89 research outputs found
Quantum transport in ultracold atoms
Ultracold atoms confined by engineered magnetic or optical potentials are
ideal systems for studying phenomena otherwise difficult to realize or probe in
the solid state because their atomic interaction strength, number of species,
density, and geometry can be independently controlled. This review focuses on
quantum transport phenomena in atomic gases that mirror and oftentimes either
better elucidate or show fundamental differences with those observed in
mesoscopic and nanoscopic systems. We discuss significant progress in
performing transport experiments in atomic gases, contrast similarities and
differences between transport in cold atoms and in condensed matter systems,
and survey inspiring theoretical predictions that are difficult to verify in
conventional setups. These results further demonstrate the versatility offered
by atomic systems in the study of nonequilibrium phenomena and their promise
for novel applications.Comment: 24 pages, 7 figures. A revie
Experimental Measurement of the Berry Curvature from Anomalous Transport
Geometrical properties of energy bands underlie fascinating phenomena in a
wide-range of systems, including solid-state materials, ultracold gases and
photonics. Most famously, local geometrical characteristics like the Berry
curvature can be related to global topological invariants such as those
classifying quantum Hall states or topological insulators. Regardless of the
band topology, however, any non-zero Berry curvature can have important
consequences, such as in the semi-classical evolution of a wave packet. Here,
we experimentally demonstrate for the first time that wave packet dynamics can
be used to directly map out the Berry curvature. To this end, we use optical
pulses in two coupled fibre loops to study the discrete time-evolution of a
wave packet in a 1D geometrical "charge" pump, where the Berry curvature leads
to an anomalous displacement of the wave packet under pumping. This is both the
first direct observation of Berry curvature effects in an optical system, and,
more generally, the proof-of-principle demonstration that semi-classical
dynamics can serve as a high-resolution tool for mapping out geometrical
properties
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
Abelian gauge potentials on cubic lattices
The study of the properties of quantum particles in a periodic potential
subject to a magnetic field is an active area of research both in physics and
mathematics; it has been and it is still deeply investigated. In this review we
discuss how to implement and describe tunable Abelian magnetic fields in a
system of ultracold atoms in optical lattices. After discussing two of the main
experimental schemes for the physical realization of synthetic gauge potentials
in ultracold set-ups, we study cubic lattice tight-binding models with
commensurate flux. We finally examine applications of gauge potentials in
one-dimensional rings.Comment: To appear on: "Advances in Quantum Mechanics: Contemporary Trends and
Open Problems", G. Dell'Antonio and A. Michelangeli eds., Springer-INdAM
series 201
Magnetic crystals and helical liquids in alkaline-earth fermionic gases
The joint action of a synthetic gauge potential and of atomic contact repulsion in a one-dimensional alkaline-earth(-like) fermionic gas with nuclear spin I leads to the existence of a hierarchy of fractional insulating and conducting states with intriguing properties. We unveil the existence and the features of those phases by means of both analytical bosonization techniques and numerical methods based on the density-matrix renormalization group algorithm. In particular, we show that the gapless phases can support helical modes, whereas the gapped states, which appear under certain conditions, are characterised both by density and magnetic order. Several distinct features emerge solely for spin I larger than 1/2, thus making their study with cold-atoms unique. We will finally argue that these states are related to the properties of an unconventional fractional quantum Hall effect in the thin-torus limit. The properties of this hierarchy of states can be experimentally studied in state-of-the-art cold-atom laboratories
Periodically driving a many-body localized quantum system
We experimentally study a periodically driven many-body localized system
realized by interacting fermions in a one-dimensional quasi-disordered optical
lattice. By preparing the system in a far-from-equilibrium state and monitoring
the remains of an imprinted density pattern, we identify a localized phase at
high drive frequencies and an ergodic phase at low ones. These two distinct
phases are separated by a dynamical phase transition which depends on both the
drive frequency and the drive strength. Our observations are quantitatively
supported by numerical simulations and are directly connected to the change in
the statistical properties of the effective Floquet Hamiltonian.We acknowledge support from Technical University of Munich - Institute for Advanced Study, funded by the German Excellence Initiative and the European Union FP7 under grant agreement 291763, from the DFG grant no. KN 1254/1-1, the European Commission (UQUAM, AQuS) and the Nanosystems Initiative Munich (NIM)
Exciton-polariton topological insulator
The authors thank R. Thomale for fruitful discussions. S.K. acknowledges the European Commission for the H2020 Marie SkĆodowska-Curie Actions (MSCA) fellowship (Topopolis). S.K., S.H. and M.S. are grateful for financial support by the JMU-Technion seed money program. S.H. also acknowledges support by the EPSRC âHybrid Polaritonicsâ Grant (EP/M025330/1). The WĂŒrzburg group acknowledges support by the ImPACT Program, Japan Science and Technology Agency and the State of Bavaria. T.C.H.L. and R. G. were supported by the Ministry of Education (Singapore) Grant No. 2017-T2-1-001Topological insulatorsâmaterials that are insulating in the bulk but allow electrons to flow on their surfaceâare striking examples of materials in which topological invariants are manifested in robustness against perturbations such as defects and disorder1. Their most prominent feature is the emergence of edge states at the boundary between areas with different topological properties. The observable physical effect is unidirectional robust transport of these edge states. Topological insulators were originally observed in the integer quantum Hall effect2 (in which conductance is quantized in a strong magnetic field) and subsequently suggested3,4,5 and observed6 to exist without a magnetic field, by virtue of other effects such as strong spinâorbit interaction. These were systems of correlated electrons. During the past decade, the concepts of topological physics have been introduced into other fields, including microwaves7,8, photonic systems9,10, cold atoms11,12, acoustics13,14 and even mechanics15. Recently, topological insulators were suggested to be possible in exciton-polariton systems16,17,18 organized as honeycomb (graphene-like) lattices, under the influence of a magnetic field. Exciton-polaritons are part-light, part-matter quasiparticles that emerge from strong coupling of quantum-well excitons and cavity photons19. Accordingly, the predicted topological effects differ from all those demonstrated thus far. Here we demonstrate experimentally an exciton-polariton topological insulator. Our lattice of coupled semiconductor microcavities is excited non-resonantly by a laser, and an applied magnetic field leads to the unidirectional flow of a polariton wavepacket around the edge of the array. This chiral edge mode is populated by a polariton condensation mechanism. We use scanning imaging techniques in real space and Fourier space to measure photoluminescence and thus visualize the mode as it propagates. We demonstrate that the topological edge mode goes around defects, and that its propagation direction can be reversed by inverting the applied magnetic field. Our exciton-polariton topological insulator paves the way for topological phenomena that involve lightâmatter interaction, amplification and the interaction of exciton-polaritons as a nonlinear many-body system.PostprintPeer reviewe
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