Rapid generation of Mott insulators from arrays of noncondensed atoms

We theoretically analyze a scheme for a fast adiabatic transfer of cold atoms from the atomic limit of isolated traps to a Mott insulator close to the superfluid phase. This gives access to the Bose-Hubbard physics without the need of a prior Bose-Einstein condensate. The initial state can be prepared by combining the deterministic assembly of atomic arrays with resolved Raman-sideband cooling. In the subsequent transfer the trap depth is reduced significantly. We derive conditions for the adiabaticity of this process and calculate optimal adiabatic ramp shapes. Using available experimental parameters, we estimate the impact of heating due to photon scattering and compute the fidelity of the transfer scheme. Finally, we discuss the particle number scaling behavior of the method for preparing low-entropy states. Our findings demonstrate the feasibility of the proposed scheme with state-of-the-art technology.

Figure 1

Excitation pathways in a microtrap array: interband excitations dominate in deep traps since intraband tunneling is exponentially suppressed. However, for shallower potentials, intraband tunneling prevails as long as the two-particle interaction energy $U\equiv U_{iiii}^{0000}$ remains smaller than the band gap $\hslash \omega$.

Figure 2

Comparison between results from the numerical solution of the single-particle Schrödinger equation (circles) and the approximate closed-form expressions (lines) for the Hubbard parameters. (a) Tunneling parameter $J$ as a function of the potential depth ${\mathcal{V}}_{\perp }$ for ${}^{87}\mathrm{Rb}$ atoms in a square lattice of Gaussian dipole traps with waist $w_0=0.71\mu \mathrm{m}$ and trap spacing $d=1.7\mu \mathrm{m}$. (b) The in-plane part ${\mathcal{U}}_{\perp }$ of the on-site interaction parameter versus ${\mathcal{V}}_{\perp }$ for the same parameters as in (a). (c) The out-of-plane part ${\mathcal{U}}_{\parallel }$ of the on-site interaction parameter versus ${\mathcal{V}}_{\parallel }$ for the same parameters as in (a).

Figure 3

Potential depth ${\mathcal{V}}_{\perp }\left(t\right)$ versus time $t$. The red dashed line shows the ramp resulting from the biexponential ansatz, whereas the blue solid line is the optimal adiabatic ramp.

Figure 4

The adiabatic Lagrangian functions per site ${\mathcal{L}}_{\text{al}}/M$ (dashed) and ${\mathcal{L}}_{\text{bh}}/M$ (solid) are plotted versus time $t$ for a biexponential (red) and an optimal adiabatic (blue) transfer sequence of duration $\tau =50\mathrm{ms}$.

Figure 5

The mass function per site ${\mathcal{M}}_{\text{bh}}/M$ is plotted versus the potential depth ${\mathcal{V}}_{\perp }$. The blue points represent the full mass function obtained from Eqs. (42), (43), (52), (53), (54), and (55), whereas the orange line corresponds to the approximation given in Eq. (61).

Figure 6

Optimal adiabatic potential ramp ${\mathcal{V}}_{\perp }\left(t\right)$ versus time $t$: comparison between the numerical solution of the Euler-Lagrange equation (blue solid lines) and the analytic approximation (dashed red lines) given in Eqs. (60) and (62). For $t<0.7\mathrm{ms}$ (a) interband excitations dominate, whereas for $t>1\mathrm{ms}$ (b) intraband excitations are the most relevant.

Figure 7

Figures of merit for the biexponential (dashed red) and the optimal adiabatic (solid blue) ramp versus the ramp duration $\tau$: (a) maximal value ${\mathbb{E}}_{\infty }/M$ of the adiabatic Lagrangian function per site during the ramp, (b) number of scattering events per atom $N_{\text{sc}}$ during the ramp, (c) transfer fidelity $\mathcal{F}$, (d) excess energy $\mathrm{\Delta }$ of the final state in units of the interaction energy $U$ at $t=\tau$. The results shown in (c) and (d) are obtained from a many-body calculation for a 1D lattice with periodic boundary conditions, $N=8$ particles and $M=8$ sites.

Figure 8

Joint probability $P=p_0^N$ to prepare $N$ atoms in the motional ground state of $N$ isolated traps versus particle number $N$ for various single-site success probabilities $p_0=0.9$ (blue circles), $p_0=0.92$ (red triangles), $p_0=0.94$ (green squares), $p_0=0.96$ (orange stars), and $p_0=0.98$ (violet diamonds).