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Quantum simulations of insulators and conductors

Periodic Reporting for period 3 - QUIC (Quantum simulations of insulators and conductors)

Reporting period: 2018-03-01 to 2019-02-28

Electrical conductors and insulators are at the basis of our current society, as they carry and store both energy and information. The conducting or insulating nature of materials is based on various separate ingredients of quantum nature, e.g. interactions, dimensionality, topology, disorder, etc. However, the complex interplay of such ingredients is in many cases still beyond our understanding. Notable examples are strongly-correlated superconductors and interacting topological materials. The reasons are that experiments on real materials aiming at separating the various ingredients are very difficult, and even that numerical simulations are inefficient, even for supercomputers.

With QUIC we aimed at a breakthrough in the understanding of the fundamental quantum mechanisms governing insulators and conductors by using quantum simulators, i.e. quantum computers of special purpose, based on fully controllable ultracold atomic gases. In an experiment-theory enterprise, we have engineered several different kinds of such synthetic quantum insulators and conductors, in which the various quantum ingredients are well known and can be controlled separately. Although in such neutral atomic systems the it is the mass and not the charge to be transported, they are governed by the same quantum laws of electrical conductors.

The immediate goal of QUIC has been the quantitative understanding of the subtle interplay of quantum phenomena. In some cases, we have proceeded towards the solution of long-standing open questions, such as the famous problem of Anderson localization or the existence of a paradoxical supersolid phase of matter. In other cases, we have tackled new conceptual problems, such as many-body localization, topological insulators and Majorana fermions. Our discoveries are already having an impact in the scientific community, and we are confident that theywill be very useful for the design of the quantum materials of tomorrow. In addition, we have extended the simulation capabilities of our atomic systems, through the realization of device-like systems that can simulate the behavior of the corresponding electronic and superconducting devices.

We are convinced that our work will have a long-lasting impact. The results of QUIC demonstrate also that there is still a lot of space for the discovery of new quantum phases based on novel types of interactions, topology, controlled disorder, etc. Indeed, several of the quantum simulators we have developed in QUIC are studying phenomena and systems that still do not exist in Nature. Understanding the new quantum phases with our quantum simulators will lead to the conception of new types of conductors and insulators.
After four years of work, QUIC has achieved a quantitative understanding of several key phenomena and systems that are of interest for both fundamental science and applications:

- We have studied the celebrated problem of Anderson localization of non-interacting particles in 3D disorder, measuring key properties such as the spectral function and the mobility edge. We have also attacked the even more challenging phenomenon of localization of interacting particles in disorder, many-body localization.
- We have studied quantum transport in low dimensions with both fermionic and bosonic particles, both in electronic device-like structures and in more conceptual setups. For example, we have realized synthetic, fully tunable quantum point contacts and quantum wires, which have allowed to study non-equilibrium physics of heat and matter transport.
- We have studied the effects of superfluidity in quantum mixtures of Bose-Einstein condensates, revealing the spin superfluidity, which shows up in the propagation of undamped spin oscillations.
- We have explored topological phenomena in graphene-like structures realized with ultracold atoms. The first milestone of QUIC has been indeed the realization of the celebrated topological Haldane model with ultracold fermionic atoms.
- Using innovative methods in theory and experiments, we have studied fundamental phenomena at the frontier of our knowledge: supersolidity in spin-orbit coupled systems, Andreev-Lifschitz-Chester supersolidity in lattice models, Majorana fermions, topological time crystals.
- We have developed theory of topological order and monitored applications for experiments with quantum random walks of photons and ultracold atom in synthetic dimensions. We have pioneered applications of machine learning, neural networks and related methods to detect and characterize quantum phases. We laid the foundations of information theory for quantum thermodynamics and non-equilibrium physics.
- The second milestone of QUIC was the realization of a strongly-correlated antiferromagnetic phase using an innovative quantum synthesis approach based on quantum-non-demolition measurements. This has opened a promising new path to create strongly-correlated quantum phases without having to rely on ultra-low temperatures.
- We have discovered exotic quantum phases that are raising a lot of interest in the scientific community: the quantum droplet phase, which has properties similar to those of the celebrated superfluid helium nanodroplets; the supersolid phase of strongly magnetic atoms, which shows coexistence of periodic order and global phase coherence, and it is promising to solve fundamental open questions in physics.
- We have realized novel quantum simulators based on ultracold quantum gases in unprecedented regimes: Bose-Einstein condensates with an unprecedented stability of the magnetic field, accessing the yet unexplored domain of Sine-Gordon Hamiltonians, of relevance to quantum simulations of high-energy physics; Fermi systems in 2D, with engineered Bernoulli-type disorder and tunable interaction, to study the open problems of Anderson localization and of the BEC-BCS crossover in the presence of disorder.
The quantum simulations we have performed in QUIC were never attempted before, and the quantum simulators we have realized are totally new. We have discovered novel quantum phases, improved our capabilities of controlling and manipulating the atomic quantum systems, and developed new ideas for simulating fundamental physical phenomena in quantum matter.

We expect that QUIC will have at least two groups of direct impacts on the society:
- The discoveries of novel phenomena and novel regime in QUIC will bring huge direct impacts to quantum material science, for designing materials with on-demand conducting properties.
- The methods of control of disordered systems developed in QUIC will be of enormous importance for the developments of the hybrid quantum-classical computing approaches that are nowadays considered the most promising.

In conclusion, since conductors and insulators will continue to be at the basis of any future technology, the quantum simulations we have carried out in QUIC will continue to be the key for a rapid advancement of science and technology. Our dream is that, in a not too far future, our findings on the synthetic quantum materials obtained with our ultracold quantum gases will allow to realize engineered real materials with novel capabilities deriving from the laws of quantum mechanics.
Basic components of atomic quantum simulators