Moiré Superradiance in Cavity Quantum Electrodynamics with Quantum Atom Gas

TL;DR

The paper investigates moiré effects in a one-dimensional cold-atom cavity QED system by mapping to an extended open Dicke model. A moiré parameter $M$ controls the dissipative superradiant phase transition, with a softening of atom-polariton modes $w_j^s$ and a reduction of the critical pump $\eta_c$ due to a moiré scattering channel $w_{j=2f_n-f_{n+1}}^s$. Observables include the cavity field spectrum $S(\omega)$ and anomalous atomic diffusion, both revealing moiré signatures and the nonequilibrium quantum dynamics of the system. The work provides a route to moiré metrology in a driven-dissipative quantum gas and points to extensions to fermionic systems and many-body localization contexts.

Abstract

As a novel platform for exploring exotic quantum phenomena, the moiré lattice has garnered significant interest in solid-state physics, photonics, and cold atom physics. While moiré lattices in two- and three-dimensional systems have been proposed for neutral cold atoms, the simpler one-dimensional moiré effect remains largely unexplored. We present a scheme demonstrating moiré effects in a one-dimensional cold atom-cavity coupling system, which resembles a generalized open Dicke model exhibiting superradiant phase transitions. We reveal a strong link between the phase transition critical point and the one-dimensional moiré parameter. Evidences of the one-dimensional moiré effect are explicitly explored, including cavity field spectrum, phase transition dynamics, and anomalous atomic diffusion. This work provides a new route for testing one-dimensional moiré effects with cold atoms and open new possibility of moiré metrology.

Figures (7)

• Figure 1: Schematic diagram for dissipative phase transition in a cavity-assisted moiré lattice. Atoms are trapped by a optical lattice potential $V_{l} \cos^{2}(k_{l} x)$ along the cavity axis. Atoms scatter the side pump laser $\varepsilon_{p}$ into the cavity mode $\cos(k_{c} x+\phi)$. The inset shows that atoms are scattered into a few different modes in the combined 1D moiré lattice. Cavity decay rate is $\kappa$.
• Figure 2: (a) Scaled mean-field value $| \alpha |$ versus scaled pumping strength $\eta / \eta_c$ for different $M$. The black solid line is the case without the external optical lattice. The inset present steady state momentum distribution for $M = 5$. (b) The eigenvalues imaginary parts of atom polariton excitations versus $\eta$ are shown for two major scattering channels at $M = 5$, in which the absolute values of the pair $j = 2 f_n - f_{n+1}$ is much smaller than those of $j = f_{n+1}$, thus determining the phase transition point. The pair $j = f_{n+1}$ would converge to $0$ at around $\eta = \eta_c$ without the occurrence of phase transition, as indicated by the black-dashed lines. The vertical grey line indicate the analytical phase transition point. Red-dashed line showcase incoherent cavity excitation. The steady states and excitations are calculated for $V_l = -1$, $N U_0 = -80$, $\Delta_c = -100$ and $\kappa = 20$.
• Figure 3: TWA simulation results with $N=1000$ obtained from sample of $500$ trajectory runs. (a) Steady state population in cavity mode (left panel) and homogeneous atomic mode $\psi_0$ (right panel) versus pumping strength $\eta$. The black solid line is the case without the external optical lattice. (b) Cavity field population dynamics at $M = 3$ along with $\eta$ ramps to the value of $0.6 \eta_c$. (c) Wigner distributions of cavity light field at the instant marked by the vertical grey dashed line in (b). The parameters are the same as those in Fig. \ref{['fig:dissipation']}, noticeably that TWA however predicts the superradiant phase transition to occur at lower $\eta$.
• Figure 4: The logarithm of the cavity field spectrum $S(\omega)$ as a function of $\omega$ and relative pumping $\eta$. From left to right: (a) $M = 1$, (b) $M = 3$, (c) $M = 5$. The vertical gray bar indicate the critical pumping strength at which phase transition takes place for each cases. Below threshold two pairs of sideband peaks are visible, corresponding to frequencies of two types of quasi-particle excitations as specified in the main text. Upon the onset of superradiant phase transition, more peaks appear and they are intimately related to the moiré parameter $M$.
• Figure 5: (a) Time scaling $\nu$ of atomic diffusion versus pumping strength $\eta$ for $M = 3$ (green-dashed line) and $M = 5$ (red-dashed line). The horizontal black-dashed line of $\nu = 1/2$ indicates the critical scaling. (b) Atomic diffusion dynamics simulated for M31 ($M = 3, \eta = 0.46 \eta_c$), M32 ($M = 3, \eta = 0.5 \eta_c$), M51 ($M = 5, \eta = 0.4 \eta_c$) and M52 ($M = 5, \eta = 0.46 \eta_c$), which were also indicated in (a). The black line indicates the normal diffusion of $\nu = 1/2$ that separates superdiffusion ($\nu > 1/2$) and subdiffusion ($\nu < 1/2$) regions. Atoms are initially prepared in a Gaussian wavepacket with width $w = 1/k_c$. The other parameters are the same as before.