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A. Simoni

Publications and source records attributed to A. Simoni.

At least 19 recordsLinked to original sources
arXiv2022

Exploring ultracold collisions in $^6$Li-$^{53}$Cr Fermi mixtures: Feshbach resonances and scattering properties of a novel alkali-transition metal system

We investigate ultracold collisions in a novel mixture of $^6$Li and $^{53}$Cr fermionic atoms, discovering more than 50 interspecies Feshbach resonances via loss spectroscopy. Building a full coupled-channel model, we unambiguously characterize the $^{6}$Li-$^{53}$Cr scattering properties and yield predictions for other isotopic pairs. In particular, we identify various Feshbach resonances that enable the controlled tuning of elastic $s$- and $p$-wave $^{6}$Li-$^{53}$Cr interactions. Our studies thus make lithium-chromium mixtures emerge as optimally-suited platforms for the experimental search of elusive few- and many-body regimes of highly-correlated fermionic matter, and for the realization of a new class of ultracold polar molecules possessing both electric and magnetic dipole moments.

cond-mat.quant-gas↗
arXiv2016

The quantum-to-classical transition: contraction of associative products

The quantum-to-classical transition is considered from the point of view of contractions of associative algebras. Various methods and ideas to deal with contractions of associative algebras are discussed that account for a large family of examples. As an instance of them, the commutative algebra of functions in phase space, corresponding to classical physical observables, is obtained as a contraction of the Moyal star-product which characterizes the quantum case. Contractions of associative algebras associated to Lie algebras are discussed, in particular the Weyl-Heisenberg and $SU(2)$ groups are considered.

quant-ph↗
arXiv2013

Groupoids and the tomographic picture of quantum mechanics

The existing relation between the tomographic description of quantum states and the convolution algebra of certain discrete groupoids represented on Hilbert spaces will be discussed. The realizations of groupoid algebras based on qudit, photon-number (Fock) states and symplectic tomography quantizers and dequantizers will be constructed. Conditions for identifying the convolution product of groupoid functions and the star--product arising from a quantization--dequantization scheme will be given. A tomographic approach to construct quasi--distributions out of suitable immersions of groupoids into Hilbert spaces will be formulated and, finally, intertwining kernels for such generalized symplectic tomograms will be evaluated explicitly.

math-ph↗
arXiv2013

Realization of associative products in terms of Moyal and tomographic symbols

The quantizer-dequantizer method allows to construct associative products on any measure space. Here we consider an inverse problem: given an associative product is it possible to realize it within the quantizer-dequantizer framework? The answer is positive in finite dimensions and we give a few examples in infinite dimensions.

math-ph↗
arXiv2012

A pedagogical presentation of a $C^\star$-algebraic approach to quantum tomography

It is now well established that quantum tomography provides an alternative picture of quantum mechanics. It is common to introduce tomographic concepts starting with the Schrodinger-Dirac picture of quantum mechanics on Hilbert spaces. In this picture states are a primary concept and observables are derived from them. On the other hand, the Heisenberg picture,which has evolved in the $C^\star-$algebraic approach to quantum mechanics, starts with the algebra of observables and introduce states as a derived concept. The equivalence between these two pictures amounts essentially, to the Gelfand-Naimark-Segal construction. In this construction, the abstract $% C^\star-$algebra is realized as an algebra of operators acting on a constructed Hilbert space. The representation one defines may be reducible or irreducible, but in either case it allows to identify an unitary group associated with the $C^\star-$algebra by means of its invertible elements. In this picture both states and observables are appropriate functions on the group, it follows that also quantum tomograms are strictly related with appropriate functions (positive-type)on the group. In this paper we present, by means of very simple examples, the tomographic description emerging from the set of ideas connected with the $C^\star-$algebra picture of quantum mechanics. In particular, the tomographic probability distributions are introduced for finite and compact groups and an autonomous criterion to recognize a given probability distribution as a tomogram of quantum state is formulated.

quant-ph↗
arXiv2012

On the tomographic description of classical fields

After a general description of the tomographic picture for classical systems, a tomographic description of free classical scalar fields is proposed both in a finite cavity and the continuum. The tomographic description is constructed in analogy with the classical tomographic picture of an ensemble of harmonic oscillators. The tomograms of a number of relevant states such as the canonical distribution, the classical counterpart of quantum coherent states and a new family of so called Gauss--Laguerre states, are discussed. Finally the Liouville equation for field states is described in the tomographic picture offering an alternative description of the dynamics of the system that can be extended naturally to other fields.

math-ph↗
arXiv2010

On the Tomographic Picture of Quantum Mechanics

We formulate necessary and sufficient conditions for a symplectic tomogram of a quantum state to determine the density state. We establish a connection between the (re)construction by means of symplectic tomograms with the construction by means of Naimark positive-definite functions on the Weyl-Heisenberg group. This connection is used to formulate properties which guarantee that tomographic probabilities describe quantum states in the probability representation of quantum mechanics.

