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arXiv:2101.04309 · Physical Review A

Dark-state sideband cooling in an atomic ensemble

Chang Cang Huang, Shijie Chai, Shau-Yu Lan

Published Jan 6, 2021• 8 citations
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Abstract

We utilize the dark state in a $\mathrm{\ensuremath{\Lambda}}$-type three-level system to cool an ensemble of $^{85}\mathrm{Rb}$ atoms in an optical lattice [Morigi et al., Phys. Rev. Lett. 85, 4458 (2000)]. The common suppression of the carrier transition of atoms with different vibrational frequencies allows them to reach a subrecoil temperature of 100 nK after being released from the optical lattice. A nearly zero vibrational quantum number is determined from the time-of-flight measurements and adiabatic expansion process. The features of sideband cooling are examined in various parameter spaces. Our results show that dark-state sideband cooling is a simple and compelling method for preparing a large ensemble of atoms into their vibrational ground state of a harmonic potential and can be generalized to different species of atoms and molecules for studying ultracold physics that demands recoil temperature and below.

DOI
10.1103/physreva.103.013305

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We utilize the dark state in a \ensuremathΛ\mathrm{\ensuremath{\Lambda}}\ensuremathΛ-type three-level system to cool an ensemble of 85Rb^{85}\mathrm{Rb}85Rb atoms in an optical lattice [Morigi et al., Phys. Rev. Lett. 85, 4458 (2000)]. The common suppression of the carrier transition of atoms with different vibrational frequencies allows them to reach a subrecoil temperature of 100 nK after being released from the optical lattice. A nearly zero vibrational quantum number is determined from the time-of-flight measurements and adiabatic expansion process. The features of sideband cooling are examined in various parameter spaces. Our results show that dark-state sideband cooling is a simple and compelling method for preparing a large ensemble of atoms into their vibrational ground state of a harmonic potential and can be generalized to different species of atoms and molecules for studying ultracold physics that demands recoil temperature and below.
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We demonstrate the laser cooling of 85Rb^{85}\mathrm{Rb}85Rb atoms in a two-dimensional optical lattice. We follow the two-step degenerate Raman sideband cooling scheme [Kerman et al., Phys. Rev. Lett. 84, 439 (2000)], where a fast cooling of atoms to an auxiliary state is followed by a slow cooling to a dark state. This method has the advantage of independent control of the heating rate and cooling rate from the optical pumping beam. We operate the lattice at a Lamb-Dicke parameter $\ensuremath{\eta}=0.45$ and show the cooling of spin-polarized 85Rb^{85}\mathrm{Rb}85Rb atoms to the recoil temperature in both dimensions within 2.4 ms with the aid of adiabatic cooling.
This dissertation reports on quantum state preparation of cesium atoms in a two-dimensional optical lattice, by resolved-sideband Raman cooling. An optical lattice is a periodic potential produced by the light shift interaction between an atom and light field. Laser cooled atoms can become strongly localized about the bottom of potential wells in an optical lattice, where they occupy a discrete spectrum of bound vibrational energy levels. The distribution over vibrational levels of atoms in the lattice is characterized by the mean vibrational excitation, n . In an optical lattice, absorption and emission of photons from lattice beams causes n to increase in time. This source of heating is always present, but its rate can be greatly reduced in a lattice detuned far from the atomic resonance. Sideband cooling is an efficient means of transferring atoms from higher into lower-lying vibrational levels and, thus, it reduces n for the ensemble. If the sideband cooling rate is much greater than the heating rate, then n approaches zero and virtually all atoms are in the lowest vibrational level in their potential wells. Our sideband cooling scheme involves stimulated Raman transitions between bound states in the potential wells of a pair of magnetic sublevels, followed by optical pumping, for a net loss of one quantum of vibration per cooling cycle. The process accumulates 98% of atoms in the ground vibrational level of a potential well associated with a single Zeeman substate. Each atom in the lattice is then very close to a pure state. For two-dimensional lattice with sideband cooling we find nx≈ny≈0.008 &parl0;16&parr0; . Various issues related to state preparation and sideband cooling are also discussed in the context of a one dimensional lin ⊥ lin optical lattice. These include improvement of laser cooling in a near resonance lattice by application of weak magnetic fields, transfer of atoms from near into far off-resonance lattices, and heating rates in far off-resonance lattices.
We demonstrate laser cooling of 85Rb atoms in a two-dimensional optical lattice. We follow the two-step degenerate Raman sideband cooling scheme, Kerman el al., Phys. Rev. Lett. 84, 439 (2000), where a fast cooling of atoms to an auxiliary state followed by a slow cooling to a dark state. This method has the advantage of independent control of the heating rate and cooling rate from the optical pumping beam. We operate the lattice at Lamb-Dicke parameter eta=0.45 and show the cooling of spin-polarized 85Rb atoms to the recoil temperature in both dimension within 2.4 ms with 90% of initial atom numbers.
We present a simple and general optical cooling method based on 3D degenerate Raman sideband cooling with adiabatic release that goes significantly beyond the density and temperature limitations of optical molasses. In 10 ms we cool a sample of 3×108 cesium atoms to a temperature of 330 nK at a density of 1.1×1011 cm−3, which corresponds to a phase-space density nλdB3=1/500.We further propose to cool atoms or molecules inside an optical cavity that enhances the scattering of blue-detuned photons and show that the dissipative mechanism can be viewed as a cavity-induced generalized Doppler cooling. Since the cooling depends on the atom’s internal level structure only through the photon scattering rate, cavity Doppler cooling is applicable to particles that do not possess a closed optical transition, which may allow one to extend laser cooling to a greater class of atoms or molecules. Large samples are cooled at the same rate as single atoms if the effect of one atom on the cavity resonance frequency is small. We also show how to achieve 3D cooling with a single optical cavity.
We propose a scheme that combines velocity-selective coherent population trapping (CPT) and Raman sideband cooling (RSC) for subrecoil cooling of optically trapped atoms outside the Lamb-Dicke regime. This scheme is based on an inverted Y\mathsf{Y}Y configuration in an alkali-metal atom. It consists of a $\mathrm{\ensuremath{\Lambda}}$ formed by two Raman transitions between the ground hyperfine levels and the DDD transition, allowing RSC along two paths and formation of a CPT dark state. Using the state-dependent difference in vibration frequency of the atom in a circularly polarized trap, we can tune the $\mathrm{\ensuremath{\Lambda}}$ to make only the motional ground state a CPT dark state. We call this scheme motion-selective coherent population trapping (MSCPT). We write the master equations for RSC and MSCPT and solve them numerically for a 87Rb^{87}\mathrm{Rb}87Rb atom in a one-dimensional optical lattice when the Lamb-Dicke parameter is 1. Although MSCPT reaches the steady state slowly compared with RSC, the former consistently produces colder atoms than the latter. The numerical results also show that subrecoil cooling by MSCPT outside the Lamb-Dicke regime is possible under a favorable, yet experimentally feasible, condition. We explain this performance quantitatively by calculating the relative darkness of each motional state. Finally, we discuss the application of the MSCPT scheme to an optically trapped diatomic polar molecule whose Stark shift and vibration frequency exhibit large variations depending on the rotational quantum number.