Invariant vector fields and the prolongation method for supersymmetric quantum systems

The kinematical and dynamical symmetries of equations describing the time evolution of quantum systems like the supersymmetric harmonic oscillator in one space dimension and the interaction of a non-relativistic spin one-half particle in a constant magnetic field are reviewed from the point of view of the vector field prolongation method. Generators of supersymmetries are then introduced so that we get Lie superalgebras of symmetries and supersymmetries. This approach does not require the introduction of Grassmann valued differential equations but a specific matrix realization and the concept of dynamical symmetry. The Jaynes-Cummings model and supersymmetric generalizations are then studied. We show how it is closely related to the preceding models. Lie algebras of symmetries and supersymmetries are also obtained.Comment: 37 pages, 7 table

On supersymmetric quantum mechanics

This paper constitutes a review on N=2 fractional supersymmetric Quantum Mechanics of order k. The presentation is based on the introduction of a generalized Weyl-Heisenberg algebra W_k. It is shown how a general Hamiltonian can be associated with the algebra W_k. This general Hamiltonian covers various supersymmetrical versions of dynamical systems (Morse system, Poschl-Teller system, fractional supersymmetric oscillator of order k, etc.). The case of ordinary supersymmetric Quantum Mechanics corresponds to k=2. A connection between fractional supersymmetric Quantum Mechanics and ordinary supersymmetric Quantum Mechanics is briefly described. A realization of the algebra W_k, of the N=2 supercharges and of the corresponding Hamiltonian is given in terms of deformed-bosons and k-fermions as well as in terms of differential operators.Comment: Review paper (31 pages) to be published in: Fundamental World of Quantum Chemistry, A Tribute to the Memory of Per-Olov Lowdin, Volume 3, E. Brandas and E.S. Kryachko (Eds.), Springer-Verlag, Berlin, 200

Right-unitary transformation theory and applications

We develop a new transformation theory in quantum physics, where the transformation operators, defined in the infinite dimensional Hilbert space, have right-unitary inverses only. Through several theorems, we discuss the properties of state space of such operators. As one application of the right-unitary transformation (RUT), we show that using the RUT method, we can solve exactly various interactions of many-level atoms with quantized radiation fields, where the energy of atoms can be two levels, three levels in Lambda, V and equiv configurations, and up to higher (>3) levels. These interactions have wide applications in atomic physics, quantum optics and quantum electronics. In this paper, we focus on two typical systems: one is a two-level generalized Jaynes-Cummings model, where the cavity field varies with the external source; the other one is the interaction of three-level atom with quantized radiation fields, where the atoms have Lambda-configuration energy levels, and the radiation fields are one-mode or two-mode cavities.Comment: 51 pages, RevTeX; Figures not included but may be obtained from author by snail-mail; Accepted for publication by Phys. Rev.

Determination of reference values for optical properties of liquid phantoms based on Intralipid and India ink

A multi-center study has been set up to accurately characterize the optical properties of diffusive liquid phantoms based on Intralipid and India ink at near-infrared (NIR) wavelengths. Nine research laboratories from six countries adopting different measurement techniques, instrumental set-ups, and data analysis methods determined at their best the optical properties and relative uncertainties of diffusive dilutions prepared with common samples of the two compounds. By exploiting a suitable statistical model, comprehensive reference values at three NIR wavelengths for the intrinsic absorption coefficient of India ink and the intrinsic reduced scattering coefficient of Intralipid-20% were determined with an uncertainty of about 2% or better, depending on the wavelength considered, and 1%, respectively. Even if in this study we focused on particular batches of India ink and Intralipid, the reference values determined here represent a solid and useful starting point for preparing diffusive liquid phantoms with accurately defined optical properties. Furthermore, due to the ready availability, low cost, long-term stability and batch-to-batch reproducibility of these compounds, they provide a unique fundamental tool for the calibration and performance assessment of diffuse optical spectroscopy instrumentation intended to be used in laboratory or clinical environment. Finally, the collaborative work presented here demonstrates that the accuracy level attained in this work for optical properties of diffusive phantoms is reliable

Towards spatially dense time-domain multi-view detection in diffuse optical tomography with single-photon avalanche diodes and integrated TCSPC electronics

The advent of high timing resolution (<50ps) single photon avalanche diodes (SPADs) and progresses in time-correlated single photon counting (TCSPC) integrated electronics opens the way to multi-view higher spatial detection density time-domain (TD) diffuse optical tomography (DOT) scanners with unprecedented temporal resolution down to possibly below 30ps. The alternative to achieve high spatial density TD optical detection is to resort to time-gated cameras. However, such cameras have timing resolutions of ~300ps, and the time gate over which photons are acquired needs to be scanned resulting in a waste of useful photons and increased acquisition times compared to what could possibly be achieved. In recent years my group has been developing a TD DOT scanner for small animal imaging using discrete detectors and high performance TCSPC electronics. A first generation scanner using photomultiplier tubes (PMTs) has been realized, achieving a temporal resolution of ~200 ps. This scanner comprises 7 dual-wavelength channels for detecting excitation and fluorescence light. Its performances in terms of number of channels, acquisition time, and temporal resolution are, however, limited by the use of PMTs, expensive TCSPC cards and routers. Recently, work has been initiated on the development of a second generation scanner using SPADs and fully parallel TCSPC electronics (one TCSPC channel per detector). The development of the first generation scanner and a first prototype of the second generation scanner will be presented, along with results obtained therewith. Future work and promising applications of such technology, notably in in vivo FLIM-FRET imaging will also be described

Time-of-flight computed tomography - proof of principle

Computed tomography has greatly improved over the last decade, especially through x-ray dose exposure reduction while maintaining image quality. Herein, a new concept is proposed to improve the contrast-to-noise ratio (CNR) by including the time-of-flight (TOF) information of individual photons to obtain further insight on the photon's trajectory and to reject scatter contribution. The proof of the concept relies on both simulation and experimental measurements in a cone-beam computed tomography arrangement. Results show a statistical difference between the TOF of scattered and primary photons exploitable in TOF computed tomography. For a large volume of the size of a human abdomen, a scatter reduction from 296% to 4% is achieved in our simulation setup with perfect timing measurements which yields a 110% better CNR, or a dose reduction by a factor of four. Cup artifacts are also reduced from 24.7% to 0.8%, and attenuation inaccuracies are improved from −26.3% to −0.8%. With 100 ps and 10 ps FWHM timing jitters, respectively 75% and 95% of the scatter contribution can be removed with marginal gains below 10 ps. Experimental measurements confirm the feasibility of measuring statistical differences between the TOF of scattered and primary photons