Prospects for sympathetic cooling of molecules in electrostatic, ac and microwave traps

We consider how trapped molecules can be sympathetically cooled by ultracold atoms. As a prototypical system, we study LiH molecules co-trapped with ultracold Li atoms. We calculate the elastic and inelastic collision cross sections of 7LiH + 7Li with the molecules initially in the ground state and in the first rotationally excited state. We then use these cross sections to simulate sympathetic cooling in a static electric trap, an ac electric trap, and a microwave trap. In the static trap we find that inelastic losses are too great for cooling to be feasible for this system. The ac and microwave traps confine ground-state molecules, and so inelastic losses are suppressed. However, collisions in the ac trap can take molecules from stable trajectories to unstable ones and so sympathetic cooling is accompanied by trap loss. In the microwave trap there are no such losses and sympathetic cooling should be possible

Deceleration and trapping of heavy diatomic molecules using a ring-decelerator

We present an analysis of the deceleration and trapping of heavy diatomic molecules in low-field seeking states by a moving electric potential. This moving potential is created by a 'ring-decelerator', which consists of a series of ring-shaped electrodes to which oscillating high voltages are applied. Particle trajectory simulations have been used to analyze the deceleration and trapping efficiency for a group of molecules that is of special interest for precision measurements of fundamental discrete symmetries. For the typical case of the SrF molecule in the (N,M) = (2, 0) state, the ring-decelerator is shown to outperform traditional and alternate-gradient Stark decelerators by at least an order of magnitude. If further cooled by a stage of laser cooling, the decelerated molecules allow for a sensitivity gain in a parity violation measurement, compared to a cryogenic molecular beam experiment, of almost two orders of magnitude

Ultracold molecules for quantum simulation: rotational coherence in CaF and RbCs

Polar molecules offer a new platform for quantum simulation of systems with long-range interactions, based on the electrostatic interaction between their electric dipole moments. Here, we report the development of coherent quantum state control using microwave fields in $^{40}$Ca$^{19}$F and $^{87}$Rb$^{133}$Cs molecules, a crucial ingredient for many quantum simulation applications. We perform Ramsey interferometry measurements with fringe spacings of $\sim 1~\rm kHz$ and investigate the dephasing time of a superposition of $N=0$ and $N=1$ rotational states when the molecules are confined. For both molecules, we show that a judicious choice of molecular hyperfine states minimises the impact of spatially varying transition-frequency shifts across the trap. For magnetically trapped $^{40}$Ca$^{19}$F we use a magnetically insensitive transition and observe a coherence time of 0.61(3)~ms. For optically trapped $^{87}$Rb$^{133}$Cs we exploit an avoided crossing in the AC Stark shifts and observe a maximum coherence time of 0.75(6)~ms

On the role of the magnetic dipolar interaction in cold and ultracold collisions: Numerical and analytical results for NH(3Σ−^3\Sigma^-) + NH(3Σ−^3\Sigma^-)

We present a detailed analysis of the role of the magnetic dipole-dipole interaction in cold and ultracold collisions. We focus on collisions between magnetically trapped NH molecules, but the theory is general for any two paramagnetic species for which the electronic spin and its space-fixed projection are (approximately) good quantum numbers. It is shown that dipolar spin relaxation is directly associated with magnetic-dipole induced avoided crossings that occur between different adiabatic potential curves. For a given collision energy and magnetic field strength, the cross-section contributions from different scattering channels depend strongly on whether or not the corresponding avoided crossings are energetically accessible. We find that the crossings become lower in energy as the magnetic field decreases, so that higher partial-wave scattering becomes increasingly important \textit{below} a certain magnetic field strength. In addition, we derive analytical cross-section expressions for dipolar spin relaxation based on the Born approximation and distorted-wave Born approximation. The validity regions of these analytical expressions are determined by comparison with the NH + NH cross sections obtained from full coupled-channel calculations. We find that the Born approximation is accurate over a wide range of energies and field strengths, but breaks down at high energies and high magnetic fields. The analytical distorted-wave Born approximation gives more accurate results in the case of s-wave scattering, but shows some significant discrepancies for the higher partial-wave channels. We thus conclude that the Born approximation gives generally more meaningful results than the distorted-wave Born approximation at the collision energies and fields considered in this work.Comment: Accepted by Eur. Phys. J. D for publication in Special Issue on Cold Quantum Matter - Achievements and Prospects (2011

Modeling sympathetic cooling of molecules by ultracold atoms

We model sympathetic cooling of ground-state CaF molecules by ultracold Li and Rb atoms. The molecules are moving in a microwave trap, while the atoms are trapped magnetically. We calculate the differential elastic cross sections for CaF-Li and CaF-Rb collisions, using model Lennard-Jones potentials adjusted to give typical values for the s-wave scattering length. Together with trajectory calculations, these differential cross sections are used to simulate the cooling of the molecules, the heating of the atoms, and the loss of atoms from the trap. We show that a hard-sphere collision model based on an energy-dependent momentum transport cross section accurately predicts the molecule cooling rate but underestimates the rates of atom heating and loss. Our simulations suggest that Rb is a more effective coolant than Li for ground-state molecules, and that the cooling dynamics is less sensitive to the exact value of the s-wave scattering length when Rb is used. Using realistic experimental parameters, we find that molecules can be sympathetically cooled to 100μK in about 10 s. By applying evaporative cooling to the atoms, the cooling rate can be increased and the final temperature of the molecules can be reduced to 1 μK within 30 s

Long rotational coherence times of molecules in a magnetic trap

Polar molecules in superpositions of rotational states exhibit long-range dipolar interactions, but maintaining their coherence in a trapped sample is a challenge. We present calculations that show many laser-coolable molecules have convenient rotational transitions that are exceptionally insensitive to magnetic fields. We verify this experimentally for CaF where we find a transition with sensitivity below 5 Hz G−1 and use it to demonstrate a rotational coherence time of 6.4(8) ms in a magnetic trap. Simulations suggest it is feasible to extend this to more than 1 s using a smaller cloud in a biased magnetic trap

Alternating gradient focusing and deceleration of polar molecules

Beams of polar molecules can be focused using an array of electrostatic lenses in alternating gradient (AG) configuration. They can also be accelerated or decelerated by applying an appropriate high-voltage switching sequence to the lenses. AG focusing is applicable to molecules in both low-field- and high-field-seeking states and is particularly well suited to the problem of decelerating heavy molecules and those in their ground rotational state. We describe the principles of AG deceleration and set out criteria to be followed in decelerator design, construction and operation. We calculate the longitudinal and transverse focusing properties of a decelerator, and exemplify this by 2D-imaging studies of a decelerated beam of metastable CO molecules