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

Laser Physics

Where is the energy of slow light stored?

R. N. Shakhmuratov, J. Odeurs

Published May 1, 2007• 3 citations
Publisher

Abstract

We analyze the energy storage process of light propagating with slow group velocity in a sample where electromagnetically induced transparency (EIT) is created by a strong coupling field. We compare the formation of slow light in EIT and in self-induced transparency (SIT). For SIT, soliton-like propagation of light with essentially reduced group velocity takes place because of the temporary storage of an appreciable part of the pulse energy in the atoms. For EIT, no energy of the probe is stored in the atoms. This energy is transformed to the coupling field and leaves the sample with phase velocity c without absorption. Slow light is formed by a low frequency coherence induced at the input by the probe and coupling fields in a two-quantum excitation process. This coherence propagates as a “spin wave” with small group velocity, and at a large distance from the input, the coherence rules the process of the energy transformation from the coupling field to the probe, reproducing exactly the temporal profile of the probe at the input.

DOI
10.1134/s1054660x07050088

Related papers

Two types of adiabatons in electromagnetically induced transparency

R. N. Shakhmuratov, J. Odeurs

We analyze the energy transformation of light propagating with slow group velocity in a three-level medium. Depending on the excitation scheme, the energy of the probe can be transformed into the coupling field or into the atomic excitation. As a result a zero-energy adiabaton develops for the lambda scheme or an energy carrying adiabaton is formed for the ladder scheme. In both cases slow light is produced by the atoms, also feeding this light by the energy stored in the metastable state (ladder scheme) or borrowing the energy from the coupling field (lambda scheme).

Physical Review A•Oct 5, 2006•13 citations

Two-photon absorption and imaging at low-light levels

D. Manuszak, G. Y. Yin, Stephen E. Harris

Summary form only given. The recent observation of slow light propagation by Harris and Hau (1999) motivates the study of nonlinear optical processes under conditions where slow group velocity, or equivalently large nonlinearity, is the dominant feature of the problem. By combining electromagnetically induced transparency (EIT) and cold atom technology, a sharp resonance is created with a transmission linewidth much less than the natural linewidth of the atoms. A pulse of light propagating in this medium has a phase velocity of c and a group velocity that can be less than 10/sup -7/ c. As a light pulse of sufficiently wide bandwidth enters a cold-atom, EIT medium, the pulse shape, electric field strength, and power density remain nominally unchanged. Concurrently, because the group velocity is decreased, the stored energy per volume must increase. This increase occurs by spatial compression of the travelling pulse. A pulse measuring 300 m in free space compresses to 30 /spl mu/m within the cold-atom medium.

Quantum Electronics and Laser Science Conference•Jan 1, 2000•0 citations

Quantum interference and slow light propagation in cold samples of open three-level atoms

Elena Cerboneschi, Ferruccio Renzoni, E. Arimondo

We investigate theoretically the propagation of a probe laser pulse through a cold sample of three-level atoms in the presence of a strong coupling field. Our numerical analysis shows that the electromagnetically induced transparency phenomenon produces very small group velocities for the probe pulse even if the three-level atomic system is open, i.e. in the presence of decay channels to levels not excited by the laser radiation. The role of the atomic momentum on the slow light propagation is briefly discussed.

Journal of Optics B Quantum and Semiclassical Optics•Aug 1, 2002•3 citations

Electromagnetically induced transparency and extremely slow light in ultracold atomic gases in traps

A. S. Troshin, N. A. Vasil’ev

For the known, experimentally realized conditions, the detailed analysis of the field-induced transparency and formation of exceptionally low group velocity of probe light is performed. The secondary fields being due to the atomic polarization induced by the two propagating light pulses - coupling (or dressing) and probe ones, resonant to the adjoining transitions in a three-level scheme, are explicitly taken into account. Partly linear (relative to the probe pulse field) and completely non-linear regimes are considered. Particularly, the outputting coupled wave is shown to be slightly amplified, when the probe light pulse “disappears” inside the medium.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 20, 2004•0 citations

Information storage and retrieval by stopping pulses of light1

R. Bullough, H. M. Gibbs

Despite the importance of quantum interference and coherent population trapping to the theory of electromagnetically induced transparency (EIT), it is shown that the recent experiments which slow down and even stop a light pulse in a dielectric really rely on a linear, refractive index type theory. From this point of view and in considerable contrast, the experiment on degenerate self-induced transparency (SIT) done 27 years ago which slowed down an optical pulse (in principle to zero velocity) was based on an intrinsically nonlinear (soliton type) theory. In quantum mechanical terms both theories are developed at the level of expectation values only and at this level the two different theories come together in terms of the storage and retrieval of information. In the Appendix we analyse the nature of this information in terms of the quantum equations governing linear EIT and nonlinear SIT.

