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

Spontaneous-emission-induced transition rates between atomic states in optical lattices

Jean-Félix Riou, Aaron Reinhard, Laura A. Zundel, David S. Weiss

Published Sep 11, 2012• 9 citations
Publisher

Abstract

We derive a general expression for the spontaneous-emission-induced transition rates between the atomic states of atoms trapped in far-detuned optical potentials, taking into account both their internal and external degrees of freedom. We apply this result to atoms trapped in deep optical lattices. For one- and two-dimensional lattices, we quantify the correlations among excitations in the tightly confined directions, the loosely trapped directions, and the internal state of the atom. We emphasize the differences in excitations between red- and blue-detuned lattices.

DOI
10.1103/physreva.86.033412

Related papers

Heating rates for an atom in a far-detuned optical lattice

Fabrice Gerbier, Yvan Castin

We calculate single-atom heating rates in a far-detuned optical lattice, in connection with recent experiments. We first derive a master equation, which includes a realistic atomic internal structure and a quantum treatment of the atomic motion in the lattice. The experimental feature that optical lattices are obtained by superimposing laser standing waves of different frequencies is also included, which leads to a micromotional correction to the light shift that we evaluate. We then calculate, and compare to experimental results, two heating rates, the total heating rate (which corresponds to the increase of the total mechanical energy of the atom in the lattice), and the ground-band heating rate (which corresponds to the increase of energy within the ground energy band of the lattice). The total heating rate remarkably is independent of the atomic state and of the sign of the laser detuning. In contrast, the ground-band heating rate in the deep lattice limit is strongly suppressed for blue-detuned lattices with respect to red-detuned lattices.

arXiv:1002.5018•Physical Review A•Jul 13, 2010•78 citations

Analysis of non-Markovian coupling of a lattice-trapped atom to free space

Michael Stewart, Ludwig Krinner, Arturo Pazmiño +1 more

Behavior analogous to that of spontaneous emission in photonic band-gap materials has been predicted for an atom-optical system consisting of an atom confined in a well of a state-dependent optical lattice that is coupled to free space through an internal-state transition [de Vega et al., Phys. Rev. Lett. 101, 260404 (2008)]. Using the Weisskopf-Wigner approach and considering a one-dimensional geometry, we analyze the properties of this system in detail, including the evolution of the lattice-trapped population, the momentum distribution of emitted matter waves, and the detailed structure of an evanescent matter-wave state below the continuum boundary. We compare and contrast our findings for the transition from Markovian to non-Markovian behaviors to those previously obtained for three dimensions.

arXiv:1709.01470•Physical Review A•Jan 24, 2017•16 citations

Mean-field approach to dipole-dipole interaction in an optical lattice

C. Menotti, Helmut Ritsch

We compare the influence of quantum statistics and atom-atom interaction in bright and dark one-dimensional optical lattices for atoms using quantum rate equations. Via a Hartree-Fock--type mean-field approach we derive an effective nonlinear single-atom equation and solve it self-consistently for a prescribed atomic density. Using a simplified dipole-dipole interaction potential, we show that the atomic energy bands are very sensitive to the mean atomic density, even in a parameter regime where temperature and band populations exhibit only a very small density dependence. Bright lattices show energy shifts towards smaller band separations, while the effect is in the opposite direction and smaller for dark lattices. In general, dipole-dipole interaction strongly dominates the influence of quantum statistics, except for very large detunings, where the spontaneous emission rate is very small.

Physical Review A•Oct 1, 1999•8 citations

Spontaneous emission of a moving atom in vacuum

Wei Guo

Spontaneous emission of an excited two-level nonrelativistic atom is examined in the Schr\"odinger picture by treating the atom's external and internal degrees of freedom on the same quantum footing. After all atomic transitions that lead to the evolution of this atom-vacuum system are analyzed, it is found that the atom's spontaneous emission rate is reduced by its center-of-mass motion. It is also found that, as a result of the entanglement between atomic and photonic states, the spontaneous emission process cannot be explained as a process that takes place in one coordinate system moving with the atom but is observed in another stationary system.

