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

Journal of Experimental and Theoretical Physics

Self-induced transparency for ultrashort pulses propagating in a multilevel quantum medium

A. Yu. Parkhomenko, С. В. Сазонов

Published Nov 1, 1998• 35 citations
Publisher

Abstract

We study theoretically the phenomenon of self-induced transparency for ultrashort pulses (videopulses) propagating in a multilevel quantum medium under conditions in which the method of slowly varying amplitudes and phases breaks down and the pulse spectrum substantially overlaps the quantum transitions. A special class of transitions with one common level is considered. We find that the dynamics of the videopulses in such a medium is described by a double sine-Gordon equation. We establish the conditions under which steady-state traveling 0 π -, 2 π -, and 4 π -videosolitons are formed. It is found that 4 π -videosolitons can propagate both in equilibrium media and in some nonequilibrium media, while 0 π -videosolitons can propagate only in nonequilibrium media. We study amplification processes in highly nonequilibrium systems and show that, depending on the initial state of the medium, 2 π -and qπ -pulses (0< q <1) with increasing amplitudes may be formed. We conclude that the amplification of an ultrashort pulse occurs due to an increase in the photon number density and to an increase in the frequency of each photon. Finally, we study the possibility of an electromagnetic autosoliton being formed in a nonequilibrium dissipative medium.

DOI
10.1134/1.558734

Related papers

Soliton regimes of ultrashort pulse propagation through an array of asymmetric quantum objects

С. В. Сазонов, N. V. Ustinov

Nonlinear regimes of two-component ultrashort pulse propagation through an array of anisotropic quantum systems are analyzed theoretically under conditions when the slowly varying envelope approximation is inapplicable. It is shown that if the spectral width of the pulse is much larger than the quantum transition frequency, then the dynamics of its ordinary component can be described by a modified sine-Gordon equation that belongs to the class of integrable models but has never been used in physical applications. It is shown that the extraordinary pulse component responsible for the dynamic Stark shift of the transition frequency is coupled to its ordinary component by an algebraic relation. The soliton solutions to the derived equation are classified. Depending on the pulse duration, the solutions have the form of 2π pulses (kinks and antikinks) or steady traveling 0π pulses having no counterparts in isotropic models (neutral kinks). Interactions between the medium and solitons of different types and soliton collisions are analyzed.

Journal of Experimental and Theoretical Physics•Oct 1, 2006•11 citations

Optical pulse probing of coherency gradient in Λ-medium

Igor V. Kazinets, I. E. Mazets, Boris G. Matisov

Quantum coherence and interference in atomic systems can lead to interesting optical phenomena such as nonabsorbing resonances, lasing without inversion, generating an ultrahigh index of refraction without absorption, propagation of light pulses without losses. In the last-named is given the title transparency. Up to now it is known some types of transparency in multi-level resonant media. One of them is electromagnetically induced transparency (EIT). The phenomenon of EIT in the propagation of laser radiation through an absorbing medium has been recently investigated and explained in terms of quantum coherence and interference for multi-level atomic system. For instance in the (Lambda) -system, if the atomic medium is prepared in a quantum superposition of states, matched pulses, i.e., a pair of optical pulses whose amplitude and phase have a well defined relation, propagate without absorption. The mechanism of coherent population trapping is responsible for EIT in a (Lambda) -system. There is another, well known mechanism for creating transparency in a two-state atom: self-induced transparency, or SIT. Here, a single pulse whose area (the integral of its Rabi frequency over time) is 2(pi) is applied to the medium. Such a pulse causes the atoms to cycle smoothly from the ground to the excited state and then back again. In principle, such a pulse can propagate over long distances. SIT can be generalized to multi-level systems and multiple quasi-monochromatic fields. Generalization of SIT in a (Lambda) -system was obtained in reference 2. In this report we present a new type of transparency (combined transparency). This type describes propagation of laser pulse through a (Lambda) -type medium where the initial atomic state is prepared in the form of spatially varying coherent superposition of low-energetic states (initial coherency gradient). The common envelope behaves as usual 2(pi) hyperbolic secant pulse, but the ratio between the components of frequencies transitions 1> yields 3> and 2> yields 3> changes due to coherent Raman scattering so (phi) equals atan(E1/E2) equals (pi) /2-Gz, where z is the coordinate, G is the constant determined by both the incident pulse parameters and the initial coherence between the atomic states. Our solution demonstrates a direct connection of EIT in adiabatic regime to the SIT effects. This type of a transparency is given the title screw-type transparency, because for the given form of incident pulse (pitch of screw) medium is transparent, if medium's the initial coherence gradient is correspondingly prepared (thread on a engine nut). Besides a transparency, this phenomenon contains a transformation of the incident pulse frequency during the process of the propagation. This property of the phenomena can be result in a complete conversion of the frequency.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 5, 1999•0 citations

Self-induced transparency with level degeneracy

Roy M. Gundersen

The propagation of ultrashort coherent light pulses through a resonant atomic medium, modelled by a two-quantum level of absorbers, is studied including the effects of level degeneracy. The governing equations, a sequence of n-tuple sine-Gordon (SG) equations, are solved by quadrature for the Q-transition, with an approximate method indicated for the (mathematically) more difficult P- and R- transitions. It is shown, in particular, that there is a surprisingly close relation between the usual SG equation and the double SG equation. A simple theorem is proved which shows that each travelling wave solution of the former immediately leads to a solution of the latter, which thus admits a restricted Backlund transformation. This direct solution of nonlinear dispersive equations, which apparently cannot be solved by the inverse method, has an interesting by-product: an approximate method for finding travelling wave solutions of relatively arbitrary Klein-Gordon equations.

