Weekly speakers and their seminar titles and abstracts:

Week 12:

Jutho Haegeman
Continuous matrix product states and the Quantum Gross-Pitaevskii Equation (KITP Seminar, Tues, Nov 29, 10am)

I will introduce the continuum limit of matrix product states (MPS) for the description of quantum many body systems in the continuum such as e.g. cold atomic gasses. By projecting the Schrodinger equation onto this nonlinear manifold of continuous MPS, we obtain a matrix-valued generalization of the famous Gross-Pitaevskii (GP) equation, where the non-commutative auxiliary degrees of freedom can model the entanglement in the system. This framework can systematically improve upon the mean field predictions provided by the GP equation, which breaks down for strongly interacting quasi one-dimensional systems. Finally, by linearizing around an equilibrium solution, we also obtain a non-commutative analogue of the Bogoliubov-de Gennes equations, which can be used to study linear response or to probe the excitation spectrum of the theory.


Week 6:

Jeremy Levy (University of Pittsburgh)
Synthesizing Quantum Matter Using Complex Oxides (KITP Seminar, Wed, Oct 19, 3.30pm)

The “toolbox” of an ideal quantum emulator includes the ability to control lattice structure, particle statistics, and interactions, at sufficiently low temperatures, in a physical system whose fundamental physical description is well understood. To create synthetic quantum matter in a laboratory, one must identify a physical platform with quantum degrees of freedom that are easily manipulated and probed. In addition to well-known platforms based on ultracold atoms and ion traps, we introduce an approach to creating synthetic quantum matter based on reconfigurable nanostructures formed at the interface between two normally insulating oxides, LaAlO3 and SrTiO3. The potential landscape at this interface can be controlled with high precision (~ 2 nm), smaller than the average electron separation. Electron-electron interactions can be tuned between attractive (at low density) to repulsive (at high density) regimes. The attractive regime leads to electron pairing and superconductivity, while the latter leads to fermionic behavior with repulsive interactions. Many elements of the “quantum transport” toolbox have already been demonstrated, including superconducting single-electron transistors, Fabry-Perot interference and ballistic (quantized) transport of electrons and Cooper pairs in dissipationless electron waveguides. The challenges and promise of this approach will be described within the context of a parallel quest to understand the underlying mechanism of electron pairing in SrTiO3.




Week 5:

Ian Spielman (NIST)
(KITP Seminar, Tues, Oct 11, 10am)

Because global topological properties are robust against local perturbations, understanding and manipulating the topological properties of physical systems is essential in advancing quantum science and technology. For example, topologically protected quantum control gives robust high-fidelity gate operations and the bulk topology of quantum Hall system leads to the quantization of the Hall conductivity. Topological order is quantified in terms of singularities called topological defects that reside in an extended parameter space. Here we engineered such a singularity argued in non- Abelian gauge theories - a Yang monopole - using atomic Bose-Einstein condensates in a parameter space. We quantified its field by measuring the Chern numbers on enclosing manifolds. While the 1st Chern number vanished, the 2nd Chern number didn’t. By displacing the manifold, we observed a transition from “topological” to “trivial” as the monopole left the manifold. Our work illustrates the synthesis of a noble topological defect in a quantum system.

Curt von Keyserlingk (Princeton University)
The pi spin-glass/time crystal phase (KITP Seminar, Wed, Oct 12, 10am)

Recent work shows that there is a sharp notion of ‘phase of matter’ in periodically driven many-body localised systems. In this talk I give a pedagogical review of perhaps the simplest such driven phase of matter, known as the pi spin-glass/ time crystal. A key feature of this phase is that in the thermodynamic limit, for fairly generic initial states, generic local observable show persistent oscillations at late times commensurate with the driving period.

Adolfo Grushin (UC Berkeley)
Signatures of inhomogenous Weyl semi-metals (KITP Seminar, Thurs, Oct 13, 10am)



Week 4:

Oskar Painter (Caltech)
Integrated optomechanical and superconducting quantum circuits (KITP Seminar, Tues, Oct 4, 10am)

I will present recent work at Caltech on the integration of optomechanical crystals for light and sound with electronic superconducting quantum circuits. Utilizing the silicon-on-insulator (SOI) wafer platform, we have made key advances in the fabrication and integration of extremely low loss microwave phonon structures and low loss microwave superconducting resonators of high impedance. These technical advancements offer several intriguing opportunities for quantum information processing and networking with phonons, photons and electrons in an integrated, wafer-scale platform. Discussion of several concepts along these lines being pursued at Caltech will be presented.

