Protocol for autonomous rearrangement of cold atoms into low-entropy configurations

The preparation of low-entropy starting conditions is a key requirement for many experiments involving neutral atoms. Here we propose a method to autonomously assemble arbitrary spatial configurations of atoms within arrays of optical tweezers or lattice sites, enabled by a combination of tunneling and ground-state laser cooling. In contrast to previous methods, our protocol does not rely on either imaging or evaporative cooling. This circumvents limitations associated with imaging fidelity and loss, especially in systems with small spatial scales, while providing a substantial improvement in speed relative to evaporative approaches. These features may make it well suited for preparing arbitrary initial conditions for Bose-Hubbard or Rydberg interacting systems.

Figure 1

(a) Conceptual overview of method. An array of lattice sites, consisting of target (outer circles) and reservoir (no circles) sites is initially loaded in a stochastic manner. After subsequent cycles of directional tunneling into target sites and between reservoir sites, interleaved with dissipative cooling steps, target states within the array are occupied. Atoms remaining in the reservoir sites are then removed, leaving a tailored low-entropy configuration. (b) Basic building block of implementation. (i) An optical potential consisting of two neighboring wells is imbalanced to create a tunneling resonance between the ground state of the reservoir site (right well) and the first motionally excited state of the target site (left well). An atom occupying the reservoir site will then tunnel into an empty target site either resonantly or through an adiabatic ramp of the relative well depths (inset). (ii) If an atom already occupies the target site, contact interactions shift the tunneling resonance, preventing double occupation of the target site. (iii) After tunneling, ground-state laser cooling is applied to return atoms to the ground state of their respective sites, providing dissipation and preventing future tunneling away from the target site.

Figure 2

Applications to different geometries. (a) Target sites can be defined within a two-dimensional lattice by applying local optical potentials to these sites, for example, with optical tweezers. Shift operations transfer atoms into target sites from neighboring reservoir sites. (b) The same concept can be applied to the filling of layers within a three-dimensional lattice. Here shift operations are applied between layers, and tunneling within layers enables reservoir atoms to find empty target sites. An auxiliary potential (light sheet) is used to shift the energy of the target plane relative to its neighbors. (c) A continuous region can be filled by repeatedly shifting atoms towards a potential barrier, represented by the gray region on the left of the array. In all protocols, atoms are removed from the reservoir sites after filling of the target sites or layers is complete (see Appendix pp4)

Figure 3

Protocol for filling uniform regions without additional dimensions. By alternately shifting even and odd pairs of atoms, atoms are shuffled to one side, where they bunch up against a barrier (barrier not pictured). The shift operations are implemented in parallel by superimposing an optical lattice (red sinusoidal lines) with an auxiliary potential (blue nonsinusoidal lines) that both creates an imbalance between neighboring wells and pushes down the barrier in the combined potential (black lines), enabling rapid tunneling. The phase of the additional potential is shifted relative to the lattice to shift even (upper) or odd (lower) pairs. Right: The shuffle operation can easily be extended to two dimensions simply by applying shuffle operations to many rows in parallel. Shuffling of each row is independent of others.

Figure 4

Effects of errors on target site (left column) and layer filling (right column) protocols. Red (light grayscale) (black) points represent 50% initial filling, with $F=1,\left(0.9\right)$. Blue (dark grayscale) points represent 90% intitial filling, with $F=1$. (a) Filling fraction $1-\xi$ versus number of cycles. Vertical lines represent the number of steps $n_{99}$ required to reach 99% filling for each condition. Loss not included. Inset: effect of tunneling fidelity on $n_{99}$. For moderate infidelities, the effect is minor. Gray line is intuitive approximation discussed in text. (b) Minimum hole fraction $\xi$ fraction versus per-cycle loss, for same conditions as (a).

Figure 5

Shuffling performance in idealized case and with imperfect fidelity and loss. (a) Example of lattice site occupation versus number of shuffling cycles, with perfect tunneling and no loss. Each cycle consists of either an even or an odd shift. After an initial traffic jam, the atoms shuffle at a rate of one site per step until they are blocked by other atoms. (b) Number of cycles required to reach 99% filling ($n_{99}$) for different target region lengths $N$. Dashed black line is the prediction from the text, and dashed gray line is $N$. (c) Example of lattice site occupation versus number of shuffling cycles in the presence of finite shift fidelity ($F=0.9$) and loss per cycle $(\epsilon =0.01$). (d) Prevalence of holes in the final array versus loss $\epsilon$ and $N$.

Figure 6

Tunneling properties within nearest-neighbor subsystem. (a, b) The motional excited state into which the atoms tunnel is twofold degenerate, with a node either along the vertical (a) or horizontal (b) axis. Atoms tunneling into the target site populate one of these two states, depending on whether they tunneled horizontally or vertically. During the tunneling process, an atom is thus confined to its original row or column but can tunnel through the target site to the reservoir site directly opposite (not shown) After cooling, both motionally excited states are cooled to the ground state of the target site. (c) The probability of a target site being filled depends on the number and configuration of filled neighboring reservoir sites. Here we show the unique filling possibilities (omitting those that are equivalent up to reflection or rotation of the system), along with the associated probability for filling the target site, assuming a perfect adiabatic ramp of the target site depth.