Gabriele De Chiara

Entanglement entropy dynamics of Heisenberg chains

By means of the time dependent density matrix renormalization group algorithm we study the zero-temperature dynamics of the Von Neumann entropy of a block of spins in a Heisenberg chain after a sudden quench in the anisotropy parameter. In the absence of any disorder the block entropy increases linearly with time and then saturates. We analyse the velocity of propagation of the entanglement as a function of the initial and final anisotropies and compare our results, wherever possible, with those obtained by means of conformal field theory. In the disordered case we find a slower (logarithmic) evolution which may signal the onset of entanglement localization.

Experimental Reconstruction of Work Distribution and Study of Fluctuation Relations in a Closed Quantum System

We report the experimental reconstruction of the nonequilibrium work probability distribution in a closed quantum system, and the study of the corresponding quantum fluctuation relations. The experiment uses a liquid-state nuclear magnetic resonance platform that offers full control on the preparation and dynamics of the system. Our endeavors enable the characterization of the out-of-equilibrium dynamics of a quantum spin from a finite-time thermodynamics viewpoint.

Berry Phase for a Spin 1=2 Particle in a Classical Fluctuating Field

The effect of fluctuations in the classical control parameters on the Berry phase of a spin 1/2 interacting with an adiabatically cyclically varying magnetic field is analyzed. It is explicitly shown that in the adiabatic limit dephasing is due to fluctuations of the dynamical phase.

Entanglement spectrum, critical exponents, and order parameters in quantum spin chains.

We investigate the entanglement spectrum near criticality in finite quantum spin chains. Using finite size scaling we show that when approaching a quantum phase transition, the Schmidt gap, i.e., the difference between the two largest eigenvalues of the reduced density matrix λ(1), λ(2), signals the critical point and scales with universal critical exponents related to the relevant operators of the corresponding perturbed conformal field theory describing the critical point. Such scaling behavior allows us to identify explicitly the Schmidt gap as a local order parameter.

Structural phase transitions in low-dimensional ion crystals

A chain of singly charged particles, confined by a harmonic potential, exhibits a sudden transition to a zigzag configuration when the radial potential reaches a critical value, depending on the particle number. This structural change is a phase transition of second order, whose order parameter is the crystal displacement from the chain axis. We study analytically the transition using Landau theory and find full agreement with numerical predictions by Schiffer [Phys. Rev. Lett. 70, 818 (1993)] and Piacente et al. [Phys. Rev. B 69, 045324 (2004)]. Our theory allows us to determine analytically the systems behavior at the transition point.

From perfect to fractal transmission in spin chains

Perfect state transfer is possible in modulated spin chains [Phys. Rev. Lett. 92, 187902 (2004)], imperfections, however, are likely to corrupt the state transfer. We study the robustness of this quantum communication protocol in the presence of disorder both in the exchange couplings between the spins and in the local magnetic field. The degradation of the fidelity can be suitably expressed, as a function of the level of imperfection and the length of the chain, in a scaling form. In addition the time signal of fidelity becomes fractal. We further characterize the state transfer by analyzing the spectral properties of the Hamiltonian of the spin chain.

Quantifying, characterizing, and controlling information flow in ultracold atomic gases

