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.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 AFeb 13, 20014 citations

Transient Hamiltonian chaos in the interaction of an electromagnetic field with two-level atoms

K. N. Alekseev, G. P. Berman

Journal of Experimental and Theoretical PhysicsMar 1, 19943 citations

Electromagnetically induced transparency with coherent and stochastic fields

Abraham G. Kofman

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.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.

Physical Review ASep 1, 199718 citations

Dynamical evolution of a two-level atom in a monomode chaotic field

C. Riti, G. Vetri

Optics CommunicationsDec 1, 198214 citations

Electromagnetically induced transparency in degenerate two-level systems

I. V. Zelensky, Vyacheslav A. Mironov

The evolution of an electromagnetic wave with slowly varying polarization, which interacts resonantly with the medium formed by degenerate two-level atoms, is studied using the wave function approach under the conditions of electromagnetically induced transparency. It is shown that the amplitude of the wave field propagates at the velocity of light in such a medium. The equation obtained for the polarization parameter has a solution in the form of a simple wave. The breaking length is determined. It is shown that the velocity of propagation of polarization waves may be much smaller than the velocity of light. The proposed approach is common for two-level systems with an arbitrary degeneracy. The case of a system with Zeeman degeneracy is analyzed in detail. The dependence of the velocity of propagation of the polarization structure on the amplitude and polarization is determined for an arbitrary level degeneracy. The evolution of the polarization structure in such a medium is discussed.The evolution of an electromagnetic wave with slowly varying polarization, which interacts resonantly with the medium formed by degenerate two-level atoms, is studied using the wave function approach under the conditions of electromagnetically induced transparency. It is shown that the amplitude of the wave field propagates at the velocity of light in such a medium. The equation obtained for the polarization parameter has a solution in the form of a simple wave. The breaking length is determined. It is shown that the velocity of propagation of polarization waves may be much smaller than the velocity of light. The proposed approach is common for two-level systems with an arbitrary degeneracy. The case of a system with Zeeman degeneracy is analyzed in detail. The dependence of the velocity of propagation of the polarization structure on the amplitude and polarization is determined for an arbitrary level degeneracy. The evolution of the polarization structure in such a medium is discussed.

Journal of Experimental and Theoretical PhysicsMay 1, 20025 citations

Quantum Chaos in Two-Level Systems Interacting with Resonant Radiation Field

トシヒコオオノ, Toshihiko Ohno

福山大学工学部紀要Jan 1, 19880 citations

{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.