Mark Fischer (Weizmann)
Dynamics of a Many-Body-Localized system coupled to a Markovian bath (KITP Seminar, Tues, Oct 5, 10am)



Week 3:

Arijeet Pal (Oxford)
Aspects of dynamical nuclear polarization in GaAs double quantum dots (KITP Seminar, Tues, Sept 27, 10am)

Experiments have achieved a remarkable degree of quantum control of states of a few electrons confined in gate-defined quantum dots. The spin degree of freedom of the trapped electrons are promising building blocks for quantum information processing. In these experiments the environment of nuclear spins plays an important role in manipulating the electronic states. I will present the experimental progress and the associated theoretical description, in understanding the interplay of dynamical nuclear polarization and spin-orbit interaction in GaAs double quantum dots.

Mohammed Hafezi (U. Maryland)
Driven quantum Hall models in photonic systems (KITP Seminar, Wed, Sept 28, 10am)

Following the measurement of topological invariants in silicon ring resonator systems [1], I discuss the progress on investigation of quantum transport of light in the presence of synthetic gauge fields, with and without strong interaction. First, in the absence of interaction, we analyze the transport properties of two-photon wavefunctions in a disordered structure with protected topological edge bands, and examine the robustness of quantum transport properties [2]. Moreover, I discuss a design for photonic crystals with topological properties [3]. Such structures can be integrated with nonlinear quantum emitters such as color centers to mediate strong interaction. In the second part, I discuss the strongly interacting driven-dissipative regime of photons, where surprises can be seen even in a driven-dissipative 1D Bose-Hubbard model [4]. More specifically, I will talk about the possibility of realization of topologically ordered states, such as Laughlin states, in photonic systems in the driven-dissipative regime. Finally, the effect of interacting disorder in these systems and the stability of these states will be examined [5].

[1] http://lanl.arxiv.org/abs/1504.00369
[2] http://lanl.arxiv.org/abs/1605.04894
[3] http://lanl.arxiv.org/abs/1605.08822
[4] http://lanl.arxiv.org/abs/1601.06857
[5] Wade DeGottardi, M.H. in prep.

Christiane P. Koch (University of Kassel)
Controlling open quantum systems: Tools, achievements, limitations (KITP Seminar, Thurs, Sept 29, 10am)

Quantum control is an important prerequisite for quantum devices. A major obstacle is the fact that a quantum system can never completely be isolated from its environment. The interaction with the environment causes decoherence. Optimal control theory is a tool that can be used to identify control strategies in the presence of decoherence. I will show how to adapt optimal control theory to quantum information tasks for open quantum systems and present examples for cold atoms and superconducting qubits. In particular, I will discuss how non-Markovianity of the open system time evolution can be exploited for control.

The perspective on decoherence only as the adversary of quantum control is nevertheless too narrow. There exist a number of control tasks, such as cooling and measurement, that can only be achieved by an interplay of control and dissipation. I will show how to utilize optimal control theory to derive efficient cooling strategies when the timescales of coherent dynamics and dissipation are very different. Our approach can be generalized to quantum reservoir engineering, opening up new avenues for control.



Week 2:

Jens Eisert (Freie Universität Berlin)
Synthetic quantum systems out of equilibrium (and the quest for quantum supremacy for quantum simulators)

Synthetic or designer quantum systems - constituted notably by cold atoms in optical lattices - allow to probe a plethora of physical phenomena related to the physics of quantum systems out of equilibrium. In this talk, we will consider questions of equilibration, Gaussification, the dynamics of quantum phase transitions and the absence of thermalisation - present in disordered interacting models that show features of the multi-faceted phenomenon of many-body localisation.

We discuss both new theoretical results, as well as tools used in collaborations with experimentalists working with cold atoms in optical lattices and on atom chips. In the last part of the talk, we will have a brief look at work in progress on conceptual questions that seem to be key to the idea of a quantum simulator: This in on the one hand one of how to devise quantum simulators that have the potential of computationally outperforming classical devices, discussing variants of IQP circuits. On the other hand, it the question of the certification of quantum simulators for which no classical simulation algorithm is known.


