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

How can humans understand their automated cars? HMI principles, problems and solutions

As long as vehicles do not provide full automation, the design and function of the Human Machine Interface (HMI) is crucial for ensuring that the human “driver” and the vehicle-based automated systems collaborate in a safe manner. When the driver is decoupled from active control, the design of the HMI becomes even more critical. Without mutual understanding, the two agents (human and vehicle) will fail to accurately comprehend each other’s intentions and actions. This paper proposes a set of design principles for in-vehicle HMI and reviews some current HMI designs in the light of those principles. We argue that in many respects, the current designs fall short of best practice and have the potential to confuse the driver. This can lead to a mismatch between the operation of the automation in the light of the current external situation and the driver’s awareness of how well the automation is currently handling that situation. A model to illustrate how the various principles are interrelated is proposed. Finally, recommendations are made on how, building on each principle, HMI design solutions can be adopted to address these challenges

Cumulative Effects in 100 kHz Repetition-Rate Laser-Induced Plasma Filaments in Air

Cumulative effects are crucial for applications of laser filaments, such as for the remote transfer of energy and the control of electric discharges. Up to now, studies of cumulative effects in the air of high-repetition-rate pulse trains have been performed at lower rates than 10 kHz. Herein, the nonlinear effects associated with short plasma filaments produced by pulses of moderate energy (0.4 mJ per pulse) and repetition rates up to 100 kHz are experimentally characterized. With increasing repetition rate, a decrease in absorption, fluorescence emission, and breakdown voltage and concurrently an increase in peak intensity and third-harmonic-generation efficiency are observed. Hydrodynamic simulations of the heated gas show that the observed decreases are directly related to a quasi-stationary state of reduced gas density in the filament. However, further investigations are required to fully understand the physics underpinning the observed sharp reduction of the breakdown voltage at 100 kHz repetition rates. The results may prove relevant for energy and information delivery applications by laser-induced air waveguide or electric discharge and lightning control