Fig. 1. Experimental setup for observing time-crystalline order.

a, NV centers in a nanobeam fabricated from black diamond are illuminated by a focused green laser beam and irradiated by a microwave source. Spins are prepared in the $(|m_s=0\rangle +|m_s=-1\rangle )/\sqrt{2}$ state using a microwave (−π/2)-pulse along the $\widehat{y}$ axis. Subsequently, within one Floquet cycle, the spins evolve under a dipolar interaction and microwave field Ω_x aligned along the $\widehat{x}$ axis for duration τ₁, immediately followed by a global microwave θ-pulse along the $\widehat{y}$ axis. After n repetitions of the Floquet cycle, the spin polarization the $\widehat{x}$ axis is read out. We choose τ₁ as an integer multiple of 2π/Ω_x to minimize accidental dynamical decoupling¹³. b-d, Representative time traces of the normalized spin polarization P(nT) and respective Fourier spectra, |S(ν)|², for different values of interaction time τ₁ and θ: (b) τ₁ = 92 ns, θ = π, (c) τ₁ = 92 ns, θ = 1.034π, and (d) τ₁ = 989 ns, θ = 1.034π. Dashed lines in c indicate ν = 1/2 ± (θ − π)/2π. Data are averaged over more than 2 ⋅10⁴ measurements.