Trihamiltonian extensions of separable systems in the plane

A method to construct trihamiltonian extensions of a separable system is presented. The procedure is tested for systems, with a natural Hamiltonian, separable in classical sense in one of the four orthogonal separable coordinate systems of the Euclidean plane, and some explicit examples are constructed. Finally a conjecture on possible generalizations to other classes of systems is discussed: in particular, the method can be easily adapted to the eleven orthogonal separable coordinate sets of the Euclidean three-space.Comment: 20 page

Quantum detection of electronic flying qubits

We consider a model of a detector of ballistic electrons at the edge of a two-dimensional electron gas in the integer quantum Hall regime. The electron is detected by capacitive coupling to a gate which is also coupled to a passive RC circuit. Using a quantum description of this circuit, we determine the signal over noise ratio of the detector in term of the detector characteristics. The back-action of the detector on the incident wavepacket is then computed using a Feynman-Vernon influence functional approach. Using information theory, we define the appropriate notion of quantum limit for such an "on the fly" detector. We show that our particular detector can approach the quantum limit up to logarithms in the ratio of the measurement time over the RC relaxation time. We argue that such a weak logarithmic effect is of no practical significance. Finally we show that a two-electron interference experiment can be used to probe the detector induced decoherence.Comment: 15 pages, 7 figures, published versio

Toward third order ghost imaging with thermal light

Recently it has been suggested that an enhancement in the visibility of ghost images obtained with thermal light can be achieved exploiting higher order correlations [3]. This paper reports on the status of an higher order ghost imaging experiment carried on at INRIM labs exploiting a pseudo-thermal source and a CCD camera.Comment: To be published in Proceedings of Recent advances in Foundations of Quantum Mechanics and Quantum Informatio

Intensity correlations, entanglement properties and ghost imaging in multimode thermal-seeded parametric downconversion: Theory

We address parametric-downconversion seeded by multimode pseudo-thermal fields. We show that this process may be used to generate multimode pairwise correlated states with entanglement properties that can be tuned by controlling the seed intensities. Multimode pseudo-thermal fields seeded parametric-downconversion represents a novel source of correlated states, which allows one to explore the classical-quantum transition in pairwise correlations and to realize ghost imaging and ghost diffraction in regimes not yet explored by experiments.Comment: 9 pages, 3 figure

Revealing interference by continuous variable discordant states

In general, a pair of uncorrelated Gaussian states mixed in a beam splitter produces a correlated state at the output. However, when the inputs are identical Gaussian states the output state is equal to the input, and no correlations appear, as the interference had not taken place. On the other hand, since physical phenomena do have observable effects, and the beam splitter is there, a question arises on how to reveal the interference between the two beams. We prove theoretically and demonstrate experimentally that this is possible if at least one of the two beams is prepared in a discordant, i.e. Gaussian correlated, state with a third beam. We also apply the same technique to reveal the erasure of polarization information. Our experiments involves thermal states and the results show that Gaussian discordant states, even when they show a positive Glauber P-function, may be useful to achieve specific tasks.Comment: published versio

Tri-hamiltonian vector fields, spectral curves and separation coordinates

We show that for a class of dynamical systems, Hamiltonian with respect to three distinct Poisson brackets (P_0, P_1, P_2), separation coordinates are provided by the common roots of a set of bivariate polynomials. These polynomials, which generalise those considered by E. Sklyanin in his algebro-geometric approach, are obtained from the knowledge of: (i) a common Casimir function for the two Poisson pencils (P_1 - \lambda P_0) and (P_2 - \mu P_0); (ii) a suitable set of vector fields, preserving P_0 but transversal to its symplectic leaves. The frameworks is applied to Lax equations with spectral parameter, for which not only it unifies the separation techniques of Sklyanin and of Magri, but also provides a more efficient ``inverse'' procedure not involving the extraction of roots.Comment: 49 pages Section on reduction revisite

Real time decoherence of Landau and Levitov quasi-particles in quantum Hall edge channels

Quantum Hall edge channels at integer filling factor provide a unique test-bench to understand decoherence and relaxation of single electronic excitations in a ballistic quantum conductor. In this Letter, we obtain a full visualization of the decoherence scenario of energy (Landau) and time (Levitov) resolved single electron excitations at filling factor $\nu=2$. We show that the Landau excitation exhibits a fast relaxation followed by spin-charge separation whereas the Levitov excitation only experiences spin-charge separation. We finally suggest to use Hong-Ou-Mandel type experiments to probe specific signatures of these different scenarios.Comment: 14 pages, 8 figure

Realization of a twin beam source based on four-wave mixing in Cesium

Four-wave mixing (4WM) is a known source of intense non-classical twin beams. It can be generated when an intense laser beam (the pump) and a weak laser beam (the seed) overlap in a $\chi^{(3)}$ medium (here cesium vapor), with frequencies close to resonance with atomic transitions. The twin beams generated by 4WM have frequencies naturally close to atomic transitions, and can be intense (gain $\gg 1$) even in the CW pump regime, which is not the case for PDC $\chi^{(2)}$ phenomenon in non-linear crystals. So, 4WM is well suited for atom-light interaction and atom-based quantum protocols. Here we present the first realization of a source of 4-wave mixing exploiting $D_2$ line of Cesium atoms.Comment: 10 pages, 10 figure