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/0312168

Self Focussing as a Coherence Propagation Phenomena. An Application to Calculate the Coherence Length for an Atom Laser

Castellanos, L. M., Lopez, F. E.

Published Dec 19, 2003• 0 citations
arXivHTMLPDF

Abstract

A theoretical description in terms of the coherence propagation is given for self-focussing. The concept of coherence length is defined in terms of free, self-focussing propagation giving results in accordance with well known experimental criteria for the laser. Extension of the method is given for an Atom Laser showing good results in agreement with recents numerical results of Trippenbach et. al.: J. Phys. B:At. Mol. Opt. Phys. 33, 47-54 (2000).

DOI
10.48550/arxiv.quant-ph/0312168

Related papers

Spatial distortions of laser pulses in coherent on-resonance propagation: Large-scale self-focusing

Jacques de Lamare, Michel Comte, Ph.J. Kupecek

When cylindrical symmetry is assumed, a numerical study of coherent on-resonance self-focusing of laser pulses in atomic media reveals a well-defined dependence on the interaction's parameters for the focusing distance and the maximal on-axis energy density reached at the focus. We interpreted this focusing to be the result of a diaphragm effect at the edge of the pulse. This can be readily explained by considering the transverse dependence of local self-induced transparency phenomena first described by McCall and Hahn [Phys. Rev. Lett. 18, 908 (1967); Phys. Rev. 183, 457 (1969)]. From this interpretation and the well-known Maxwell-Bloch equations, we derived a theoretical quantitative model for coherent on-resonance large-scale self-focusing, that is to say, focusing of the beam as a whole. Our main results include the above-mentioned exact parametric dependence for the focusing distance, as well as predictions about the ratios of on-axis energy densities and pulse transverse sizes between the input and focus planes. All of these predictions appear to corroborate the results of an experiment on a ${\mathrm{Tm}}^{169}$ vapor.

Physical Review A•Oct 1, 1994•11 citations

Theoretical tools for atom-laser-beam propagation

J.-F. Riou, Yann Le Coq, François Impens +4 more

We present a theoretical model for the propagation of non-self-interacting atom laser beams. We start from a general propagation integral equation and we use the same approximations as in photon optics to derive tools to calculate the atom-laser-beam propagation. We discuss the approximations that allow one to reduce the general equation whether to a Fresnel-Kirchhoff integral calculated by using the stationary phase method, or to the eikonal. Within the paraxial approximation, we also introduce the $ABCD$ matrices formalism and the beam quality factor. As an example, we apply these tools to analyze the recent experiment by Riou et al. [Phys. Rev. Lett. 96, 070404 (2006)].

arXiv:0802.4039•Physical Review A•Mar 27, 2008•31 citations

Coherence length calculation for the outcoupled beam of atom laser

Abdul-Basit A. Saleh, Noori H. N. Al-Hashmiy

We use the theory of coupled Gross-Pitaevskii equations to derive an expression for the current density of the propagating atoms coupled out of the condensate under the influence of gravity. By describing the propagation vector of the atoms and using a theoretical definition of the coherence length, we calculate the coherence lengths of 37K, 141Ce, and 249Fm atom lasers numerically. Our calculation method is verified with the available experimental and theoretical data in the literature. The results showed a very good agreement.

Brazilian Journal of Physics•Sep 1, 2007•1 citation

Coherence properties of an atom laser

Marek Trippenbach, Y. B. Band, Mark Edwards +8 more

We study the coherence properties of an atom laser, which operates by extracting atoms from a gaseous Bose-Einstein condensate via a two-photon Raman process, by analysing a recent experiment (Hagley et al 1999 Phys. Rev. Lett. 83 3112). We obtain good agreement with the experimental data by solving the time-dependent Gross-Pitaevskii equation in three dimensions both numerically and with a Thomas-Fermi model. The coherence is strongly affected by the space-dependent phase developed by the condensate when the trapping potential is turned off.

arXiv:cond-mat/9906033•Journal of Physics B Atomic Molecular and Optical Physics•Dec 13, 1999•32 citations

Three-level atom laser model with results and applications

Andrew M. Smith II, Crispin W. Gardiner

We present here a fully quantum-mechanical treatment of the laser using a three-level atom model. The phase-space method employed is identical to that in a previous publication of ours [Phys. Rev. A 38, 4073 (1988)] and again results in a Fokker-Planck description of the laser without any approximations. The third level only provides extra deterministic terms and, if it is regarded as a further reservoir to the lasing levels, then the resultant stochastic equations have much improved stability. These equations are suitable for extensive theoretical analysis of both the laser and optical bistability, although in this paper we have concentrated on the adiabatically eliminated limit and calculated the leading noise terms in various regimes. However, we do use the technique of direct numerical simulation to solve exactly the full system of laser equations. The results display clearly many of the known laser characteristics.

