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

Physical Review A

Electromagnetically induced transparency with coherent and stochastic fields

Abraham G. Kofman

Published Sep 1, 1997• 18 citations
Publisher

Abstract

This paper deals with electromagnetically induced transparency (EIT), i.e., a significant suppression of absorption at a material transition (in the form of a dip in an absorption spectrum), due to a strong laser field, coupling the excited level with an auxiliary excited (unpopulated) level. A comprehensive theory of EIT is developed for the cases of coherent and Markovian phase- and amplitude-phase-fluctuating coupling fields. For a coherent coupling field, a shift of the absorption minimum from the two-photon resonance is revealed in the off-resonance case. Two models of amplitude-phase fluctuating fields are considered: the chaotic field and the uncorrelated-jump field. Closed analytical expressions for EIT line shape are derived and exact limits of different regimes of EIT are obtained, the emphasis being on the near-resonance case. The main conclusion is that an amplitude-phase-fluctuating field can induce significant transparency, though reduced in comparison to a phase-fluctuating field of the same average intensity and bandwidth. EIT decreases with the increase of the bandwidth for all stochastic models considered. EIT with a chaotic field is generally less pronounced than EIT with an uncorrelated-jump field of the same intensity and bandwidth, the difference increasing with the field intensity. The possibility of experimental verification of the results obtained is discussed.

DOI
10.1103/physreva.56.2280

Related papers

Transparency induced by a chaotic field

Abraham G. Kofman

Summary form only given. The phenomenon of electromagnetically induced transparency (EIT) has been the subject of extensive experimental and theoretical studies in recent years, since it has a fundamental significance and a host of important applications. To produce EIT one requires a strong laser field, which often undergoes random fluctuations. The case of amplitude-phase fluctuations appears to be much more complicated and richer than the case of Markovian phase fluctuations. Here we consider transparency induced by a Gaussian-Markovian amplitude-phase fluctuating (chaotic) field. The problem involves five parameters: the coupling field rms Rabi frequency, bandwidth, detuning, and the widths of the material and coupled transitions.

Quantum Electronics and Laser Science Conference•Jun 25, 2003•0 citations

Electromagnetically induced transparency and evolution of a two-level system under a strong chaotic field

Abraham G. Kofman

The present paper treats the electromagnetically induced transparency (EIT), i.e., the absorption spectrum of a weak probe field, near-resonant to a material transition, in the presence of a strong amplitude-phase fluctuating field which couples the upper level of the transition to another excited level. The coupling field is assumed to be chaotic (i.e., a complex Gaussian process with a Lorentzian spectrum) and so strong that the material relaxation and the detuning can be neglected. In addition, we consider the Fourier transform of the spectrum ${U}_{\mathrm{aa}}(t),$ which determines absorption of a probe field with a time-dependent intensity. The quantity ${U}_{\mathrm{aa}}(t)$ equals a diagonal element of the average reduced evolution operator of the two-level system (TLS), coupled by the strong field. As a starting point, we use the stationary, partially averaged stochastic Schr\"odinger equation, which has the form of a set of two second-order differential equations. The theory is developed by combining analytical and numerical approaches. For the most important regime, when the rms Rabi frequency ${V}_{0}$ is much greater than the coupling-field bandwidth $\ensuremath{\nu},$ we obtain scaling relations for the EIT line shape and the TLS evolution. In particular, the absorption at the minimum (i.e., at the resonance frequency) scales as ${\ensuremath{\nu}}^{1/3}{V}_{0}^{\ensuremath{-}4/3},$ whereas the evolution function ${U}_{\mathrm{aa}}(t)$ performs damped oscillations with the decay rate on the order of ${(V}_{0}^{2}\ensuremath{\nu}{)}^{1/3}.$ These results differ significantly from those following from the uncorrelated-jump model. The results of this paper are shown to be applicable to more general models of amplitude-phase fluctuations than the Gaussian-Markovian chaotic field.

Physical Review A•Feb 13, 2001•4 citations

Intensity-fluctuation–induced spectral structure

Abraham G. Kofman

Electromagnetically induced transparency (EIT) with chaotic field is considered for the constructive-interference case ( i.e. ,when the material transition is much narrower than the coupled one). The field intensity fluctuations are shown to induce a narrow peak at the material frequency, in addition to the familiar Autler-Towns doublet. The dependence of the fluctuation-induced peak on the field bandwidth ν is obtained analytically and numerically. EIT is shown to increase with ν for sufficiently small ν.

