Discrete time crystals enhanced by Stark potentials in Rydberg atom arrays

TL;DR

This work addresses stabilizing discrete time crystals without disorder-induced localization by introducing a Stark potential in the detuning of a periodically driven Rydberg atom array. A two-stage Floquet protocol is used to implement a Stark-enhanced, disorder-free DTC, where the Stark detuning yields approximate U(1) prethermalization rather than Stark MBL. Numerical results demonstrate improved DTC robustness to spin-flip imperfections and significantly extended lifetimes, with the effects being initial-state independent and resilient to longer-range interactions. The approach offers a practical path to observing DTCs in clean Rydberg systems with reduced experimental overhead, avoiding disorder averaging and specialized state preparation.

Abstract

Discrete time crystals (DTCs) are non-equilibrium phases in periodically driven systems that exhibit spontaneous breaking of discrete time-translation symmetry. The stabilization of most DTC phases is achieved via the disorder-induced many-body localization. In this work, we propose an experimental scheme to realize disorder-free DTCs in a periodically driven Rydberg atom array. Our scheme utilizes a linear potential in the atomic detuning to enhance the DTC order, without being tired to (Stark) many-body localization. We numerically demonstrate that the Stark potential enhances the robustness of the DTC against the flip imperfections and extends its lifetime, which are independent of initial states. Thus, our scheme provides a promising way to explore DTCs in Rydberg atom arrays without disorder averaging and special state preparation.

Figures (5)

• Figure 1: Experimental scheme. (a) Sequence diagram for periodically switching on the Raman field $\Omega$ and Stark potential $\Omega$ in stages $T_1$ and $T_2$, respectively. The sequence corresponds to the Hamiltonians $H_1$ and $H_2$ in the two stages. (b) Schematic of a one-dimensional $^{87}$Rb atom arrays. The horizontal orange laser is the Raman laser, which acts at the $T_1$ stage with a Rabi frequency $\Omega$. The vertical red laser is the optical tweezers, which are used to trap atoms and act as a Stark potential field from the $T_2$ stage. Atom at the j-th site is initialized in the ground state $\ket{r}$ and coupled to the Rydberg state $\ket{r}$ via a two-photon Raman transition with a site-dependent and linear detuning $\Delta_j=Fj$.
• Figure 2: The autocorrelator $C$ as a function of time $t/T$ for (a) $FT_2=0$ (absence of Stark potentials) and (b) $FT_2=0.25$. (c) and (d) Fourier spectra $FFT[C(t)]$ corresponding to (a) and (b), respectively. (e) and (f) Overlap $O$ between the initial state and quasi-eigenstates with respect to the quasi-eigenenergy $E_F$, which correspond to (a) and (b), respectively. The initial state in (a-f) is $|\psi(0)\rangle=\ket{111111111111}$. Other parameters are $T_1=1$, $T_2=10$, $V=0.1$, $\epsilon=0.3$, and $L=12$.
• Figure 3: (a) Amplitude of the subharmonic response $A_{\pi}$ as functions of $\epsilon$ and $FT_2$ for $V = 0.1$. (b) $A_{\pi}$ as a function of $\epsilon$ for $FT_2=0,0.2,0.3$ and fixed $V = 0.1$. (c) $A_{\pi}$ as a function of $FT_2$ for $V=0.06,0.09,0.12$ and fixed $\epsilon=0.3$. (d) $A_{\pi}$ as a function of $FT_2$ with nearest-neighbor interaction (NN), next-nearest-neighbor (NNN), next-next-nearest-neighbor (NNNN) and every atom interacting with others (ALL). Other parameters in (a-d) are $T_1=1$, $T_2=10$ and $L=10$, and the initial product states is $\ket{111111111111}$.
• Figure 4: (a) The autocorrelator $C(t)$ at stroboscopic time for $\epsilon=0.25$ and $FT_2=0.25$. The lifetime of the DTC is $N_c=t_c/T=3042$. (b) Logarithm of the lifetime $N_c$ as a function of the Stark potential strength $FT_2$ for different imperfection $\epsilon$. Other parameters are $V = 0.1$ and $L=10$.
• Figure 5: The autocorrelator $C(t)$ (the first and second row panels) and corresponding Fourier spectrum $FFT[C(t)]$ (the last row panels) for initial states $\ket{1111000000}$ (a,c,e) and $\ket{1111010010}$ (b,d,f), respectively. The Stark potential strength is $FT_2=0$ in (a,b) and $FT_2=0.4$ in (c,d). Other parameters are $T_1=1$, $T_2=10$, $V=0.1$, $\epsilon=0.25$ and $L=10$.