Figure 1

Experimental setup and control of the coupling along the resonator axis. (a) Two FFP cavities are linked with a intercavity tunneling amplitude $\mathcal{K}$. Each cavity contains $N^a$ two-level ${}^{87}\mathrm{Rb}$ atoms trapped by an external magnetic potential or dipole beam. $g$ is the coherent coupling rate between an individual atom and the cavity field; $\gamma$ and $\kappa$ are the dissipation rate of the atomic spontaneous emission and the cavity field itself, respectively. (b) The atoms are placed at a position $x$ along the cavity axis and are loaded into the optical lattice. The cavity mode (${\lambda }_{\mathrm{C}}=780\mathrm{nm}$) and far-detuned optical lattice (${\lambda }_{\mathrm{L}}=830\mathrm{nm}$) standing waves in each cavity have a variable overlap with a $6.4\mu \mathrm{m}$ period. (c) The loaded atoms show a strongly modulated coupling depending on the local overlap between lattice and cavity mode.Reuse & Permissions

Figure 2

Excitations of a polariton condensate. This diagram shows the dependence of excitation density ${\rho }^{\mathrm{ex}}$ on the coupling rate $g$ for chemical potential $(\mu -{\omega }_{\mathrm{C}})/g_{\min }\sqrt{N^a}=-1$ (red line) and the chemical potential as a function of $g$ for the excitation density ${\rho }^{\mathrm{ex}}=0.3$ (blue line). The inset shows the photon occupancy density $\rho$ as a function of the excitation density ${\rho }^{\mathrm{ex}}$ for atomic resonance (${\Delta }_{\mathrm{C}}=0$), where the red dashed line is the linear fitting.Reuse & Permissions

Figure 3

The chemical potential-current relation in the polariton condensates. (a),(b) Time evolution of the relative population (solid line) and phase (dashed line) for (a) $v=0.8v_c$ and (b) $v=1.5v_c$. (c) Dependence of the relative population (solid line) and the chemical potential difference (dashed line) on the velocity of the moving optical lattice. This diagram shows that there exists a sharp transition with the critical velocity $v_c=0.48\mu \mathrm{m}/\mu \mathrm{s}$.Reuse & Permissions