Many-body nonequilibrium dynamics in a self-induced Floquet system

Abstract

Floquet systems are periodically driven systems. In this framework, the system Hamiltonian and associated spectra of interest are modified, giving rise to new quantum phases of matter and nonequilibrium dynamics without static counterparts. Here we experimentally demonstrate a self-induced Floquet system in the interacting Rydberg gas. This originates from the photoionization of thermal Rydberg gases in a static magnetic field. Importantly, by leveraging the Rydberg electromagnetically induced transparency spectrum, we probe the nonequilibrium dynamics in the bistable regime and identify the emergence of a discrete time crystalline phase. Our work fills the experimental gap in the understanding the relation of multistability and dissipative discrete time crystalline phase. In this regard, it constitutes a highly controlled platform for exploring exotic nonequilibrium physics in dissipative interacting systems.

Figures (4)

• Figure 1: Floquet engineering of nonequilibrium states in a driven-dissipative Rydberg gas. (a) Experimental setup. The probe (red) and coupling lasers (green) are counterpropagated through the Cs vapor cell to form EIT. The transmission of the probe is detected by a photodetector (PD). A PI laser beam (blue) co-propagates in parallel with the coupling laser, ionizing the Rydberg atoms in the blue channel. A homogeneous magnetic field B is along with the probe direction. Gray, golden, and blue spheres represent the ground atoms, Rydberg atoms, and charged particles, respectively. (b) This setting can be treated as an effective two-level atom (ground and Rydberg states $|g\rangle$ and $|r\rangle$) with detuning $\Delta^{(0)}$, Rabi frequency $\Omega$ and decay rate $\gamma$. (c) and (d) In the non-interaction regime (with $\bar{V}=0$), the dissipation dominates the dynamics of the system and leads to a homogeneous phase (with a single stable state). As shown in (d), the electric fields driving with a period $T$ (highlighted with the light blue regime) make the system oscillate. (e) and (f) For intense driving laser, strong atomic interactions can induce bifurcation and result in optical bistability. In the bistable regime, the phase space consists of two BOA (highlighted with gray and orange regime). When starting from $\rho^{L}$ (low transmission), for the one period, the charges kick the system into the BOA of $\rho^{H}$, and subsequent systemic Hamiltonian $\hat{H}^{(0)}$ bring the system close to $\rho^{H}$ (high transmission), and vice versa. As shown in (f), in this regime, the periodic driving makes the system oscillate between high- and low- transmission with a doubled period $2T$. Here we set $\bar{V}=-12\gamma$, $\Omega=0.7\gamma$, and $\Delta^{(0)}=3.5\gamma$.
• Figure 2: The comparison of EIT signal without (a) and with (b) PI laser at coupling Rabi frequency of $\Omega_c/2\pi =$0.59 MHz. (c) Measured oscillation frequency as a function of the magnetic field B. The solid line displays the linear fitting through the origin. The error bars show the standard deviation of three independent measurements. Inset presents a 1 ms time dynamics of the probe transmission at $\textit{B}=14.88$ G marked with a blue circle.
• Figure 3: (a) The measurement of scanned EIT signal at the indicated Rabi frequency of $\Omega_c/2\pi =$1.08 MHz, 1.68 MHz and 2.42 MHz, respectively. (b) Measured color map of the probe transmission as a function of $\Delta$ and Rabi frequency of $\Omega_c$. (c) The measured transmission signal towards optical bistability without PI laser at the indicated Rabi frequency of $\Omega_c$. Arrows show the scan directions from red to blue detuning (red) and reverse (blue). (d) Color map of the transmission difference between two scan directions as a function of $\Omega_c$.
• Figure 4: Measured phase map of Fourier spectra as a function of the two-photon laser detuning $\Delta$ range from 70 MHz to 125 MHz at $\Omega_c = 2\pi \times$1.78 MHz. The critical point value is found with $\Delta\simeq90$ MHz (marked by the dashed line), indicating phase transition in such a system.