Sid Parameswaran (UC Irvine)
Quantum Critical Entanglement in Highly Excited States

I will discuss infinite-temperature properties of an infinite sequence of random quantum spin chains using a real-space renormalization group approach, and demonstrate that they exhibit non-ergodic behavior at strong disorder. The analysis is conveniently implemented in terms of SU(2)k anyon chains, including the random transverse-field Ising model as a special case. Highly excited eigenstates of these systems exhibit properties usually associated with quantum critical ground states. The excited-state fixed points are generically distinct from their ground state counterparts, and represent non-equilibrium critical phases of matter. I will briefly discuss related work on studying the interplay of symmetry-protected order and localization in one dimensional chains with "particle-hole symmetry".

Refs: Vasseur, Potter, SP, Phys. Rev. Lett. 114, 217201 (2015); Vasseur, Friedman, SP, Potter, Phys. Rev. B 93, 134207 (2016)

Brayden Ware (UCSB)
Discussion of "Majorana-dimer" models and fermionic topological phases

We consider a class of 'intrinsically fermionic' topological phases (and related SPT phases) that have deconfined Ising anyons but not chiral edge modes. We show that there is a model wavefunction for this phase inspired by the RVB dimer wavefunction and a corresponding exactly solvable Hamiltonian. We will discuss the extraction of topological quantities from this wavefunction and the role of (a lattice version of) spin structures in defining these fermionic topological phases.

Romain Vasseur (UC Berkeley)
Symmetry constraints far from equilibrium

In this talk, I will describe some general constraints on the existence of many-body localized (MBL) phases in the presence of global symmetries. Based only on representation theory, I will derive some general Mermin-Wagner-type principles governing the possible fates of non-equilibrium dynamics in isolated, disordered quantum systems. In particular, I will show that MBL cannot exist in the presence of non-Abelian symmetries. Consequences for the classification of MBL protected topological phases (and Floquet phases) will be discussed.




Week 1:

Hans-Peter Buechler, Stuttgart
Topological states in a microscopic model of interacting fermions

We present a microscopic model of interacting fermions where the ground state degeneracy is topologically protected. The model is based on a double-wire setup with local interactions in a particle number conserving setting. A compelling property of this model is the exact solvability for its ground states and low energy excitations. We demonstrate the appearance of topologically protected edge states and derive their braiding properties on a microscopic level. We find the non-abelian statistics of Ising anyons, which can be interpreted as Majorana-like edge states.


Maissam Barkeshli, Station Q and University of Maryland
Creating and manipulating topologically protected degeneracies through gapped boundaries in quantum many-body states

Abstract: A profound consequence of certain classes of topological quantum states of matter is the possibility of topologically protected degeneracies in the ground state spectrum of the system. No local operators can distinguish topologically degenerate states, allowing them to be particularly robust to decoherence. In this talk, I will discuss some new directions in the pursuit of creating, measuring, and manipulating topological degeneracies, which utilize the physics of gapped boundaries. Some specific results I will discuss include (1) a proposal for creating and reading out topological states without localized zero modes in bilayer Laughlin fractional quantum Hall states; and (2) ideas for how to implement topologically robust unitary transformations when the topological degeneracy is due to disconnected gapped boundaries and there are no localized zero modes.


Paul Fendley, Oxford
Strong zero modes: what they are and what they're good for

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.


Monika Schleier-Smith, Stanford
Scrambling or Preserving Quantum Information with Cold Atoms and Light

When a qubit falls into a black hole, the information is rapidly “scrambled,” i.e., entangled with the black hole’s many internal degrees of freedom. Scrambling is a manifestation of many-body quantum chaos, suggesting that strongly interacting quantum systems realizable in table-top experiments might offer insight into the dynamics of quantum information in black holes. I will describe a general experimental protocol for measuring scrambling, applicable to quantum simulations of a variety of spin models that can be engineered with neutral atoms in optical cavities, Rydberg-dressed atoms, or trapped ions. Common to all these systems is a means of “reversing time” by switching the sign of a many-body Hamiltonian. This key ingredient of our protocol is enabled by optically controlled spin-spin interactions. I will explain how such interactions are realized in cold-atom experiments and touch on broader prospects for harnessing them to access new many-body phenomena, including Floquet symmetry-protected topological phases of Rydberg-dressed atoms.