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

Resonance fluorescence from quantized one-dimensional molasses

P. Marte, Ralph Dum, Richard Taïeb, P. Zoller

Published Feb 1, 1993• 79 citations
Publisher

Abstract

We study theoretically the spectrum of resonance fluoresence from one-dimensional molasses consisting of two-level atoms with Zeeman substructure. The center-of-mass motion of the atom is treated fully quantum mechanically. The spectrum shows sidebands due to transitions between vibrational levels in optical potentials generated by the laser light. Detailed results are presented for the ${\mathit{J}}_{\mathit{g}}$=1/2\ensuremath{\rightarrow}${\mathit{J}}_{\mathit{e}}$=3/2 atomic transition in a laser configuration with two counterpropagating waves with orthogonal polarizations. We have solved the corresponding quantum master equation and calculated the relevant autocorrelation function of the atomic dipole using (i) a direct numerical solution of the master equation, (ii) a wave-function simulation of the master equation and correlation function employing periodic time-dependent Bloch wave functions, and (iii) a semiclassical bipotential calculation for the spectrum including a simple quantum correction.

DOI
10.1103/physreva.47.1378

Related papers

Spectrum of resonance fluorescence and cooling dynamics in quantized one-dimensional molasses: Effects of laser configuration

Richard Taïeb, P. Marte, Ralph Dum +1 more

We study theoretically the spectrum of resonance fluorescence and laser-cooling dynamics corresponding to quantized atomic motion in one-dimensional optical molasses. We consider an atom with a ${\mathit{J}}_{\mathit{g}}$=1\ensuremath{\rightarrow}${\mathit{J}}_{\mathit{e}}$=2 transition interacting with two counterpropagating laser beams. The laser light is assumed to be linearly polarized with an angle \ensuremath{\theta} between the polarization vectors. We discuss the spectrum of resonance fluorescence, the spectroscopy of band structure in the optical potentials, and the population of the vibrational quantum levels as a function of the angle between the polarization vectors.

Physical Review A•Jun 1, 1993•21 citations

Quantum wave function simulation of the resonance fluorescence spectrum from one-dimensional optical molasses

P. Marte, Ralph Dum, Richard Taïeb +2 more

Using recently developed quantum wave function techniques, we have performed a simulation of $^{85}\mathrm{Rb}$ atoms in a one-dimensional optical molasses, formed from counterpropagating laser beams with orthogonal linear polarizations. Both internal and external degrees of freedom are treated quantum mechanically in one dimension and the spectrum of resonance fluorescence is calculated and compared to recent experiments. Excellent agreement is obtained for the spectrum and additional insight is gained into the experimental evidence for quantized motion in the optical potentials.

Physical Review Letters•Aug 30, 1993•72 citations

Quantum motion of laser trapped atoms

Poul Jessen

In two recent experiments Verkerk et al. and our group have observed quantization of the center-of-mass motion of laser cooled atoms in sub-wavelength sized potential wells formed by the light field of a 1-dimensional optical molasses. Our 1-dimensional optical molasses consists of a pair of counterpropagating laser beams of orthogonal, linear polarization, creating a series of potential wells separated by {lambda}/4. Polarization gradient laser cooling reduces the thermal energy of the atoms until they are trapped in well resolved vibrational levels near the bottom of the wells. Transitions between these vibrational levels are seen in a high resolution spectrum of fluorescence, where they give rise to a Rayleigh peak centered at the laser frequency, and well resolved Raman sidebands shifted by a frequency {plus_minus}{omega}, typically on the order of 100 kHz. We find quantitative agreement between the measured level separation h{omega} and the results of a calculation of the bandstructure in the periodic optical potential. Based on the observed ratio of the strength of the blue to the red sideband we determine the temperature of the atoms, and find agreement with theoretical predictions. Based on the level spacing and temperature we find the atoms to be localized to {approx}/15, withmore » up to 50-60% of the population of the trapped atoms in the vibrational ground state. We observe intriguing differences between fluorescence radiated by localized atoms, and the fluorescence radiated by non-localized atoms in a 1-dimensional optical molasses composed of a pair of counterpropagating laser beams of opposite circular polarization. The prospect of observing quantum motion and spatial order in 2 and 3 dimensions, and the consequences for the spectrum of fluorescence, will be discussed.« less

