We will develop tightly focussed optical tweezers into a versatile tool for deterministically assembling an interacting quantum system one molecule at a time. We will explore two approaches to load each microtrap of the tweezer array with single molecules: (i) single RbCs molecules will be formed inside the microtraps by association of single trapped Rb and Cs atoms; (ii) single CaF molecules will be captured from a MOT. The insight gained from this project will be invaluable to our work on lattices.

Making Tweezer Traps

The tweezer trap, or microtrap, is a tightly focussed red-detuned optical dipole trap. The confining force is based on the polarizability, α, of the atom or molecule at the frequency of the trapping light. Because the light is detuned far from any resonances, the confinement has little dependence on the hyperfine or rotational state of a molecule. Such tweezer traps for single atoms have been made by several groups, and our design follows these established methods. Unlike loading of an optical lattice, where the molecule density should be similar to the density of lattice sites, a single molecule can be loaded into a microtrap from a source of far lower density. Indeed, in previous work with atoms, the microtrap typically loads in about 10 ms from a MOT of only ∼105 atoms. We will use custom microscope objectives that provide near-diffraction-limited performance. We choose the trapping laser wavelength and power to give sufficiently large trap depth and trap frequency, while keeping the scattering rate, which heats the trapped particle, below 1 photon/s.

LOADING Rb, Cs, & CaF INTO MICROTRAPS

Single atoms of Rb and Cs will be loaded into the microtraps from MOTs. The simplest loading method ensures that the trap always contains either zero or one atom, each with 50% probability, because when two atoms enter the same trap both are ejected by light- assisted collisions. By using light blue-detuned from the D1 transition to tailor the light-assisted collisions, the probability of loading a single atom can approach unity. This enables the rapid loading of uniformly filled arrays of atoms. We will use real-time monitoring of the trap occupancy by fluorescence imaging, to ensure that a single atom of each species is loaded. The two microtraps for Rb and Cs will be loaded sequentially. First, a single Rb atom will be loaded from a MOT into an 880 nm microtrap. This trap has no effect on Cs because its polarizability is zero at this wavelength. Then, a single Cs atom will be loaded into an 1064 nm microtrap, spatially offset from the Rb trap. Finally, with all near-resonant light turned off, the two traps will be merged by translating the 880 nm beam using an acousto-optic deflector, then gradually turning off the 880 nm light, leaving both atoms in the 1064 nm trap.

Single molecules of CaF will be loaded from the MOT. It seems likely that light-assisted collisions will again ensure an occupancy of either zero or one molecule, just as for single atoms. Once again, we aim for real-time imaging to determine the presence of a trapped molecule. We expect an initial temperature of a few hundred μK. There is a great advantage in cooling to lower temperatures, especially for the experiments that will follow. Therefore, we will first focus on applying sub-Doppler cooling techniques to the trapped molecule.

Sideband Cooling

For all three species, Rb, Cs, and CaF, we will apply a method of Raman sideband cooling to drive the particle towards the motional ground state of the microtrap. Since its application to atoms has been established, we focus here on how we will apply the method to CaF. The figure below illustrates our scheme.

Scheme for Raman sideband cooling of CaF molecules in tweezer microtraps. Solid lines are laser-driven transitions, dashed lines are spontaneous emission. Steps (i) & (ii) are applied repeatedly until the molecule reaches the motional ground state.

Forming Single RbCs Molecules

After merging both Rb and Cs into a single microtrap, a magnetic field swept across a Feshbach resonance will associate the two atoms into a single molecule. The formation of molecules by magnetoassociation in macroscopic traps is well established, but has never before been used to produce single molecules in microtraps. We expect the situation to be similar to that in optical lattices, where near-unity association efficiency has been demonstrated. Cooling the atoms close to their ground states of motion and careful merging of the two microtraps will be important in achieving high association efficiency in the tweezer. The weakly bound molecule will be transferred to the ground rovibrational state using STIRAP.  Both the magnetoassociation step and STIRAP transfer have already been demonstrated for RbCs in a macroscopic 3D trap in Durham.

Unlike CaF, RbCs molecules cannot be detected by fluorescence imaging as there are no known closed transitions. Instead we will reverse the association sequence to return to two atoms in the microtrap. It may be possible to image atoms directly in a single microtrap, but light-assisted collisions may make this difficult. For a more robust detection protocol, we will tweeze the atoms apart by re-introducing the 880 nm microtrap and spatially translating it away from the 1064 nm trap so that the two atoms can be imaged separately.

Control of Interacting Molecules

Once we have mastered the control of single molecules in microtraps, we will begin studying pairs of trapped molecules. Our apparatus will incorporate two acousto-optic deflectors to control the position of a single microtrap in two orthogonal directions. By driving these deflectors with two frequencies, we produce two separate microtraps whose spacing can be controlled with nm precision through the frequency difference. With this setup, we can first load two well-spaced microtraps and cool towards the motional ground state, prepare each molecule in the rotational ground-state, and then bring the two molecules close together. They can be brought to within about 500 nm before the two microtraps merge into a single trap. At these small separations, the dipole-dipole interaction enables coherent operations to be applied on the joint state of the pair.

To study molecule-molecule interactions, we will begin by mapping out the set of levels in CaF shown below by microwave spectroscopy. This will feed directly into our theoretical work, which in turn will improve our understanding of this relatively simple interacting system. Using the dipole-dipole interactions, we will demonstrate a quantum-controlled NOT gate, the basic building block in the quantum computation scheme proposed by David DeMille, which has become a paradigm of the field. We will test our control protocols and investigate decoherence effects pertinent to molecules. Subsequently, we will extend our experiments to arrays of three and four molecules, where the dynamics is more complex. We expect the insight gained using the four-molecule square array to prove important to the lattice projects.

Energy eigenvalues for two CaF molecules versus separation. The joint rotational state is N1 + N2 = 1. The zero of energy is 2B. The inset shows the upper group of levels at larger separations.

Theoretical Advances

To understand more fully the interactions in small arrays, and interpret the pattern of energy levels we measure, the calculation outlined above needs extending in several ways. First, we need to include the nuclear spins. This introduces additional degrees of freedom and multiplies the size of the basis set needed. For 2Σ molecules (CaF and YbCs) we need to include electron-spin–nuclear spin couplings and the interactions formally take place on multiple coupled electronic potential energy surfaces. We will wish to consider the molecular pair in the presence of external electric and magnetic fields, which introduce additional axes and couplings. These fields will give us new ways to control the interactions, once we understand the crossings and avoided-crossings between levels as the fields are varied. If the molecules are not so tightly confined, their centre-of-mass motions must be considered, requiring coupled-channel methods to solve the resulting problem in 1, 2 or 3 extra degrees of freedom. Such methods are implemented in the BOUND program, but have not previously been applied to problems of this complexity, and challenging theoretical extensions will be needed.