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arXiv:1703.05957 · Physical Review Letters

Relaxation of an Isolated Dipolar-Interacting Rydberg Quantum Spin System

Asier Piñeiro Orioli, Adrien Signoles, H. Wildhagen, G. Günter, Jürgen Berges, S. Whitlock, Matthias Weidemüller

Published Feb 5, 2018• 89 citations
arXivHTMLPDF

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.

DOI
10.1103/physrevlett.120.063601

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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 fundamental question in many-body physics is how closed quantum systems reach equilibrium.We address this question experimentally and theoretically in an ultracold large-spin Fermi gas where we find a complex interplay between internal and motional degrees of freedom.The fermions are initially prepared far from equilibrium with only a few spin states occupied.The subsequent dynamics leading to redistribution among all spin states is observed experimentally and simulated theoretically using a kinetic Boltzmann equation with full spin coherence.The latter is derived microscopically and provides good agreement with experimental data without any free parameters.We identify several collisional processes that occur on different time scales.By varying density and magnetic field, we control the relaxation dynamics and are able to continuously tune the character of a subset of spin states from an open to a closed system.
Understanding the dynamics of strongly interacting disordered quantum systems is one of the most challenging problems in modern science, due to features such as the breakdown of thermalization and the emergence of glassy phases of matter.We report on the observation of anomalous relaxation dynamics in an isolated XXZ quantum spin system realized by an ultracold gas of atoms initially prepared in a superposition of two different Rydberg states.The total magnetization is found to exhibit subexponential relaxation analogous to classical glassy dynamics, but in the quantum case this relaxation originates from the buildup of nonclassical correlations.In both experiment and semiclassical simulations, we find the evolution toward a randomized state is independent of the strength of disorder up to a critical value.This hints toward a unifying description of relaxation dynamics in disordered isolated quantum systems, analogous to the generalization of statistical mechanics to out-of-equilibrium scenarios in classical spin glasses.
A fundamental question in many-body physics is how closed quantum systems reach equilibrium. We address this question experimentally and theoretically in an ultracold large-spin Fermi gas where we find a complex interplay between internal and motional degrees of freedom. The fermions are initially prepared far from equilibrium with only a few spin states occupied. The subsequent dynamics leading to redistribution among all spin states is observed experimentally and simulated theoretically using a kinetic Boltzmann equation with full spin coherence. The latter is derived microscopically and provides good agreement with experimental data without any free parameters. We identify several collisional processes, which occur on different time scales. By varying density and magnetic field, we control the relaxation dynamics and are able to continuously tune the character of a subset of spin states from an open to a closed system.
I will discuss the spin dynamics of two magnetic atoms trapped in an external trap. Assuming that initially the atoms are in their orbital ground state I will discuss in details all possible elementary processes of spin flipping. Dipole-dipole interactions couple spin degrees of freedom of the two particles to their quantized orbital motion. Because of conservation of the total angular momentum if a magnetization of the system changes the system acquires an orbital angular momentum and atoms circulate around the center of the trap. I show that spin dynamics driven by dipolar interactions is possible only when the energies of the initial and the final sates are equal. In a case of weak magnetic moments of atoms this condition can be fulfilled utilizing a resonant external magnetic field, which tunes energies of involved states via the linear Zeeman effect. I will illustrate the resonant dynamics comparing the theoretical predictions to some results of experiments on Chromium atoms.
