Seminars from 2017

At very high disorder a generic closed quantum system becomes completely localized. I argue that this (many body) localization is preempted by a wide regime of non-ergodic behavior that displays a number of unusual properties. A good system to study these effects are Josephson junction arrays in a somewhat unusual regime. In the main part of the talk I will discuss the localization of single particles on random regular graphs that provide a toy model capturing the main physics of the many body localization. I will develop a simplified analytical theory of the non-ergodic phase in this models that extends the approach developed in the work of Abou Chakra, Thouless and Anderson and compare the results with the direct numerical simulations.

We revisit the analytic number theory of factoring numbers N=xy, product of two primes, in order to build a new approach suitable for statistical analysis. This is readily translated to the physics of a system in two dimensions with bound trajectories. After semiclassical quantization we get that the statistics of the energies for these trajectories lead to the statistics of the primes pi (x) < pi ( sqrt N). The result is fully equivalent to obtaining the prime factors of N from the quantum theory of this simulator in a way entirely alternative to Shor’s algorithm.
Finally we advance the result that this quantum system can be experimentally implemented and show our proposal for the experimental setup.

We show that quantum chaotic dynamic may not result in thermalization in certain bosonic models that can be realized as an array of Josephson junctions. This model exhibits a many-body localization transition which separates insulating and metallic phases. Localization prevents the system to thermalize in the insulating phase. We show that there is a intermediate
region in the phase diagram, between Many-Body localized and ergodic phases, in which the system behaves as a metal but it is not described by the laws of Statistical Mechanics.

Experimental advances in the control and measurement of quantum systems are driving the development of quantum technologies across multiple experimental platforms, from trapped ions and cold atoms, to superconducting circuits and nanomechanical setups [1]. Among the most promising practical applications of these devices lies quantum-enhanced sensing, where individual or quantum-correlated particles are used to accurately measure observables, from magnetic fields to gravity. Extending this paradigm, recent work has highlighted the potential of single quantum systems to probe strongly-correlated quantum systems [2].
In this talk, I will present a quantum protocol that uses multiple atomic impurities to measure N-point correlations in strongly-correlated quantum systems [3], and discuss ongoing experimental efforts at Oxford to implement it with a two-species cold-atom setup [4].
[1] G. Kurizki et al., PNAS 110, 3866-3873 (2014); K. Bongs et al., Proc. SPIE 9900, 990009 (2016).
[2] See, e.g., D. Hangleiter et al., Phys. Rev. A 91, 013611 (2015); T.H. Johnson et al., Phys. Rev. A 93, 053619 (2016).
[3] M. Streif, A. Buchleitner, D. Jaksch & J. Mur-Petit, Phys. Rev. A 94, 053634 (2016).
[4] E. Bentine et al., J. Phys. B 50 094002 (2017).

Every point on the wave front of a propagating wave is a source of secondary wavelets, which spread forward at the same speed as the source wave. The wave front at later times is then given by the surface tangent to the secondary wavelets. This principle was proposed by Christiaan Huygens in 1678, to explain the laws of reflection and refraction. It was used again more than a century later, in 1816, by Augustin-Jean Fresnel, to intepret the diffraction effects that occur when visible light encounters slits, edges and screens.

The principle provides crucial insight into the nature of wave propagation and it is a milestone in the physics of ondulatory phenomena. For this reason, its universal validity is usually taken for granted. However, yet one century later, Jacques Hadamard noticed that Huygens’ principle is valid only when waves propagate in an odd number n>1 of spatial dimensions.

Both quantum mechanics and quantum field theory make use of wave equations in their formulation. It is therefore interesting to ask whether Huygens’ principle holds for the seminal equations that are the backbone of these theories. The Schrodinger equation, being non-relativistic, does not admit a satisfactory formulation of this question. What about the Dirac equation?

We discuss the validity of Huygens’ principle for the massless Dirac-Weyl equation. We find that the principle holds for odd space dimension n, while it is invalid for even n. We explicitly discuss the cases n=1,2 and 3.

Any quantum system is never isolated and represents an open system. As result, the environment that surrounds the system introduces decoherence spoiling its quantum properties. Employing an alternative formalism to study open quantum systems, the Stochastic Surrogate Hamiltonian, we analyze dissipation and dephasing processes produced by a spin bath. For dissipation, we show that the Stochastic Surrogate Hamiltonian enables the simulation of thermalization beyond the weak and Markovian regimes. For dephasing, the relation with temperature is studied, showing that the effect depends on the dephasing mechanism itself.
Refs:
[1] E. Torrontegui and R. Kosloff, New J. Phys. 18, 093001 (2016).
[2] R. Baer and R. Kosloff, J. Chem. Phys. 106, 21 (1997).
[3] G. Katz, M. A. Ratner, and R. Kosloff, J. Phys. Chem. C 118, 21798 (2014).

The standard energy conditions usually associated to general relativity are (mostly) linear in the stress-energy tensor, and have clear physical interpretations in terms of geodesic focussing, but suffer the significant drawback that they are often violated by semi-classical quantum effects. In contrast, it is possible to develop non-standard energy conditions that are intrinsically non-linear in the stress-energy tensor, and which exhibit much better well-controlled behaviour when semi-classical quantum effects are introduced, at the cost of a less direct applicability to geodesic focussing. In this talk I will review the standard energy conditions and their various limitations. Then, I will briefly introduce the averaged energy conditions, and present in detail the nonlinear and the semi-classical energy conditions.

