rb D 1 line have been used to simulate the probe response. The simulated probe absorption shows a gain-like structure depending on the relative field intensities. The spectral features of the probe response exhibit substantial differences under thermal averaging as compared to a Doppler-free condition. The splitting of simulated probe absorption can be explained by the dressed state model. Electromagnetically induced absorption (EIA) is observed in the simulated probe response curve when the spontaneous decay of the population from the uppermost excited state to the lower ground state is absent.
We have studied nonlinear quantum optical effects in a doubly driven four-level atomic system in a homogeneously broadened regime. On application of two strong fields the system can be made to display double electromagnetically induced transparency (EIT) because of constructive quantum interference giving rise to nonlinear absorption at three-photon resonance condition. This fact may be used to obtain other phenomena like the effect of photon switching in a pulsed regime and large cross phase modulation (XPM) effect. We also show that the behaviour of spatial modulation of transparency of the weak probe beam in a three-level system interacted with a strong standing wave pump field can be dramatically changed in our four-level ladder type system. Here, strong coupling field acting on the uppermost transition is represented by a standing wave whereas strong pump and weak probe fields acting successively on the lower transitions are represented by travelling waves. The effect of double EIT on nonlinear light generation based on the four-wave-mixing (FWM) technique is also investigated. We have examined that the four wave mixing efficiency can be effectively controlled by varying the strength of the pump field.