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 Modern Optics

Velocity selection in a Doppler-broadened ensemble of atoms interacting with a monochromatic laser beam

Ifan G. Hughes

Published May 22, 2017• 8 citations
Publisher

Abstract

There is extensive use of monochromatic lasers to select atoms with a narrow range of velocities in many atomic physics experiments. For the commonplace situation of the inhomogeneous Doppler-broadened (Gaussian) linewidth exceeding the homogeneous (Lorentzian) natural linewidth by typically two orders of magnitude, a substantial narrowing of the velocity class of atoms interacting with the light can be achieved. However, this is not always the case, and here we show that for a certain parameter regime there is essentially no selection – all of the atoms interact with the light in accordance with the velocity probability density. An explanation of this effect is provided, emphasizing the importance of the long tail of the constituent Lorentzian distribution in a Voigt profile.

DOI
10.1080/09500340.2017.1328749

Related papers

Inhomogeneous broadening

Luigi Lugiato, Franco Prati, Massimo Brambilla

Up to this point we have always assumed that all the atoms which interact with the radiation field have the same atomic transition frequency, with an atomic linewidth given by γ ⊥ . This configuration is called homogeneous broadening. However, in the great majority of lasers the linewidth is inhomogeneously broadened , because the atomic frequency follows a distribution. For example, in solid-state lasers such as the ruby laser and fiber lasers the inhomogeneity is due to the imperfections in the crystalline structure of the material. In gas lasers, where the atoms or molecules are free to move, the inhomogeneous broadening is due to the Doppler effect, for which a molecule moving with velocity v in a field of frequency ω and wave vector k experiences an effective frequency ω ′ = ω − k · v [8]. Since what matters is the difference between the atomic transition frequency and the field frequency, we can keep the field frequency fixed and imagine that the field interacts with different groups of atoms that move with different velocities and therefore have different transition frequencies. The realistic velocity distribution is a Gaussian, for which the corresponding distribution for the modulus of the velocity is Maxwellian. However, in the following we will mainly analyze the case of a Lorentzian distribution for the atomic transition frequency, because this allows an analytical treatment. Again for the sake of simplicity, we will limit our analysis to the case of a ring cavity. In Section 15.1 we will generalize to the inhomogeneous-broadening configuration the modal equations for the case of homogeneous broadening, which were formulated in Chapter 12. In Section 15.2 we will specialize to the single-mode model and discuss its stationary solutions for the laser case. Multimode dynamical equations The atomic transition frequency of the generic group of atoms is given by ω a + δ D , where ω a is the central atomic frequency and δ D takes positive and negative values. We call ω c the frequency of the cavity mode nearest to ω a and denote by δ ac the difference ω a − ω c .

Cambridge University Press eBooks•Feb 28, 2015•2 citations

Laser-induced fluorescence line narrowing in atomic vapors

Th. Meier, Hans A. Schuessler

The use of highly monochromatic light permits the selective excitation of atoms in vapors if excitation and detection of the fluorescence is carried out collinearly. The atoms capable of absorbing light then form an atomic beam of well-defined velocity along the direction of the laser beam, but no velocity selection occurs perpendicular to it. The potential of the technique for Doppler-free atomic spectroscopy and for the study of excited atom collisions is demonstrated by using the Na D1 line as an example.

NASA STI/Recon Technical Report N•Sep 1, 1983•0 citations

Laser-induced fluorescence line narrowing in atomic vapors

Th. Meier, Hans A. Schuessler

The use of highly monochromatic light permits the selective excitation of atoms in vapors if excitation and detection of the fluorescence is carried out collinearly. The atoms capable of absorbing light then form an atomic beam of well-defined velocity along the direction of the laser beam, but no velocity selection occurs perpendicular to it. The potential of the technique for Doppler-free atomic spectroscopy and for the study of excited atom collisions is demonstrated by using the Na D1 line as an example.

