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

Dark-state cooling in the presence of gravity: Gravitational limit of laser cooling

Ralph Dum, Maxim Olshanii

Published Feb 1, 1997• 3 citations
Publisher

Abstract

Dark-state cooling of atoms in the presence of a uniform external (gravity) field is investigated. The external field leads to a finite lifetime for the dark state and thereby to a lower limit for the temperatures obtainable. The minimum temperature in the presence of a gravity field is found to be ${\mathrm{k}}_{\mathrm{B}}$${\mathrm{T}}_{\mathrm{grav}}$\ensuremath{\sim}Mg\ensuremath{\lambda}/2\ensuremath{\pi} (where M is the atom mass, \ensuremath{\lambda} the wavelength of the cooling laser). This limit is shown to be a universal limit for any laser-cooling scheme.

DOI
10.1103/physreva.55.1217

Related papers

Raman cooling of atoms below the gravitational limit

Alexander Soroko

Raman cooling of non-zero-spin atoms in the presence of gravitational and external magnetic fields is investigated. The magnetic field is adjusted so as to compensate for the gravitational force acting on ground-state atoms. A dark state is created and supported in momentum space with additional velocity-selective two-photon transitions. The minimum allowed temperature is found to be determined only by the width of velocity selection, and therefore can be much less than the gravitational limit. A complete set of analytical formulas describing cooling of a dilute atomic sample is derived. They serve as the basis for numerical simulations which are carried out in the one-dimensional case.

arXiv:physics/9804034•Physical Review A•Nov 1, 1998•2 citations

Study of laser cooling in deep optical lattice: two-level quantum model

Прудников Олег Николаевич, R. Ya. Ilenkov, А. В. Тайченачев +2 more

We study a possibility of laser cooling of 24 Mg atoms in deep optical lattice formed by intense off-resonant laser field in a presence of cooling field resonant to narrow (3 s 3 s ) 1 S 0 → (3 s 3 p ) 3 P 1 (λ = 457 nm) optical transition. For description of laser cooling with taking into account quantum recoil effects we consider two quantum models. The first one is based on direct numerical solution of quantum kinetic equation for atom density matrix and the second one is simplified model based on decomposition of atom density matrix over vibration states in the lattice wells. We search cooling field intensity and detuning for minimum cooling energy and fast laser cooling.

Journal of Physics Conference Series•Jan 1, 2018•0 citations

Cooling atoms in dark gravitational laser traps

Yu. B. Ovchinnikov, Johannes Söding, Rudolf Grimm

We propose a trap based on an evanescent light wave which is formed on the surface of a conical or a pyramidal cavity in a glass substrate. The far blue-detuned evanescent wave acts as a mirror for atoms, bouncing on it in the gravitational field. In addition, fast and deep Sisyphus cooling in the evanescent wave can be organized for alkali atoms. This leads to the cooling of the atoms down to the recoil-limited temperature and their collection in the field- free region near the bottom of the trap, to form an atomic gas of extremely high density.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 6, 1996•0 citations

Laser cooling of trapped atoms to the ground state: A dark state in position space

Giovanna Morigi, J. I. Cirac, K. Ellinger +1 more

We propose a scheme that allows us to laser cool trapped atoms to the ground state of a one-dimensional confining potential. The scheme is based on the creation of a dark state by designing the laser profile, so that the hottest atoms are coherently pumped to another internal level, and then repumped back. The scheme works beyond the Lamb-Dicke limit. We present results of a full quantum treatment for a one-dimensional model.

arXiv:quant-ph/9710034•Physical Review A•Apr 1, 1998•18 citations

One-dimensional laser cooling below the Doppler limit

Vladimir Finkelstein, P. R. Berman, Jingzhong Guo

A theoretical analysis is given for one-dimensional laser cooling below the Doppler limit of J=1/2 ground-state atoms. The laser field consists of a pair of counterpropagating, linearly polarized, low-power beams, whose polarization directions differ by an angle \ensuremath{\theta} (0\ensuremath{\le}\ensuremath{\theta}\ensuremath{\le}\ensuremath{\pi}/2). For \ensuremath{\theta}\ensuremath{\ll}1, the effective optical-pumping time is shown to increase strongly near the nodes of the standing wave, and the cooling force can be much larger than that for \ensuremath{\theta}=\ensuremath{\pi}/2. Moreover, for \ensuremath{\theta}\ensuremath{\ll}1, it can be shown that the stimulated part of the atomic diffusion is reduced considerably as compared with that for \ensuremath{\theta}=\ensuremath{\pi}/2. As a consequence it is possible to achieve an equilibrium atomic distribution that, for \ensuremath{\theta}\ensuremath{\ll}1, is characterized by a mean kinetic energy that is lower than that predicted to occur for \ensuremath{\theta}=\ensuremath{\pi}/2. The equilibrium velocity distribution is not necessarily Maxwellian, and thus the temperature of the atomic ensemble may not be well defined. The achievable kinetic energy is so small that the cooled atoms may be trapped in the vicinity of the laser-field nodes.

