Direct measurement of general quantum states using weak measurement

Recent work [J.S. Lundeen et al. Nature, 474, 188 (2011)] directly measured the wavefunction by weakly measuring a variable followed by a normal (i.e. `strong') measurement of the complementary variable. We generalize this method to mixed states by considering the weak measurement of various products of these observables, thereby providing the density matrix an operational definition in terms of a procedure for its direct measurement. The method only requires measurements in two bases and can be performed `in situ', determining the quantum state without destroying it.Comment: This is a later and very different version of arXiv:1110.0727v3 [quant-ph]. New content: a method to directly measure each element of the density matrix, specific Hamiltonians to weakly measure the product of non-commuting observables, and references to recent related wor

Direct Measurement of the Quantum Wavefunction

Central to quantum theory, the wavefunction is the complex distribution used to completely describe a quantum system. Despite its fundamental role, it is typically introduced as an abstract element of the theory with no explicit definition. Rather, physicists come to a working understanding of the wavefunction through its use to calculate measurement outcome probabilities via the Born Rule. Presently, scientists determine the wavefunction through tomographic methods, which estimate the wavefunction that is most consistent with a diverse collection of measurements. The indirectness of these methods compounds the problem of defining the wavefunction. Here we show that the wavefunction can be measured directly by the sequential measurement of two complementary variables of the system. The crux of our method is that the first measurement is performed in a gentle way (i.e. weak measurement) so as not to invalidate the second. The result is that the real and imaginary components of the wavefunction appear directly on our measurement apparatus. We give an experimental example by directly measuring the transverse spatial wavefunction of a single photon, a task not previously realized by any method. We show that the concept is universal, being applicable both to other degrees of freedom of the photon (e.g. polarization, frequency, etc.) and to other quantum systems (e.g. electron spin-z quantum state, SQUIDs, trapped ions, etc.). Consequently, this method gives the wavefunction a straightforward and general definition in terms of a specific set of experimental operations. We expect it to expand the range of quantum systems scientists are able to characterize and initiate new avenues to understand fundamental quantum theory

Impact of model physics on estimating the surface mass balance of the Greenland ice sheet

Long-term predictions of sea level rise from increased Greenland ice sheet melting have been derived using Positive Degree Day models only. It is, however, unknown precisely what uncertainties are associated with applying this simple surface melt parameterization for future climate. We compare the behavior of a Positive Degree Day and Energy Balance/ Snowpack model for estimating the surface mass balance of the Greenland ice sheet under a warming climate. Both models were first tuned to give similar values for present-day mass balance using 10 years of ERA-40 climatology and were then run for 300 years, forced with the output of a GCM in which atmospheric CO2 increased to 4 times preindustrial levels. Results indicate that the Positive Degree Day model is more sensitive to climate warming than the Energy Balance model, generating annual runoff rates almost twice as large for a fixed ice sheet geometry. Roughly half of this difference was due to differences in the volume of melt generated and half was due to differences in refreezing rates in the snowpack. Our results indicate that the modeled snowpack properties evolve on a multidecadal timescale to changing climate, with a potentially large impact on the mass balance of the ice sheet; an evolution that was absent from the Positive Degree Day model. Copyright 2007 by the American Geophysical Union

Object surface recovery using a multi-light photometric stereo technique for non-Lambertian surfaces subject to shadows and specularities

This paper presents a new multi-light source photometric stereo system for reconstructing images of various characteristics of non-Lambertian rough surfaces with widely varying texture and specularity. Compared to the traditional three-light photometric stereo method, extra lights are employed using a hierarchical selection strategy to eliminate the effects of shadows and specularities, and to make the system more robust. We also show that six lights is the minimum needed in order to apply photometric stereo to the entire visible surface of any convex object. Experiments on synthetic and real scenes demonstrate that the proposed method can extract surface reflectance and orientation effectively, even in the presence of strong shadows and highlights. Hence, the method offers advantages in the recovery of dichromatic surfaces possessing rough texture or deeply relieved topographic features, with applications in reverse engineering and industrial surface inspection. Experimental results are presented in the paper

Rapid scanning wide-field clutter elimination in epi-optoacoustic imaging using comb LOVIT

Epi-style optoacoustic (OA) imaging provides flexibility by integrating the irradiation optics and ultrasound receiver, yet clutter generated by optical absorption near the probe obscures deep OA sources. Localised vibration tagging (LOVIT) retrieves OA signal from images that are acquired with and without a preceding ultrasonic pushing beam: Radiation force leads to a phase shift of signals coming from the focal area resulting in their visibility in a difference image, whereas clutter from outside the pushing beam is eliminated. Disadvantages of a single-focus approach are residual clutter from inside the pushing beam above the focus, and time-intensive scanning of the focus to retrieve a large field-of-view. To speed up acquisition, we propose to create multiple foci in parallel, forming comb-shaped ARF patterns. By subtracting OA images obtained with interleaved combs, this technique moreover results in greatly improved clutter reduction in phantoms mimicking optical, acoustic and elastic properties of breast tissue. Keywords: Photoacoustic, Imaging depth, Handheld, Ultrasound, Radiation force, Shear wave, Image contras

Ultrasound transducer array

An ultrasonic transducer array and method of making an ultrasonic transducer array. The array comprising a plurality of individual array elements made from a piezoelectric composite which is made from a plurality of individual piezoelectric segments; a passive filler between the piezoelectric segments; and, one or more electrodes for driving the array elements formed from the piezoelectric segments; wherein the spatial pattern of the piezoelectric segments of the piezoelectric composite defines one or more non-linear, irregular channels which separate the piezoelectric segments thereby minimising interaction between the individual array elements and minimising spurious modes in the ultrasound transducer array