Physical Review A•Jun 23, 2008•8 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

Lifetime and emission characteristics of collective electronic excitations in two-dimensional optical lattices

Hashem Zoubi, Helmut Ritsch

Collective electronic excitations in planar optical lattices exhibit strong modifications of the radiative damping rate and directional emission pattern as compared to a single excited atom. Collective excitations for long wave numbers and polarizations orthogonal to the lattice plane exhibit superradiance with a very short lifetime and a tightly confined emission direction. For shorter wavelength and in-plane polarization, they can possess a long lifetime, which, beyond a critical wave number, tends to infinity. Those excitations thus become metastable and decoupled from the free radiation field. They can store a single energy quantum for a long time and transfer the excitation over long distances. In general the spatial, polarization, and frequency dependence of the emission pattern can provide us with optical and electronic properties of optical lattices.

arXiv:1103.2949•Physical Review A•Jun 23, 2011•25 citations
We derive a general expression for the spontaneous-emission-induced transition rates between the atomic states of atoms trapped in far-detuned optical potentials, taking into account both their internal and external degrees of freedom. We apply this result to atoms trapped in deep optical lattices. For one- and two-dimensional lattices, we quantify the correlations among excitations in the tightly confined directions, the loosely trapped directions, and the internal state of the atom. We emphasize the differences in excitations between red- and blue-detuned lattices.
We calculate single-atom heating rates in a far-detuned optical lattice, in connection with recent experiments. We first derive a master equation, which includes a realistic atomic internal structure and a quantum treatment of the atomic motion in the lattice. The experimental feature that optical lattices are obtained by superimposing laser standing waves of different frequencies is also included, which leads to a micromotional correction to the light shift that we evaluate. We then calculate, and compare to experimental results, two heating rates, the total heating rate (which corresponds to the increase of the total mechanical energy of the atom in the lattice), and the ground-band heating rate (which corresponds to the increase of energy within the ground energy band of the lattice). The total heating rate remarkably is independent of the atomic state and of the sign of the laser detuning. In contrast, the ground-band heating rate in the deep lattice limit is strongly suppressed for blue-detuned lattices with respect to red-detuned lattices.
Behavior analogous to that of spontaneous emission in photonic band-gap materials has been predicted for an atom-optical system consisting of an atom confined in a well of a state-dependent optical lattice that is coupled to free space through an internal-state transition [de Vega et al., Phys. Rev. Lett. 101, 260404 (2008)]. Using the Weisskopf-Wigner approach and considering a one-dimensional geometry, we analyze the properties of this system in detail, including the evolution of the lattice-trapped population, the momentum distribution of emitted matter waves, and the detailed structure of an evanescent matter-wave state below the continuum boundary. We compare and contrast our findings for the transition from Markovian to non-Markovian behaviors to those previously obtained for three dimensions.
We compare the influence of quantum statistics and atom-atom interaction in bright and dark one-dimensional optical lattices for atoms using quantum rate equations. Via a Hartree-Fock--type mean-field approach we derive an effective nonlinear single-atom equation and solve it self-consistently for a prescribed atomic density. Using a simplified dipole-dipole interaction potential, we show that the atomic energy bands are very sensitive to the mean atomic density, even in a parameter regime where temperature and band populations exhibit only a very small density dependence. Bright lattices show energy shifts towards smaller band separations, while the effect is in the opposite direction and smaller for dark lattices. In general, dipole-dipole interaction strongly dominates the influence of quantum statistics, except for very large detunings, where the spontaneous emission rate is very small.
Spontaneous emission of an excited two-level nonrelativistic atom is examined in the Schr\"odinger picture by treating the atom's external and internal degrees of freedom on the same quantum footing. After all atomic transitions that lead to the evolution of this atom-vacuum system are analyzed, it is found that the atom's spontaneous emission rate is reduced by its center-of-mass motion. It is also found that, as a result of the entanglement between atomic and photonic states, the spontaneous emission process cannot be explained as a process that takes place in one coordinate system moving with the atom but is observed in another stationary system.
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.
Collective electronic excitations in planar optical lattices exhibit strong modifications of the radiative damping rate and directional emission pattern as compared to a single excited atom. Collective excitations for long wave numbers and polarizations orthogonal to the lattice plane exhibit superradiance with a very short lifetime and a tightly confined emission direction. For shorter wavelength and in-plane polarization, they can possess a long lifetime, which, beyond a critical wave number, tends to infinity. Those excitations thus become metastable and decoupled from the free radiation field. They can store a single energy quantum for a long time and transfer the excitation over long distances. In general the spatial, polarization, and frequency dependence of the emission pattern can provide us with optical and electronic properties of optical lattices.