Abstract
Sideband cooling is a popular method for cooling atoms to the ground state of an optical trap. Applying the same method to molecules requires a number of challenges to be overcome. Strong tensor Stark shifts in molecules cause the optical trapping potential, and corresponding trap frequency, to depend strongly on rotational, hyperfine and Zeeman state. Consequently, transition frequencies depend on the motional quantum number and there are additional heating mechanisms, either of which can be fatal for an effective sideband cooling scheme. We develop the theory of sideband cooling in state-dependent potentials, and derive an expression for the heating due to photon scattering. We calculate the ac Stark shifts of molecular states in the presence of a magnetic field, and for any polarization. We show that the complexity of sideband cooling can be greatly reduced by applying a large magnetic field to eliminate electron- and nuclear-spin degrees of freedom from the problem. We consider how large the magnetic field needs to be, show that heating can be managed sufficiently well, and present a simple recipe for cooling to the ground state of motion.
Highlights
In recent years there has been rapid progress in the development of techniques for producing and manipulating ultracold molecules [1,2,3,4,5,6,7,8,9,10,11,12]
Laser-cooled molecules were captured in tweezer traps for the first time [20]
An important current challenge is how to cool these molecules to the ground state of motion in tweezer traps or lattices
Summary
In recent years there has been rapid progress in the development of techniques for producing and manipulating ultracold molecules [1,2,3,4,5,6,7,8,9,10,11,12]. In order to selectively drive the red sideband of the transition, the linewidth must be narrow compared to the energy spacing of the motional levels of the trapped atom; typical trap frequencies are of order 100 kHz. The second step provides the dissipation necessary for cooling by optically pumping the atom back to its original internal state. When the potentials are identical, different motional states of the two potentials are orthogonal and the probability of changing n depends only on the Lamb-Dicke parameter, the square root of the ratio of the photon recoil energy to the level spacing of the traps Provided this parameter is small, transitions that change the motional quantum.
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