Bulletin of the American Physical Society•May 1, 1993•0 citations

Quantized 1D- and 2D optical molasses: Laser cooling and spectrum of resonance fluorescene

P. Marte, Ralph Dum, Richard Taïeb +1 more

We present results for laser cooling of optical molasses and the spectrum of resonance fluorescene based on a fully quantum mechanical treatment of the atomic center-of-mass motion for 1D and 2D laser configurations. Our calculations based on recently developed wave function simulations of the quantum master equation for laser cooling.

Bulletin of the American Physical Society•May 1, 1993•0 citations

Monte Carlo simulation of quantized atomic motion in one-dimensional optical molasses

P. Marte, Ralph Dum, A. R. Taieb +1 more

A Monte Carlo simulation method is developed to model quantized atomic motion in one-dimensional optical molasses.1 We calculate atomic absorption and emission spectra and energy distribution functions for various J → J′ transitions coupled to linear and circularly polarized light for standing wave configurations.2 We are particularly interested in generation of sidebands in atomic spectra corresponding to quantized atomic motion.3 Our Monte Carlo method is based on propagating an atomic center-of-mass wave packet and simulating a sequence of spontaneous emissions between families of Bloch states in the periodic laser-induced potentials. Propagation of the (periodic part of the) atomic wave function in time is performed by using a variant of the split-operator FFT algorithm. Band structure calculations for these atomic configurations are presented.

Annual Meeting Optical Society of America•Jan 1, 1992•0 citations

Observation of quantized motion in optical potential wells in 1-D optical molasses

Poul Jessen, R. J. C. Speeuw, Christoph Ira Westbrook +2 more

We have measured the spectrum of fluorescence from 85Rb in 1-D optical molasses. The spectrum consists of a central peak and one set of sidebands characteristic of quantized atomic motion. In a 1-D molasses consisting of two counterpropagating, linear, and orthogonally polarized laser beams, optical potential wells are spaced λ/4 apart where the polarization is circular. Polarization gradient cooling reduces the temperature to a point where the atoms are trapped in these wells. The atomic motion is approximated by a quantum mechanical harmonic oscillator. We interpret the central peak as transitions beginning and ending in the same bound level and the sidebands as Raman transitions changing the vibrational quantum number by ±1. The observed level spacing in the well is proportional to the square root of the light shift. The relative strength of the blue and red sideband is given by a Boltzman factor, allowing us to determine the temperature. As expected, the temperature increases linearly with the light shift.

