Observation of a Superradiant Mott Insulator in the Dicke-Hubbard Model

It is well known that the bosonic Hubbard model possesses a Mott insulator phase. Likewise, it is known that the Dicke model exhibits a self-organized superradiant phase. By implementing an optical lattice inside of a high-finesse optical cavity, both models are merged such that an extended Hubbard model with cavity-mediated infinite range interactions arises. In addition to a normal superfluid phase, two superradiant phases are found, one of them coherent and hence superfluid and one incoherent Mott insulating.

Figure 1

Experimental setup. The beam diameters and the BEC are not drawn to scale.

Figure 2

(a) The intracavity photon number is plotted versus the effective detuning ${\delta }_{\text{eff}}$ and the strength ${ϵ}_p$ of the pump wave. The HSF-SSF phase boundary is highlighted by a thick dashed-dotted black line. Six locations in the phase diagram are highligted by capital letters $A$, $B$, $C$, $D$, $E$, $F$. Three trajectories, $\overline{\mathrm{ABCD}}$, $\overline{\mathrm{DCD}}$, and $\overline{\mathrm{EFE}}$, are indicated along which the degree of coherence of the atomic sample is observed. The black squares labeled by greek letters $\alpha ,\beta ,\gamma$ show the observed boundary between the SSF and the SMI phase. Corresponding BDMFT calculations are shown by the white-bordered black disks. (b) The upper panel quantifies the tuning of ${\delta }_{\text{eff}}$ (black squares) and ${ϵ}_p$ (green disks) along the path $\overline{\mathrm{ABCD}}$ in (a). In the lower panel, the intracavity photon number $N_p$ (red disks) and the width (FWHM) $\mathcal{W}$ of the observed zero momentum Bragg resonance (blue diamonds) with regard to the $z$ direction are plotted. The red and blue solid lines are linear fits, including the data points highlighted by black margins. The red dashed line corresponds to the white delimited data points. The HSF-SSF and the SSF-SMI phase boundaries are defined by the intersections of the red and blue lines with the $(N_p=0)$ and $(\mathcal{W}=1)$ lines, respectively. In (c), momentum spectra (in the ($k_y,k_z$) plane) are shown recorded at the locations on the path $\overline{\mathrm{ABCD}}$ indicated by the black arrows in (b).

Figure 3

Intracavity photon number $N_p$ and width (FWHM) of the zero momentum Bragg peak $\mathcal{W}$ plotted versus time for the paths $\overline{\mathrm{DCD}}$ (a) and $\overline{\mathrm{EFE}}$ (b) indicated in Fig. 2. In (a), the pump lattice well depth ${ϵ}_p$ is linearly tuned from zero at D to $5.12E_{\text{rec}}$ at C and back to zero at D with constant ${\delta }_{\text{eff}}/2\pi =-11\mathrm{kHz}$. Correspondingly, in (b), ${\delta }_{\text{eff}}/2\pi =-18\mathrm{kHz}$, and ${ϵ}_p$ is tuned between ${ϵ}_p(E)=0$ and ${ϵ}_p(F)=8.45E_{\text{rec}}$. The red and blue lines are linear fits including the data points highlighted by black edges. The HSF-SSF and the SSF-SMI phase boundaries are defined by the intersections of the red and blue lines with the $(N_p=0)$ and $(\mathcal{W}=1)$ lines, respectively.