Physical realization of coupled Hilbert-space mirrors for quantum-state engineering

Manipulation of superpositions of discrete quantum states has a mathematical counterpart in the motion of a unit-length statevector in an N-dimensional Hilbert space. Any such statevector motion can be regarded as a succession of two-dimensional rotations. But the desired statevector change can also be treated as a succession of reflections, the generalization of Householder transformations. In multidimensional Hilbert space such reflection sequences offer more efficient procedures for statevector manipulation than do sequences of rotations. We here show how such reflections can be designed for a system with two degenerate levels - a generalization of the traditional two-state atom - that allows the construction of propagators for angular momentum states. We use the Morris-Shore transformation to express the propagator in terms of Morris-Shore basis states and Cayley-Klein parameters, which allows us to connect properties of laser pulses to Hilbert-space motion. Under suitable conditions on the couplings and the common detuning, the propagators within each set of degenerate states represent products of generalized Householder reflections, with orthogonal vectors. We propose physical realizations of this novel geometrical object with resonant, near-resonant and far-off-resonant laser pulses. We give several examples of implementations in real atoms or molecules.Comment: 15 pages, 6 figure

Focusing and Compression of Ultrashort Pulses through Scattering Media

Light scattering in inhomogeneous media induces wavefront distortions which pose an inherent limitation in many optical applications. Examples range from microscopy and nanosurgery to astronomy. In recent years, ongoing efforts have made the correction of spatial distortions possible by wavefront shaping techniques. However, when ultrashort pulses are employed scattering induces temporal distortions which hinder their use in nonlinear processes such as in multiphoton microscopy and quantum control experiments. Here we show that correction of both spatial and temporal distortions can be attained by manipulating only the spatial degrees of freedom of the incident wavefront. Moreover, by optimizing a nonlinear signal the refocused pulse can be shorter than the input pulse. We demonstrate focusing of 100fs pulses through a 1mm thick brain tissue, and 1000-fold enhancement of a localized two-photon fluorescence signal. Our results open up new possibilities for optical manipulation and nonlinear imaging in scattering media

Estimating EQ-5D utilities based on the Short-Form Long Term Conditions Questionnaire (LTCQ-8)

Purpose: The aim of this work was to develop a mapping algorithm for estimating EuroQoL 5 Dimension (EQ-5D) utilities from responses to the Long-Term Conditions Questionnaire (LTCQ), thus increasing LTCQ’s potential as a comprehensive outcome measure for evaluating integrated care initiatives. Methods: We combined data from three studies to give a total sample of 1334 responses. In each of the three datasets, we randomly selected 75% of the sample and combined the selected random samples to generate the estimation dataset, which consisted of 1001 patients. The unselected 25% observations from each dataset were combined to generate an internal validation dataset of 333 patients. We used direct mapping models by regressing responses to the LTCQ-8 directly onto EQ-5D-5L and EQ-5D-3L utilities as well as response (or indirect) mapping to predict the response level that patients selected for each of the five EQ-5D-5L domains. Several models were proposed and compared on mean squared error and mean absolute error. Results: A two-part model with OLS was the best performing based on the mean squared error (0.038) and mean absolute error (0.147) when estimating the EQ-5D-5L utilities. A multinomial response mapping model using LTCQ-8 responses was used to predict EQ-5D-5L responses levels. Conclusions: This study provides a mapping algorithm for estimating EQ-5D utilities from LTCQ responses. The results from this study can help broaden the applicability of the LTCQ by producing utility values for use in economic analyses