## Final Report Summary - NEWFQS (New Frontiers in Quantum Simulation)

- CONTEXT -

The description of quantum systems is a challenge that defies the most powerful supercomputers in the world. Physicists know a few quantum models that are exactly solvable, but they are the exception rather than the norm. Even systems with a few dozen atoms are so complicated that the memory required to describe their quantum state exceeds what can be possibly achieved with current or future classical computers.

And yet we need to understand better quantum many-body systems. This is necessary, for example, to engineer new materials, sensors or simply to keep on advancing our knowledge in this exciting research field. Physicists have developed a wide set of tools that can be used to address the description of complex quantum systems, mostly relying on approximations, such as mean-field theory or renormalization group methods. Most of what we know about solid-state physics and complex quantum systems rely on those approximate methods.

NewFQS has explored a different, alternative, approach. We have designed and studied analog quantum simulators – devices where interactions can be tuned to mimic the dynamics of quantum models. Quantum simulators are an alternative to exact numerical calculations and they use a similar technology to quantum computers. Furthermore this project has allowed us to collaborate with an experimental group in which some of our ideas have been put into practice, opening up a new research direction in many-body physics.

Why quantum simulators are useful? First all, they allow us to investigate quantum states of matter under controlled conditions and thus to experiment looking for new phases of matter or useful properties. Furthermore, they can also guide us in finding novel theoretical or computational methods. For example, an experiment may unveil new phenomena and guide theorists to find out an explanation – in the process we can discover new theoretical ideas and algorithms.

- RESULTS -

Workpackage 1 – Spin-Boson Quantum Simulation

Our project has been mostly focused on applications with trapped ion quantum simulators. These are devices where ionized atoms are trapped by electromagnetic potentials and they form crystals that can vary in size from a few ions to around 50 or even 100 ions.

Each ion in the crystal has its own spin. In a sense a spin is the smallest possible quantum system. However a collection of many spins can show a wide range of exciting phenomena like phase transitions and exotic quantum orders. Ions in a crystal can also vibrate and those vibrations can interact with the spins. In quantum mechanics, vibrations are described in terms of quanta of excitations known as phonons. Phonons are actually the simplest example of a bosonic excitation.

A trapped ion quantum simulator can be thus understood as a quantum system that is made up of spins interacting with phonons. In NewFQS we have shown that those very basic ingredients are enough to realize a variety of interesting quantum simulations. For example, one can use phonons to impose a symmetry on the simulator that is well known in particle physics, namely, gauge symmetry. By doing that we have predicted, together with Pedro Nevado (a PhD in the group), a rich quantum phase diagram with a first-order phase transition, see Ref. 5 in the list below.

Another way in which phonons can be exploited for quantum simulation is as mediators of spin-spin interactions. For example, we have shown that trapped ion spins can interact in a complex, frustrated, way, Ref. 4. What we mean here by “frustration” is that interactions between spins alternate signs in such a way that they impose a very complex magnetic structure in which the direction in which spins have to point to is not very clearly defined. This may seem like an exotic scenario, but actually, the investigation of magnetic frustration is closely related to the optimization that is carried out by some quantum computers.

The project has allowed the principal investigator to carry out a collaboration with Tobias Schaetz’ group at University of Freiburg, where a spin-boson model was simulated with trapped ion crystals of up to 5 atoms. In a sense, this was one of the simplest possible quantum simulations in which we simply observed the relaxation of a crystal after an initial excitation. This configuration has allowed us to investigate the process of quantum thermalization. This is the not very-well understood process by which an isolated quantum system reaches a thermal equilibrium even in the absence of contact with a thermal bath. Our experiment (Ref. 1) allowed us to investigate thermalization and to obtain information on the time-scales of this process, something that has motivated more theoretical work in the group.

Workpackage 2 – Quantum Lattice Laser

One of the more exciting prospects of quantum simulation is the possibility of implementing quantum phases which do not strictly speaking correspond to materials found in Nature, but which still are interesting from fundamental point of view.

