Fernando Galve

Non-homogeneous chain environments (e.g. segmented ion traps) are investigated through an exact diagonalization approach. Different spectral densities, including band-gaps, can be engineered to separately assess memory effects. Environment non-Markovianity is quantified with recently introduced measures of information flow-back and non-divisibility of the system dynamical map. By sweeping the bath spectrum via tuning of the system frequency we show strongest memory effect at band-gap edges and provide an interpretation based on energy flow between system and environment. A system weakly coupled to a stiff chain ensures a Markovian dynamics, while the size of the environment as well as the local density of modes are not substantial factors. We show an opposite effect when increasing the temperature inside or outside the spectral band-gap. Further, non-Markovianity arises for larger (negative and positive) powers of algebraic spectral densities, being the Ohmic case not always the most Markovian one.

It is known that arrays of trapped ions can be used to efficiently simulate a variety of many-body quantum systems. Here, we show how it is possible to build a model representing a spin chain interacting with bosons which is exactly solvable. The exact spectrum of the model at zero temperature and the ground state properties are studied. We show that a quantum phase transition occurs when the coupling between spins and bosons reaches a critical value, which corresponds to a level crossing in the energy spectrum. Once the critical point is reached, the number of bosonic excitations in the ground state, which can be assumed as an order parameter, starts to be different from zero. The population of the bosonic mode is accompanied by a macroscopic magnetization of the spins. This double effect could represent an useful resource for the phase transition detection since a measure on the phonon can give information about the phase of the spin system. A finite temperature phase diagram is also given in the adiabatic regime.

We consider the thermodynamic properties of the squeezed vacuum state of a frequency--modulated quantum harmonic oscillator. We analytically relate the squeezing parameter to the irreversible work and the degree of nonadiabaticity of the frequency transformation. We furthermore determine the optimal modulation that leads to maximal squeezing, and discuss its implementation as well as the detection of squeezing in single cold ion traps.