Where do bosons actually belong?

We explore a variety of reasons for considering su(1,1) instead of the customary h(1) as the natural unifying frame for characterizing boson systems. Resorting to the Lie-Hopf structure of these algebras, that shows how the Bose-Einstein statistics for identical bosons is correctly given in the su(1,1) framework, we prove that quantization of Maxwell's equations leads to su(1,1), relativistic covariance being naturally recognized as an internal symmetry of this dynamical algebra. Moreover su(1,1) rather than h(1) coordinates are associated to circularly polarized electromagnetic waves. As for interacting bosons, the su(1,1) formulation of the Jaynes-Cummings model is discussed, showing its advantages over h(1).Comment: 9 pages, to appear in J. Phys. A: Math. Theo

New quantumness domains through generalized squeezed states

Current definitions of both squeezing operator and squeezed vacuum state are critically examined on the grounds of consistency with the underlying su(1,1) algebraic structure. Accordingly, the generalized coherent states for su(1,1) in its Schwinger two-photon realization are proposed as squeezed states. The physical implication of this assumption is that two additional degrees of freedom become available for the control of quantum optical systems. The resulting physical predictions are evaluated in terms of quadrature squeezing and photon statistics, while the application to a Mach–Zehnder interferometer is discussed to show the emergence of nonclassical regions, characterized by negative values of Mandel’s parameter, which cannot be anticipated by the current formulation, and then outline future possible use in quantum technologies

Incoherent scattered radiation in diatomic molecules

Raman spectra excited in diatomic gases by the line λ2536 of mercury have been photographed with a quartz spectrograph. An apparatus for using gases at pressures from ten to fifteen atmospheres has been built, with great improvement as compared with the use of gases at atmospheric pressure. Results obtained with H2, N2, O2, NO are reported. A particularly complete investigation has been made of the hydrogen spectrum, leading to an accurate determination of the constants of the molecule in the normal electronic state. The numerical values are (in cm-1) B0=h/8π2I0c=59.40; ω0/1=4162.1. For N2, the corresponding values resulted to be: B0=1.992; ω0/1=2330.7. For O2: B0=1.436; ω0/1=1554.7. All these molecules are in Σ states, and the Raman spectra consist of Q-, double R-, and double P- form branches, as deduced from the Kramers-Heisenberg formula by the author and by Hill and Kemble. Nitric oxide is the only molecule so far investigated which is in a 2II state. The transition between the two terms of the doublet has been observed in the scattered radiation

Quantum geometry and quantum algorithms

Motivated by algorithmic problems arising in quantum field theories whose dynamical variables are geometric in nature, we provide a quantum algorithm that efficiently approximates the colored Jones polynomial. The construction is based on the complete solution of Chern-Simons topological quantum field theory and its connection to Wess-Zumino-Witten conformal field theory. The colored Jones polynomial is expressed as the expectation value of the evolution of the q-deformed spin-network quantum automaton. A quantum circuit is constructed capable of simulating the automaton and hence of computing such expectation value. The latter is efficiently approximated using a standard sampling procedure in quantum computation.Comment: Submitted to J. Phys. A: Math-Gen, for the special issue ``The Quantum Universe'' in honor of G. C. Ghirard

Quantum global vortex strings in a background field

We consider quantum global vortex string correlation functions, within the Kalb-Ramond framework, in the presence of a background field-strength tensor and investigate the conditions under which this yields a nontrivial contribution to those correlation functions. We show that a background field must be supplemented to the Kalb-Ramond theory, in order to correctly describe the quantum properties of the vortex strings. The explicit form of this background field and the associated quantum vortex string correlation function are derived. The complete expression for the quantum vortex creation operator is explicitly obtained. We discuss the potential applicability of our results in the physics of superfluids and rotating Bose-Einstein condensates.Comment: To appear in Journal of Physics A: Mathematical and Genera

Spin networks, quantum automata and link invariants

The spin network simulator model represents a bridge between (generalized) circuit schemes for standard quantum computation and approaches based on notions from Topological Quantum Field Theories (TQFT). More precisely, when working with purely discrete unitary gates, the simulator is naturally modelled as families of quantum automata which in turn represent discrete versions of topological quantum computation models. Such a quantum combinatorial scheme, which essentially encodes SU(2) Racah--Wigner algebra and its braided counterpart, is particularly suitable to address problems in topology and group theory and we discuss here a finite states--quantum automaton able to accept the language of braid group in view of applications to the problem of estimating link polynomials in Chern--Simons field theory.Comment: LateX,19 pages; to appear in the Proc. of "Constrained Dynamics and Quantum Gravity (QG05), Cala Gonone (Italy) September 12-16 200

Generalized Gibbs ensembles for time dependent processes

An information theory description of finite systems explicitly evolving in time is presented for classical as well as quantum mechanics. We impose a variational principle on the Shannon entropy at a given time while the constraints are set at a former time. The resulting density matrix deviates from the Boltzmann kernel and contains explicit time odd components which can be interpreted as collective flows. Applications include quantum brownian motion, linear response theory, out of equilibrium situations for which the relevant information is collected within different time scales before entropy saturation, and the dynamics of the expansion

Reconstructing Quantum Geometry from Quantum Information: Spin Networks as Harmonic Oscillators

Loop Quantum Gravity defines the quantum states of space geometry as spin networks and describes their evolution in time. We reformulate spin networks in terms of harmonic oscillators and show how the holographic degrees of freedom of the theory are described as matrix models. This allow us to make a link with non-commutative geometry and to look at the issue of the semi-classical limit of LQG from a new perspective. This work is thought as part of a bigger project of describing quantum geometry in quantum information terms.Comment: 16 pages, revtex, 3 figure