Europhysics Letters (EPL)•Apr 15, 1999•2 citations

Effect of closely-spaced excited states on electromagnetically induced transparency

Saesun Kim, Alberto M. Marino

Electromagnetically induced transparency (EIT) is a well-known phenomenon due in part to its applicability to quantum devices such as quantum memories and quantum gates. EIT is commonly modeled with a three-level lambda system; however, this simplified model does not capture all the physics of EIT experiments with real systems. We present a theoretical study of the effect of two closely-spaced excited states on EIT and off-resonance Raman transitions. In addition to the expected broadening of the EIT resonance and reduction in EIT transparency due to multiple excited states, we find some unexpected and interesting results. A comparison with a model that does not allow for coupling of the excited states shows that the coherent interaction of the fields with two excited states whose separation is smaller than their Doppler broadened linewidth can enhance the EIT transparency under some conditions and can enhance and shift the resonance frequency of off-resonance Raman absorption. Furthermore, through a dressed state analysis of the full four-level system, we find that the underlying mechanism for the reduction in EIT transparency is a shift in the two-photon resonance due to unequal dipole moments of the transitions coupled by the control field. Complete transparency can only be recovered for systems with equal dipole moments or when the separation between the two excited states is at least of the order of the Doppler width. To support our theoretical study, we present experimental EIT measurements in the D1 lines of 85Rb and 87Rb that agree with our predictions of an enhancement or reduction of EIT transparency under specific conditions. The experimental results also verify the roles that the dipole moments and the separation between the two excited states have on recovering the EIT transparency.

arXiv:1912.12267•OSA Continuum•Nov 29, 2021•0 citations

Intensity-fluctuation-induced spectral structure

Abraham G. Kofman

Summary form only given. It is well known that strong resonant laser radiation can significantly modify absorption and emission spectra of matter, producing such features, as the Autler-Towns doublet, the dark resonance, etc. Laser fluctuations, which are often inevitable, usually tend to smear out the field-induced spectral features. Here, however, we show that in an experimental scheme, usually used to obtain electromagnetically induced transparency (EIT), intensity fluctuations of a strong coupling field can induce a narrow peak in the probe absorption spectrum.

Quantum Electronics and Laser Science Conference•Jan 20, 2003•0 citations

Electromagnetically induced transparency in a thin film

David Petrosyan, Yu. P. Malakyan

Summary form only given. We have developed a formalism for rendering the (near)resonant interaction of two electromagnetic fields with an inhomogeneously broadened system consisting of three-level /spl Lambda/-atoms confined in an ultrathin cell of thickness 10 /spl mu/m or less. The peculiar features of this model stem from the fact that the free interaction time of atoms with two laser fields is solely determined by the wall-to-wall time of atomic flight. Unusual absorptive and dispersive properties of this system have been found. Thus, we show that the absorption spectrum of the probe field and the fluorescence signal from the upper atomic level contain two sub-Doppler dips. One of them is originated from the optical pumping due to the leak of atomic population from the upper atomic level, white the other much narrower dip corresponds to the electromagnetically induced transparency (EIT) effect established in the medium due to the coherent population trapping of the atoms. When the coupling field is tuned into the exact resonance with the corresponding atomic transition, the locations of the two dips on the frequency scale coincide, whereas in the case of nonzero detuning of the coupling field, the two dips are shifted from each other by the amount of this detuning. This is because the EIT is very sensitive to the Raman resonance condition, while the OP is most efficient in the vicinity of the resonance of the probe field with the atomic transition frequency.

