Preparation and Spectroscopy of a Metastable Mott-Insulator State with Attractive Interactions

We prepare and study a metastable attractive Mott-insulator state formed with bosonic atoms in a three-dimensional optical lattice. Starting from a Mott insulator with Cs atoms at weak repulsive interactions, we use a magnetic Feshbach resonance to tune the interactions to large attractive values and produce a metastable state pinned by attractive interactions with a lifetime on the order of 10 s. We probe the (de)excitation spectrum via lattice modulation spectroscopy, measuring the interaction dependence of two- and three-body bound-state energies. As a result of increased on-site three-body loss we observe resonance broadening and suppression of tunneling processes that produce three-body occupation.

Figure 1

Stability of the many-body system for attractive interactions (a) BEC fraction $x_{\mathrm{BEC}}$ as a function of $a_S$ with $t_H=50\mathrm{ms}$. The narrow shaded areas indicate the locations of Feshbach resonances. The inset shows the region around $a_S=0a_0$. (b) Number of remaining atoms $N_A$ as a function of $a_S$ with the same settings as in (a). (c) $N_A$ (top) and $x_{\mathrm{BEC}}$ (bottom) as a function of $t_H$ for $a_S=+220a_0$ (circles), $a_S=-240a_0$ (squares), and $a_S=-2000a_0$ (diamonds). The solid lines are exponential fits giving $1/e$-decay times of $28.3\pm 0.9\mathrm{s}$ ($+220a_0$), $25.2\pm 1.8\mathrm{s}$ ($-240a_0$), and $19.5\pm 0.5\mathrm{s}$ ($-2000a_0$) for $N_A$ and $14.2\pm 0.6\mathrm{s}$ ($+220a_0$), $13.7\pm 0.6\mathrm{s}$ ($-240a_0$), and $11.4\pm 0.4\mathrm{s}$ ($-2000a_0$) for $x_{\mathrm{BEC}}$. (d) Top: $x_{\mathrm{BEC}}$ as a function of $t_H$ at $a_S=-100a_0$ for $V_0=20E_R$ (circles, $|U|/J=159$, deep in the Mott regime), $V_0=14E_R$ (squares, $|U|/J=36$, near the transition), and $V_0=12E_R$ (diamonds, $|U|/J=21$, in the superfluid regime). Bottom: $x_{\mathrm{BEC}}$ as a function of $t_H$ at $a_S=+15a_0$ (circles) and $a_S=-15a_0$ (squares) for $V_0=20E_R$ ($|U|/J=24$). The solid lines are double exponential fits to guide the eye. We attribute the reduced initial value for $x_{\mathrm{BEC}}$ in (d) to the increased dwell time in the region of low $|a_S|$ as the magnetic field settles to its final value.

Figure 2

Excitation spectrum for a Mott insulating state with attractive interactions (a) BEC fraction $x_{\mathrm{BEC}}$ as a function of $f_M$ for high (low) initial density shown as circles (squares) at $a_S=-306a_0$. The solid lines are double Gaussian fits. (b) Normalized molecule number $N_M$ as a function of $f_M$ at $a_S=-306a_0$. (c) Set of excitation spectra with $x_{\mathrm{BEC}}$ as a function of $f_M$ as $a_S$ is varied: $a_S=-111a_0$ (top) to $a_S=-2334a_0$ (bottom). The three-body resonance is indicated by an arrow.

Figure 3

Excitation energies $\Delta E$ into two- and three-body bound states for negative $a_S$. Two-body bound-state excitation energy (circles), three-body bound-state excitation energy (squares), and first excited two-body bound-state excitation energy (diamonds, obtained by doubling the measured values) are shown as a function of $a_S$. The solid (dashed) line is the calculated excitation energy for the two-body (three-body) bound state and the dotted line is the calculated excitation energy for the first excited two-body bound state. The dash-dotted line is the standard BH model calculation. The shaded area indicates the variation for the calculated $\Delta E$ as $V_0$ is varied from 19 to $21E_R$. The inset shows the two-body (circles) and three-body (squares) bound-state excitation energies for the full range of $a_S$ accessible in our experiment, where the data for $a_S>0$ are taken from Ref. 29, augmented by new measurements for $a_S>1000a_0$.

Figure 4

Broadening of the three-body excitation resonance. (a) Set of excitation spectra showing the normalized BEC fraction $x_{\mathrm{BEC}}$ as a function of $f_M$ for various values of $a_S$ as indicated. The resonance peak connected to the two-body (three-body) bound state is located at lower (higher) frequency. The solid lines are double-peaked Gaussian fits, from which the width (FWHM) of the resonances is deduced. (b) FWHM of the three-body excitation resonance as a function of $a_S$ for attractive interactions. (c) For comparison, we show the FWHM of the three-body excitation resonance as a function of $a_S$ for repulsive interactions [29].