The InAs/GaSb double quantum well (DQW), a tunable two dimensional (2D) electron-hole system, was recently proposed as a 2D topological insulator (TI) [1]. While convincing evidence for transport by edge states in micrometer-sized devices has been reported in several experiments [2, 3, 4], the topological origin of these transport properties is still under debate [5]. In the present work we test the transport by edge states in several DQW’s with diferrent sizes InAs/GaSb to cover from normal insulator (NI) and TI samples up to unprecedented length scales and high magnetic fields. First of all, we address the low-temperature electrical transport in a local measurement configuration (Fig.1 (a)), both in zero-field and in the integer quantum Hall regime (Fig.1 (c)), with the latter indicating the realization of a non-trivial system [6]. Successively, making use of non-local transport measurements (Fig.1 (b), (d)), we consistently find evidence for transport by edge states over sub-millimeter distances, as tested using the methodology of Refs.[2, 3] and applying a resistor network model analogous to the one of Ref.[4]. Under high magnetic fields (up to B = 30 T), we detect persistent transport by edge states, with a clear suppression of backscattering in the case of perpendicular orientation. We analyse the response of the edge states to systematic inversions of the current contacts and/or of the polarity of the magnetic field. Many-body interactions can produce exotic novel ground states in these systems. An interacting electron and hole can spontaneously form excitons, i.e. a neutral bound state, provided that the exciton binding energy exceeds the energy separation between the single particle states.

References
[1] C.X. Liu, T.L Hughes, X.L. Qi, K. Wang and S.C Zhang, Phys. Rev. Lett. 100, 236601 (2008).
[2] K. Suzuki, Y. Harada, K. Onomitsu, and K. Muraki, Phys. Rev. B 87, 235311 (2013).
[3] K. Suzuki, Y. Harada, K. Onomitsu, and K. Muraki, Phys. Rev. B 91, 245309 (2015).
[4] S. Mueller et al:, Phys. Rev. B 92, 081303(R) (2015).
[5] F. Nichele et al:, arXiv:1511.01728.
[6] B. Büttner et al:, Nature Phys. 7, 418 (2011).

As we know, spacetime is not flat at the cosmological scale. In order to describe spacetime, in General Relativity theory (GR), we need a continuous and differentiable manifold and a formal way to account for the continuous distortion of the metrics. The main point is that changing coordinate systems should not affect physics laws (General Covariance). However at the Planck length, matter is not continuous and obeys Quantum Theory (QT). Although one century has passed, finding an intrinsically discrete counterpart of GR is still an open question. In fact, discretized GR does not turn out in just a mere finite difference scheme of the old formula.
I recently showed that one way to describe a discrete curved spacetime is by using Quantum Walks. From a physical perspective a QW describes situations where a quantum particle is taking steps on a discrete grid conditioned on its internal state (say, spin states). The particle dynamically explores a large Hilbert space associated with the positions of the lattice and allows thus to simulate a wide range of transport phenomena.
It is surprising that this unitary and local dynamics, defined on a rigid space-time lattice coincides in the continuous limit with the dynamical behavior of a quantum spinning-particle spreading on a curved spacetime. This could really turn out to be a powerful quantum numerical method to discretize GR.

Recent experimental developments in nanophotonics [1], circuit QED [2] and cold atoms [3] allow to engineer systems where quantum emitters couple to low dimensional photon-like reservoirs with non-trivial energy dispersion. Compared to three-dimensional and structureless baths, the interactions induced by such structured environments can be strongly enhanced and have long-range character.

In this talk, I will show several phenomena that can emerge in these scenarios such as the existence of multi-photon bound states around single quantum emitters [4], the generation of tuneable long-range coherent interactions [5], or how one can boost the fidelities and efficiencies of non-classical states of light [6].

[1] Nature 508, 241–244 (2014), Nature Communications 5, 3808 (2014), Rev. Mod. Phys. 87, 347 (2015)
[2] Nature Physics 13 (1), 48-52 (2017)
[3] Nature Physics 8, 267–276 (2012),Physical Rev Lett. 101 (26), 260404 (2010)
[4] Physical Review X 6 (2), 021027 (2016)
[5] Nature Photonics 9 (5), 320-325 (2015), PNAS, 201603777 (2016)
[6] Physical Review Letters 115 (16), 163603 (2015), New Journal of Physics 18 (4), 043041 (2016) arXiv:1603.01243

The concept of symmetry is one cornerstone of modern theoretical physics,
quantum mechanics is another. Sometimes they are incompatible with each other.
These incompatibilities are called anomalies.
They constrain possible fermion spectra of gauge theories and explain otherwise
forbidden processes such as the decay of the neutral pion into two photons.
In the recent years however anomalies play an ever bigger role in a totally different
realm of physics: condensed matter. In particular anomalies induce exotic new
transport phenomena such as the chiral magnetic and the chiral vortical effects.
I will review of chiral anomalies, anomaly induced transport phenomena and
discuss some of its applications in a new exciting class of materials: the Weyl semimetals.

Statistical learning theory is rich in results that changed the way we process and think about data. Furthermore, the theory offered a fresh perspective on artificial intelligence. Applications are countless and much progress has been made in applying learning schemes in quantum control problems. Quantum information processing and quantum computing are the next frontier for machine learning, but benefits work both ways: quantum-enhanced learning is also a promising research direction, but we must generalize known classical results to the quantum case to fully understand the limits and possibilities. This talk gives an introduction to the core concepts in learning theory, and then looks at the major challenges in the intersection of machine learning, artificial intelligence, and quantum information processing.