arXiv subjects

Paolo Facchi

Publications and source records attributed to Paolo Facchi.

At least 127 records · Page 7Linked to original sources

arXiv2015

Split and overlapped binary solitons in optical lattices

We analyze the energetic and dynamical properties of bright-bright (BB) soliton pairs in a binary mixture of Bose-Einstein condensates subjected to the action of a combined optical lattice, acting as an external potential for the first species, while modulating the intraspecies coupling constant of the second. In particular, we use a variational approach and direct numerical integrations to investigate the existence and stability of BB solitons in which the two species are either spatially separated (split soliton) or located at the same optical lattice site (overlapped soliton). The dependence of these solitons on the interspecies interaction parameter is explicitly investigated. For repulsive interspecies interaction we show the existence of a series of critical values at which transitions from an initially overlapped soliton to split solitons occur. For attractive interspecies interaction only single direct transitions from split to overlapped BB solitons are found. The possibility to use split solitons for indirect measurements of scattering lengths is also suggested.

cond-mat.quant-gas↗

arXiv2015

Tomography: mathematical aspects and applications

In this article we present a review of the Radon transform and the instability of the tomographic reconstruction process. We show some new mathematical results in tomography obtained by a variational formulation of the reconstruction problem based on the minimization of a Mumford-Shah type functional. Finally, we exhibit a physical interpretation of this new technique and discuss some possible generalizations.

math-ph↗

arXiv2015

Quantum systems with time-dependent boundaries

We present here a set of lecture notes on quantum systems with time-dependent boundaries. In particular, we analyze the dynamics of a non-relativistic particle in a bounded domain of physical space, when the boundaries are moving or changing. In all cases, unitarity is preserved and the change of boundaries does not introduce any decoherence in the system.

math-ph↗

arXiv2015

Quantum Typicality and Initial Conditions

If the state of a quantum system is sampled out of a suitable ensemble, the measurement of some observables will yield (almost) always the same result. This leads us to the notion of quantum typicality: for some quantities the initial conditions are immaterial. We discuss this problem in the framework of Bose-Einstein condensates.

quant-ph↗

arXiv2015

Typical observables in a two-mode Bose system

A class of k-particle observables in a two-mode system of Bose particles is characterized by typicality: if the state of the system is sampled out of a suitable ensemble, an experimental measurement of that observable yields (almost) always the same result. We investigate the general features of typical observables, the criteria to determine typicality and finally focus on the case of density correlation functions, which are related to spatial distribution of particles and interference.

quant-ph↗

arXiv2014

Hamiltonian Purification

The problem of Hamiltonian purification introduced by Burgarth et al. [D. K. Burgarth et al., Nat. Commun. 5, 5173 (2014)] is formalized and discussed. Specifically, given a set of non-commuting Hamiltonians {h1, . . ., hm} operating on a d-dimensional quantum system Hd, the problem consists in identifying a set of commuting Hamiltonians {H1,...,Hm} operating on a larger dE-dimensional system H_{dE} which embeds H_d as a proper subspace, such that hj = PHjP with P being the projection which allows one to recover Hd from HdE . The notions of spanning-set purification and generator purification of an algebra are also introduced and optimal solutions for u(d) are provided.

quant-ph↗

arXiv2014

Phase randomization and typicality in the interference of two condensates

Interference is observed when two independent Bose-Einstein condensates expand and overlap. This phenomenon is typical, in the sense that the overwhelming majority of wave functions of the condensates, uniformly sampled out of a suitable portion of the total Hilbert space, display interference with maximal visibility. We focus here on the phases of the condensates and their (pseudo) randomization, which naturally emerges when two-body scattering processes are considered. Relationship to typicality is discussed and analyzed.

cond-mat.quant-gas↗

arXiv2014

Quantum Computing in Plato's Cave

We show that mere observation of a quantum system can turn its dynamics from a very simple one into a universal quantum computation. This effect, which occurs if the system is regularly observed at short time intervals, can be rephrased as a modern version of Plato's Cave allegory. More precisely, while in the original version of the myth, the reality perceived within the Cave is described by the projected shadows of some more fundamental dynamics which is intrinsically more complex, we found that in the quantum world the situation changes drastically as the "projected" reality perceived through sequences of measurements can be more complex than the one that originated it. After discussing examples we go on to show that this effect is generally to be expected: almost any quantum dynamics will become universal once "observed" as outlined above. Conversely, we show that any complex quantum dynamics can be "purified" into a simpler one in larger dimensions.

quant-ph↗

arXiv2013

Non-Abelian Phases from a Quantum Zeno Dynamics

A connection is estabilished between the non-Abelian phases obtained via adiabatic driving and those acquired via a quantum Zeno dynamics induced by repeated projective measurements. In comparison to the adiabatic case, the Zeno dynamics is shown to be more flexible in tuning the system evolution, which paves the way to the implementation of unitary quantum gates and applications in quantum control.

