D. Porras

We show that the quasi-adiabatic evolution of a system governed by the Dicke Hamiltonian can be described in terms of a self-induced quantum many-body metrological protocol. This effect relies on the sensitivity of the ground state to a small symmetry-breaking perturbation at the quantum phase transition, that leads to the collapse of the wavefunciton into one of two possible ground states. The scaling of the final state properties with the number of atoms and with the intensity of the symmetry breaking field, can be interpreted in terms of the precession time of an effective quantum metrological protocol. We show that our ideas can be tested with spin-phonon interactions in trapped ion setups. Our work points to a classification of quantum phase transitions in terms of the capability of many-body quantum systems for parameter estimation.

We show an analogy between static quantum emitters coupled to a single mode of a quantum field and accelerated Unruh-DeWitt detectors. We envision a way to simulate a variety of relativistic quantum field settings beyond the reach of current computational power, such as high number of qubits coupled to a quantum field following arbitrary non-inertial trajectories. Our scheme may be implemented with trapped ions and circuit QED set-ups.

The vibrations of a collection of ions in a microtrap array can be described in terms of hopping phonons. We show theoretically that the vibrational couplings may be tailored by using a gradient of the microtrap frequencies, together with a periodic driving of the trapping potential. These ingredients allow us to induce effective gauge fields on the vibrational excitations, such that phonons mimic the behavior of charged particles in a magnetic field. In particular, microtrap arrays are ideally suited to realize the famous Aharonov-Bohm effect, and observe the paradigmatic edge states typical from quantum-Hall samples and topological insulators.

We show that the vibrations of a chain of trapped ions offer an interesting route to explore the physics of disordered quantum systems. By preparing the internal state of the ions in a quantum superposition, we show how the local vibrational energy becomes a stochastic variable, being its statistical properties inherited from the underlying quantum parallelism of the internal state. We describe a minimally-perturbing measurement of the resonance fluorescence, which allows us to study effects like Anderson localization without the need of ground-state cooling or individual addressing, and thus paves the way towards high-temperature ion experiments.

We propose and theoretically analyse an experimental configuration in which lasers induce 3-spin interactions between trapped ions.By properly choosing the intensities and frequencies of the lasers, 3-spin couplings may be dominant or comparable to 2-spin terms and magnetic fields. In this way, trapped ions can be used to study exotic quantum phases which do not have a counterpart in nature. We study the conditions for the validity of the effective 3-spin Hamiltonian, and predict qualitatively the quantum phase diagram of the system.

Trapped ions arranged in Coulomb crystals provide us with the elements to study the physics of a single spin coupled to a boson bath. In this work we show that optical forces allow us to realize a variety of spin-boson models, depending on the crystal geometry and the laser configuration. We study in detail the Ohmic case, which can be implemented by illuminating a single ion with a travelling wave. The mesoscopic character of the phonon bath in trapped ions induces new effects like the appearance of quantum revivals in the spin evolution.

We propose and analyze a new method to produce single and entangled photons which does not require cavities. It relies on the collective enhancement of light emission as a consequence of the presence of entanglement in atomic ensembles. Light emission is triggered by a laser pulse, and therefore our scheme is deterministic. Furthermore, it allows one to produce a variety of photonic entangled states by first preparing certain atomic states using simple sequences of quantum gates. We analyze the feasibility of our scheme, and particularize it to: ions in linear traps, atoms in optical lattices, and in cells at room temperature.

The vibrations of a chain of trapped ions can be considered, under suitable experimental conditions, as an ensemble of interacting phonons, whose quantum dynamics is governed by a Bose--Hubbard Hamiltonian. In this work we study the quantum phases which appear in this system, and show that thermodynamical properties, such as critical parameters and critical exponents, can be measured in experiments with a limited number of ions. Besides that, interacting phonons in trapped ions offer us the possibility to access regimes which are difficult to study with ultracold bosons in optical lattices, like models with attractive or site--dependent phonon-phonon interactions.

We show that a large number of ions stored in a Penning trap, and forming a 2D Coulomb crystal, provides an almost ideal system for scalable quantum computation and quantum simulation. In particular, the coupling of the internal states to the motion of the ions transverse to the crystal plane, allows one to implement two qubit quantum gates. We analyze in detail the decoherence induced by anharmonic couplings with in--plane hot vibrational modes, and show that very high gate fidelities can be achieved with current experimental set--ups.

A system of trapped ions under the action of off--resonant standing--waves can be used to simulate a variety of quantum spin models. In this work, we describe theoretically quantum phases that can be observed in the simplest realization of this idea: quantum Ising and XY models. Our numerical calculations with the Density Matrix Renormalization Group method show that experiments with ion traps should allow one to access general properties of quantum critical systems. On the other hand, ion trap quantum spin models show a few novel features due to the peculiarities of induced effective spin--spin interactions which lead to interesting effects like long--range quantum correlations and the coexistence of different spin phases.

We show that the dynamics of phonons in a set of trapped ions interacting with lasers is described by a Bose-Hubbard model whose parameters can be externally adjusted. We investigate the possibility of observing several quantum many-body phenomena, including (quasi) Bose-Einstein condensation as well as a superfluid-Mott insulator quantum phase transition.

We show that the physical system consisting of trapped ions interacting with lasers may undergo a rich variety of quantum phase transitions. By changing the laser intensities and polarizations the dynamics of the internal states of the ions can be controlled, in such a way that an Ising or Heisenberg-like interaction is induced between effective spins. Our scheme allows us to build an analogue quantum simulator of spin systems with trapped ions, and observe and analyze quantum phase transitions with unprecedent opportunities for the measurement and manipulation of spins.