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 A

Photonic band gaps in optical lattices

Ivan Deutsch, R. J. C. Spreeuw, S. L. Rolston, William D. Phillips

Published Aug 1, 1995• 196 citations
Publisher

Abstract

We study photonic band gaps in a one-dimensional optical lattice of laser-cooled trapped atoms. We solve for the self-consistent equilibrium positions of the atoms, accounting for the backaction of the atoms on the trapping beams. This solution depends strongly on the sign of the trapping laser detuning. For red-detuned trapping lasers, the resulting lattice exhibits a one-dimensional photonic band gap for frequencies between the trapping laser frequency and the atomic resonance. For blue detuning the stop band extends symmetrically about resonance, typically for hundreds of atomic linewidths, except for the small region between atomic resonance and the lattice frequency, which is excluded. We calculate the reflection spectrum for a lattice of Cs atoms for various trapping laser detunings and interpret its behavior as a function of the lattice size and density. For a mean density of ${10}^{11}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$, and 1000 planes, 55% reflection of a weak probe beam should be observed. We also consider Bragg scattering in a three-dimensional optical lattice as a means of probing the long-range order in the atomic density correlation function.

DOI
10.1103/physreva.52.1394

Related papers

Tunable three photonic band-gaps coherently induced in one-dimensional cold atomic lattices

Nuo Ba, Lei Wang, Yan Zhang

Using the technique of electromagnetically induced transparency, three photonic bandgaps can be established and manipulated at any time due to the refraction modulated periodically by the one-dimensional optical lattice in a tripod atomic system which is trapped in a one-dimensional optical lattice with a Gaussian density distribution. Using the density-matrix equations to describe the interaction between laser and atoms and the transfer-matrix equation to describe the scattering of light waves in periodic media, we can obtain the steady reflection and transmission spectra. It can be found that the position and width as well as the reflectivity of the photonic band-gap could be tuned by changing the detunings and intensities of the coupling fields and the geometric Bragg detuning.

Acta Physica Sinica•Jan 1, 2014•2 citations

Photonic spectrum of bichromatic optical lattices

Stefan Rist, Patrizia Vignolo, Giovanna Morigi

We study the photonic spectrum of a one-dimensional optical lattice possessing a double primitive cell, when the atoms are well localized at the lattice minima. While a one-dimensional lattice with a simple Wigner-Seitz cell always possesses a photonic band gap at the atomic resonance, in this configuration the photonic transmission spectrum may exhibit no, double, or multiple photonic band gaps depending on the ratio between the interparticle distance $\ensuremath{\varrho}$ inside the cell and the cell size $a$. The transmission spectra of a weak incident probe are evaluated when the atoms are trapped in free space and inside an optical resonator for realistic experimental parameters.

arXiv:0901.2295•Physical Review A•May 13, 2009•14 citations

Dynamically controlled two-color photonic band gaps via balanced four-wave mixing in one-dimensional cold atomic lattices

Hong Wei Yang, Liu Shuan Yang, Xiao-Chang Wang +3 more

We study an ensemble of cold atoms driven to the four-level double-$\ensuremath{\Lambda}$ configuration and trapped in the one-dimensional optical lattices for achieving dynamically controlled photonic band gaps (PBGs) via the balanced four-wave mixing interaction. Numerical results show that a pair of PBGs characterized by high platforms of probe reflectivities and reduced density of photonic states are established, simultaneously, on both probe transitions in one symmetric driving scheme. Such two-color PBGs can be easily manipulated in position and width by modulating, e.g., the balanced Rabi frequencies of two coupling fields and the Gaussian widths of atomic density distributions, to change the equal probe detunings fulfilling both Bragg conditions. Each two-color PBG as predicted in the coherent atomic lattices may be explored to attain robust light entanglement, even for single-probe photons, via an efficient frequency conversion during the nonlinearly correlated reflection.

Physical Review A•Dec 18, 2013•23 citations

Multiple reflections and diffuse scattering in Bragg scattering at optical lattices

Sebastian Slama, C. von Cube, M. Kohler +2 more

We study Bragg scattering at one-dimensional atomic lattices. Cold atoms are confined by optical dipole forces at the antinodes of a standing wave generated inside a laser-driven cavity. The atoms arrange themselves into an array of lens-shaped layers located at the antinodes of the standing wave. Light incident on this array at a well-defined angle is partially Bragg reflected. We measure reflectivities as high as $30%$. In contrast to a previous experiment devoted to the thin grating limit [S. Slama et al., Phys. Rev. Lett. 94, 193901 (2005)] we now investigate the thick grating limit characterized by multiple reflections of the light beam between the atomic layers. In principle, multiple reflections give rise to a photonic stop band, which manifests itself in the Bragg diffraction spectra as asymmetries and minima due to destructive interference between different reflection paths. We show that close to resonance however disorder favors diffuse scattering, hinders coherent multiple scattering and impedes the characteristic suppression of spontaneous emission inside a photonic band gap.

arXiv:quant-ph/0511258•Physical Review A•Feb 27, 2006•37 citations

Dynamic manipulation of three-color light reflection in a defective atomic lattice

Tianming Li, Maohua Wang, Chengping Yin +2 more

We extend a recent theoretical work [ Phys. Rev. A 101 , 053856 ( 2020 ) 10.1103/PhysRevA.101.053856 ] by replacing disorders characterized by varied atomic densities with defects characterized by vacant lattice cells to evaluate again three-color reflection in a one-dimensional optical lattice filled with cold 87Rb atoms. This is based on the consideration that trapped atoms may escape from some lattice cells and effects of vacant cells on light propagation are of major importance from both fundamental and applied research viewpoints. We consider two types of defective atomic lattices where vacant cells are randomly or continuously distributed among filled cells. Numerical results show that the wider reflection band in a large detuning region of negligible off-resonance absorption is quite sensitive to, while the narrower reflection bands in two near-resonant regions of electromagnetically induced transparency are rather robust against, the number of random vacant cells. In contrast, all three reflection bands exhibit strong robustness against the number of continuous vacant cells. Note, however, that both narrower reflection bands may become widened and exhibit a blue shift when continuous vacant cells appear in the front of our atomic lattice due to the joint contributions of Bragg scattering and quantum interference.