Physical Review A•Feb 1, 1992•48 citations

Operator description of laser cooling below the Doppler limit

Gerard Nienhuis, P. van der Straten, S-Q. Shang

We give a general theoretical description of radiative forces on atoms in a monochromatic radiation field. The driven transition has a lower level consisting of several substates, and we consider the limit of low velocities and weak intensities. This situation comprises the schemes where cooling to temperatures below the Doppler limit is possible. After expressing the atomic dipole in terms of the polarizability tensor, we obtain an expression of the force as the sum of the radiation pressure, the dipole force, and a contribution from the gradient of the polarization. This latter contribution contains a part resulting from redistribution of photons between the plane waves that compose the field, and a part resulting from fluorescence. We express the average force and the momentum-diffusion tensor in terms of a closed evolution equation for the lower-state density matrix. We show by a scaling argument that in any case of cooling, the final temperature goes down linearly with the intensity, until the recoil limit is approached. The description is valid for a weak and monochromatic, but otherwise arbitrary field, and it allows for the presence of an external magnetic field, and of hyperfine splitting. It is applicable to cooling in one, two, or three dimensions. We give numerical results for the average force in a number of specific cases of two counterrunning plane waves.

Physical Review A•Jul 1, 1991•81 citations
Dark-state cooling of atoms in the presence of a uniform external (gravity) field is investigated. The external field leads to a finite lifetime for the dark state and thereby to a lower limit for the temperatures obtainable. The minimum temperature in the presence of a gravity field is found to be {\mathrm{k}}_{\mathrm{B}}$${\mathrm{T}}_{\mathrm{grav}}\ensuremath{\sim}Mg\ensuremath{\lambda}/2\ensuremath{\pi} (where M is the atom mass, \ensuremath{\lambda} the wavelength of the cooling laser). This limit is shown to be a universal limit for any laser-cooling scheme.
Raman cooling of non-zero-spin atoms in the presence of gravitational and external magnetic fields is investigated. The magnetic field is adjusted so as to compensate for the gravitational force acting on ground-state atoms. A dark state is created and supported in momentum space with additional velocity-selective two-photon transitions. The minimum allowed temperature is found to be determined only by the width of velocity selection, and therefore can be much less than the gravitational limit. A complete set of analytical formulas describing cooling of a dilute atomic sample is derived. They serve as the basis for numerical simulations which are carried out in the one-dimensional case.
We study a possibility of laser cooling of 24 Mg atoms in deep optical lattice formed by intense off-resonant laser field in a presence of cooling field resonant to narrow (3 s 3 s ) 1 S 0 → (3 s 3 p ) 3 P 1 (λ = 457 nm) optical transition. For description of laser cooling with taking into account quantum recoil effects we consider two quantum models. The first one is based on direct numerical solution of quantum kinetic equation for atom density matrix and the second one is simplified model based on decomposition of atom density matrix over vibration states in the lattice wells. We search cooling field intensity and detuning for minimum cooling energy and fast laser cooling.
We propose a trap based on an evanescent light wave which is formed on the surface of a conical or a pyramidal cavity in a glass substrate. The far blue-detuned evanescent wave acts as a mirror for atoms, bouncing on it in the gravitational field. In addition, fast and deep Sisyphus cooling in the evanescent wave can be organized for alkali atoms. This leads to the cooling of the atoms down to the recoil-limited temperature and their collection in the field- free region near the bottom of the trap, to form an atomic gas of extremely high density.
A theoretical analysis is given for one-dimensional laser cooling below the Doppler limit of J=1/2 ground-state atoms. The laser field consists of a pair of counterpropagating, linearly polarized, low-power beams, whose polarization directions differ by an angle \ensuremath{\theta} (0\ensuremath{\le}\ensuremath{\theta}\ensuremath{\le}\ensuremath{\pi}/2). For \ensuremath{\theta}\ensuremath{\ll}1, the effective optical-pumping time is shown to increase strongly near the nodes of the standing wave, and the cooling force can be much larger than that for \ensuremath{\theta}=\ensuremath{\pi}/2. Moreover, for \ensuremath{\theta}\ensuremath{\ll}1, it can be shown that the stimulated part of the atomic diffusion is reduced considerably as compared with that for \ensuremath{\theta}=\ensuremath{\pi}/2. As a consequence it is possible to achieve an equilibrium atomic distribution that, for \ensuremath{\theta}\ensuremath{\ll}1, is characterized by a mean kinetic energy that is lower than that predicted to occur for \ensuremath{\theta}=\ensuremath{\pi}/2. The equilibrium velocity distribution is not necessarily Maxwellian, and thus the temperature of the atomic ensemble may not be well defined. The achievable kinetic energy is so small that the cooled atoms may be trapped in the vicinity of the laser-field nodes.
We give a general theoretical description of radiative forces on atoms in a monochromatic radiation field. The driven transition has a lower level consisting of several substates, and we consider the limit of low velocities and weak intensities. This situation comprises the schemes where cooling to temperatures below the Doppler limit is possible. After expressing the atomic dipole in terms of the polarizability tensor, we obtain an expression of the force as the sum of the radiation pressure, the dipole force, and a contribution from the gradient of the polarization. This latter contribution contains a part resulting from redistribution of photons between the plane waves that compose the field, and a part resulting from fluorescence. We express the average force and the momentum-diffusion tensor in terms of a closed evolution equation for the lower-state density matrix. We show by a scaling argument that in any case of cooling, the final temperature goes down linearly with the intensity, until the recoil limit is approached. The description is valid for a weak and monochromatic, but otherwise arbitrary field, and it allows for the presence of an external magnetic field, and of hyperfine splitting. It is applicable to cooling in one, two, or three dimensions. We give numerical results for the average force in a number of specific cases of two counterrunning plane waves.