quant-ph↗

arXiv2013

Defining quantumness via the Jordan product

We propose alternative definitions of classical states and quantumness witnesses by focusing on the algebra of observables of the system. A central role will be assumed by the anticommutator of the observables, namely the Jordan product. This approach turns out to be suitable for generalizations to infinite dimensional systems. We then show that the whole algebra of observables can be generated by three elements by repeated application of the Jordan product.

math-ph↗

arXiv2013

A quantum particle in a box with moving walls

We analyze the non-relativistic problem of a quantum particle that bounces back and forth between two moving walls. We recast this problem into the equivalent one of a quantum particle in a fixed box whose dynamics is governed by an appropriate time-dependent Schroedinger operator.

math-ph↗

arXiv2013

Typical Entanglement

Let a pure state ψbe chosen randomly in an NM-dimensional Hilbert space, and consider the reduced density matrix ρof an N-dimensional subsystem. The bipartite entanglement properties of ψare encoded in the spectrum of ρ. By means of a saddle point method and using a "Coulomb gas" model for the eigenvalues, we obtain the typical spectrum of reduced density matrices. We consider the cases of an unbiased ensemble of pure states and of a fixed value of the purity. We finally obtain the eigenvalue distribution by using a statistical mechanics approach based on the introduction of a partition function.

math-ph↗

arXiv2013

Entropy-Driven Phase Transitions of Entanglement

We study the behavior of bipartite entanglement at fixed von Neumann entropy. We look at the distribution of the entanglement spectrum, that is the eigenvalues of the reduced density matrix of a quantum system in a pure state. We report the presence of two continuous phase transitions, characterized by different entanglement spectra, which are deformations of classical eigenvalue distributions.

quant-ph↗

arXiv2013

A dynamical composition law for boundary conditions

We analyze the quantum dynamics of a non-relativistic particle moving in a bounded domain of physical space, when the boundary conditions are rapidly changed. In general, this yields new boundary conditions, via a dynamical composition law that is a very simple instance of superposition of different topologies. In all cases unitarity is preserved and the quick change of boundary conditions does not introduce any decoherence in the system. Among the emerging boundary conditions, the Dirichlet case (vanishing wave function at the boundary) plays the role of an attractor. Possible experimental implementations with superconducting quantum interference devices are explored and analyzed.

quant-ph↗

arXiv2012

Unearthing wave-function renormalization effects in the time evolution of a Bose-Einstein condensate

We study the time evolution of a Bose-Einstein condensate in an accelerated optical lattice. When the condensate has a narrow quasimomentum distribution and the optical lattice is shallow, the survival probability in the ground band exhibits a steplike structure. In this regime we establish a connection between the wave-function renormalization parameter $Z$ and the phenomenon of resonantly enhanced tunneling.

quant-ph↗

arXiv2012

Domain wall suppression in trapped mixtures of Bose-Einstein condensates

The ground state energy of a binary mixture of Bose-Einstein condensates can be estimated for large atomic samples by making use of suitably regularized Thomas-Fermi density profiles. By exploiting a variational method on the trial densities the energy can be computed by explicitly taking into account the normalization condition. This yields analytical results and provides the basis for further improvement of the approximation. As a case study, we consider a binary mixture of $^{87}$Rb atoms in two different hyperfine states in a double well potential and discuss the energy crossing between density profiles with different numbers of domain walls, as the number of particles and the inter-species interaction vary.

cond-mat.quant-gas↗

arXiv2012

Quantum Zeno dynamics of a field in a cavity

We analyze the quantum Zeno dynamics that takes place when a field stored in a cavity undergoes frequent interactions with atoms. We show that repeated measurements or unitary operations performed on the atoms probing the field state confine the evolution to tailored subspaces of the total Hilbert space. This confinement leads to non-trivial field evolutions and to the generation of interesting non-classical states, including mesoscopic field state superpositions. We elucidate the main features of the quantum Zeno mechanism in the context of a state-of-the-art cavity quantum electrodynamics experiment. A plethora of effects is investigated, from state manipulations by phase space tweezers to nearly arbitrary state synthesis. We analyze in details the practical implementation of this dynamics and assess its robustness by numerical simulations including realistic experimental imperfections. We comment on the various perspectives opened by this proposal.

quant-ph↗

arXiv2011

Quantumness and Entanglement Witnesses

We analyze the recently introduced notion of quantumness witness and compare it to that of entanglement witness. We show that any entanglement witness is also a quantumness witness. We then consider some physically relevant examples and explicitly construct some witnesses.

math-ph↗