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:1310.1647 · Annual review of cold atoms and molecules

ONE-DIMENSIONAL PHOTONIC BAND GAPS IN OPTICAL LATTICES

Marina Samoylova, Nicola Piovella, Michael Holynski, Ph. W. Courteille, Romain Bachelard

Published Mar 31, 2014• 1 citation
arXivHTMLPDF

Abstract

The phenomenon of photonic band gaps in one-dimensional optical lattices is reviewed using a microscopic approach. Formally equivalent to the transfer matrix approach in the thermodynamic limit, a microscopic model is required to study finite-size effects, such as deviations from the Bragg condition. Microscopic models describing both scalar and vectorial light are proposed, as well as for two- and three-level atoms. Several analytical results are compared to experimental data, showing a good agreement.

DOI
10.1142/9789814590174_0004

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 band gaps in optical lattices

Ivan Deutsch, R. J. C. Spreeuw, S. L. Rolston +1 more

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.

Physical Review A•Aug 1, 1995•196 citations

Controlling emission and propagation of light with photonic band gap crystals

Elahe Yeganegi Dastgerdi

In certain three-dimensional crystals, a frequency range exist for all polarizations for which light is not allowed to propagate in any direction, called the 3D photonic band gap: a frequency range where the density of vacuum fluctuations vanishes in an ideal infinitely large and perfect system. The complete absence of vacuum fluctuations can be interpreted as zero density of states and vice versa. It is well known that the characteristics of spontaneous emission of light depend strongly on the environment of the light source. According to quantum electrodynamics, the emission rate of a two-level quantum emitter as described by Fermi’s “golden rule”, is factorized into one part describing the emitter’s properties and a second part describing the effect of the environment on the light field via the local density of optical state (LDOS). The radiative decay rate of the emitters is proportional to the LDOS. The absence of vacuum fluctuations or the zero LDOS leads to complete inhibition of the spontaneous emission. While many great advances towards a band gap have been made, no complete inhibition has ever been observed to date. In this thesis, for the first time, we have studied the spontaneous emission of PbS quantum dots inside real 3D photonic band gap crystal as a function of frequency throughout the band gap. In our experiments we have observed an inhibited emission of 18x in the band gap. The time-resolved decay curves show evidence for intriguing finite-size effects whereby vacuum fluctuations tunnel into the band gap. Unfortunately, most theories assume crystals of infinite extent, where the inhibition in the band gap is also infinite, as vacuum fluctuations don’t exist inside the crystal. Here we propose an original model to calculate the LDOS in the band gap of a finite photonic crystal based on tunneling of the vacuum fluctuations into the crystal. We validate our model for the one-dimensional situation with a direct comparison to the analytic calculations which exist for one-dimensional photonic crystals. For three dimensional crystals, the theory shows an excellent match to the experiment.

•Oct 1, 2014•0 citations

Light propagation in atomic stratified media: breakdown of the transfer-matrix method at high density

Sokolov, Igor M., William Guerin

The transfer-matrix method is a standard approach to wave propagation in stratified media. With the advent of cold-atom-based quantum and photonic technologies, several experiments and many proposals consider light propagation in one-dimensional optical lattices, using the transfer matrices as the main tool for the simulation. Here, we study the validity of this method by comparing its results to the microscopic coupled-dipole model, which is exact in the linear-optics regime. We show that the transfer-matrix method works very well at low density, even for thin disordered slices, and breaks down at high density because the dipole-dipole interaction induces a collective response from the atoms such that the properties of one layer are influenced by the others. We determine the boundary values of atomic densities for which this method is still applicable for describing experiments. Our findings are relevant for experimental realizations using ultra-cold atoms.