The quantum lattice laser is one of those examples. It consists of an array of nano-lasers that are synchronized by some kind of coupling. This model could be implemented, for example, in trapped ion crystals where each ion would play the role of a microscopic laser. Also other systems, such as lattices of superconducting qubits. Actually, one of the first results that we obtained was to prove that the basic element of a quantum lattice of lasers, namely, a nano-laser, can be implemented very efficiently with a single superconducting qubit (Ref. 7).

Together with one of the PhD students at Sussex (Samuel Fernandez-Lorenzo) we have been able to predict the phase diagram of the system and found a strong analogy with the case of a Bose-Einstein condensate in a lattice (Ref. 3). Our results will have applications in quantum sensing and metrology.

Workpackage 3 – Quantum Simulators for Quantum Metrology

In one of the most interesting aspects of the project, we have explored the possibility that quantum simulators not only help us advance our knowledge of many-body systems, but also they can be the basis for applications. Actually, we know that simulators have complex phases that are very sensitive to external parameters, so, why not using them for quantum sensing.

Together with Samuel Fernandez-Lorenzo, we have explored how dissipative simulators can actually be used as “quantum compasses” that are extremely sensitive to external electromagnetic fields (Refs. 3 and 9). This is an exciting research line that we hope to continue in the future.

IMPACT

The project has had several impacts, let us stress here a few important ones

- Our work on quantum thermalization was covered by a News Feature article in Nature, Vol 551, Issue 7678, Nov 2017, “The new thermodynamics: how quantum physics is bending the rules”.

- One of our works on Quantum Simulation (Ref. 6) is a theoretical proposal for quantum simulation that has been implemented by an experimental group in the US. at University of Illinois at Urbana-Champaign (see “Correlated Spin-Flip Tunneling in a Fermi Lattice Gas” arXiv:1711.02061, by Wenchao Xu, William Morong, Hoi-Yin Hui, Vito W. Scarola and Brian DeMarco.

- We have established academic collaborations between University of Sussex (UK), University of Freiburg (Germany) and CSIC (Madrid) that will be kept after completion of this project.

- Some of NewFQS’ results have motivated recent funding applications and further theoretical work by the group.

The description of quantum systems is a challenge that defies the most powerful supercomputers in the world. Physicists know a few quantum models that are exactly solvable, but they are the exception rather than the norm. Even systems with a few dozen atoms are so complicated that the memory required to describe their quantum state exceeds what can be possibly achieved with current or future classical computers.

And yet we need to understand better quantum many-body systems. This is necessary, for example, to engineer new materials, sensors or simply to keep on advancing our knowledge in this exciting research field. Physicists have developed a wide set of tools that can be used to address the description of complex quantum systems, mostly relying on approximations, such as mean-field theory or renormalization group methods. Most of what we know about solid-state physics and complex quantum systems rely on those approximate methods.

NewFQS has explored a different, alternative, approach. We have designed and studied analog quantum simulators – devices where interactions can be tuned to mimic the dynamics of quantum models. Quantum simulators are an alternative to exact numerical calculations and they use a similar technology to quantum computers. Furthermore this project has allowed us to collaborate with an experimental group in which some of our ideas have been put into practice, opening up a new research direction in many-body physics.

Why quantum simulators are useful? First all, they allow us to investigate quantum states of matter under controlled conditions and thus to experiment looking for new phases of matter or useful properties. Furthermore, they can also guide us in finding novel theoretical or computational methods. For example, an experiment may unveil new phenomena and guide theorists to find out an explanation – in the process we can discover new theoretical ideas and algorithms.

- RESULTS -

Workpackage 1 – Spin-Boson Quantum Simulation

Our project has been mostly focused on applications with trapped ion quantum simulators. These are devices where ionized atoms are trapped by electromagnetic potentials and they form crystals that can vary in size from a few ions to around 50 or even 100 ions.

Each ion in the crystal has its own spin. In a sense a spin is the smallest possible quantum system. However a collection of many spins can show a wide range of exciting phenomena like phase transitions and exotic quantum orders. Ions in a crystal can also vibrate and those vibrations can interact with the spins. In quantum mechanics, vibrations are described in terms of quanta of excitations known as phonons. Phonons are actually the simplest example of a bosonic excitation.