Journal of the Optical Society of America B•Apr 1, 1984•1 citation

Atomic-Motion-Induced Quasi-Collective Effects in Laser Spectroscopy of Atomic Gases

Valeriy I. Yudin, А. В. Тайченачев, M. Yu. Basalaev +2 more

We develop the theory of propagation of laser wave in a gas of two-level atoms (with an optical transition frequency $\omega^{}_0$) under the condition of inhomogeneous Doppler broadening, considering the self-consistent solution of the Maxwell-Bloch equations in the mean-field approximation and for one-atomic density matrix. The nonlinear effects in the atomic density $n$, caused by the free motion of atoms, are found. These effects distort the lineshape (shift, asymmetry, broadening), but are not associated with atom-atom interaction. Moreover, in the case $nk^{-3}_0<1$ (where $k^{}_0=\omega^{}_0/c$) and temperatures $T\gtrsim 300$~K, these quasi-collective effects exceed the well-known influence of the dipole-dipole interatomic interaction (e.g., Lorentz-Lorenz shift) by more than one order of magnitude. It was also found that for some area of parameters, the frequency interval appears, within which the non-trivial self-consistent solution of the Maxwell-Bloch equations is absent at all. Thus, the physical picture of collective effects in a gas medium should be substantially revised.

•Aug 17, 2021•0 citations

Quantum-limited linewidth of a bad-cavity laser with inhomogeneous broadening

Antonio Zelaquett Khoury, Mikhail I. Kolobov, L. Davidovich

We derive a general expression for the linewidth of inhomogeneously broadened traveling-wave gas lasers, without any assumption on the relative magnitude of the atomic and field decay constants, and for several types of atomic pumping statistics, ranging from Poissonian to regular. For small inhomogeneous broadening, an important linewidth narrowing occurs in the bad-cavity limit. This effect disappears, however, in the large inhomogeneous broadening limit (Doppler limit). \textcopyright{} 1996 The American Physical Society.

Physical Review A•Feb 1, 1996•13 citations

Power-dependent line-shape corrections for quantitative spectroscopy

Thomas M. Stace, Gar-Wing Truong, James D. Anstie +2 more

The Voigt profile---a convolution of a Gaussian and a Lorentzian---accurately describes the absorption lines of atomic and molecular gases at low probe powers. Fitting experimental absorption data to such a Voigt profile yields both the Lorentzian natural linewidth and the Gaussian Doppler broadening. However, as the probe power increases, saturation effects change the absorption line shape, such that it is no longer accurately described by a Voigt profile. Naively fitting a simple Voigt profile to the absorption line therefore introduces spurious power dependence into the extracted Doppler component. Using a simple atomic model, we calculate power-dependent corrections to the Voigt profile, which are parametrized by the Gaussian Doppler width, the Lorentzian natural linewidth, and the optical depth. We show numerically and experimentally that including the correction term substantially reduces the spurious power dependence in the fitted Gaussian width.