Journal of Physics A Mathematical and General•Oct 7, 1990•3 citations

Self-induced transparency for the supremely short pulses in conditions of partially spectral exceeding of the quantum transitions

С. В. Сазонов, A. F. Sobolevskii

Without using the slowly varying amplitude approximation a nonlinear propagation of supremely short pulses in the three-level quantum medium have been investigated. At this by the pulse spectral wide is exceeding only one of quantum transitions. The nonlinear wave equations of 'sin-Gordon + Korteweg-de Vries'-type and 'sin-Gordon + Korteweg- de Vries'-type, which describe pulse dynamics, was obtained. On the basis of approximate solution we come to a conclusion about minimum temporal duration of propagating pulse.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jan 14, 2000•0 citations

Self-induced-transparency soliton propagation under the influence of a far-from-resonance transition line

Victor V. Kozlov, Evald E. Fradkin

The results of theoretical research of the propagation effect of an ultrashort optical pulse under the conditions of coherent interaction with two resonant transitions are presented. One of the transitions is tuned to exact resonance with the pulse carrier frequency; the other is distanced by much more than the pulse spectral width, thus the adiabatic following approximation may be applied to it. The interaction between the pulse and the far-from-resonance transition is described by the wave equation with the nonlinear index of refraction in the form of the Lorentz function of the field amplitude. This wave equation is solved together with the Bloch equations for the exact resonant transition. The solution in the form of the stationary phase-modulated pulse is obtained, and (pi) -pulse of self-induced transparency is the special case of this solution. The obtained solution has the area under the pulse envelope less than (pi) , and with increasing the absorption coefficient of the far-from-resonance transition the pulse area decreases. The effect can be used for reducing the transparency threshold of the resonant medium below (pi) .

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jun 10, 1997•0 citations

Nonlinear regimes of propagation of resonant pulses in multilevel quantum media

С. В. Сазонов

An approximate operator approach that is equivalent to the mathematical Wentzel-Kramers-Brillouin method and allows one to solve the set of constitutive equations for an N -level quantum medium resonantly interacting with multifrequency optical pulses is proposed. The transitions occurring via a common level with the ordinal number j are considered in detail. It is shown that, for j =1, the self-induced transparency regime is realized, whereas, at j=N , the regime of electromagnetically induced transparency is realized. Within the framework of the WKB approximation, an expression that represents the area theorem for multifrequency resonant pulses is derived.

