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

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Light scattering from a randomly occupied optical lattice. I. Born approximation

Wei Guo, Sudhakar Prasad

Published May 19, 2003• 4 citations
Publisher

Abstract

A theoretical study of the scattering of light from a randomly occupied optical lattice of resonant atoms is presented to reveal both the characteristics of the lattice and the properties of light scattered from the lattice. In the first-order Born approximation we discuss here, a number of interesting effects are established, including sideband Stokes scattering, a finite angular coherence of the scattered light, and spectral line narrowing. Specifically, the degree of angular coherence of the scattered light is calculated, and it is shown that such coherence is strongly influenced by the regularity and size of the underlying lattice structure. The previously observed phenomenon of the sideband spectral line narrowing is also explained in terms of the localization of atoms in the trapping potential wells. Important information about the lattice can thus be recovered by analyzing the scattered light in the Born approximation.

DOI
10.1103/physreve.67.056614

Related papers

Light scattering from a randomly occupied optical lattice. II. The multiple scattering problem

Wei Guo, Sudhakar Prasad

In this paper, we study the problem of multiple scattering of light from a randomly occupied optical lattice, thereby extending the first-order Born analysis of the previous paper. A full multiple-scattering analysis is essential to a complete understanding of the nature of light propagation inside a medium. Our calculations show that the incident wave, when resonant with the atomic medium, is rapidly extinguished due to multiple scattering. The decay constant depends critically on the incident wavelength, the lattice constant, the average number density of atoms, and their polarizability. Both the Bragg scattering amplitudes and directions are modified as a result of multiple scattering. Because of the random site occupation of an otherwise regular lattice structure, a coherent enhancement of the scattering cross section is also predicted to occur along a discrete set of directions that are related to the strictly backward direction by reciprocal lattice vectors.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•May 19, 2003•6 citations

Recurrent scattering of spontaneous radiation from a randomly occupied optical lattice

Wei Guo

The problem of recurrent scattering of spontaneous radiation from a randomly occupied optical lattice is discussed herein theoretically. The intensity of the scattered radiation is calculated and averaged over the random distribution of atoms trapped inside the lattice. From the intensity of the scattered radiation, two properties of random lasing are derived. First, the random lasing's strongest oscillation has a wavelength comparable to the lattice constant and, second, its emission spectrum is discontinuous. In the present paper, a quantity, the number of multiple scattering channels based on the long-range regularity possessed by an optical lattice, is defined. This quantity is found to significantly determine the magnitudes of the mean intensity of the scattered radiation and the wave decay constant.

Physical Review E•Mar 19, 2004•3 citations

Bragg Scattering from Atoms in Optical Lattices

G. Birkl, M. Gatzke, Ivan Deutsch +2 more

We observe coherently enhanced reflection (Bragg scattering) of a near resonant laser beam from cesium atoms ordered by a periodic array of optical potential wells known as an optical lattice. The reflected light is enhanced by a factor of $\ensuremath{\sim}{10}^{5}$ over scattering from a disordered atomic sample. We measure the magnitude of the reflectivity and its detuning dependence as functions of the density and the degree of localization of the atoms. The change in lattice constant due to the frequency-dependent effective index of refraction seen by the lattice light field is observed.

Physical Review Letters•Oct 9, 1995•218 citations

Thermal effects in light scattering from ultracold bosons in an optical lattice

Kazimierz Łakomy, Zbigniew Idziaszek, Marek Trippenbach

We study the scattering of a weak and far-detuned light from a system of ultracold bosons in one-dimensional and three-dimensional optical lattices. We show the connection between angular distributions of the scattered light and statistical properties of a Bose gas in a periodic potential. The angular patterns are determined by the Fourier transform of the second-order correlation function, and thus they can be used to retrieve information on particle number fluctuations and correlations. We consider superfluid and Mott-insulator phases of the Bose gas in a lattice and we analyze in detail how the scattering depends on the system dimensionality, temperature, and atom-atom interactions.

