Quantum simulators by design: Many-body physics in reconfigurable arrays of tunnel-coupled traps

We present a platform for the bottom-up construction of itinerant many-body systems: ultracold atoms transferred from a Bose-Einstein condensate into freely configurable arrays of microlens generated focused-beam dipole traps. This complements traditional optical lattices and provides a different access to the field of two-dimensional quantum simulators. The ultimate control of topology, well depth, atom number, and interaction strength is matched by sufficient tunneling. We characterize the required light fields, derive the Bose-Hubbard parameters for several alkali-metal species, and investigate the loading procedures and heating mechanisms. To demonstrate the potential of this approach, we analyze coupled annular Josephson contacts exhibiting many-body resonances.

Figure 1

Optical intensities for a set of trap configurations for a novel type quantum simulator. Optical intensity $\mathcal{I}\left(\mathbf{x}\right)$ of planar lattice-type geometries of focused-beam dipole traps separated by $1.7\mu \mathrm{m}$: (a) Measured intensity in a square lattice with designed lattice defect, (b) simulated intensity for an atomtronic diode, (c) simulated graphenelike lattice with several point defects on the right, and (d) simulated molecular structure of quinolones, a family of antibiotics.

Figure 2

Experimental setup for flexible creation of 2D potential geometries (red from left) and site-selective control of the tunneling rates (blue from right). Both light fields are generated by a combination of microlens arrays and a spatial light modulators controlling the illumination of each lenslet. The resulting focal planes are re-imaged into a vacuum chamber by two demagnifying relay lens systems. For out-of-plane confinement of the atoms via $V_{\parallel }$ an additional light sheet is applied in the $x-y$ plane.

Figure 3

Coupled Josephson rings. (a) Josephson point contact of two ring lattices with $M=6$ sites per ring. (b) Simulated optical intensity $\mathcal{I}\left(\mathbf{x}\right)$ using a hexagonal MLA. (c) and (d) Simulation of the population inversion subject to the Bose-Hubbard Hamilton operator with $N=4$ particles for $K=0.1J$: $U=0$ [(c) dotted blue line], $U=0.02J$ [(c) solid red line] compared to the perturbation theory result of Eq. (2) [(c) dashed black line], $U=J$ [(d) solid black line], $U=3J$ [(d) dash-dotted red line], $U=5.07J$ [(d) dashed green line], and $U=11.7J$ [(d) dotted blue line].

Figure 4

Self-trapping and many-body resonances. (a) Minimal value ${\zeta }_m\left(U\right)$ of the population inversion between two coupled ring lattices for $M=6$ sites and $N=4$ particles versus the interaction strength $U$ exhibiting many-body resonances. They correspond to the population oscillations shown in Figs. 3 and 3. (b) Eigenenergies of this system for different distributions of the particles between the two rings. These energies correspond to states of the form $|N_A{,j\rangle }_A\otimes {|N-N_A,j^{\prime }\rangle }_B$.

Figure 5

Measured light field of a square lattice of optical microtraps: (a) Central part of the intensity distribution and (b) section of the intensity distribution (black squares) along the horizontal line (a). The dashed blue line is a Gaussian fit to the experimental intensity distribution and the red line is the result of a simulation of the optical system.

Figure 6

Bose-Hubbard parameters. Ratio of the Bose-Hubbard interaction energy $U$ and tunneling energy $J$ versus the optical potential depth $V_{0\perp }$ (thick black line) for ${}^{87}\mathrm{Rb}$ in a lattice with $d=1.7\mu \mathrm{m}$ and further parameters given in Table 1. The horizontal lines mark the predicted superfluid–Mott-insulator phase transition for 1D and 2D geometries at unit filling [3, 37].