arXiv:1203.2828•Physical Review A•Jul 17, 2012•16 citations
There is extensive use of monochromatic lasers to select atoms with a narrow range of velocities in many atomic physics experiments. For the commonplace situation of the inhomogeneous Doppler-broadened (Gaussian) linewidth exceeding the homogeneous (Lorentzian) natural linewidth by typically two orders of magnitude, a substantial narrowing of the velocity class of atoms interacting with the light can be achieved. However, this is not always the case, and here we show that for a certain parameter regime there is essentially no selection – all of the atoms interact with the light in accordance with the velocity probability density. An explanation of this effect is provided, emphasizing the importance of the long tail of the constituent Lorentzian distribution in a Voigt profile.
Up to this point we have always assumed that all the atoms which interact with the radiation field have the same atomic transition frequency, with an atomic linewidth given by γ ⊥ . This configuration is called homogeneous broadening. However, in the great majority of lasers the linewidth is inhomogeneously broadened , because the atomic frequency follows a distribution. For example, in solid-state lasers such as the ruby laser and fiber lasers the inhomogeneity is due to the imperfections in the crystalline structure of the material. In gas lasers, where the atoms or molecules are free to move, the inhomogeneous broadening is due to the Doppler effect, for which a molecule moving with velocity v in a field of frequency ω and wave vector k experiences an effective frequency ω ′ = ω − k · v [8]. Since what matters is the difference between the atomic transition frequency and the field frequency, we can keep the field frequency fixed and imagine that the field interacts with different groups of atoms that move with different velocities and therefore have different transition frequencies. The realistic velocity distribution is a Gaussian, for which the corresponding distribution for the modulus of the velocity is Maxwellian. However, in the following we will mainly analyze the case of a Lorentzian distribution for the atomic transition frequency, because this allows an analytical treatment. Again for the sake of simplicity, we will limit our analysis to the case of a ring cavity. In Section 15.1 we will generalize to the inhomogeneous-broadening configuration the modal equations for the case of homogeneous broadening, which were formulated in Chapter 12. In Section 15.2 we will specialize to the single-mode model and discuss its stationary solutions for the laser case. Multimode dynamical equations The atomic transition frequency of the generic group of atoms is given by ω a + δ D , where ω a is the central atomic frequency and δ D takes positive and negative values. We call ω c the frequency of the cavity mode nearest to ω a and denote by δ ac the difference ω a − ω c .
The use of highly monochromatic light permits the selective excitation of atoms in vapors if excitation and detection of the fluorescence is carried out collinearly. The atoms capable of absorbing light then form an atomic beam of well-defined velocity along the direction of the laser beam, but no velocity selection occurs perpendicular to it. The potential of the technique for Doppler-free atomic spectroscopy and for the study of excited atom collisions is demonstrated by using the Na D1 line as an example.
The use of highly monochromatic light permits the selective excitation of atoms in vapors if excitation and detection of the fluorescence is carried out collinearly. The atoms capable of absorbing light then form an atomic beam of well-defined velocity along the direction of the laser beam, but no velocity selection occurs perpendicular to it. The potential of the technique for Doppler-free atomic spectroscopy and for the study of excited atom collisions is demonstrated by using the Na D1 line as an example.
We develop the theory of propagation of laser wave in a gas of two-level atoms (with an optical transition frequency ω0\omega^{}_0ω0​) under the condition of inhomogeneous Doppler broadening, considering the self-consistent solution of the Maxwell-Bloch equations in the mean-field approximation and for one-atomic density matrix. The nonlinear effects in the atomic density nnn, caused by the free motion of atoms, are found. These effects distort the lineshape (shift, asymmetry, broadening), but are not associated with atom-atom interaction. Moreover, in the case nk0−3<1nk^{-3}_0<1nk0−3​<1 (where k0=ω0/ck^{}_0=\omega^{}_0/ck0​=ω0​/c) and temperatures T≳300T\gtrsim 300T≳300~K, these quasi-collective effects exceed the well-known influence of the dipole-dipole interatomic interaction (e.g., Lorentz-Lorenz shift) by more than one order of magnitude. It was also found that for some area of parameters, the frequency interval appears, within which the non-trivial self-consistent solution of the Maxwell-Bloch equations is absent at all. Thus, the physical picture of collective effects in a gas medium should be substantially revised.
We derive a general expression for the linewidth of inhomogeneously broadened traveling-wave gas lasers, without any assumption on the relative magnitude of the atomic and field decay constants, and for several types of atomic pumping statistics, ranging from Poissonian to regular. For small inhomogeneous broadening, an important linewidth narrowing occurs in the bad-cavity limit. This effect disappears, however, in the large inhomogeneous broadening limit (Doppler limit). \textcopyright{} 1996 The American Physical Society.
The Voigt profile---a convolution of a Gaussian and a Lorentzian---accurately describes the absorption lines of atomic and molecular gases at low probe powers. Fitting experimental absorption data to such a Voigt profile yields both the Lorentzian natural linewidth and the Gaussian Doppler broadening. However, as the probe power increases, saturation effects change the absorption line shape, such that it is no longer accurately described by a Voigt profile. Naively fitting a simple Voigt profile to the absorption line therefore introduces spurious power dependence into the extracted Doppler component. Using a simple atomic model, we calculate power-dependent corrections to the Voigt profile, which are parametrized by the Gaussian Doppler width, the Lorentzian natural linewidth, and the optical depth. We show numerically and experimentally that including the correction term substantially reduces the spurious power dependence in the fitted Gaussian width.