We demonstrate the possibility of realizing a neural network in a chain of trapped ions with induced long range interactions. Such models permit one to store information distributed over the whole system. The storage capacity of such a network, which depends on the phonon spectrum of the system, can be controlled by changing the external trapping potential. We analyze the implementation of error resistant universal quantum information processing in such systems.

Atom number states are a valuable resource for ultracold chemistry, atom interferometry, and quantum information processing. Recent experiments have achieved their deterministic preparation in trapped few-fermion systems. We analyze the tunneling decay of these states, in terms of both the survival probability and the nonescape probability, which can be extracted from measurements of the full counting statistics. At short times, both probabilities exhibit deviations from the exponential law. The decay is governed by the multiparticle Zeno time, which exhibits a signature of quantum statistics and contact interactions. The subsequent exponential regime governs most of the dynamics, and we provide accurate analytical expressions for the associated decay rates. Both dynamical regimes are illustrated in a realistic model. Finally, a global picture of multiparticle quantum decay is presented.

Heat rectifiers are systems that conduct heat asymmetrically for forward and reversed temperature gradients. We present an analytical study of heat rectification in linear quantum systems. We demonstrate that asymmetric heat currents can be induced in a linear system only if it is dynamically driven. The rectification can be further enhanced, even achieving maximal performance, by detuning the oscillators of the driven network. Finally, we demonstrate the feasibility of such driven harmonic network to work as a thermal transistor, quantifying its efficiency through the dynamical amplification factor.Rectifiers are physical systems capable of conducting energy asymmetrically -whether electric, magnetic, thermal...-and are an essential building block in many technological applications. Although thermal rectifiers are crucial components to manipulate heat currents and construct phononic devices, so far no efficient and feasible thermal diodes have been found. Such device, when connected to two thermal baths at different temperatures, conducts heat asymmetrically if the temperatures of the baths are interchanged. This effect allows for an effective heat dissipation with a suppressed backflow reaction.To date, most theoretical proposals on classical heat rectifiers (see [1] and references therein) have been based either on the use of inohomogenous materials [2-7] exploiting nonlinear interactions, or doping the systems with impurities while remaining in the linear regime [8]. Also, the feasibility of microscopic systems acting as thermal devices has been recently addressed in, for instance, phononic refrigerators in the classical [9] and quantum [10] regimes, or heat rectifiers in diferent platforms: quantum dots [11], nonlinear solid-state quantum circuits [12], few-level systems [13,14], or hybrid configurations [15].Here, we address analytically and in full generality heat rectification in quantum systems under generic linear interactions. To this aim, we assume a network of harmonic oscillators coupled to two thermal reservoirs and investigate how asymmetric heat fluxes can be induced in such setup. First, we revisit the static scenario showing that linearity forbids heat rectification, regardless of any asymmetry in the harmonic network or in its coupling with the baths. Second, we demonstrate that heat rectification in a linear quantum system is possible if the system is periodically driven. This is our main result. Such feature is a consequence of two facts: (i) injecting/extracting work into/from a system by an external agent is a useful resource to redistribute energy and (ii) by periodically driven a system, new asymmetric heat transport processes -that have no analog in static scenarios-are induced. By using the Floquet formalism we identify precisely the quantum processes leading to heat rectification. Finally, we also demonstrate the suitability of driven harmonic net-works as heat transistors. Q r 1 FIG. 1. Sketch of a heat rectification setup where a system S with linear interactions V (t) is connected ...

We describe the preparation of atom-number states with strongly interacting bosons in one dimension, or spin-polarized fermions. The procedure is based on a combination of weakening and squeezing of the trapping potential. For the resulting state, the full atom number distribution is obtained. Starting with an unknown number of particles $N_i$, we optimize the sudden change in the trapping potential which leads to the Fock state of $N_f$ particles in the final trap. Non-zero temperature effects as well as different smooth trapping potentials are analyzed. A simple criterion is provided to ensure the robust preparation of the Fock state for physically realistic traps.Comment: 5 pages, 5 figure

We investigate the possibility of forming high-fidelity atomic Fock states by gradual reduction of a quasione-dimensional trap containing spin-polarized fermions or strongly interacting bosons in the Tonk-Girardeau regime. Making the trap shallower and simultaneously squeezing it can lead to the preparation of an ideal atomic Fock state as one approaches either the sudden or the adiabatic limits. Nonetheless, the fidelity of the resulting state is shown to exhibit nonmonotonic behavior with the time scale in which the trapping potential is changed.