We study quantum information flow in a model comprising of an impurity qubit immersed in a Bose-Einstein condensed reservoir. We demonstrate how information flux between the qubit and the condensate can be manipulated by engineering the ultracold reservoir within experimentally realistic limits. We place a particular emphasis on non-Markovian dynamics, characterized by a reversed flow of information from the background gas to the qubit and identify a controllable crossover between Markovian and non-Markovian dynamics in the parameter space of the model. Introduction- In the last decades high precision con- trol of ultracold atomic gases has allowed the realization of beautiful experiments unveiling fundamental phenom- ena in the physics of many-body quantum systems at low temperatures. Key examples are the observation of Anderson localization (1), the superfluid-Mott insulator transition (2), the creation of Tonks-Girardeau gases (3), and the atom laser (4), just to mention a few. More recently, hybrid systems composed of quantum dots, single trapped ions and optical lattices coupled to Bose-Einstein condensates (BECs) have been studied both theoretically and experimentally (5). These systems are studied in the framework of open quantum systems (6), effectively described as one or more two-level sys- tems (qubits) interacting with a reservoir consisting of the ultracold gas. The possibility of manipulating cru- cial parameters of the reservoir, such as the scattering length (7), combined with the continuous improvements in quantum control of qubits highlights the enormous po- tential of hybrid systems as quantum simulators of both condensed matter models and open quantum systems. Lately, the open systems community has given substan- tial interest to the dynamics of quantum information flow due to several proposals to link it to the division of quan- tum processes into Markovian and non-Markovian ones (8-11). The latter ones have been defined as processes where an open system recovers some previously lost infor- mation and therefore temporarily combats the destruc- tive effect of the environment as a sink for quantum prop- erties. Such processes are very desirable from a quantum information processing point of view, since they increase the operational time of qubits (12). Sophisticated con- trol over detrimental environmental effects enabled by, for example, hybrid quantum systems will be very bene- ficial for state-of-the-art quantum processors. Moreover, understanding of the decoherence processes in hybrid systems gives insight into the basic physical mech- anisms ruling the interaction of the qubit and the cold atomic cloud surrounding it. It is also a key pre-requisite to the realization of quantum simulators since it allows for the identification of the relevant parameters for on- demand control of the exchange of quantum information between a qubit and its ultracold environment. We present here the first characterization of non- Markovian effects in the context of ultracold gases. More specifically, inspired by a model introduced in Ref. (13), we consider an impurity atom in a double well potential, i.e., an effective qubit system, interacting with a BEC environment. We study information flow using the non- Markovianity quantifier presented in Ref. (8) and show how information flux can be manipulated by experimen- tally achievable means such as changing the scattering length, the effective dimension of the background gas or the trapping geometry of the qubit. We find a crossover between Markovian and non-Markovian dynamics in the parameter space of the model and uncover the physical mechanisms at the root of non-Markovian phenomena induced by the ultracold background gas. Our findings pave the way to the realization of quantum simulators for non-Markovian open quantum system models with ultracold atomic gases. The model- We consider an impurity atom trapped in a deep double well potential VA(r). The impurity atom forms a qubit system with the two qubit states repre- sented by the occupation of the impurity atom in the left or the right well, |Li and |Ri respectively. The impurity atom couples to a bosonic background gas B trapped in a shallow potential VB(r), which forms a Bose-Einstein condensed environment for the qubit system. The Hamil- tonian for this system, derived in Ref. (13), is

Entanglement detection in hybrid optomechanical systems

We study a device formed by a Bose-Einstein condensate (BEC) coupled to the field of a cavity with a moving end mirror and find a working point such that the mirror-light entanglement is reproduced by the BEC-light quantum correlations. This provides an experimentally viable tool for inferring mirror-light entanglement with only a limited set of assumptions. We prove the existence of tripartite entanglement in the hybrid device, persisting up to temperatures of a few milli-Kelvin, and discuss a scheme to detect it.

Quantum cloning in spin networks

We introduce an approach to quantum cloning based on spin networks and we demonstrate that phase covariant cloning can be realized using no external control but only with a proper design of the Hamiltonian of the system. In the 1! 2 cloning we find that the XY model saturates the value for the fidelity of the optimal cloner and gives values comparable to it in the general N! M case. We finally discuss the effect of external noise. Our protocol is much more robust to decoherence than a conventional procedure based on quantum

Phase Diagram of Spin-1 Bosons on One-Dimensional Lattices

Spinor Bose condensates loaded in optical lattices have a rich phase diagram characterized by different magnetic order. Here we apply the density matrix renormalization group to accurately determine the phase diagram for spin-1 bosons loaded on a one-dimensional lattice. The Mott lobes present an even or odd asymmetry associated to the boson filling. We show that for odd fillings the insulating phase is always in a dimerized state. The results obtained in this work are also relevant for the determination of the ground state phase diagram of the S = 1 Heisenberg model with biquadratic interaction.