A trapped ion quantum simulator can be thus understood as a quantum system that is made up of spins interacting with phonons. In NewFQS we have shown that those very basic ingredients are enough to realize a variety of interesting quantum simulations. For example, one can use phonons to impose a symmetry on the simulator that is well known in particle physics, namely, gauge symmetry. By doing that we have predicted, together with Pedro Nevado (a PhD in the group), a rich quantum phase diagram with a first-order phase transition, see Ref. 5 in the list below.

Another way in which phonons can be exploited for quantum simulation is as mediators of spin-spin interactions. For example, we have shown that trapped ion spins can interact in a complex, frustrated, way, Ref. 4. What we mean here by “frustration” is that interactions between spins alternate signs in such a way that they impose a very complex magnetic structure in which the direction in which spins have to point to is not very clearly defined. This may seem like an exotic scenario, but actually, the investigation of magnetic frustration is closely related to the optimization that is carried out by some quantum computers.

The project has allowed the principal investigator to carry out a collaboration with Tobias Schaetz’ group at University of Freiburg, where a spin-boson model was simulated with trapped ion crystals of up to 5 atoms. In a sense, this was one of the simplest possible quantum simulations in which we simply observed the relaxation of a crystal after an initial excitation. This configuration has allowed us to investigate the process of quantum thermalization. This is the not very-well understood process by which an isolated quantum system reaches a thermal equilibrium even in the absence of contact with a thermal bath. Our experiment (Ref. 1) allowed us to investigate thermalization and to obtain information on the time-scales of this process, something that has motivated more theoretical work in the group.

Workpackage 2 – Quantum Lattice Laser

One of the more exciting prospects of quantum simulation is the possibility of implementing quantum phases which do not strictly speaking correspond to materials found in Nature, but which still are interesting from fundamental point of view.

The quantum lattice laser is one of those examples. It consists of an array of nano-lasers that are synchronized by some kind of coupling. This model could be implemented, for example, in trapped ion crystals where each ion would play the role of a microscopic laser. Also other systems, such as lattices of superconducting qubits. Actually, one of the first results that we obtained was to prove that the basic element of a quantum lattice of lasers, namely, a nano-laser, can be implemented very efficiently with a single superconducting qubit (Ref. 7).

Together with one of the PhD students at Sussex (Samuel Fernandez-Lorenzo) we have been able to predict the phase diagram of the system and found a strong analogy with the case of a Bose-Einstein condensate in a lattice (Ref. 3). Our results will have applications in quantum sensing and metrology.

Workpackage 3 – Quantum Simulators for Quantum Metrology

In one of the most interesting aspects of the project, we have explored the possibility that quantum simulators not only help us advance our knowledge of many-body systems, but also they can be the basis for applications. Actually, we know that simulators have complex phases that are very sensitive to external parameters, so, why not using them for quantum sensing.

Together with Samuel Fernandez-Lorenzo, we have explored how dissipative simulators can actually be used as “quantum compasses” that are extremely sensitive to external electromagnetic fields (Refs. 3 and 9). This is an exciting research line that we hope to continue in the future.

IMPACT

The project has had several impacts, let us stress here a few important ones

- Our work on quantum thermalization was covered by a News Feature article in Nature, Vol 551, Issue 7678, Nov 2017, “The new thermodynamics: how quantum physics is bending the rules”.

- One of our works on Quantum Simulation (Ref. 6) is a theoretical proposal for quantum simulation that has been implemented by an experimental group in the US. at University of Illinois at Urbana-Champaign (see “Correlated Spin-Flip Tunneling in a Fermi Lattice Gas” arXiv:1711.02061, by Wenchao Xu, William Morong, Hoi-Yin Hui, Vito W. Scarola and Brian DeMarco.

- We have established academic collaborations between University of Sussex (UK), University of Freiburg (Germany) and CSIC (Madrid) that will be kept after completion of this project.

- Some of NewFQS’ results have motivated recent funding applications and further theoretical work by the group.