## Non-ergodicity in many body systems and disordered random graphs; application to the phase diagram Josephson junction chain

## Quantum Simulator of the factorization problem

Finally we advance the result that this quantum system can be experimentally implemented and show our proposal for the experimental setup.

## Multifractal metal in a disordered Josephson Junctions Array

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.

## Probing quantum correlations with multiple atomic impurities

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).

## Huygens principle and Dirac equation

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.

## Decoherence produced by a spin bath

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).

## Classical and semiclassical energy conditions

## Edge transport over sub-millimeter distance in the 2D Topological Insulator InAs/GaSb

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).

## Quantum Walks Gravity Simulation

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.

## Quantum optics in low dimensions: from fundamentals to applications

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

## Anomalies (in) matter

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.