Annual Meeting Optical Society of America•Jan 1, 1992•0 citations
We study theoretically the spectrum of resonance fluoresence from one-dimensional molasses consisting of two-level atoms with Zeeman substructure. The center-of-mass motion of the atom is treated fully quantum mechanically. The spectrum shows sidebands due to transitions between vibrational levels in optical potentials generated by the laser light. Detailed results are presented for the Jg{\mathit{J}}_{\mathit{g}}Jg​=1/2\ensuremath{\rightarrow}Je{\mathit{J}}_{\mathit{e}}Je​=3/2 atomic transition in a laser configuration with two counterpropagating waves with orthogonal polarizations. We have solved the corresponding quantum master equation and calculated the relevant autocorrelation function of the atomic dipole using (i) a direct numerical solution of the master equation, (ii) a wave-function simulation of the master equation and correlation function employing periodic time-dependent Bloch wave functions, and (iii) a semiclassical bipotential calculation for the spectrum including a simple quantum correction.
We study theoretically the spectrum of resonance fluorescence and laser-cooling dynamics corresponding to quantized atomic motion in one-dimensional optical molasses. We consider an atom with a Jg{\mathit{J}}_{\mathit{g}}Jg​=1\ensuremath{\rightarrow}Je{\mathit{J}}_{\mathit{e}}Je​=2 transition interacting with two counterpropagating laser beams. The laser light is assumed to be linearly polarized with an angle \ensuremath{\theta} between the polarization vectors. We discuss the spectrum of resonance fluorescence, the spectroscopy of band structure in the optical potentials, and the population of the vibrational quantum levels as a function of the angle between the polarization vectors.
Using recently developed quantum wave function techniques, we have performed a simulation of 85Rb^{85}\mathrm{Rb}85Rb atoms in a one-dimensional optical molasses, formed from counterpropagating laser beams with orthogonal linear polarizations. Both internal and external degrees of freedom are treated quantum mechanically in one dimension and the spectrum of resonance fluorescence is calculated and compared to recent experiments. Excellent agreement is obtained for the spectrum and additional insight is gained into the experimental evidence for quantized motion in the optical potentials.
In two recent experiments Verkerk et al. and our group have observed quantization of the center-of-mass motion of laser cooled atoms in sub-wavelength sized potential wells formed by the light field of a 1-dimensional optical molasses. Our 1-dimensional optical molasses consists of a pair of counterpropagating laser beams of orthogonal, linear polarization, creating a series of potential wells separated by {lambda}/4. Polarization gradient laser cooling reduces the thermal energy of the atoms until they are trapped in well resolved vibrational levels near the bottom of the wells. Transitions between these vibrational levels are seen in a high resolution spectrum of fluorescence, where they give rise to a Rayleigh peak centered at the laser frequency, and well resolved Raman sidebands shifted by a frequency {plus_minus}{omega}, typically on the order of 100 kHz. We find quantitative agreement between the measured level separation h{omega} and the results of a calculation of the bandstructure in the periodic optical potential. Based on the observed ratio of the strength of the blue to the red sideband we determine the temperature of the atoms, and find agreement with theoretical predictions. Based on the level spacing and temperature we find the atoms to be localized to {approx}/15, withmore » up to 50-60% of the population of the trapped atoms in the vibrational ground state. We observe intriguing differences between fluorescence radiated by localized atoms, and the fluorescence radiated by non-localized atoms in a 1-dimensional optical molasses composed of a pair of counterpropagating laser beams of opposite circular polarization. The prospect of observing quantum motion and spatial order in 2 and 3 dimensions, and the consequences for the spectrum of fluorescence, will be discussed.« less
A Monte Carlo simulation method is developed to model quantized atomic motion in one-dimensional optical molasses.1 We calculate atomic absorption and emission spectra and energy distribution functions for various J → J′ transitions coupled to linear and circularly polarized light for standing wave configurations.2 We are particularly interested in generation of sidebands in atomic spectra corresponding to quantized atomic motion.3 Our Monte Carlo method is based on propagating an atomic center-of-mass wave packet and simulating a sequence of spontaneous emissions between families of Bloch states in the periodic laser-induced potentials. Propagation of the (periodic part of the) atomic wave function in time is performed by using a variant of the split-operator FFT algorithm. Band structure calculations for these atomic configurations are presented.
We have measured the spectrum of fluorescence from 85Rb in 1-D optical molasses. The spectrum consists of a central peak and one set of sidebands characteristic of quantized atomic motion. In a 1-D molasses consisting of two counterpropagating, linear, and orthogonally polarized laser beams, optical potential wells are spaced λ/4 apart where the polarization is circular. Polarization gradient cooling reduces the temperature to a point where the atoms are trapped in these wells. The atomic motion is approximated by a quantum mechanical harmonic oscillator. We interpret the central peak as transitions beginning and ending in the same bound level and the sidebands as Raman transitions changing the vibrational quantum number by ±1. The observed level spacing in the well is proportional to the square root of the light shift. The relative strength of the blue and red sideband is given by a Boltzman factor, allowing us to determine the temperature. As expected, the temperature increases linearly with the light shift.