Adiabatic perturbation theory and geometry of periodically-driven systems

We give a systematic review of the adiabatic theorem and the leading non-adiabatic corrections in periodically-driven (Floquet) systems. These corrections have a two-fold origin: (i) conventional ones originating from the gradually changing Floquet Hamiltonian and (ii) corrections originating from changing the micro-motion operator. These corrections conspire to give a Hall-type linear response for non-stroboscopic (time-averaged) observables allowing one to measure the Berry curvature and the Chern number related to the Floquet Hamiltonian, thus extending these concepts to periodically-driven many-body systems. The non-zero Floquet Chern number allows one to realize a Thouless energy pump, where one can adiabatically add energy to the system in discrete units of the driving frequency. We discuss the validity of Floquet Adiabatic Perturbation Theory (FAPT) using five different models covering linear and non-linear few and many-particle systems. We argue that in interacting systems, even in the stable high-frequency regimes, FAPT breaks down at ultra slow ramp rates due to avoided crossings of photon resonances, not captured by the inverse-frequency expansion, leading to a counter-intuitive stronger heating at slower ramp rates. Nevertheless, large windows in the ramp rate are shown to exist for which the physics of interacting driven systems is well captured by FAPT.The authors would like to thank M. Aidelsburger, M. Atala, E. Dalla Torre, N. Goldman, M. Heyl, D. Huse, G. Jotzu, C. Kennedy, M. Lohse, T. Mori, L. Pollet, M. Rudner, A. Russomanno, and C. Schweizer for fruitful discussions. This work was supported by AFOSR FA9550-16-1-0334, NSF DMR-1506340, ARO W911NF1410540, and the Hungarian research grant OTKA Nos. K101244, K105149. M. K. was supported by Laboratory Directed Research and Development (LDRD) funding from Berkeley Lab, provided by the Director, Office of Science, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. The authors are pleased to acknowledge that the computational work reported in this paper was performed on the Shared Computing Cluster which is administered by Boston University's Research Computing Services. The authors also acknowledge the Research Computing Services group for providing consulting support which has contributed to the results reported within this paper. The study of the driven non-integrable transverse-field Ising model was carried out using QuSpin [185] - an open-source state-of-the-art Python package for dynamics and exact diagonalization of quantum many body systems, available to download here. (FA9550-16-1-0334 - AFOSR; DMR-1506340 - NSF; W911NF1410540 - ARO; K101244 - Hungarian research grant OTKA; K105149 - Hungarian research grant OTKA; DE-AC02-05CH11231 - Laboratory Directed Research and Development (LDRD) funding from Berkeley Lab)https://arxiv.org/pdf/1606.02229.pd

Observation of Bose-Einstein Condensation in a Strong Synthetic Magnetic Field

Extensions of Berry's phase and the quantum Hall effect have led to the discovery of new states of matter with topological properties. Traditionally, this has been achieved using gauge fields created by magnetic fields or spin orbit interactions which couple only to charged particles. For neutral ultracold atoms, synthetic magnetic fields have been created which are strong enough to realize the Harper-Hofstadter model. Despite many proposals and major experimental efforts, so far it has not been possible to prepare the ground state of this system. Here we report the observation of Bose-Einstein condensation for the Harper-Hofstadter Hamiltonian with one-half flux quantum per lattice unit cell. The diffraction pattern of the superfluid state directly shows the momentum distribution on the wavefuction, which is gauge-dependent. It reveals both the reduced symmetry of the vector potential and the twofold degeneracy of the ground state. We explore an adiabatic many-body state preparation protocol via the Mott insulating phase and observe the superfluid ground state in a three-dimensional lattice with strong interactions.Comment: 6 pages, 5 figures. Supplement: 6 pages, 4 figure

Entanglement entropy in a periodically driven Ising chain

In this work we study the entanglement entropy of a uniform quantum Ising chain in transverse field undergoing a periodic driving of period \u3c4. By means of Floquet theory we show that, for any subchain, the entanglement entropy tends asymptotically to a value \u3c4-periodic in time. We provide a semi-analytical formula for the leading term of this asymptotic regime: It is constant in time and obeys a volume law. The entropy in the asymptotic regime is always smaller than the thermal one: because of integrability the system locally relaxes to a generalized Gibbs ensemble (GGE) density matrix. The leading term of the asymptotic entanglement entropy is completely determined by this GGE density matrix. Remarkably, the asymptotic entropy shows marked features in correspondence to some non-equilibrium quantum phase transitions undergone by a Floquet state analog of the ground state

Learning Control of Quantum Systems

This paper provides a brief introduction to learning control of quantum systems. In particular, the following aspects are outlined, including gradient-based learning for optimal control of quantum systems, evolutionary computation for learning control of quantum systems, learning-based quantum robust control, and reinforcement learning for quantum control.Comment: 9 page

Determinants of social participation of visually impaired older adults

PURPOSE: To assess determinants of social participation among visually impaired older adults. METHODS: This cross-sectional study included visually impaired persons (>/=55 years; n = 173) who were referred to a low-vision rehabilitation center. Determinants (i.e., sociodemographic, physical, social and psychological factors, and personal values) of participation were identified in four domains of participation: (1) domestic life; (2) interpersonal interactions and relationships; (3) major life areas; and (4) community, social, and civic life. Study participants completed telephone interviews. RESULTS: Age, physical fitness, and helplessness were determinants of participation in domestic life. Social network size was associated with participation in major life areas. The personal value attached to participation (i.e., perceived importance) was a determinant of participation in interpersonal interactions and relationships, major life areas, and community, social and civic life. Vision-related characteristics (i.e., self-perceived vision and degree of visual impairment) were not associated with participation. CONCLUSIONS: Across the participation domains, perceived importance is a major determinant of social participation among visually impaired older adults. Physical health along with social and psychological status, also affect participation. Knowing how participation is determined can be used to develop rehabilitation interventions to enhance participation of visually impaired older adults