Observation of a Dissipative Time Crystal

We present the first experimental realization of a time crystal stabilized by dissipation. The central signature in our implementation in a driven open atom-cavity system is a period doubled switching between distinct checkerboard density wave patterns, induced by the interplay between controlled cavity dissipation, cavity-mediated interactions, and external driving. We demonstrate the robustness of this dynamical phase against system parameter changes and temporal perturbations of the driving.

Figure 1

Dissipative time crystal. (a) Schematic diagram of the transversely pumped atom-cavity system. (b) Time sequence for the pump with modulation strength $f_0=0.3$ and modulation period $T_D=0.25\mathrm{ms}$. In the time interval delimited by dashed lines, $f_0$ is linearly ramped from zero to its desired value. (c) The corresponding response of the intracavity photon number $N_P$ (red) and the relative phase $\varphi$ between the pump and the cavity light field (blue). (d)–(h) Top panels: momentum distributions measured at instances of time marked by dashed arrows in (c). Bottom panels: corresponding mean-field results for the single-particle density distribution, which shows periodic switching between even and odd DWs at twice the driving period.

Figure 2

Dynamical regimes. Dynamics of the relative phase $\varphi$ for (a) $f_0=0.05$, (b) $f_0=0.25$, and (c) $f_0=0.95$ with fixed ${\omega }_D=2\pi \times 4\mathrm{kHz}$. (d)–(f) Corresponding Fourier spectra of the dynamics in (a)–(c). As the modulation strength is increased, the system transforms from a DW to a DTC phase. Strong modulation leads to heating and chaotic behavior. (g)–(j) Dynamical phase diagram showing the relative crystalline fraction $\mathrm{\Xi }$ as a function of the modulation frequency ${\omega }_D$ and strength $f_0$ for (g) clean modulation, (h) weak noise strength $n=9.6$, (i) intermediate noise strength $n=15.9$, and (j) large noise strength $n=22.3$. The diagram is constructed by dividing the parameter space into $18\times 18$ plaquettes and within each averaging over multiple experimental runs (at least four realizations). Red crosses in (g)–(j) mark the modulation parameters used in Figs. 3. Increasingly large noise strengths shrink the area in the phase diagram where a stable DTC phase prevails.

Figure 3

Robustness of subharmonic response. (a)–(d) Single-shot experimental runs for the noise strengths applied in Figs. 2 and for values of ${\omega }_D$ and $f_0$ according to the red crosses in these figures. Top panels: single-shot protocols for the pump strength. Bottom panel: corresponding time evolution of the relative phase $\varphi$ (blue trace) and intracavity photon number $N_P$ (red trace). (e) Dependence of the relative crystalline fraction $\mathrm{\Xi }$ on the noise strength averaged over 7 experimental runs with $f_0=0.2$ and ${\omega }_D=2\pi \times 4\mathrm{kHz}$. The gray dashed lines mark the noise strengths used in (a)–(d).

Figure 4

Short-range interaction and atom loss. Numerical results from TWA for the dynamics of (a) the intracavity photon number $N_P$ and (b) the nonequal time correlation $C$ of the photons for different values of the collisional interaction energy $E_a$ and the atom loss rate $\gamma$. To increase the quality of the presentation, the black, red, green, and blue traces in a are plotted with different offsets $0,15,30,45\times {10}^3$, respectively. The modulation parameters are ${\omega }_D=2\pi \times 4\mathrm{kHz}$ and $f_0=0.2$.