quant-ph↗
arXiv2009

An introduction to the tomographic picture of quantum mechanics

Starting from the famous Pauli problem on the possibility to associate quantum states with probabilities, the formulation of quantum mechanics in which quantum states are described by fair probability distributions (tomograms, i.e. tomographic probabilities) is reviewed in a pedagogical style. The relation between the quantum state description and the classical state description is elucidated. The difference of those sets of tomograms is described by inequalities equivalent to a complete set of uncertainty relations for the quantum domain and to nonnegativity of probability density on phase space in the classical domain. Intersection of such sets is studied. The mathematical mechanism which allows to construct different kinds of tomographic probabilities like symplectic tomograms, spin tomograms, photon number tomograms, etc., is clarified and a connection with abstract Hilbert space properties is established. Superposition rule and uncertainty relations in terms of probabilities as well as quantum basic equation like quantum evolution and energy spectra equations are given in explicit form. A method to check experimentally uncertainty relations is suggested using optical tomograms. Entanglement phenomena and the connection with semigroups acting on simplexes are studied in detail for spin states in the case of two qubits. The star-product formalism is associated with the tomographic probability formulation of quantum mechanics.

quant-ph↗
arXiv2009

Collisional and molecular spectroscopy in an ultracold Bose-Bose mixture

The route toward a Bose-Einstein condensate of dipolar molecules requires the ability to efficiently associate dimers of different chemical species and transfer them to the stable rovibrational ground state. Here, we report on recent spectroscopic measurements of two weakly bound molecular levels and newly observed narrow d-wave Feshbach resonances. The data are used to improve the collisional model for the Bose-Bose mixture 41K87Rb, among the most promising candidates to create a molecular dipolar BEC.

cond-mat.other↗
arXiv2009

Feshbach resonances in ultracold atom-molecule collisions

We investigate the presence of Feshbach resonances in ultracold alkali-dialkali reactive collisions. Quantum scattering calculations are performed on a new Na_3 quartet potential energy surface. An analysis of scattering features is performed through a systematic variation of the nonadditive three-body interaction potential. Our results should provide useful information for interpreting future atom-molecule collision experiments.

quant-ph↗
arXiv2008

Semigroup of positive maps for qudit states and entanglement in tomographic probability representation

Stochastic and bistochastic matrices providing positive maps for spin states (for qudits) are shown to form semigroups with dense intersection with the Lie groups $IGL(n, \mathbb{R})$ and $GL(n, \mathbb{R})$ respectively. The density matrix of a qudit state is shown to be described by a spin tomogram determined by an orbit of the bistochastic semigroup acting on a simplex. A class of positive maps acting transitively on quantum states is introduced by relating stochastic and quantum stochastic maps in the tomographic setting. Finally, the entangled states of two qubits and Bell inequalities are given in the framework of the tomographic probability representation using the stochastic semigroup properties.

quant-ph↗
arXiv2008

Accurate near-threshold model for ultracold KRb dimers from interisotope Feshbach spectroscopy

We investigate magnetic Feshbach resonances in two different ultracold K-Rb mixtures. Information on the K(39)-Rb(87) isotopic pair is combined with novel and pre-existing observations of resonance patterns for K(40)-Rb(87). Interisotope resonance spectroscopy improves significantly our near-threshold model for scattering and bound-state calculations. Our analysis determines the number of bound states in singlet/triplet potentials and establishes precisely near threshold parameters for all K-Rb pairs of interest for experiments with both atoms and molecules. In addition, the model verifies the validity of the Born-Oppenheimer approximation at the present level of accuracy.

cond-mat.other↗
arXiv2007

A tomographic setting for quasi-distribution functions

The method of constructing the tomographic probability distributions describing quantum states in parallel with density operators is presented. Known examples of Husimi-Kano quasi-distribution and photon number tomography are reconsidered in the new setting. New tomographic schemes based on coherent states and nonlinear coherent states of deformed oscillators, including q-oscillators, are suggested. The associated identity decompositions providing Gram-Schmidt operators are explicitly given, and contact with the Agarwal-Wolf $Ω$-operator ordering theory is made.

quant-ph↗
arXiv2007

Feshbach resonances in ultracold K(39)

We discover several magnetic Feshbach resonances in collisions of ultracold K(39) atoms, by studying atom losses and molecule formation. Accurate determination of the magnetic-field resonance locations allows us to optimize a quantum collision model for potassium isotopes. We employ the model to predict the magnetic-field dependence of scattering lengths and of near-threshold molecular levels. Our findings will be useful to plan future experiments on ultracold potassium atoms and molecules.

physics.atom-ph↗
arXiv2007

39-K Bose-Einstein condensate with tunable interactions

We produce a Bose-Einstein condensate of 39-K atoms. Condensation of this species with naturally small and negative scattering length is achieved by a combination of sympathetic cooling with 87-Rb and direct evaporation, exploiting the magnetic tuning of both inter- and intra-species interactions at Feshbach resonances. We explore tunability of the self-interactions by studying the expansion and the stability of the condensate. We find that a 39-K condensate is interesting for future experiments requiring a weakly interacting Bose gas.

cond-mat.other↗
arXiv2006

Tomography in abstract Hilbert spaces

The tomographic description of a quantum state is formulated in an abstract infinite dimensional Hilbert space framework, the space of the Hilbert-Schmidt linear operators, with trace formula as scalar product. Resolutions of the unity, written in terms of over-complete sets of rank-one projectors and of associated Gram-Schmidt operators taking into account their non-orthogonality, are then used to reconstruct a quantum state from its tomograms. Examples of well known tomographic descriptions illustrate the exposed theory.

quant-ph↗