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Sub-Doppler Laser Cooling of 40K with Raman Gray Molasses on the D2 Line

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Sub-Doppler Laser Cooling of 40K with Raman Gray Molasses on the D2 Line Journal of Physics B: Atomic, Molecular and Optical Physics J. Phys. B: At. Mol. Opt. Phys. 50 (2017) 095002 (7pp) https://doi.org/10.1088/1361-6455/aa65ea Sub-Doppler laser cooling of 40K with Raman gray molasses on the D 2 line G D Bruce1,2, E Haller1, B Peaudecerf1, D A Cotta1, M Andia1,SWu3, M Y H Johnson1,2, B W Lovett2 and S Kuhr1,4 1 University of Strathclyde, Department of Physics, SUPA, Glasgow G4 0NG, United Kingdom 2 SUPA School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews KY16 9SS, United Kingdom 3 Department of Physics, State Key Laboratory of Surface Physics and Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education), Fudan University, Shanghai 200433, Peopleʼs Republic of China E-mail: [email protected] Received 14 December 2016, revised 20 February 2017 Accepted for publication 10 March 2017 Published 12 April 2017 Abstract Gray molasses is a powerful tool for sub-Doppler laser cooling of atoms to low temperatures. For alkaline atoms, this technique is commonly implemented with cooling lasers which are blue-detuned from either the D1 or D2 line. Here we show that efficient gray molasses can be implemented on the 40 D2 line of K with red-detuned lasers. We obtained temperatures of 482()m K, which enables direct loading of 9.2() 3´ 106 atoms from a magneto-optical trap into an optical dipole trap. We support our findings by a one-dimensional model and three-dimensional numerical simulations of the optical Bloch equations which qualitatively reproduce the experimentally observed cooling effects. Keywords: atomic physics, gray molasses, laser cooling, ultracold atoms, sub-Doppler cooling (Some figures may appear in colour only in the online journal) 1. Introduction on a Sisyphus-like cooling effect in which atoms climb potential hills created by polarization or intensity gradients, Ultracold quantum gases have attracted much interest in thereby losing kinetic energy before being optically pumped recent years, and have become a versatile tool to investigate to a lower energy level. In the case of Li and K, the only strongly interacting and strongly correlated quantum systems alkalines with stable fermionic isotopes, polarization gradient [1]. Cooling of an atomic gas to ultralow temperatures cooling in a standard optical molasses is less efficient because requires a multi-stage cooling process, which starts with a the smaller excited state hyperfine splitting leads to a higher laser cooling phase in a magneto-optical trap (MOT), fol- excitation probability of transitions other than the ones used lowed by evaporative cooling in magnetic or optical traps. for cooling. Nonetheless, sub-Doppler temperatures were Directly after collecting atoms in a MOT, lower temperatures achieved for K [3–6] and Li [7] at low atom densities using a and a higher phase space density can be achieved by sub- red-detuned optical molasses. In most experimental setups, Doppler laser cooling techniques [2].A‘standard’ red- the MOT uses light near-red detuned to the FFF¢=+1 detuned optical molasses allows the heavier alkaline atoms cycling transition of the D2 (nSnP12 32) line (n is the Rb and Cs to be cooled well below the Doppler limit. It relies principal quantum number). It was also shown that Doppler cooling on the narrower linewidth nSnP12+()1 32 4 Author to whom any correspondence should be addressed. transition can achieve low temperature at high density in 6Li [8, 9] and 40K [10], but this technique requires lasers in the ultraviolet or blue wavelength range. Original content from this work may be used under the terms Gray molasses is another powerful method for sub-Dop- of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and pler laser cooling to high densities and low temperatures the title of the work, journal citation and DOI. [11, 12], and it relies on the presence of bright and dark states. 