Alfredo Luis

Degree of coherence for vectorial electromagnetic fields as the distance between correlation matrices

We assess the degree of coherence of vectorial electromagnetic fields in the space-frequency domain as the distance between the cross-spectral density matrix and the identity matrix representing completely incoherent light. This definition is compared with previous approaches. It is shown that this distance provides an upper bound for the degree of coherence and visibility for any pair of scalar waves obtained by linear combinations of the original fields. This same approach emerges when applying a previous definition of global coherence to a Young interferometer.

Chirality quantum phase transition in the Dirac oscillator

We study a relativistic spin-1/2 fermion subjected to a Dirac oscillator coupling and a constant magnetic field. An interplay between opposed chirality interactions culminates in the appearance of a relativistic quantum phase transition, which can be fully characterized. We obtain analytical expressions for the energy gap, order parameter, and canonical quantum fluctuations across the critical point. Moreover, we also discuss the effect of this phase transition on the statistics of the chiral bosonic ensemble, where its super- or sub-Poissonian nature can be controlled by means of external parameters. Finally, we study the entanglement properties between the degrees of freedom in the relativistic ground state, where an interesting transition between a biseparable and a genuinely tripartite entangled state occurs.

Precision quantum metrology and nonclassicality in linear and nonlinear detection schemes.

We examine whether metrological resolution beyond coherent states is a nonclassical effect. We show that this is true for linear detection schemes but false for nonlinear schemes, and propose a very simple experimental setup to test it. We find a nonclassicality criterion derived from quantum Fisher information.

Nonrelativistic limit in the 2+1 Dirac oscillator: A Ramsey-interferometry effect

We study the nonrelativistic limit of a paradigmatic model in relativistic quantum mechanics, the two-dimensional Dirac oscillator. Remarkably, we find a different kind of Zitterbewegung which persists in this nonrelativistic regime, and leads to an observable deformation of the particle orbit. This effect can be interpreted in terms of a Ramsey-interferometric phenomenon, allowing an insightful connection between relativistic quantum mechanics and quantum optics. Furthermore, subsequent corrections to the nonrelativistic limit, which account for the usual spin-orbit Zitterbewegung, can be neatly understood in terms of a Mach-Zehnder interferometer.

Irreversible effects of random unitary transformations on coherence properties of partially polarized electromagnetic fields

We demonstrate monotonic, irreversible effects on the entropy, the degree of polarization, and different degrees of coherence when random, energy-preserving unitary transformations are applied to vectorial electromagnetic fields.

Polarization correlations in quantum optics

We introduce a formalism to assess polarization correlations based on a suitably defined probability distribution for polarization (the SU(2) Q function). Polarization correlations are measured as the distance between the joint distribution and the product of individual distributions. We show that this formalism is superior to previous approaches based on the Stokes parameters. We apply it to some relevant field states focusing on the relation between polarization correlations and the degree of polarization of the individual modes. We introduce also a degree of two-mode polarization. The examples analyzed reveal the complementarity between polarization correlations and the degree of two-mode polarization.

Characterization of quantum angular-momentum fluctuations via principal components

We elaborate an approach to quantum fluctuations of angular momentum based on the diagonalization of the covariance matrix in two versions: real symmetric and complex Hermitian. At difference with previous approaches this is SU(2) invariant and avoids any difficulty caused by nontrivial commutators. Meaningful uncertainty relations are derived which are nontrivial even for vanishing mean angular momentum. We apply this approach to some relevant states.

Overall degree of coherence for vectorial electromagnetic fields and the Wigner function

We elaborate the overall degree of coherence for vectorial electromagnetic waves within paraxial approximation, expressing it in terms of a polarization Wigner function and the spatial-angular Stokes parameters.

Ray picture of polarization and coherence in a Young interferometer

We apply a polarization Wigner formalism to the propagation of polarization in a Young interferometer within paraxial approximation. With a very simple ray picture, we obtain complete and rigorous information about polarization evolution via the superposition of the spatial-angular Stokes parameters associated with three light rays. We compare the degree of polarization in the interference region with several measures of the degree of coherence for vectorial fields.

Quantum mechanics as a geometric phase: phase-space interferometers

It is shown that basic quantum commutation relations are equivalent to a geometric phase. We propose two interferometric arrangements that are able to measure this quantum geometric phase via interference in phase space.