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Abstract

In this thesis, we present the realization of an isolated Heisenberg XXZ spin 1/2 system with an off-diagonal disorder in the coupling constants using cold atoms in highly excited Rydberg states. We select a set of Rydberg states that interact via van der Waals interaction which can be mapped onto an interacting spin system. We investigate the out-of-equilibrium dynamics of the spin system after it has been initialized in a fully magnetized state. Following unitary evolution governed by the Heisenberg spin Hamiltonian, we measure the magnetization as a function of the evolution time. By fitting a stretched exponential function to the resulting magnetization dynamics be obtain a stretched exponent of β = 0.32 revealing a slow relaxation of the spin system, similar to what is found in spin glasses. By choice, the initial state is an eigenstate of the mean-field Hamiltonian and thus the observed relaxation indicates that the dynamics are triggered by quantum fluctuations. We find that varying the distribution of coupling constants by means of the so-called dipole blockade effect has no impact on the stretching exponent indicating that it is a universal parameter of the system independent of the microscopic details for the range of disorder explored in the experiment. It also allows us to combine the different datasets by re-scaling the time domain with the characteristic interaction strength. The combined datasets expand our measurements to two orders of magnitude in the re-scaled time-domain showing that slow dynamics is a persistent effect for long evolution times.