arXiv:2601.14715•Jan 21, 2026•0 citations

Cavity quantum electrodynamics with three-dimensional photonic band gap crystals

Willem L. Vos, Léon A. Woldering

Introduction The propagation of light in periodically ordered photonic crystals bears a strong analogy to the wave propagation of conduction electrons in atomic crystals. The development of Bloch modes and dispersion are determined by the interference of waves that are diffracted by lattice planes [19, 52]. The periodicity commensurate with the wavelength (a ≈ λ/2) gives rise to Bragg diffraction that is associated with frequency windows for which waves are forbidden to propagate in a particular direction. Such stop gaps have long been known to arise for electromagnetic waves, notably for X-rays in atomic crystals [214]. At optical frequencies, the stop gaps that occur in one-dimensional periodic structures, known as Bragg stacks, are widely used in optical laboratories as broadband highly reflecting dielectric mirrors [556]. The distinguishing feature of three-dimensional (3D) photonic crystals is that a common stop gap can be achieved for all directions and for all polarizations simultaneously: the widely pursued 3D photonic band gap . Historically a 3D band gap has never been considered for the propagation of X-rays in periodic media, since a gap requires a high refractive index contrast of order unity, whereas the refractive index varies by less then 10 −4 in the X-ray range. At frequencies inside the 3D photonic band gap, the density of optical states (DOS) completely vanishes. As the density of states can also be interpreted as the density of vacuum fluctuations [334], a 3D band gap thus serves as an effective shield to these fluctuations. The total absence of optical modes in a photonic band gap has implications beyond classical optics that break the analogy between the behavior of light in photonic crystals and the behavior of electrons in atomic crystals. 3D photonic band gap crystals play an important role in cavity quantum electrodynamics (cQED) [64, 549], where they offer at least five prospects for new physics. Firstly, probably the most eagerly pursued phenomenon is the complete inhibition of spontaneous emission: an excited quantum emitter – such as an atom, molecule, or quantum dot – embedded in a crystal with its transition frequency tuned to within the 3D band gap remains forever excited since it cannot decay to the ground state by emitting a photon.

Cambridge University Press eBooks•Nov 30, 2014•12 citations

Light propagation in atomic stratified media: breakdown of the textbook transfer-matrix method at high density

Igor Sokolov, William Guerin

The transfer-matrix method is a standard approach to wave propagation in stratified media. With the advent of cold-atom-based quantum and photonic technologies, several experiments and many proposals consider light propagation in one-dimensional optical lattices, using the transfer matrices as the main tool for the simulation. Here, we study the validity of this method by comparing its results to the microscopic coupled-dipole model, which is exact in the linear-optics regime. We show that the transfer-matrix method works very well at low density, even for thin disordered slices, and breaks down at high density because the dipole–dipole interaction induces a collective response from the atoms such that the properties of one layer are influenced by the others. We determine the boundary values of atomic densities for which this method is still applicable for describing experiments. Our findings are relevant for experimental realizations using ultra-cold atoms.

