No Arabic abstract
All light has structure, but only recently it has become possible to construct highly controllable and precise potentials so that most laboratories can harness light for their specific applications. In this chapter, we review the emerging techniques for high-resolution and configurable optical trapping of ultracold atoms. We focus on optical deflectors and spatial light modulators in the Fourier and direct imaging configurations. These optical techniques have enabled significant progress in studies of superfluid dynamics, single-atom trapping, and underlie the emerging field of atomtronics. The chapter is intended as a complete guide to the experimentalist for understanding, selecting, and implementing the most appropriate optical trapping technology for a given application. After introducing the basic theory of optical trapping and image formation, we describe each of the above technologies in detail, providing a guide to the fundamental operation of optical deflectors, digital micromirror devices, and liquid crystal spatial light modulators. We also describe the capabilities of these technologies for manipulation of trapped ultracold atoms, where the potential is dynamically modified to enable experiments, and where time-averaged potentials can realise more complex traps. The key considerations when implementing time-averaged traps are described.
Ultracold atoms confined in a dipole trap are submitted to a potential whose depth is proportional to the real part of their dynamic dipole polarizability. The atoms also experience photon scattering whose rate is proportional to the imaginary part of their dynamic dipole polarizability. In this article we calculate the complex dynamic dipole polarizability of ground-state erbium, a rare-earth atom that was recently Bose-condensed. The polarizability is calculated with the sum-over-state formula inherent to second-order perturbation theory. The summation is performed on transition energies and transition dipole moments from ground-state erbium, which are computed using the Racah-Slater least-square fitting procedure provided by the Cowan codes. This allows us to predict 9 unobserved odd-parity energy levels of total angular momentum J=5, 6 and 7, in the range 25000-31000 cm-1 above the ground state. Regarding the trapping potential, we find that ground-state erbium essentially behaves like a spherically-symmetric atom, in spite of its large electronic angular momentum. We also find a mostly isotropic van der Waals interaction between two ground-state erbium atoms, characterized by a coefficient C_6^{iso}=1760 a.u.. On the contrary, the photon-scattering rate shows a pronounced anisotropy, since it strongly depends on the polarization of the trapping light.
We measure the conductivity of neutral fermions in a cubic optical lattice. Using in-situ fluorescence microscopy, we observe the alternating current resultant from a single-frequency uniform force applied by displacement of a weak harmonic trapping potential. In the linear response regime, a neutral-particle analogue of Ohms law gives the conductivity as the ratio of total current to force. For various lattice depths, temperatures, interaction strengths, and fillings, we measure both real and imaginary conductivity, up to a frequency sufficient to capture the transport dynamics within the lowest band. The spectral width of the real conductivity reveals the current dissipation rate in the lattice, and the integrated spectral weight is related to thermodynamic properties of the system through a sum rule. The global conductivity decreases with increased band-averaged effective mass, which at high temperatures approaches a T-linear regime. Relaxation of current is observed to require a finite lattice depth, which breaks Galilean invariance and enables damping through collisions between fermions.
Scalable, coherent many-body systems can enable the realization of previously unexplored quantum phases and have the potential to exponentially speed up information processing. Thermal fluctuations are negligible and quantum effects govern the behavior of such systems with extremely low temperature. We report the cooling of a quantum simulator with 10,000 atoms and mass production of high-fidelity entangled pairs. In a two-dimensional plane, we cool Mott insulator samples by immersing them into removable superfluid reservoirs, achieving an entropy per particle of $1.9^{+1.7}_{-0.4} times 10^{-3} k_{text{B}}$. The atoms are then rearranged into a two-dimensional lattice free of defects. We further demonstrate a two-qubit gate with a fidelity of 0.993 $pm$ 0.001 for entangling 1250 atom pairs. Our results offer a setting for exploring low-energy many-body phases and may enable the creation of large-scale entanglement
We report on the controlled creation of a valence bond state of delocalized effective-spin singlet and triplet dimers by means of a bichromatic optical superlattice. We demonstrate a coherent coupling between the singlet and triplet states and show how the superlattice can be employed to measure the singlet-fraction employing a spin blockade effect. Our method provides a reliable way to detect and control nearest-neighbor spin correlations in many-body systems of ultracold atoms. Being able to measure these correlations is an important ingredient to study quantum magnetism in optical lattices. We furthermore employ a SWAP operation between atoms being part of different triplets, thus effectively increasing their bond-length. Such SWAP operation provides an important step towards the massively parallel creation of a multi-particle entangled state in the lattice.
We demonstrate the experimental implementation of an optical lattice that allows for the generation of large homogeneous and tunable artificial magnetic fields with ultracold atoms. Using laser-assisted tunneling in a tilted optical potential we engineer spatially dependent complex tunneling amplitudes. Thereby atoms hopping in the lattice accumulate a phase shift equivalent to the Aharonov-Bohm phase of charged particles in a magnetic field. We determine the local distribution of fluxes through the observation of cyclotron orbits of the atoms on lattice plaquettes, showing that the system is described by the Hofstadter model. Furthermore, we show that for two atomic spin states with opposite magnetic moments, our system naturally realizes the time-reversal symmetric Hamiltonian underlying the quantum spin Hall effect, i.e., two different spin components experience opposite directions of the magnetic field.