Conference on Lasers and Electro-Optics•Aug 29, 2005•2 citations
This paper deals with electromagnetically induced transparency (EIT), i.e., a significant suppression of absorption at a material transition (in the form of a dip in an absorption spectrum), due to a strong laser field, coupling the excited level with an auxiliary excited (unpopulated) level. A comprehensive theory of EIT is developed for the cases of coherent and Markovian phase- and amplitude-phase-fluctuating coupling fields. For a coherent coupling field, a shift of the absorption minimum from the two-photon resonance is revealed in the off-resonance case. Two models of amplitude-phase fluctuating fields are considered: the chaotic field and the uncorrelated-jump field. Closed analytical expressions for EIT line shape are derived and exact limits of different regimes of EIT are obtained, the emphasis being on the near-resonance case. The main conclusion is that an amplitude-phase-fluctuating field can induce significant transparency, though reduced in comparison to a phase-fluctuating field of the same average intensity and bandwidth. EIT decreases with the increase of the bandwidth for all stochastic models considered. EIT with a chaotic field is generally less pronounced than EIT with an uncorrelated-jump field of the same intensity and bandwidth, the difference increasing with the field intensity. The possibility of experimental verification of the results obtained is discussed.
Summary form only given. The phenomenon of electromagnetically induced transparency (EIT) has been the subject of extensive experimental and theoretical studies in recent years, since it has a fundamental significance and a host of important applications. To produce EIT one requires a strong laser field, which often undergoes random fluctuations. The case of amplitude-phase fluctuations appears to be much more complicated and richer than the case of Markovian phase fluctuations. Here we consider transparency induced by a Gaussian-Markovian amplitude-phase fluctuating (chaotic) field. The problem involves five parameters: the coupling field rms Rabi frequency, bandwidth, detuning, and the widths of the material and coupled transitions.
The present paper treats the electromagnetically induced transparency (EIT), i.e., the absorption spectrum of a weak probe field, near-resonant to a material transition, in the presence of a strong amplitude-phase fluctuating field which couples the upper level of the transition to another excited level. The coupling field is assumed to be chaotic (i.e., a complex Gaussian process with a Lorentzian spectrum) and so strong that the material relaxation and the detuning can be neglected. In addition, we consider the Fourier transform of the spectrum Uaa(t),{U}_{\mathrm{aa}}(t),Uaa​(t), which determines absorption of a probe field with a time-dependent intensity. The quantity Uaa(t){U}_{\mathrm{aa}}(t)Uaa​(t) equals a diagonal element of the average reduced evolution operator of the two-level system (TLS), coupled by the strong field. As a starting point, we use the stationary, partially averaged stochastic Schr\"odinger equation, which has the form of a set of two second-order differential equations. The theory is developed by combining analytical and numerical approaches. For the most important regime, when the rms Rabi frequency V0{V}_{0}V0​ is much greater than the coupling-field bandwidth $\ensuremath{\nu},$ we obtain scaling relations for the EIT line shape and the TLS evolution. In particular, the absorption at the minimum (i.e., at the resonance frequency) scales as ${\ensuremath{\nu}}^{1/3}{V}_{0}^{\ensuremath{-}4/3},$ whereas the evolution function Uaa(t){U}_{\mathrm{aa}}(t)Uaa​(t) performs damped oscillations with the decay rate on the order of ${(V}_{0}^{2}\ensuremath{\nu}{)}^{1/3}.$ These results differ significantly from those following from the uncorrelated-jump model. The results of this paper are shown to be applicable to more general models of amplitude-phase fluctuations than the Gaussian-Markovian chaotic field.
Electromagnetically induced transparency (EIT) with chaotic field is considered for the constructive-interference case ( i.e. ,when the material transition is much narrower than the coupled one). The field intensity fluctuations are shown to induce a narrow peak at the material frequency, in addition to the familiar Autler-Towns doublet. The dependence of the fluctuation-induced peak on the field bandwidth ν is obtained analytically and numerically. EIT is shown to increase with ν for sufficiently small ν.
Electromagnetically induced transparency (EIT) is a well-known phenomenon due in part to its applicability to quantum devices such as quantum memories and quantum gates. EIT is commonly modeled with a three-level lambda system; however, this simplified model does not capture all the physics of EIT experiments with real systems. We present a theoretical study of the effect of two closely-spaced excited states on EIT and off-resonance Raman transitions. In addition to the expected broadening of the EIT resonance and reduction in EIT transparency due to multiple excited states, we find some unexpected and interesting results. A comparison with a model that does not allow for coupling of the excited states shows that the coherent interaction of the fields with two excited states whose separation is smaller than their Doppler broadened linewidth can enhance the EIT transparency under some conditions and can enhance and shift the resonance frequency of off-resonance Raman absorption. Furthermore, through a dressed state analysis of the full four-level system, we find that the underlying mechanism for the reduction in EIT transparency is a shift in the two-photon resonance due to unequal dipole moments of the transitions coupled by the control field. Complete transparency can only be recovered for systems with equal dipole moments or when the separation between the two excited states is at least of the order of the Doppler width. To support our theoretical study, we present experimental EIT measurements in the D1 lines of 85Rb and 87Rb that agree with our predictions of an enhancement or reduction of EIT transparency under specific conditions. The experimental results also verify the roles that the dipole moments and the separation between the two excited states have on recovering the EIT transparency.
Summary form only given. It is well known that strong resonant laser radiation can significantly modify absorption and emission spectra of matter, producing such features, as the Autler-Towns doublet, the dark resonance, etc. Laser fluctuations, which are often inevitable, usually tend to smear out the field-induced spectral features. Here, however, we show that in an experimental scheme, usually used to obtain electromagnetically induced transparency (EIT), intensity fluctuations of a strong coupling field can induce a narrow peak in the probe absorption spectrum.
Summary form only given. We have developed a formalism for rendering the (near)resonant interaction of two electromagnetic fields with an inhomogeneously broadened system consisting of three-level /spl Lambda/-atoms confined in an ultrathin cell of thickness 10 /spl mu/m or less. The peculiar features of this model stem from the fact that the free interaction time of atoms with two laser fields is solely determined by the wall-to-wall time of atomic flight. Unusual absorptive and dispersive properties of this system have been found. Thus, we show that the absorption spectrum of the probe field and the fluorescence signal from the upper atomic level contain two sub-Doppler dips. One of them is originated from the optical pumping due to the leak of atomic population from the upper atomic level, white the other much narrower dip corresponds to the electromagnetically induced transparency (EIT) effect established in the medium due to the coherent population trapping of the atoms. When the coupling field is tuned into the exact resonance with the corresponding atomic transition, the locations of the two dips on the frequency scale coincide, whereas in the case of nonzero detuning of the coupling field, the two dips are shifted from each other by the amount of this detuning. This is because the EIT is very sensitive to the Raman resonance condition, while the OP is most efficient in the vicinity of the resonance of the probe field with the atomic transition frequency.