0953-4075/17/095002+07$33.00 1 © 2017 IOP Publishing Ltd Printed in the UK J. Phys. B: At. Mol. Opt. Phys. 50 (2017) 095002 G D Bruce et al A spatially varying light shift of the bright states allows the D2 line. The cooling light is red-detuned by D =-12.3 G moving atoms to undergo a Sisyphus-like cooling effect [2],in from the FF=¢=92 92 transition and the repumper a way that hot atoms are transferred from a dark to a bright light is detuned by D - d from the FF=¢=72 92 state at a potential minimum of the bright state and back again transition (see level scheme in figure 1(d)). into a dark state at a potential maximum. The coupling between Using the method outlined in [22], we calculated eigen- the dark and bright states is velocity-selective, such that the states and light shifts, ò, of the dressed states (see appendix), coldest atoms are trapped in the dark states with substantially and the photon scattering rate γ for each of the states. The reduced interaction with the light field. Most early experiments eigenstates correspond to the bare mF states at positions of using gray molasses created Zeeman dark states by using pure s+ - polarization (figure 1(b)) and for arbitrary polar- circularly polarized light on FF¢=F [13, 14] or ization, they are predominantly superpositions of the mF fi FFF¢=-1 transitions [15–17] within the D2 line, and states within a speci c F manifold. The eigenstates can be blue-detuned lasers so that the energy of bright states lay above grouped into dark states (g ~ 0 at all positions) and bright those of the dark states. In those experiments with Rb and Cs, states (g > 0 at all positions). The dark states are pre- the large hyperfine splitting in the P32states allows a large dominantly superpositions of the mF states from the F = 7 2 detuning of the gray molasses laser from the other transitions manifold, and the bright states are superpositions of mF states (in particular from the MOT FF¢+1 cycling transition) predominantly from the F = 9 2 manifolds with small such that the gray molasses provides the dominant light-scat- admixtures of states from the F¢=11 2 manifold. The tering process. In contrast, the poorly-resolved P32states in Li energy of the bright states is spatially varying (blue curves in and K increase the probability of undergoing transitions on the figure 1(b)) with the dominant light-shift contribution from MOT cycling transition, which was thought to limit the the FF=¢=92 112 transition, while the light shifts effectiveness of the gray molasses. Efficient implementations of the dark eigenstates have negligible spatial variation (green of gray molasses with 39K [18–20], 40K [21, 22], 6Li [22, 23] curves in figure 1(b)). For negative two-photon detuning 7 [ ] and Li 24 have therefore used transitions of the D1 line (d < 0), the energy of the dark states is below the bright states (nSnP12 12 transitions), requiring the use of additional (figure 1(b)), and above for positive detunings. lasers. In some of these experiments, cooling was found to be We calculated the optical pumping rate, gD, which is the enhanced at a Raman resonance between the cooling and rate at which an atom scatters a photon and returns to a dif- repumping light fields [18, 22, 24]. This Λ configuration cre- ferent state (see appendix), at each point in space by num- ates additional, coherent dark states, as in velocity-selective erical solution of the optical Bloch equations [22]. Atoms are coherent population trapping schemes [25, 26]. preferentially depumped from the bright states at positions of In this work, we demonstrate that such Raman dark states pure linear polarization (figure 1(c)), which occurs at the 40 can be utilized for cooling of K to high atom densities in a potential maxima of the lowest-lying bright state. The prob- red-detuned gray molasses using only light at a frequency ability of motional coupling is largest when the energy dif- close to the FFF¢=+1 transition on the D2 line. In ference between bright and dark states is smallest [27].By contrast to the D1-line or narrow-line cooling schemes, our choosing δ such that the dark states have lower energy than all scheme requires minimal experimental overhead, because the the bright states (in our case d =-0.17 G), we ensure that lasers are the same as the ones used for the MOT. Our paper is motional coupling is strongest between the dark state and structured as follows. Firstly, we model the gray molasses by lowest-energy bright state at the potential minima. computing the energy levels and photon scattering rates of It is critical for our scheme that the bright states belong bright and dark states by numerical solution of the optical mostly to the F = 9 2 manifold and the dark states to the Bloch equations. We present experimental evidence that our F = 7 2 manifold, with smaller F. Only in this case it is method reaches sub-Doppler temperatures and efficiently possible that the energetically lowest bright state experiences loads atoms into an optical dipole trap (ODT). We analyze the strongest light shift (at z = l 8) while its depumping rate our results using a semi-classical Monte Carlo simulation and to the dark states is actually lowest. The main component of find qualitative agreement with our experimental data. this bright state at z = l 8 is from the stretched Fm==92,F 92 state whose scattering rate is highest.
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