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arXiv:physics/9804034 · Physical Review A

Raman cooling of atoms below the gravitational limit

Alexander Soroko

Published Nov 1, 1998• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.58.3963

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Bulletin of the American Physical Society•May 1, 1993•0 citations
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.
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 kB{\mathrm{k}}_{\mathrm{B}}kB​Tgrav{\mathrm{T}}_{\mathrm{grav}}Tgrav​\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.
A technique for cooling atoms in two dimensions to temperatures below the single photon recoil limit k{sub B}T{sub rec} = (hk){sup 2}/2M is demonstrated. This technique combines velocity selection using stimulated Raman transitions and dissipation by spontaneous emission. It is an extension of the one dimensional cooling technique that was demonstrated recently. Experimental results for sodium atoms are presented, and the limits on the minimal cooling temperatures are analyzed. Finally, the possibility of applying the Raman cooling technique to atoms in a dipole trap is discussed.
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.
We develop a unified many-body theory of two-photon dark-state laser cooling, the workhorse for preparing trapped ions close to their motional quantum ground state. For ions with a ΛΛΛ level structure, driven by Raman lasers, we identify an ion-number-dependent crossover between weak and strong coupling where both the cooling rate and final temperature are simultaneously optimized. We obtain simple analytic results in both extremes: In the weak coupling limit, we show a Lorentzian spin-absorption spectrum determines the cooling rate and final occupation of the motional state, which are both independent of the number of ions. We also highlight the benefit of including an additional spin dependent force in this case. In the strong coupling regime, our theory reveals the role of collective dynamics arising from phonon exchange between dark and bright states, allowing us to explain the enhancement of the cooling rate with increasing ion number. Our analytic results agree closely with exact numerical simulations and provide experimentally accessible guidelines for optimizing cooling in large ion crystals, a key step toward scalable, high-fidelity trapped-ion quantum technologies.
We experimentally realize an enhanced Raman control scheme for neutral atoms that features an intrinsic suppression of the two-photon carrier transition, but retains the sidebands which couple to the external degrees of freedom of the trapped atoms. This is achieved by trapping the atom at the node of a blue detuned standing wave dipole trap, that acts as one field for the two-photon Raman coupling. The improved ratio between cooling and heating processes in this configuration enables a five times lower fundamental temperature limit for resolved sideband cooling. We apply this method to perform Raman cooling to the two-dimensional vibrational ground state and to coherently manipulate the atomic motion. The presented scheme requires minimal additional resources and can be applied to experiments with challenging optical access, as we demonstrate by our implementation for atoms strongly coupled to an optical cavity.
We have observed a new type of sub-Doppler laser cooling with neither polarization gradients nor magnetic fields. All known sub-Doppler laser cooling methods require one of these two to resdistribute the atomic population among the energy levels. This allows the irreversible processes of optical pumping vels. This allows the irreversible processes of optical pumping (OP) to manipulate the conservative force of light shifts (e.g. resonant exchange between the two beams comprising a standing wave) into a damping force. Our scheme employs stimulated Raman transitions between ground state hyperfine levels of Rb with a bichromatic standing wave, accompanied by a momentum change of {Delta}p = 2{h_bar}k. OP, with {Delta}p = 1{h_bar}k, creates a population imbalance allowing repetition of the Raman process. When the detuning of the light from Raman resonance {delta} is properly chosen, the net momentum exchange damps the atomic motion. Changing {delta} by only {gamma}/6(1 MHz) replaces cooling by heating. This process separates the velocity selective Raman resonance and OP processes differently from others, and helps clarify the role of these different mechanisms.