This thesis presents several experiments investigating the regimes of behaviour of a proto-typical open quantum many-body system far away from equilibrium. The experimental platform is based on ultracold atoms laser-excited to Rydberg states, which we engineer to emulate a strongly interacting, driven-dissipative quantum spin system. The high degree of control over the relevant microscopic processes and their parameters, as well as the ability to widely tune interaction and driving strengths provides the means to address fundamental questions on how different regimes of dynamical behaviour emerge in complex open quantum systems and how they can be characterised. \n \nIn the first part, we discuss how control over the relevant properties of Rydberg spin systems, like temperature, density, long evolution times, strong interactions, tunable driving, and dissipation can be achieved. We introduce the new experimental apparatus developed during this thesis, which combines both single-photon and two-photon Rydberg excitation schemes with high atom densities and long excitation times using an optical dipole trap. Additionally, we investigate theoretically how long coherence times exceeding motional timescales combined with strong many-body interactions can be achieved in such a system. We identify an optimal parameter regime for two-photon excitation where such conditions can be generated with coherence times and interaction strengths comparable to what is achievable for single-photon excitation. \n \nIn the second part we explore the macroscopic non-equilibrium behaviour of our system and devise suitable observables for characterising different regimes of behaviour. We discover that the slow atom loss inherent to our system provides a convenient observable for the many-body state of the system. Focussing on evolution times where the effect of the atom loss on the evolution is small, we discover that the rate of atom loss exhibits powerlaw scaling with the driving strength over several orders of magnitude. The measured scaling exponents reveal the non-equilibrium phase structure of the many-body system and allow us to distinguish dissipation-dominated, paramagnetic and critical regimes, as well as an instability. In the observed critical regime, collectively enhanced driving dominates over dissipation, leading to scaling associated to the critical point of the non-dissipative equilibrium Rydberg spin system. Based on the known microscopic processes of our system, we perform classical many-body rate equation simulations, which agree well with the observed phase structure as well as the position and associated scaling exponents of the individual regimes. These findings open up new means to study and classify out of equilibrium systems based on slow particle loss and powerlaw scaling. \n \nIn the last part of this thesis we reveal a second type of criticality in our system, which is genuinely non-equilibrium in character and arises from an absorbing state phase transition. The critical state of this phase transition dominates the system evolution at late times where particle loss is no longer negligible. We identify self-organisation as the mechanism driving the system to this critical state, which we observe through powerlaw scaling of the non-equilibrium steady-state. These experiments establish Rydberg atoms as a well controlled platform for implementing and exploring models of absorbing state phase transitions and self-organised criticality with unprecedented access to the underlying microscopic properties of the system.
In this thesis, we consider the forms of non-equilibrium phenomena that can arise in atoms or polar molecules trapped in a deep optical lattice and coupled by dipolar internal degrees of freedom. We specifically focus on only two internal states, which results in the systems studied behaving as spin−1/2-1/2−1/2 models with long-range interactions. We first study a closed system with both static and resonant near-field dipole interactions under an external drive. By studying the uniform mean-field dynamics of the system, we find the dynamics are given by Rabi oscillations, with a bifurcation in the dynamics as a function of drive strength between small scale and large scale oscillations. Analysing the stability of these oscillations to small fluctuations reveals that interactions tend to cause the oscillations to decohere. However, we find parameter regimes where coherent oscillations can persist for high enough intensity drive. We then consider the effects of an environment on the non-equilibrium dynamics of the near-field dipole model. We find that within the mean-field approximation, an environment causes the system to relax to many novel steady state spin configurations, such as spin density waves, antiferromagnetism and long-time oscillations, as well as bistabilities between these phases. To assess the validity of the mean-field approximation, we compare our mean-field results to small quantum systems. We carry out a similar analysis on a system with far-field dipole interactions, where it is necessary to introduce nonlocal dissipation, which results in several decay modes into the environment. These decay modes lead to instabilities of many of the steady state phases that occurred in the near-field dipole system, leading to the emergence of more spin density wave and oscillatory phases. Finally, we examine the dynamics on the approach to steady state in a dissipative dipolar system by studying Rydberg atoms coupled to a photonic crystal waveguide, which mediates an effective dipole-dipole interaction between the atoms. We find that if two excitations exist in the system, then bound states can form, with nonlocal dissipation resulting in a momentum dependent decay rate of the bound states and also greater freedom in engineering the bound state energy dispersion.