Journal of Modern Optics•Jan 1, 2004•7 citations

Storing and processing optical information with ultraslow light in Bose-Einstein condensates

Zachary Dutton, Lene Vestergaard Hau

We theoretically explore coherent information transfer between ultraslow light pulses and Bose-Einstein condensates (BEC's) and find that storing light pulses in BEC's allows the coherent condensate dynamics to process optical information. We consider BEC's of alkali atoms with a $\ensuremath{\Lambda}$ energy level configuration. In this configuration, one laser (the coupling field) can cause a pulse of a second pulsed laser (the probe field) to propagate with little attenuation (electromagnetically induced transparency) at a very slow group velocity $(\ensuremath{\sim}10\phantom{\rule{0.3em}{0ex}}\mathrm{m}∕\mathrm{s})$ and be spatially compressed to lengths smaller than the BEC. These pulses can be fully stopped and later revived by switching the coupling field off and on. Here we develop a formalism, applicable in both the weak- and strong-probe regimes, to analyze such experiments and establish several results: (1) We show that the switching can be performed on time scales much faster than the adiabatic time scale for electromagnetically induced transparancy even in the strong-probe regime. We also study the behavior of the system changes when this time scale is faster than the excited state lifetime. (2) Stopped light pulses write their phase and amplitude information onto spatially dependent atomic wave functions, resulting in coherent two-component BEC dynamics during long storage times. We investigate examples relevant to $^{87}\mathrm{Rb}$ experimental parameters and see a variety of novel dynamics occur, including interference fringes, gentle breathing excitations, and two-component solitons, depending on the relative scattering lengths of the atomic states used and the probe to coupling intensity ratio. We find that the dynamics when the levels $\ensuremath{\mid}F=1,{M}_{F}=\ensuremath{-}1⟩$ and $\ensuremath{\mid}F=2,{M}_{F}=+1⟩$ are used could be well suited to designing controlled processing of the information input on the probe. (3) Switching the coupling field on after the dynamics writes the evolved BEC wave functions density and phase features onto a revived probe pulse, which then propagates out. We establish equations linking the BEC wave function to the resulting output probe pulses in both the strong- and weak-probe regimes. We then identify sources of deviations from these equations due to absorption and distortion of the pulses. These deviations result in imperfect fidelity of the information transfer from the atoms to the light fields and we calculate this fidelity for Gaussian-shaped features in the BEC wave functions. In the weak-probe case, we find that the fidelity is affected both by absorption of very-small-length-scale features and absorption of features occupying regions near the condensate edge. We discuss how to optimize the fidelity using these considerations. In the strong-probe case, we find that when the oscillator strengths for the two transitions are equal the fidelity is not strongly sensitive to the probe strength, while when they are unequal the fidelity is worse for stronger probes. Applications to distant communication between BEC's, squeezed light generation, and quantum information are anticipated.

