Future directions in non-ergodic dynamics in quantum systems

Robust edge zero modes guaranteeing ground-state degeneracy are common in a topological phase of matter. A more dramatic effect occurs in the Ising/Majorana/Kitaev chain: “strong” edge zero modes result in identical spectra in the entire even and odd fermion-number sectors, up to exponentially small finite-size corrections. A strong zero mode in a clean system is not a free-fermionic fluke. In the XYZ chain/coupled Majorana wires, its presence guarantees infinite coherence time for the edge spin, even with an infinite-temperature initial state. In non-integrable systems like the Ising chain with four-fermion interactions, an “almost” strong zero mode results in a very long coherence time, falling off very slowly with system size.

Professor Paul Fendley, Oxford University, UK

Professor Paul Fendley, Oxford University, UK

Paul Fendley is Senior Research Fellow at All Souls College and Professor at the Rudolf Peierls Centre for Theoretical Physics, University of Oxford. His research is on statistical mechanics, condensed matter, and mathematical physics, with a particular emphasis on integrable systems and other non-perturbative approaches. He is a Fellow of the American Physical Society and the Institute of Physics.

The long time dynamics of generic strongly interacting quantum systems presents a fundamental challenge for theory and computation. Matrix product states, useful for describing quantum ground states, are commonly thought to be inadequate for description of dynamics. The main obstruction is the linear growth of the entanglement entropy in time, which implies exponential growth of the required matrix sizes. In his talk Altman will discuss a new approach to overcome this obstruction and accurately describe the chaotic dynamics and emergent hydrodynamic behaviour at long times using matrix product states. The key idea is that local observables thermalize quickly when subject to generic evolution and consequently follow effective classical hydrodynamics. This suggests that the entanglement growth can be truncated after the local equilibration time without sacrificing information about local observables. Our scheme for implementing this truncation is based on the time dependent variational principle, which ensures that the approximate dynamics respects all conservation laws and can be systematically improved by increasing the bond dimension. Altman will present results for thus obtained transport coefficients and chaos characteristics in the Ising model subject to both transverse and longitudinal fields.

Professor Ehud Altman, University of California Berkeley, USA

Professor Ehud Altman, University of California Berkeley, USA

Professor Ehud Altman received his PhD from the Technion, Haifa in 2002. He was then a postdoctoral fellow at Harvard university for three years before joining the faculty of the Weizmann Institute of Science as a Yigal Alon fellow in 2005. He was promoted to the rank of Associate professor there in 2011. In 2010 he was awarded the young investigator prize from the Israel Physical Society and the Krill prize of the Wolf foundation. During the academic year 2012-2013 he was a Miller visiting professor at UC Berkeley. He joined the Physics department of UC Berkeley as a professor in the summer of 2016.

Atomic gases cooled to Nanokelvin temperatures are a new exciting tool to study a broad range of quantum phenomena. In particular, an outstanding and rapid control over the fundamental parameters, such as interaction strength, spin composition, and dimensionality allows to realize and observe many different situations far from equilibrium. Long-standing questions such as the coupling to an environment can be investigated. In her talk, Kollath will address the question of the influence of a coupling to an environment on the system dynamics in bosonic optical lattice gases. The interplay between the interaction, the kinetic energy and the coupling to the environment causes a critical dynamics with algebraic decaying observable or a glass-like dynamics. Also the propagation of correlations will be discussed.

Professor Corinna Kollath, University of Bonn, Germany

Professor Corinna Kollath, University of Bonn, Germany

Professor Corinna Kollath obtained her PhD in 2005 from RWTH Aachen. Between 2005 and 2007, Kollath completed a postdoc at the University of Geneva, working with Thierry Giamarchi. During the period 2005 to 2007, Corinna became a Junior Research Chair of the network ‘Triangle de la Physique’. In 2008 she was at Chargé de Recherche de 2eme class (CNRS) at CPHT, École Polytechnique. Between 2011 to 2013, Kollath became the Associate Professor at the University of Geneva, Switzerland. Since 2013, Corinna has been a Professor at the University of Bonn, Germany.

A novel feature of cold gases is the possibility to couple the motional dynamics of a quantum many body system to (one or more) quantized bosonic modes, describing the light fields in optical cavities. Such matter-light coupled systems show interesting forms of collective dynamics. They are subject to dissipation through fluctuations/damping of the cavity mode.  Cooper will present theoretical results that demonstrate examples of these novel collective dynamics, both in uniform and disordered settings, focusing on the question of whether or not the dissipative dynamics drive the system to a unique steady state.

Professor Nigel Cooper, University of Cambridge, UK

Professor Nigel Cooper, University of Cambridge, UK

Nigel Cooper is a condensed matter theorist, working on many-particle quantum systems. His work spans both the traditional solid-state setting of semiconductor materials and the field of ultra-cold atomic gases. He obtained a PhD from Oxford (1994), and held research positions at Harvard, Institut Laue-Langevin (Grenoble), Cambridge and Birmingham (as Royal Society University Research Fellow). He joined the Cavendish Laboratory in Cambridge in 2000, where he is now Professor of Theoretical Physics. He was awarded the 2007 Maxwell Medal and Prize by the Institute of Physics, a Humboldt Research Award (2013) and an EPSRC Established Career Fellowship (2013).

