Superfluidity of Interacting Bosonic Mixtures in Optical Lattices

We report the observation of many-body interaction effects for a homonuclear bosonic mixture in a three-dimensional optical lattice with variable state dependence along one axis. Near the superfluid-to-Mott insulator transition for one component, we find that the presence of a second component can reduce the apparent superfluid coherence, most significantly when the second component either experiences a strongly localizing lattice potential or none at all. We examine this effect by varying the relative populations and lattice depths, and discuss the observed behavior in view of recent proposals for atomic-disorder and polaron-induced localization.

Figure 1

State-dependent transition from the superfluid to the Mott regime. (a) Surfaces of equal probability density ($1/e^2$) for (noninteracting) atoms of type $|a⟩$ (red [dark grey]) and $|b⟩$ (blue [medium grey]) in a three-dimensional lattice with depths of $12E_R^{\perp }$ in the transverse directions ($x$, $y$), and $15(3.8)E_R$ along $z$ for $|a⟩$ ($|b⟩$) atoms. (b) Time-of-flight (TOF) absorption image after release of a balanced mixture ($f_a\approx f_b$). The aspect ratio $l_z/l_x$ is given by $k_z/k_{\perp }$. (c) TOF images after Stern-Gerlach separation. The $|a⟩$ component (red [medium grey]) enters the Mott regime ($t_a/U_{aa}\approx 1/39$, $t_{\perp }/U_{aa}\approx 1/38$), whereas the $|b⟩$ component (blue [dark grey]) remains superfluid. The bottom graph illustrates the state-dependent $z$-lattice ramp. The transverse lattice ramp (not shown) follows a 115 ms long sigmoid curve and reaches its full depth of $12E_R^{\perp }$ as the $z$ lattice reaches half of its maximum depth.

Figure 2

Effects of a background medium on superfluid coherence. (I; left column) $|a⟩$ atoms ($V_a=8.3E_R$) in contact with superfluid $|b⟩$ atoms ($V_b=2.1E_R$) and (II; right column) $|b⟩$ atoms ($V_b=7.8E_R$) in contact with localized $|a⟩$ atoms ($V_b=31E_R$). (a) Stern-Gerlach separated TOF images (for $f_a\approx f_b$) after a gravitational phase shift. The circles in (I) denote apertures used to determine visibility. (b) Dependence of the visibility and peak width on the relative population of the background medium, with constant total atom number $1.7(1)\times {10}^5$; the insets show corresponding data for the background medium. Open circles denote reference measurements without background medium, in which the atom numbers are varied correspondingly. Ramp shapes are as in Fig. 1, with $V_{\perp }=12E_R^{\perp }$.

Figure 3

Dependence of superfluid coherence on the localization of the second component. Visibility (${\gamma }_a$) and peak width (${\sigma }_a$) (filled circles) of the $|a⟩$ component, with fixed lattice parameters of $V_a=12E_R$ and $V_{\perp }=12E_R^{\perp }$, in the presence of $|b⟩$ atoms ($f_b\approx 3/4$, $N_a+N_b=3.7(2)\times {10}^5$) as $V_b$ is increased. In references (open circles) taken without $|b⟩$ atoms and with $N_a=1.0(1)\times {10}^5$, the visibility and peak width are roughly constant at 0.52(3) and 0.26(2) (dashed lines). Data points are averaged over 3–5 runs, with statistical error bars shown. Uncertainties in lattice depth are $\sim 5\%$ (not shown).