Relaxation of an Isolated Dipolar-Interacting Rydberg Quantum Spin System

Abstract

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.

A generalized phase space approach for solving quantum spin dynamics

“…in combination with variational Monte-Carlo evolution [11][12][13][14]), or dilute systems (e.g. by making use of a clusterization [15,16]).…”

“…In particular, models of coupled spin-particles with long-range interactions have become a topic of intensive research because of important experimental progress. While models with spin S=1/2 have been implemented with many different setups, e.g.using polar molecules [15,17], Rydberg atoms [16,[18][19][20][21][22][23], trapped ions [24][25][26] and cavity QED systems [27,28], recently also models with larger spins S>1/2 have become a research focus in particular for experiments with magnetic atoms [29][30][31][32][33][34]. The large spin degrees of freedom in S>1/2 systems poses a much more stringent requirement for numerical treatment compared to S=1/2 systems.…”

“…Our method thus allows us to study the TWA time-evolution not only of spin operators, but the full spin-density matrix and thus allows us to extract experimentally relevant time-dependent observables such as spin-state populations, and fundamentally relevant quantities such as entanglement. In the limit of S=1/2 our generalized discrete TWA approach (GDTWA), reduces to the previously proposed discrete TWA method (DTWA) [44], which has been remarkably successful in predicting S=1/2 model dynamics [16,[45][46][47][48][49].…”

Optical Control of the Resonant Dipole-Dipole Interaction between Rydberg Atoms

“…One can encode a spin-1/2 between the ground-state and a Rydberg level, use the van der Waals interactions between two identical Rydberg states and map the system onto an Ising-like Hamiltonian [21]. In this case, the spins can be manipulated globally by a resonant laser field and local addressing has been demonstrated using a far red-detuned focused laser beam shifting the ground-state energy of a particular atom in the ensemble [11].In addition to Ising Hamiltonian, the long-range XY Hamiltonian [22][23][24][25][26][27] can naturally be implemented with Rydberg atoms by using the dipolar spin-exchange interaction [28][29][30][31][32]. For principal quantum number n ∼ 60, the direct dipoledipole coupling U = C 3 /R 3 between two atoms in Rydberg levels with orbital angular momentum differing by ±1 ensures strong interaction energies in the 1 − 10 MHz range for atoms separated by ∼ 10 µm.…”

“…In addition to Ising Hamiltonian, the long-range XY Hamiltonian [22][23][24][25][26][27] can naturally be implemented with Rydberg atoms by using the dipolar spin-exchange interaction [28][29][30][31][32]. For principal quantum number n ∼ 60, the direct dipoledipole coupling U = C 3 /R 3 between two atoms in Rydberg levels with orbital angular momentum differing by ±1 ensures strong interaction energies in the 1 − 10 MHz range for atoms separated by ∼ 10 µm.…”