Coherence Times of Bose-Einstein Condensates beyond the Shot-Noise Limit via Superfluid Shielding

We demonstrate a new way to extend the coherence time of separated Bose-Einstein condensates that involves immersion into a superfluid bath. When both the system and the bath have similar scattering lengths, immersion in a superfluid bath cancels out inhomogeneous potentials either imposed by external fields or inherent in density fluctuations due to atomic shot noise. This effect, which we call superfluid shielding, allows for coherence lifetimes beyond the projection noise limit. We probe the coherence between separated condensates in different sites of an optical lattice by monitoring the contrast and decay of Bloch oscillations. Our technique demonstrates a new way that interactions can improve the performance of quantum devices.

Figure 1

Schematic of superfluid shielding. (a) Before applying a tilt, the atoms are in a superfluid, which is approximately described by a coherent state on each site. The chemical potential is constant across the cloud. (b) In the limit of a strong tilt ($\mathrm{\Delta }\gg J$), the wave function at each lattice site is projected onto the number basis, leading to fluctuations in the number of atoms and chemical potential from site to site. (c) If the gas has two components, one which is localized by the tilt, and one which remains superfluid, the itinerant component can compensate for fluctuations in the localized component. (d)–(f) Momentum distribution over the course of a single Bloch oscillation after ten cycles. (d) Without superfluid shielding, the diffuse cloud indicates decoherence of the condensate. (e) The itinerant component feels no force and does not Bloch oscillate. (f) For the shielded component, the Bloch oscillation contrast is high. (g) Exponential decay of the Bloch oscillation contrast for a one-component (blue dots) and two-component (red squares) gas, for a transverse lattice depth of $11E_r$ and $\sim 8\times 10^3$ atoms.

Figure 2

Superfluid shielding of external fields, applied by increasing the trap frequency. The vertical dashed line is the initial trap frequency that corresponds to a linear chemical potential for the $|\downarrow ⟩$ atoms. We compare the contrast after 25 Bloch oscillation cycles for unshielded (blue dots) and shielded (red squares) components. In this figure only, for technical reasons, one of the transverse lattices had a spacing of 392.5 nm.

Figure 3

Superfluid shielding for different atom numbers and densities. Shown are the exponential decay lifetimes of spin $|\downarrow ⟩$ Bloch oscillating component for unshielded (blue dots) and shielded (red squares) cases vs chemical potential. In (a), the chemical potential is changed by varying atom number from $\sim 6\times 10^3$ to $\sim 2\times 10^4$ while keeping the lattice depths at $10E_r$ in both transverse directions. In (b), the chemical potential is varied by changing the transverse lattice depth from $4E_r$ to $11E_r$. In both plots, the dashed lines represent the projection noise limit given by two theoretical models (see text).

Figure 4

Contrast lifetime versus shielding fraction. Exponential decay lifetime of spin $|\downarrow ⟩$ Bloch oscillating component upon varying the number of atoms in spin $|\uparrow ⟩$ state (i.e., fraction of atoms in $|\uparrow ⟩$ state over total number of atoms) indicates that shielding is effective beyond projection noise limits once more than $\sim 25\%$ atoms are in the $|\uparrow ⟩$ state.