Recent experiments [1,2] indicate that selective optical driving of phonons may generate or enhance ordered phases in strongly correlated quantum materials. In his talk Jaksch will discuss quantum optically inspired models that may help explain and engineer such phenomena. Specifically, Jaksch will consider a driven fermionic Hubbard model in the strongly correlated limit where the onsite interaction dominates over the kinetic energy [3]. The driving is modelled as an alternating periodic modulation of the lattice site energy offsets. He will demonstrate how this modulation suppresses tunnelling and induces exchange interactions. The combination of these effects changes the nature of the system into an attractive Luttinger liquid and leads to enhanced fermion pairing in one spatial dimension. Jaksch will present results at zero and finite temperatures and discuss the prospect of observing driven out-of-equilibrium superconductivity in this model system.

1. D. Fausti, R.I. Tobey, N. Dean, S. Kaiser, A. Dienst, M.C. Hoffmann, S. Pyon, T. Takayama, H. Takagi, and A. Cavalleri, Light-Induced Superconductivity in a Stripe-Ordered Cuprate. Science 331, 189 (2011).
2. M. Mitrano, A. Cantaluppi, D. Nicoletti, S. Kaiser, A. Perucchi, S. Lupi, P. Di Pietro, D. Pontiroli, M. Ricco, S.R. Clark, D. Jaksch and A. Cavalleri, Possible light-induced superconductivity in K3C60 at high temperature. Nature 530, 461-464 (2016). 
3. J. Coulthard, S.R. Clark, S. Al-Assam, A. Cavalleri and D. Jaksch, Enhancement of super-exchange pairing in the periodically-driven Hubbard model, arXiv:1608.03964 (2016).

Professor Dieter Jaksch, University of Oxford, UK

Professor Dieter Jaksch, University of Oxford, UK

Dieter Jaksch is the Head of Atomic and Laser Physics at the University of Oxford. He has worked on strongly correlated quantum systems and their non-equilibrium dynamics since 1998 starting with a proposal for achieving a superfluid to Mott insulator transition in ultracold gases. It was followed by theoretical work that helped laying the foundations of the research field of strongly correlated ensembles of ultracold atoms in optical lattices and realisations of quantum simulators with neutral atoms. His current research interests include developing quantum algorithms for early generation quantum computers, eg, for solving non-linear partial differential equations and optimisation problems, and extending quantum optical techniques towards controlling quantum materials.

The statistical properties of the entanglement spectrum of a disordered many-particle system are studied, in order to identify the localized to extended transition as function of interaction strength and excitation energy expected from the many-body localization transition. In his talk, Berkovits shows that an indication of such a transition is indeed observed, and some of the features may be interpreted as a signature of non-ergodic behaviour.

Professor Richard Berkovits, Bar-Ilan University, Israel

Professor Richard Berkovits, Bar-Ilan University, Israel

Richard Berkovits is a Professor of Physics at Bar-Ilan University. His speciality is theoretical condensed matter Physics. Berkovits received his PhD in Physics from Bar-Ilan in 1989. He continued on as a post-doc in UCLA and MIT and then returned to Bar-Ilan in 1992 as a faculty member in the Department of Physics, which he chaired between 2008 and 2012. He spent a sabbatical year in Princeton University and NEC Labs.

The time-dependent microscopic control available in experiments with systems of ultracold atoms has opened new opportunities to explore many-body dynamics, addressing fundamental questions both in and out of equilibrium. This control can also be extended beyond the coherent dynamics of the system, as in typical experimental regimes the dominant mechanisms for dissipation can both be described microscopically from first principles, and can be controlled with external fields. Such control originates in the separation of timescales for coupling to a reservoir and for the relaxation of the reservoir, which is typical in quantum optics. This allows us to calculate and explore the effect of dissipation on the many-body dynamics, including on the ergodicity of dynamics after a parameter quench. We can also go further, especially in engineering dissipative processes that will drive the system into specific interacting many-body states. Daley will discuss his group’s recent work in this direction, especially looking at the microscopic description of dissipation for cold atoms in optical lattices in the presence of light scattering or with the addition of a second species that acts as a reservoir, and describe applications towards the generation of strongly correlated many-body states, and the investigation of out-of-equilibrium dynamics (including in systems exhibiting many-body-localisation).

Professor Andrew Daley, University of Strathclyde, UK

Professor Andrew Daley, University of Strathclyde, UK

Andrew Daley is Professor of Theoretical Quantum Optics in the Department of Physics at the University of Strathclyde in Glasgow, Scotland. Originally from Auckland, New Zealand, he completed his doctoral studies at the University of Innsbruck, Austria, in 2005, and was a senior scientist in Innsbruck and then an Assistant Professor at the University of Pittsburgh before moving to Scotland in 2013. His research centres on the interface between quantum optics and many-body physics, especially exploring new possibilities to study out-of-equilibrium dynamics with strongly interacting quantum gases of atoms and molecules in optical potentials. He is currently PI of an EPSRC Programme Grant on ‘Designing out of equilibrium many-body quantum systems’.