arXiv:0904.2927•Physical Review A•Oct 7, 2009•16 citations

Local and global properties of light-bound atomic lattices investigated by Bragg diffraction

Matthias Weidemüller, Axel Görlitz, Theodor W. Hänsch +1 more

We explore Bragg diffraction from atomic lattices bound by light as a diagnostic tool for studying properties of optical lattices not accessible so far. A weak laser beam at a wavelength of about half the wavelength of the lattice field is diffracted from the (100) and (130) lattice planes of a Rb optical lattice. The observation of well-defined Bragg spots confirms the long-range order in optical lattices. From the acceptance angle for Bragg diffraction we deduce the range over which crystalline order is preserved. The comparison of two Bragg spots diffracted from different lattice planes allows us to directly measure the position spread of the atomic wave packets oscillating in the light-induced potential wells. By combining conventional probe transmission spectroscopy with Bragg diffraction we study the motion of atoms that are deeply bound inside the potential wells. We show experimentally and theoretically how backaction of the bound atoms on the trapping field influences the lattice constant. We develop a model for the modification of the refractive index by the highly ordered atomic medium. Based on first-order scattering theory the model explicitly includes the influence of atomic localization on the resulting lattice constant. By measuring the change of the Bragg angle, we observe a decrease of the lattice plane separation for increasing atomic density. We report experimental evidence for the correction to the refractive index due to the finite position spread of the atoms.

Physical Review A•Dec 1, 1998•44 citations

Light scattering from ultracold atoms in optical lattices as an optical probe of quantum statistics

Igor B. Mekhov, Christoph Maschler, Helmut Ritsch

We study off-resonant collective light scattering from ultracold atoms trapped in an optical lattice. Scattering from different atomic quantum states creates different quantum states of the scattered light, which can be distinguished by measurements of the spatial intensity distribution, quadrature variances, photon statistics, or spectral measurements. In particular, angle-resolved intensity measurements reflect global statistics of atoms (total number of radiating atoms) as well as local statistical quantities (single-site statistics even without optical access to a single site) and pair correlations between different sites. As a striking example we consider scattering from transversally illuminated atoms into an optical cavity mode. For the Mott-insulator state, similar to classical diffraction, the number of photons scattered into a cavity is zero due to destructive interference, while for the superfluid state it is nonzero and proportional to the number of atoms. Moreover, we demonstrate that light scattering into a standing-wave cavity has a nontrivial angle dependence, including the appearance of narrow features at angles, where classical diffraction predicts zero. The measurement procedure corresponds to the quantum nondemolition measurement of various atomic variables by observing light.