Journal of the Optical Society of America B•Apr 23, 2026•0 citations
The phenomenon of photonic band gaps in one-dimensional optical lattices is reviewed using a microscopic approach. Formally equivalent to the transfer matrix approach in the thermodynamic limit, a microscopic model is required to study finite-size effects, such as deviations from the Bragg condition. Microscopic models describing both scalar and vectorial light are proposed, as well as for two- and three-level atoms. Several analytical results are compared to experimental data, showing a good agreement.
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 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 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$, 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.
In certain three-dimensional crystals, a frequency range exist for all polarizations for which light is not allowed to propagate in any direction, called the 3D photonic band gap: a frequency range where the density of vacuum fluctuations vanishes in an ideal infinitely large and perfect system. The complete absence of vacuum fluctuations can be interpreted as zero density of states and vice versa. It is well known that the characteristics of spontaneous emission of light depend strongly on the environment of the light source. According to quantum electrodynamics, the emission rate of a two-level quantum emitter as described by Fermi’s “golden rule”, is factorized into one part describing the emitter’s properties and a second part describing the effect of the environment on the light field via the local density of optical state (LDOS). The radiative decay rate of the emitters is proportional to the LDOS. The absence of vacuum fluctuations or the zero LDOS leads to complete inhibition of the spontaneous emission. While many great advances towards a band gap have been made, no complete inhibition has ever been observed to date. In this thesis, for the first time, we have studied the spontaneous emission of PbS quantum dots inside real 3D photonic band gap crystal as a function of frequency throughout the band gap. In our experiments we have observed an inhibited emission of 18x in the band gap. The time-resolved decay curves show evidence for intriguing finite-size effects whereby vacuum fluctuations tunnel into the band gap. Unfortunately, most theories assume crystals of infinite extent, where the inhibition in the band gap is also infinite, as vacuum fluctuations don’t exist inside the crystal. Here we propose an original model to calculate the LDOS in the band gap of a finite photonic crystal based on tunneling of the vacuum fluctuations into the crystal. We validate our model for the one-dimensional situation with a direct comparison to the analytic calculations which exist for one-dimensional photonic crystals. For three dimensional crystals, the theory shows an excellent match to the experiment.
The transfer-matrix method is a standard approach to wave propagation in stratified media. With the advent of cold-atom-based quantum and photonic technologies, several experiments and many proposals consider light propagation in one-dimensional optical lattices, using the transfer matrices as the main tool for the simulation. Here, we study the validity of this method by comparing its results to the microscopic coupled-dipole model, which is exact in the linear-optics regime. We show that the transfer-matrix method works very well at low density, even for thin disordered slices, and breaks down at high density because the dipole-dipole interaction induces a collective response from the atoms such that the properties of one layer are influenced by the others. We determine the boundary values of atomic densities for which this method is still applicable for describing experiments. Our findings are relevant for experimental realizations using ultra-cold atoms.
Introduction The propagation of light in periodically ordered photonic crystals bears a strong analogy to the wave propagation of conduction electrons in atomic crystals. The development of Bloch modes and dispersion are determined by the interference of waves that are diffracted by lattice planes [19, 52]. The periodicity commensurate with the wavelength (a ≈ λ/2) gives rise to Bragg diffraction that is associated with frequency windows for which waves are forbidden to propagate in a particular direction. Such stop gaps have long been known to arise for electromagnetic waves, notably for X-rays in atomic crystals [214]. At optical frequencies, the stop gaps that occur in one-dimensional periodic structures, known as Bragg stacks, are widely used in optical laboratories as broadband highly reflecting dielectric mirrors [556]. The distinguishing feature of three-dimensional (3D) photonic crystals is that a common stop gap can be achieved for all directions and for all polarizations simultaneously: the widely pursued 3D photonic band gap . Historically a 3D band gap has never been considered for the propagation of X-rays in periodic media, since a gap requires a high refractive index contrast of order unity, whereas the refractive index varies by less then 10 −4 in the X-ray range. At frequencies inside the 3D photonic band gap, the density of optical states (DOS) completely vanishes. As the density of states can also be interpreted as the density of vacuum fluctuations [334], a 3D band gap thus serves as an effective shield to these fluctuations. The total absence of optical modes in a photonic band gap has implications beyond classical optics that break the analogy between the behavior of light in photonic crystals and the behavior of electrons in atomic crystals. 3D photonic band gap crystals play an important role in cavity quantum electrodynamics (cQED) [64, 549], where they offer at least five prospects for new physics. Firstly, probably the most eagerly pursued phenomenon is the complete inhibition of spontaneous emission: an excited quantum emitter – such as an atom, molecule, or quantum dot – embedded in a crystal with its transition frequency tuned to within the 3D band gap remains forever excited since it cannot decay to the ground state by emitting a photon.
The transfer-matrix method is a standard approach to wave propagation in stratified media. With the advent of cold-atom-based quantum and photonic technologies, several experiments and many proposals consider light propagation in one-dimensional optical lattices, using the transfer matrices as the main tool for the simulation. Here, we study the validity of this method by comparing its results to the microscopic coupled-dipole model, which is exact in the linear-optics regime. We show that the transfer-matrix method works very well at low density, even for thin disordered slices, and breaks down at high density because the dipole–dipole interaction induces a collective response from the atoms such that the properties of one layer are influenced by the others. We determine the boundary values of atomic densities for which this method is still applicable for describing experiments. Our findings are relevant for experimental realizations using ultra-cold atoms.