Ultracold Atoms in a Disordered Crystal of Light: Towards a Bose Glass

We use a bichromatic optical lattice to experimentally realize a disordered system of ultracold strongly interacting ${}^{87}\mathrm{Rb}$ bosons. In the absence of disorder, the atoms are pinned by repulsive interactions in the sites of an ideal optical crystal, forming one-dimensional Mott-insulator states. We measure the excitation spectrum of the system as a function of disorder strength and characterize its phase-coherence properties with a time-of-flight technique. Increasing disorder, we observe a broadening of the Mott-insulator resonances and the transition to a state with vanishing long-range phase coherence and a flat density of excitations, which suggest the formation of a Bose-glass phase.

Figure 1

Phase diagram for disordered interacting bosons [2]. Depending on the ratio between tunneling energy $J$, interaction energy $U$, and disorder $\Delta$, the system forms a superfluid (SF), a Mott insulator (MI), or a Bose glass (BG).

Figure 2

In a homogeneous MI the tunneling of one boson from a site to a neighboring one has an energy cost $\Delta E=U$. In the presence of disorder this excitation energy becomes $\Delta E=U\pm {\Delta }_j$, where ${\Delta }_j$ is the local site-to-site energy difference.

Figure 3

(a) A collection of 1D Bose gases in a deep 2D lattice experience the bichromatic potential $V(x)$. (b) Potential energy $V(x)$ for $s_1=16$ and $s_2=1$. (c) Histogram of the calculated energy differences between neighboring sites for $s_2=1$.

Figure 4

(a)–(e) Excitation spectra for $s_1=16$ and different values of $s_2$. (f) Effect of the modulation at frequency $\nu =1.9\mathrm{kHz}$ as a function of $s_2$. The points correspond to the $1/\sqrt{e}$ half-width of a Gaussian fit of the central density peak after modulation and TOF. The line in (a) is a fit to the experimental points, while the curves in (b)–(f) are calculated from a model of inhomogeneous broadening of the MI resonances.

Figure 5

(a) Density distribution after time-of-flight for different values of $s_1$ and $s_2=2.5$. (b) Coherent fraction as a function of $s_1$ for $s_2=0$ and $s_2=2.5$ and sketch of the corresponding scans in the phase diagrams. Each point corresponds to a different set of images ($\approx 10$ images per set).