arXiv:quant-ph/0702193•Physical Review A•Nov 21, 2007•56 citations
A theoretical study of the scattering of light from a randomly occupied optical lattice of resonant atoms is presented to reveal both the characteristics of the lattice and the properties of light scattered from the lattice. In the first-order Born approximation we discuss here, a number of interesting effects are established, including sideband Stokes scattering, a finite angular coherence of the scattered light, and spectral line narrowing. Specifically, the degree of angular coherence of the scattered light is calculated, and it is shown that such coherence is strongly influenced by the regularity and size of the underlying lattice structure. The previously observed phenomenon of the sideband spectral line narrowing is also explained in terms of the localization of atoms in the trapping potential wells. Important information about the lattice can thus be recovered by analyzing the scattered light in the Born approximation.
In this paper, we study the problem of multiple scattering of light from a randomly occupied optical lattice, thereby extending the first-order Born analysis of the previous paper. A full multiple-scattering analysis is essential to a complete understanding of the nature of light propagation inside a medium. Our calculations show that the incident wave, when resonant with the atomic medium, is rapidly extinguished due to multiple scattering. The decay constant depends critically on the incident wavelength, the lattice constant, the average number density of atoms, and their polarizability. Both the Bragg scattering amplitudes and directions are modified as a result of multiple scattering. Because of the random site occupation of an otherwise regular lattice structure, a coherent enhancement of the scattering cross section is also predicted to occur along a discrete set of directions that are related to the strictly backward direction by reciprocal lattice vectors.
The problem of recurrent scattering of spontaneous radiation from a randomly occupied optical lattice is discussed herein theoretically. The intensity of the scattered radiation is calculated and averaged over the random distribution of atoms trapped inside the lattice. From the intensity of the scattered radiation, two properties of random lasing are derived. First, the random lasing's strongest oscillation has a wavelength comparable to the lattice constant and, second, its emission spectrum is discontinuous. In the present paper, a quantity, the number of multiple scattering channels based on the long-range regularity possessed by an optical lattice, is defined. This quantity is found to significantly determine the magnitudes of the mean intensity of the scattered radiation and the wave decay constant.
We observe coherently enhanced reflection (Bragg scattering) of a near resonant laser beam from cesium atoms ordered by a periodic array of optical potential wells known as an optical lattice. The reflected light is enhanced by a factor of $\ensuremath{\sim}{10}^{5}$ over scattering from a disordered atomic sample. We measure the magnitude of the reflectivity and its detuning dependence as functions of the density and the degree of localization of the atoms. The change in lattice constant due to the frequency-dependent effective index of refraction seen by the lattice light field is observed.
We study the scattering of a weak and far-detuned light from a system of ultracold bosons in one-dimensional and three-dimensional optical lattices. We show the connection between angular distributions of the scattered light and statistical properties of a Bose gas in a periodic potential. The angular patterns are determined by the Fourier transform of the second-order correlation function, and thus they can be used to retrieve information on particle number fluctuations and correlations. We consider superfluid and Mott-insulator phases of the Bose gas in a lattice and we analyze in detail how the scattering depends on the system dimensionality, temperature, and atom-atom interactions.
We explore Bragg diffraction from atomic lattices bound by light as a diagnostic tool for studying properties of optical lattices not accessible so far. A weak laser beam at a wavelength of about half the wavelength of the lattice field is diffracted from the (100) and (130) lattice planes of a Rb optical lattice. The observation of well-defined Bragg spots confirms the long-range order in optical lattices. From the acceptance angle for Bragg diffraction we deduce the range over which crystalline order is preserved. The comparison of two Bragg spots diffracted from different lattice planes allows us to directly measure the position spread of the atomic wave packets oscillating in the light-induced potential wells. By combining conventional probe transmission spectroscopy with Bragg diffraction we study the motion of atoms that are deeply bound inside the potential wells. We show experimentally and theoretically how backaction of the bound atoms on the trapping field influences the lattice constant. We develop a model for the modification of the refractive index by the highly ordered atomic medium. Based on first-order scattering theory the model explicitly includes the influence of atomic localization on the resulting lattice constant. By measuring the change of the Bragg angle, we observe a decrease of the lattice plane separation for increasing atomic density. We report experimental evidence for the correction to the refractive index due to the finite position spread of the atoms.
We study off-resonant collective light scattering from ultracold atoms trapped in an optical lattice. Scattering from different atomic quantum states creates different quantum states of the scattered light, which can be distinguished by measurements of the spatial intensity distribution, quadrature variances, photon statistics, or spectral measurements. In particular, angle-resolved intensity measurements reflect global statistics of atoms (total number of radiating atoms) as well as local statistical quantities (single-site statistics even without optical access to a single site) and pair correlations between different sites. As a striking example we consider scattering from transversally illuminated atoms into an optical cavity mode. For the Mott-insulator state, similar to classical diffraction, the number of photons scattered into a cavity is zero due to destructive interference, while for the superfluid state it is nonzero and proportional to the number of atoms. Moreover, we demonstrate that light scattering into a standing-wave cavity has a nontrivial angle dependence, including the appearance of narrow features at angles, where classical diffraction predicts zero. The measurement procedure corresponds to the quantum nondemolition measurement of various atomic variables by observing light.