Physical Review A•Mar 1, 1990•14 citations

Kerr-free propagation of a near-resonant laser in an atomic vapor

Didier Bénisti, O. Gobert, Michel Comte

In this paper, we address the propagation of a near resonant laser inside an atomic vapor in the case when, due to the Kerr effect, the laser beam would either self-focus or self-defocus. We show, both theoretically and experimentally, how to get rid of such an alteration in the transverse beam profile without changing any of the characteristics of the laser light under consideration (wavelength, intensity, etc.), nor of the atomic vapor. Moreover, our proposed method offers a lot of control on the beam profile, whose transverse size after propagation may be chosen at will by making use of a second, copropagating laser, whose required wavelength and intensity may be derived analytically.

Physical Review A•Jan 30, 2014•0 citations
A theoretical description in terms of the coherence propagation is given for self-focussing. The concept of coherence length is defined in terms of free, self-focussing propagation giving results in accordance with well known experimental criteria for the laser. Extension of the method is given for an Atom Laser showing good results in agreement with recents numerical results of Trippenbach et. al.: J. Phys. B:At. Mol. Opt. Phys. 33, 47-54 (2000).
When cylindrical symmetry is assumed, a numerical study of coherent on-resonance self-focusing of laser pulses in atomic media reveals a well-defined dependence on the interaction's parameters for the focusing distance and the maximal on-axis energy density reached at the focus. We interpreted this focusing to be the result of a diaphragm effect at the edge of the pulse. This can be readily explained by considering the transverse dependence of local self-induced transparency phenomena first described by McCall and Hahn [Phys. Rev. Lett. 18, 908 (1967); Phys. Rev. 183, 457 (1969)]. From this interpretation and the well-known Maxwell-Bloch equations, we derived a theoretical quantitative model for coherent on-resonance large-scale self-focusing, that is to say, focusing of the beam as a whole. Our main results include the above-mentioned exact parametric dependence for the focusing distance, as well as predictions about the ratios of on-axis energy densities and pulse transverse sizes between the input and focus planes. All of these predictions appear to corroborate the results of an experiment on a Tm169{\mathrm{Tm}}^{169}Tm169 vapor.
We present a theoretical model for the propagation of non-self-interacting atom laser beams. We start from a general propagation integral equation and we use the same approximations as in photon optics to derive tools to calculate the atom-laser-beam propagation. We discuss the approximations that allow one to reduce the general equation whether to a Fresnel-Kirchhoff integral calculated by using the stationary phase method, or to the eikonal. Within the paraxial approximation, we also introduce the ABCDABCDABCD matrices formalism and the beam quality factor. As an example, we apply these tools to analyze the recent experiment by Riou et al. [Phys. Rev. Lett. 96, 070404 (2006)].
We use the theory of coupled Gross-Pitaevskii equations to derive an expression for the current density of the propagating atoms coupled out of the condensate under the influence of gravity. By describing the propagation vector of the atoms and using a theoretical definition of the coherence length, we calculate the coherence lengths of 37K, 141Ce, and 249Fm atom lasers numerically. Our calculation method is verified with the available experimental and theoretical data in the literature. The results showed a very good agreement.
We study the coherence properties of an atom laser, which operates by extracting atoms from a gaseous Bose-Einstein condensate via a two-photon Raman process, by analysing a recent experiment (Hagley et al 1999 Phys. Rev. Lett. 83 3112). We obtain good agreement with the experimental data by solving the time-dependent Gross-Pitaevskii equation in three dimensions both numerically and with a Thomas-Fermi model. The coherence is strongly affected by the space-dependent phase developed by the condensate when the trapping potential is turned off.
We present here a fully quantum-mechanical treatment of the laser using a three-level atom model. The phase-space method employed is identical to that in a previous publication of ours [Phys. Rev. A 38, 4073 (1988)] and again results in a Fokker-Planck description of the laser without any approximations. The third level only provides extra deterministic terms and, if it is regarded as a further reservoir to the lasing levels, then the resultant stochastic equations have much improved stability. These equations are suitable for extensive theoretical analysis of both the laser and optical bistability, although in this paper we have concentrated on the adiabatically eliminated limit and calculated the leading noise terms in various regimes. However, we do use the technique of direct numerical simulation to solve exactly the full system of laser equations. The results display clearly many of the known laser characteristics.
In this paper, we address the propagation of a near resonant laser inside an atomic vapor in the case when, due to the Kerr effect, the laser beam would either self-focus or self-defocus. We show, both theoretically and experimentally, how to get rid of such an alteration in the transverse beam profile without changing any of the characteristics of the laser light under consideration (wavelength, intensity, etc.), nor of the atomic vapor. Moreover, our proposed method offers a lot of control on the beam profile, whose transverse size after propagation may be chosen at will by making use of a second, copropagating laser, whose required wavelength and intensity may be derived analytically.