Relaxation of an Isolated Dipolar-Interacting Rydberg Quantum Spin System

How do isolated quantum systems approach an equilibrium state? We experimentally and theoretically address this question for a prototypical spin system formed by ultracold atoms prepared in two Rydberg states with different orbital angular momenta. By coupling these states with a resonant microwave driving, we realize a dipolar $XY$ spin-$1/2$ model in an external field. Starting from a spin-polarized state, we suddenly switch on the external field and monitor the subsequent many-body dynamics. Our key observation is density dependent relaxation of the total magnetization much faster than typical decoherence rates. To determine the processes governing this relaxation, we employ different theoretical approaches that treat quantum effects on initial conditions and dynamical laws separately. This allows us to identify an intrinsically quantum component to the relaxation attributed to primordial quantum fluctuations.

Figure 1

Sketch of a dipolar-interacting Rydberg spin system. (a) In an ultracold atomic gas, Rydberg excitations are optically prepared in the initial state $|\downarrow ⟩$. A microwave field is then turned on that resonantly couples the $|\downarrow ⟩$ and $|\uparrow ⟩$ states. (b) This drives coherent spin oscillations of each atom in the ensemble, as seen in the Bloch sphere representation of a single embedded spin, based on the numerical solution of the 8 spin Schrödinger equation. (c) Strong dipolar exchange interactions between the spins $J_{ij}$ compete with the driving field leading to the relaxation of the spin oscillations.

Figure 2

Nonequilibrium magnetization dynamics for various mean numbers of spins $⟨N⟩$ within a fixed volume. The experimental Rydberg data are represented by blue points. The error bars represent the standard errors of the mean. Results of a MACE simulation are also given for the unitary dynamics of a dipolar $XY$ quantum spin-$1/2$ model, starting from a pure state with all the spins pointing down (black solid line), as described in the text.

Figure 3

Relaxation dynamics computed by three theoretical methods: MACE (black solid lines), MF (green dash-dotted lines), and TWA (red dashed lines). Experimental data (blue dots) shown for comparison. (a) Magnetization as a function of time for $⟨N⟩=178$. (b) Amplitude of the Fourier transform of (a) normalized to the value expected for a full contrast oscillation. (c) Peak amplitude of the Fourier component $f=\mathrm{\Omega }$ for different interaction strengths $J$. The grey box corresponds to the above parameter choice. Error bars on the experimental data correspond to the standard deviation of the sampling distributions estimated using the bootstrap method.