Optics and Spectroscopy•Oct 1, 2003•9 citations
We study theoretically the phenomenon of self-induced transparency for ultrashort pulses (videopulses) propagating in a multilevel quantum medium under conditions in which the method of slowly varying amplitudes and phases breaks down and the pulse spectrum substantially overlaps the quantum transitions. A special class of transitions with one common level is considered. We find that the dynamics of the videopulses in such a medium is described by a double sine-Gordon equation. We establish the conditions under which steady-state traveling 0 π -, 2 π -, and 4 π -videosolitons are formed. It is found that 4 π -videosolitons can propagate both in equilibrium media and in some nonequilibrium media, while 0 π -videosolitons can propagate only in nonequilibrium media. We study amplification processes in highly nonequilibrium systems and show that, depending on the initial state of the medium, 2 π -and qπ -pulses (0< q <1) with increasing amplitudes may be formed. We conclude that the amplification of an ultrashort pulse occurs due to an increase in the photon number density and to an increase in the frequency of each photon. Finally, we study the possibility of an electromagnetic autosoliton being formed in a nonequilibrium dissipative medium.
Nonlinear regimes of two-component ultrashort pulse propagation through an array of anisotropic quantum systems are analyzed theoretically under conditions when the slowly varying envelope approximation is inapplicable. It is shown that if the spectral width of the pulse is much larger than the quantum transition frequency, then the dynamics of its ordinary component can be described by a modified sine-Gordon equation that belongs to the class of integrable models but has never been used in physical applications. It is shown that the extraordinary pulse component responsible for the dynamic Stark shift of the transition frequency is coupled to its ordinary component by an algebraic relation. The soliton solutions to the derived equation are classified. Depending on the pulse duration, the solutions have the form of 2π pulses (kinks and antikinks) or steady traveling 0π pulses having no counterparts in isotropic models (neutral kinks). Interactions between the medium and solitons of different types and soliton collisions are analyzed.
Quantum coherence and interference in atomic systems can lead to interesting optical phenomena such as nonabsorbing resonances, lasing without inversion, generating an ultrahigh index of refraction without absorption, propagation of light pulses without losses. In the last-named is given the title transparency. Up to now it is known some types of transparency in multi-level resonant media. One of them is electromagnetically induced transparency (EIT). The phenomenon of EIT in the propagation of laser radiation through an absorbing medium has been recently investigated and explained in terms of quantum coherence and interference for multi-level atomic system. For instance in the (Lambda) -system, if the atomic medium is prepared in a quantum superposition of states, matched pulses, i.e., a pair of optical pulses whose amplitude and phase have a well defined relation, propagate without absorption. The mechanism of coherent population trapping is responsible for EIT in a (Lambda) -system. There is another, well known mechanism for creating transparency in a two-state atom: self-induced transparency, or SIT. Here, a single pulse whose area (the integral of its Rabi frequency over time) is 2(pi) is applied to the medium. Such a pulse causes the atoms to cycle smoothly from the ground to the excited state and then back again. In principle, such a pulse can propagate over long distances. SIT can be generalized to multi-level systems and multiple quasi-monochromatic fields. Generalization of SIT in a (Lambda) -system was obtained in reference 2. In this report we present a new type of transparency (combined transparency). This type describes propagation of laser pulse through a (Lambda) -type medium where the initial atomic state is prepared in the form of spatially varying coherent superposition of low-energetic states (initial coherency gradient). The common envelope behaves as usual 2(pi) hyperbolic secant pulse, but the ratio between the components of frequencies transitions 1> yields 3> and 2> yields 3> changes due to coherent Raman scattering so (phi) equals atan(E1/E2) equals (pi) /2-Gz, where z is the coordinate, G is the constant determined by both the incident pulse parameters and the initial coherence between the atomic states. Our solution demonstrates a direct connection of EIT in adiabatic regime to the SIT effects. This type of a transparency is given the title screw-type transparency, because for the given form of incident pulse (pitch of screw) medium is transparent, if medium's the initial coherence gradient is correspondingly prepared (thread on a engine nut). Besides a transparency, this phenomenon contains a transformation of the incident pulse frequency during the process of the propagation. This property of the phenomena can be result in a complete conversion of the frequency.
The propagation of ultrashort coherent light pulses through a resonant atomic medium, modelled by a two-quantum level of absorbers, is studied including the effects of level degeneracy. The governing equations, a sequence of n-tuple sine-Gordon (SG) equations, are solved by quadrature for the Q-transition, with an approximate method indicated for the (mathematically) more difficult P- and R- transitions. It is shown, in particular, that there is a surprisingly close relation between the usual SG equation and the double SG equation. A simple theorem is proved which shows that each travelling wave solution of the former immediately leads to a solution of the latter, which thus admits a restricted Backlund transformation. This direct solution of nonlinear dispersive equations, which apparently cannot be solved by the inverse method, has an interesting by-product: an approximate method for finding travelling wave solutions of relatively arbitrary Klein-Gordon equations.
Without using the slowly varying amplitude approximation a nonlinear propagation of supremely short pulses in the three-level quantum medium have been investigated. At this by the pulse spectral wide is exceeding only one of quantum transitions. The nonlinear wave equations of 'sin-Gordon + Korteweg-de Vries'-type and 'sin-Gordon + Korteweg- de Vries'-type, which describe pulse dynamics, was obtained. On the basis of approximate solution we come to a conclusion about minimum temporal duration of propagating pulse.
The results of theoretical research of the propagation effect of an ultrashort optical pulse under the conditions of coherent interaction with two resonant transitions are presented. One of the transitions is tuned to exact resonance with the pulse carrier frequency; the other is distanced by much more than the pulse spectral width, thus the adiabatic following approximation may be applied to it. The interaction between the pulse and the far-from-resonance transition is described by the wave equation with the nonlinear index of refraction in the form of the Lorentz function of the field amplitude. This wave equation is solved together with the Bloch equations for the exact resonant transition. The solution in the form of the stationary phase-modulated pulse is obtained, and (pi) -pulse of self-induced transparency is the special case of this solution. The obtained solution has the area under the pulse envelope less than (pi) , and with increasing the absorption coefficient of the far-from-resonance transition the pulse area decreases. The effect can be used for reducing the transparency threshold of the resonant medium below (pi) .
An approximate operator approach that is equivalent to the mathematical Wentzel-Kramers-Brillouin method and allows one to solve the set of constitutive equations for an N -level quantum medium resonantly interacting with multifrequency optical pulses is proposed. The transitions occurring via a common level with the ordinal number j are considered in detail. It is shown that, for j =1, the self-induced transparency regime is realized, whereas, at j=N , the regime of electromagnetically induced transparency is realized. Within the framework of the WKB approximation, an expression that represents the area theorem for multifrequency resonant pulses is derived.