Optics Express•Sep 7, 2021•5 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
We study photonic band gaps in a one-dimensional optical lattice of laser-cooled trapped atoms. We solve for the self-consistent equilibrium positions of the atoms, accounting for the backaction of the atoms on the trapping beams. This solution depends strongly on the sign of the trapping laser detuning. For red-detuned trapping lasers, the resulting lattice exhibits a one-dimensional photonic band gap for frequencies between the trapping laser frequency and the atomic resonance. For blue detuning the stop band extends symmetrically about resonance, typically for hundreds of atomic linewidths, except for the small region between atomic resonance and the lattice frequency, which is excluded. We calculate the reflection spectrum for a lattice of Cs atoms for various trapping laser detunings and interpret its behavior as a function of the lattice size and density. For a mean density of 1011{10}^{11}1011 cm\ensuremath−3{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}cm\ensuremath−3, and 1000 planes, 55% reflection of a weak probe beam should be observed. We also consider Bragg scattering in a three-dimensional optical lattice as a means of probing the long-range order in the atomic density correlation function.
Using the technique of electromagnetically induced transparency, three photonic bandgaps can be established and manipulated at any time due to the refraction modulated periodically by the one-dimensional optical lattice in a tripod atomic system which is trapped in a one-dimensional optical lattice with a Gaussian density distribution. Using the density-matrix equations to describe the interaction between laser and atoms and the transfer-matrix equation to describe the scattering of light waves in periodic media, we can obtain the steady reflection and transmission spectra. It can be found that the position and width as well as the reflectivity of the photonic band-gap could be tuned by changing the detunings and intensities of the coupling fields and the geometric Bragg detuning.
We study the photonic spectrum of a one-dimensional optical lattice possessing a double primitive cell, when the atoms are well localized at the lattice minima. While a one-dimensional lattice with a simple Wigner-Seitz cell always possesses a photonic band gap at the atomic resonance, in this configuration the photonic transmission spectrum may exhibit no, double, or multiple photonic band gaps depending on the ratio between the interparticle distance $\ensuremath{\varrho}$ inside the cell and the cell size aaa. The transmission spectra of a weak incident probe are evaluated when the atoms are trapped in free space and inside an optical resonator for realistic experimental parameters.
We study an ensemble of cold atoms driven to the four-level double-$\ensuremath{\Lambda}$ configuration and trapped in the one-dimensional optical lattices for achieving dynamically controlled photonic band gaps (PBGs) via the balanced four-wave mixing interaction. Numerical results show that a pair of PBGs characterized by high platforms of probe reflectivities and reduced density of photonic states are established, simultaneously, on both probe transitions in one symmetric driving scheme. Such two-color PBGs can be easily manipulated in position and width by modulating, e.g., the balanced Rabi frequencies of two coupling fields and the Gaussian widths of atomic density distributions, to change the equal probe detunings fulfilling both Bragg conditions. Each two-color PBG as predicted in the coherent atomic lattices may be explored to attain robust light entanglement, even for single-probe photons, via an efficient frequency conversion during the nonlinearly correlated reflection.
We study Bragg scattering at one-dimensional atomic lattices. Cold atoms are confined by optical dipole forces at the antinodes of a standing wave generated inside a laser-driven cavity. The atoms arrange themselves into an array of lens-shaped layers located at the antinodes of the standing wave. Light incident on this array at a well-defined angle is partially Bragg reflected. We measure reflectivities as high as 3030%30. In contrast to a previous experiment devoted to the thin grating limit [S. Slama et al., Phys. Rev. Lett. 94, 193901 (2005)] we now investigate the thick grating limit characterized by multiple reflections of the light beam between the atomic layers. In principle, multiple reflections give rise to a photonic stop band, which manifests itself in the Bragg diffraction spectra as asymmetries and minima due to destructive interference between different reflection paths. We show that close to resonance however disorder favors diffuse scattering, hinders coherent multiple scattering and impedes the characteristic suppression of spontaneous emission inside a photonic band gap.
We extend a recent theoretical work [ Phys. Rev. A 101 , 053856 ( 2020 ) 10.1103/PhysRevA.101.053856 ] by replacing disorders characterized by varied atomic densities with defects characterized by vacant lattice cells to evaluate again three-color reflection in a one-dimensional optical lattice filled with cold 87Rb atoms. This is based on the consideration that trapped atoms may escape from some lattice cells and effects of vacant cells on light propagation are of major importance from both fundamental and applied research viewpoints. We consider two types of defective atomic lattices where vacant cells are randomly or continuously distributed among filled cells. Numerical results show that the wider reflection band in a large detuning region of negligible off-resonance absorption is quite sensitive to, while the narrower reflection bands in two near-resonant regions of electromagnetically induced transparency are rather robust against, the number of random vacant cells. In contrast, all three reflection bands exhibit strong robustness against the number of continuous vacant cells. Note, however, that both narrower reflection bands may become widened and exhibit a blue shift when continuous vacant cells appear in the front of our atomic lattice due to the joint contributions of Bragg scattering and quantum interference.
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.