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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Quantized motion of atoms in a magneto-optical potential under coherent population trapping in high-intensity laser fields

Nelly Pavlovna Konopleva, А. В. Тайченачев, Anatolii M Tumaikin, Valeriy I. Yudin

Published Aug 1, 1996• 4 citations
Publisher

Abstract

We study theoretically the quantized motion of previously cooled atoms in a one-dimensional magneto-optical potential under coherent population trapping (CPT) conditions. We consider atoms with a transition interacting with a lin lin laser field and a static uniform magnetic field in the high-intensity limit. It is shown that if the Rabi frequency is greater than the Zeeman splitting, Doppler shift, natural width and detuning, then atoms are captured in the long-lived CPT state while the excited-state population is small. We do not take into account the incoherent photon scattering and describe the atomic motion by the Schrödinger equation. The oscillation frequency, oscillation damping time and localization size are obtained for atoms moving near the bottom of potential wells in a harmonic approximation. Narrowing of the vibrational spectral lines due to the CPT effect is predicted.

DOI
10.1088/1355-5111/8/4/006

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Physical Review Letters•Jul 6, 1992•327 citations
We study theoretically the quantized motion of previously cooled atoms in a one-dimensional magneto-optical potential under coherent population trapping (CPT) conditions. We consider atoms with a transition interacting with a lin lin laser field and a static uniform magnetic field in the high-intensity limit. It is shown that if the Rabi frequency is greater than the Zeeman splitting, Doppler shift, natural width and detuning, then atoms are captured in the long-lived CPT state while the excited-state population is small. We do not take into account the incoherent photon scattering and describe the atomic motion by the Schrödinger equation. The oscillation frequency, oscillation damping time and localization size are obtained for atoms moving near the bottom of potential wells in a harmonic approximation. Narrowing of the vibrational spectral lines due to the CPT effect is predicted.
The motion of previously cooled atoms in a spatial grating formed by lin (perpendicular) lin laser field configuration and the static uniform magnetic field is considered in the case of Fg equals 1 yields Fe equals 1 transition. We show that in the case of high intensity laser fields (when Rabi frequency is greater than Zeeman splitting, Doppler shift, natural width, and detuning) atoms are captured in long-lived coherent population trapping (CPT) state while heating, incoherent photon scattering, and atom-atom photon exchange are strongly reduced. The frequency, the damping time of oscillation, and the localization size are obtained for atoms moving near the bottom of potential wells in the frame of harmonic approximation. Narrowing of vibrational spectral lines due to the CPT-effect is predicted.
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
We study the peculiarities of the coherent population trapping (CPT) dark resonance in atomic vapor confined in a finite-size cell. Taking into account the scattering of atoms on anti-relaxation coating of the walls, we analyze the line shape of the CPT resonance in 133 C s depending on various parameters, such as the width of laser radiation spectrum, the type of pumping, and the magnitude of static magnetic field for both lin || lin and l i n ⊥ l i n polarization schemes. We show that for different parameters, the dependence of the line shape on the size of a cell is different, i.e., different factors affect the CPT resonance nonadditively. Thus, in the case when CPT resonance is excited by a narrowband laser, the shape of the resonance weakly depends on the size of a cell due to the laser-induced narrowing effect. We also show that the distortion of the line shape of the CPT resonance caused by nonresonant hyperfine sublevels of atomic excited states is modified with the size of a cell. Our calculation reveals the important role of accounting for the hyperfine and Zeeman structure of atomic levels. We have shown that the contrast of the CPT resonance differs about 5 times from the prediction of the simple three-level Λ model. The obtained results can be used for the optimization of the quantum frequency standards based on the CPT effect. In the final part of the paper, on the basis of the shot noise approximation we estimate the short-term stability of such standards.
The dark magneto-optical lattice for atoms with J yields J -1 transition is considered. The periodic potential is formed using a (sigma) + - (sigma) - laser field and a uniform magnetic field orthogonal to the light waves propagation. The dynamics of slowly moving atoms is investigated for J equals 1 in the quasiclassical approximation. The cases of a weak and strong dark states destruction by the magnetic field are analyzed. The sub- Doppler cooling for a blue detuning from resonance is demonstrated for a low laser field power. The dark atomic lattice creation in the case of the light-induced shift is much less than the Zeeman splitting is predicted.
We report our study on coherent population trapping (CPT) in a $\ensuremath{\Lambda}$ configuration coupled by magnetic dipole interactions. The $\ensuremath{\Lambda}$ configuration is formed by bichromatic radio-frequency fields coupling a pair of Zeeman sublevels in one hyperfine level of an alkali-metal atom to another sublevel in the other hyperfine level. The Zeeman sublevel at the apex is coupled to a state in the nPnPnP manifold via an optical transition on one of the spectroscopic DDD lines to induce optical pumping to a dark state. The configuration is closed without leakage to other Zeeman sublevels. We use lithium atoms in an optical trap for our experimental study. The system allows independent control of the main parameters characterizing CPT, which include the upper-state decay rate and the decoherence rate as well as the Rabi frequencies. By turning off the applied fields, the system is frozen so that its quantum state can be measured precisely. We studied the line shapes and dynamics of the CPT system, and measured the phase relation of the dark superposition state to find excellent agreement with theory. The possible application of the scheme as a method to cool optically trapped atoms below the recoil limit in a manner analogous to velocity-selective coherent population trapping is discussed.
We observe transitions of laser-cooled Rb between vibrational levels in subwavelength-sized optical potential wells, using high-resolution spectroscopy of resonance fluorescence. We measure the spacing of the levels and the population distribution, and find the atoms to be localized to 1/15 of the optical wavelength. We find up to 60% of the population of trapped atoms in the vibrational ground state. The dependence of the spectrum on the parameters of the optical field provides detailed information about the dynamics of laser-cooled atoms.