arXiv:quant-ph/0404018•Physical Review A•Nov 30, 2004•68 citations
We analyze the energy storage process of light propagating with slow group velocity in a sample where electromagnetically induced transparency (EIT) is created by a strong coupling field. We compare the formation of slow light in EIT and in self-induced transparency (SIT). For SIT, soliton-like propagation of light with essentially reduced group velocity takes place because of the temporary storage of an appreciable part of the pulse energy in the atoms. For EIT, no energy of the probe is stored in the atoms. This energy is transformed to the coupling field and leaves the sample with phase velocity c without absorption. Slow light is formed by a low frequency coherence induced at the input by the probe and coupling fields in a two-quantum excitation process. This coherence propagates as a “spin wave” with small group velocity, and at a large distance from the input, the coherence rules the process of the energy transformation from the coupling field to the probe, reproducing exactly the temporal profile of the probe at the input.
We analyze the energy transformation of light propagating with slow group velocity in a three-level medium. Depending on the excitation scheme, the energy of the probe can be transformed into the coupling field or into the atomic excitation. As a result a zero-energy adiabaton develops for the lambda scheme or an energy carrying adiabaton is formed for the ladder scheme. In both cases slow light is produced by the atoms, also feeding this light by the energy stored in the metastable state (ladder scheme) or borrowing the energy from the coupling field (lambda scheme).
Summary form only given. The recent observation of slow light propagation by Harris and Hau (1999) motivates the study of nonlinear optical processes under conditions where slow group velocity, or equivalently large nonlinearity, is the dominant feature of the problem. By combining electromagnetically induced transparency (EIT) and cold atom technology, a sharp resonance is created with a transmission linewidth much less than the natural linewidth of the atoms. A pulse of light propagating in this medium has a phase velocity of c and a group velocity that can be less than 10/sup -7/ c. As a light pulse of sufficiently wide bandwidth enters a cold-atom, EIT medium, the pulse shape, electric field strength, and power density remain nominally unchanged. Concurrently, because the group velocity is decreased, the stored energy per volume must increase. This increase occurs by spatial compression of the travelling pulse. A pulse measuring 300 m in free space compresses to 30 /spl mu/m within the cold-atom medium.
We investigate theoretically the propagation of a probe laser pulse through a cold sample of three-level atoms in the presence of a strong coupling field. Our numerical analysis shows that the electromagnetically induced transparency phenomenon produces very small group velocities for the probe pulse even if the three-level atomic system is open, i.e. in the presence of decay channels to levels not excited by the laser radiation. The role of the atomic momentum on the slow light propagation is briefly discussed.
For the known, experimentally realized conditions, the detailed analysis of the field-induced transparency and formation of exceptionally low group velocity of probe light is performed. The secondary fields being due to the atomic polarization induced by the two propagating light pulses - coupling (or dressing) and probe ones, resonant to the adjoining transitions in a three-level scheme, are explicitly taken into account. Partly linear (relative to the probe pulse field) and completely non-linear regimes are considered. Particularly, the outputting coupled wave is shown to be slightly amplified, when the probe light pulse “disappears” inside the medium.
Despite the importance of quantum interference and coherent population trapping to the theory of electromagnetically induced transparency (EIT), it is shown that the recent experiments which slow down and even stop a light pulse in a dielectric really rely on a linear, refractive index type theory. From this point of view and in considerable contrast, the experiment on degenerate self-induced transparency (SIT) done 27 years ago which slowed down an optical pulse (in principle to zero velocity) was based on an intrinsically nonlinear (soliton type) theory. In quantum mechanical terms both theories are developed at the level of expectation values only and at this level the two different theories come together in terms of the storage and retrieval of information. In the Appendix we analyse the nature of this information in terms of the quantum equations governing linear EIT and nonlinear SIT.
We theoretically explore coherent information transfer between ultraslow light pulses and Bose-Einstein condensates (BEC's) and find that storing light pulses in BEC's allows the coherent condensate dynamics to process optical information. We consider BEC's of alkali atoms with a $\ensuremath{\Lambda}$ energy level configuration. In this configuration, one laser (the coupling field) can cause a pulse of a second pulsed laser (the probe field) to propagate with little attenuation (electromagnetically induced transparency) at a very slow group velocity $(\ensuremath{\sim}10\phantom{\rule{0.3em}{0ex}}\mathrm{m}∕\mathrm{s})$ and be spatially compressed to lengths smaller than the BEC. These pulses can be fully stopped and later revived by switching the coupling field off and on. Here we develop a formalism, applicable in both the weak- and strong-probe regimes, to analyze such experiments and establish several results: (1) We show that the switching can be performed on time scales much faster than the adiabatic time scale for electromagnetically induced transparancy even in the strong-probe regime. We also study the behavior of the system changes when this time scale is faster than the excited state lifetime. (2) Stopped light pulses write their phase and amplitude information onto spatially dependent atomic wave functions, resulting in coherent two-component BEC dynamics during long storage times. We investigate examples relevant to 87Rb^{87}\mathrm{Rb}87Rb experimental parameters and see a variety of novel dynamics occur, including interference fringes, gentle breathing excitations, and two-component solitons, depending on the relative scattering lengths of the atomic states used and the probe to coupling intensity ratio. We find that the dynamics when the levels $\ensuremath{\mid}F=1,{M}_{F}=\ensuremath{-}1⟩$ and $\ensuremath{\mid}F=2,{M}_{F}=+1⟩$ are used could be well suited to designing controlled processing of the information input on the probe. (3) Switching the coupling field on after the dynamics writes the evolved BEC wave functions density and phase features onto a revived probe pulse, which then propagates out. We establish equations linking the BEC wave function to the resulting output probe pulses in both the strong- and weak-probe regimes. We then identify sources of deviations from these equations due to absorption and distortion of the pulses. These deviations result in imperfect fidelity of the information transfer from the atoms to the light fields and we calculate this fidelity for Gaussian-shaped features in the BEC wave functions. In the weak-probe case, we find that the fidelity is affected both by absorption of very-small-length-scale features and absorption of features occupying regions near the condensate edge. We discuss how to optimize the fidelity using these considerations. In the strong-probe case, we find that when the oscillator strengths for the two transitions are equal the fidelity is not strongly sensitive to the probe strength, while when they are unequal the fidelity is worse for stronger probes. Applications to distant communication between BEC's, squeezed light generation, and quantum information are anticipated.