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arXiv:2205.05224 · Physical Review A

Motion-selective coherent population trapping by Raman sideband cooling along two paths in a Λ configuration

Sooyoung Park, Meung Ho Seo, Ryun Ah Kim, D. Cho

Published Aug 31, 2022• 7 citations
arXivHTMLPDF

Abstract

We report our experiment on sideband cooling with two Raman transitions in a $\mathrm{\ensuremath{\Lambda}}$ configuration that allows selective coherent population trapping (CPT) of the low-lying motional states. The cooling method is applied to $^{87}\mathrm{Rb}$ atoms in a circularly polarized one-dimensional optical lattice. Owing to the vector polarizability, the vibration frequency of a trapped atom depends on its Zeeman quantum number and the CPT resonance for a pair of bound states in the $\mathrm{\ensuremath{\Lambda}}$ configuration depends on their vibrational quantum numbers. We call this scheme motion-selective coherent population trapping (MSCPT) and it is a trapped-atom analog of the velocity-selective CPT developed for free He atoms. We observe a pronounced dip in temperature near a detuning for the Raman beams to satisfy the CPT resonance condition for the motional ground state. Although the lowest temperature we obtain is ten times the recoil limit owing to the heat load from motion along an axis, which is left uncooled, and the large Lamb-Dicke parameter of 2.3 in our apparatus, the experiment demonstrates that MSCPT enhances the effectiveness of Raman sideband cooling and enlarges the range of its application. Discussions of design parameters optimized for MSCPT on $^{87}\mathrm{Rb}$ atoms and opportunities provided by diatomic polar molecules, whose Stark shift shows a strong dependence on the rotational quantum number, are included.

DOI
10.1103/physreva.106.023323

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Physical Review A•Mar 10, 2014•7 citations
We report our experiment on sideband cooling with two Raman transitions in a \ensuremathΛ\mathrm{\ensuremath{\Lambda}}\ensuremathΛ configuration that allows selective coherent population trapping (CPT) of the low-lying motional states. The cooling method is applied to 87Rb^{87}\mathrm{Rb}87Rb atoms in a circularly polarized one-dimensional optical lattice. Owing to the vector polarizability, the vibration frequency of a trapped atom depends on its Zeeman quantum number and the CPT resonance for a pair of bound states in the \ensuremathΛ\mathrm{\ensuremath{\Lambda}}\ensuremathΛ configuration depends on their vibrational quantum numbers. We call this scheme motion-selective coherent population trapping (MSCPT) and it is a trapped-atom analog of the velocity-selective CPT developed for free He atoms. We observe a pronounced dip in temperature near a detuning for the Raman beams to satisfy the CPT resonance condition for the motional ground state. Although the lowest temperature we obtain is ten times the recoil limit owing to the heat load from motion along an axis, which is left uncooled, and the large Lamb-Dicke parameter of 2.3 in our apparatus, the experiment demonstrates that MSCPT enhances the effectiveness of Raman sideband cooling and enlarges the range of its application. Discussions of design parameters optimized for MSCPT on 87Rb^{87}\mathrm{Rb}87Rb atoms and opportunities provided by diatomic polar molecules, whose Stark shift shows a strong dependence on the rotational quantum number, are included.
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.
A method of sideband Raman cooling to the vibrational ground state of the m=0m=0m=0 Zeeman sublevel in a far-detuned two-dimensional optical lattice is proposed. In our scheme, the Raman coupling between vibrational manifolds of the adjacent Zeeman sublevels is shifted to the red sideband due to the ac Stark effect induced by a weak pump field. Thus cooling and optical pumping to m=0m=0m=0 are achieved by purely optical means with coplanar cw laser beams. The optical lattice and cooling parameters are estimated in the framework of simple theoretical models. An application of the transverse sideband cooling method to frequency standards is discussed. Coherent population trapping for the sideband Raman transitions between the degenerate vibrational levels is predicted.
Summary form only given. Laser cooled atoms play a critical role in modern designs of frequency standards such as atomic fountains. Recently, an elegant and efficient method of two-dimensional cooling to the vibrational ground state of a far-off resonance optical lattice has been demonstrated. This method is a variant of Raman sideband cooling based on the Raman transitions between the vibrational manifolds of adjacent Zeeman substates. A static magnetic field is used to tune the Zeeman levels so that Raman resonance occurs on the red sideband and results in cooling. Two circularly polarized fields are used to recycle the atoms for repetitive Raman cooling. Unfortunately, a direct application of this scheme to frequency standards meets with several difficulties. Stimulated by these concepts and results, we propose a new variant of transverse sideband cooling, where these problems are avoided, while still maintaining most of the attractive features. The field configuration used for the optical lattice consists of three linearly polarized beams having equal amplitudes and propagating in the xy plane with angles of 2/spl pi//3 between each other. The polarization vectors of these beams are tilted through a small angle with respect to the z-axis. All the beams have the same frequency far-detuned to the red of the D/sub 2/ resonance line. Raman transitions between vibrational levels of adjacent magnetic substates are induced by the small in-plane component of the field. Two other important requirements for Raman sideband cooling are a uniform energy shift of the magnetic sublevels and optical pumping.
We form a 1D optical lattices for Cs atoms using light tuned a few thousand linewidths below the 6S1/2(F equals 4) yields 6P3/2(F' equals 5) transition at 852 nm. In this far-off- resonance lattice the time scale for damping of motional coherences and kinetic energy can be orders of magnitude longer than the vibrational oscillation period for atoms trapped in the lattice potential wells. Atoms are loaded directly into deeply bound states, by adiabatic transfer from a superimposed, near-resonance optical lattice. This yields a mean vibrational excitation n approximately equals 0.3, and localization (Delta) z approximately (lambda) /20 deep in the Lamb-Dicke regime. Light scattering subsequently heats the atoms, but the initial rate is only of order 10-3 vibrational quanta per oscillation period. Low vibrational excitation, localization in the Lamb-Dicke regime and low heating rates make these atoms good candidates for resolved- sideband Raman cooling, and for the generation and study of non-classical states of center-of-mass motion. We propose a scheme for resolved-sideband Raman cooling and quantum state preparation; the scheme employs Raman coupling between magnetic sublevels induced by the lattice light field itself.
In Section 8.3.9, we mentioned that the recoil temperature was not the ultimate barrier to cooling. Several mechanisms have been conceived and implemented to concentrate the atomic velocity distribution in a range of values of width less than V R . In contrast to Doppler or Sisyphus cooling, these mechanisms do not appeal to a friction force, but rather to an optical pumping process (see Complement 2B), able to accumulate the atoms in this narrow range of velocities. We now present one such mechanism called ‘velocity-selective coherent population trapping’, considering only the case where the motion occurs in one space direction (the O z -axis). Note, however, that the method generalizes to two or three dimensions. Coherent population trapping Coherent population trapping is a phenomenon that occurs when an atom has a system of three energy levels in the ∧ configuration shown in Figure 8A.1, where each leg of the ∧ interacts with a laser L − or L + . This was discussed in detail in Section 2D.2 of Complement 2D. Here we consider the case where the two ground states g + and L − , have exactly the same energy, and the two lasers have frequencies ω + and ω − , very close to the resonance frequency ω 0 . In this situation, the selectivity of the interactions is obtained via the polarization selection rules (see Complement 2B): if g − , g + and e have magnetic quantum numbers m = −1, +1 and 0, respectively, the laser wave L − is right-circularly polarized (σ + polarization), while the laser wave L + is left-circularly polarized (σ − polarization).
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.