Nonlinear optics with less than one photon

We demonstrate suppression and enhancement of spontaneous parametric down- conversion via quantum interference with two weak fields from a local oscillator (LO). Pairs of LO photons are observed to upconvert with high efficiency for appropriate phase settings, exhibiting an effective nonlinearity enhanced by at least 10 orders of magnitude. This constitutes a two-photon switch, and promises to be useful for a variety of nonlinear optical effects at the quantum level.Comment: 8 pages, 5 figure

Doctor of Philosophy

dissertationA paleoenvironmental reconstruction is presented from the Bear River Range, southeast Idaho. Reconstructed environmental conditions are inferred from paleoecological proxies, including pollen, macrofossils, and macroscopic charcoal from lacustrine sediments taken from Plan B Pond. A second, complementary paleoenvironmental reconstruction is presented based on stable carbon and oxygen isotope measurements of speleothem calcite collected from Minnetonka Cave, located just 8 km from Plan B Pond. The paleoenvironmental reconstructions from the two Bear River Range records suggest that each record contains significant seasonal bias, with the speleothem and sedimentary charcoal records primarily recording winter-season variability over time, and the pollen and macrofossil data recording summer conditions. Together, the Bear River Range data show a comprehensive picture of Holocene hydroclimatic conditions, and refines our understanding of controls on water resource variability in the region. Based on the Bear River Range records, the study area experienced cool, wet winters, and hot, dry summers in the early Holocene (prior to ~7500 BP), as compared to modern. The middle Holocene (7500-4000 BP) was characterized by dry and consistently warming winters, with dry, warm summers. The Late Holocene (4500 BP-Modern) has been characterized by cooler summers, with generally wetter, but increasingly variable, winter conditions. The results of this study indicate that previously published paleoclimate reconstructions from the Western United States must be considered carefully when using them to understand large-scale ocean atmosphere teleconnection patterns such as El-Nino Southern Oscillation (ENSO) and Pacific Decadal Oscillation (PDO). Because these teleconnection patterns are associated with spatially consistent seasonal precipitation and temperature anomalies, paleoclimate records must be evaluated for seasonal bias, if they are to be used for reconstructing past strength or presence of the teleconnection anomalies

Optimal experiment design revisited: fair, precise and minimal tomography

Given an experimental set-up and a fixed number of measurements, how should one take data in order to optimally reconstruct the state of a quantum system? The problem of optimal experiment design (OED) for quantum state tomography was first broached by Kosut et al. [arXiv:quant-ph/0411093v1]. Here we provide efficient numerical algorithms for finding the optimal design, and analytic results for the case of 'minimal tomography'. We also introduce the average OED, which is independent of the state to be reconstructed, and the optimal design for tomography (ODT), which minimizes tomographic bias. We find that these two designs are generally similar. Monte-Carlo simulations confirm the utility of our results for qubits. Finally, we adapt our approach to deal with constrained techniques such as maximum likelihood estimation. We find that these are less amenable to optimization than cruder reconstruction methods, such as linear inversion.Comment: 16 pages, 7 figure

Classical dispersion-cancellation interferometry

Even-order dispersion cancellation, an effect previously identified with frequency-entangled photons, is demonstrated experimentally for the first time with a linear, classical interferometer. A combination of a broad bandwidth laser and a high resolution spectrometer was used to measure the intensity correlations between anti-correlated optical frequencies. Only 14% broadening of the correlation signal is observed when significant material dispersion, enough to broaden the regular interferogram by 4250%, is introduced into one arm of the interferometer.Comment: 4 pages, 3 figure

Comment on "A linear optics implementation of weak values in Hardy's paradox"

A recent experimental proposal by Ahnert and Payne [S.E. Ahnert and M.C. Payne, Phys. Rev. A 70, 042102 (2004)] outlines a method to measure the weak value predictions of Aharonov in Hardy's paradox. This proposal contains flaws such as the state preparation method and the procedure for carrying out the requisite weak measurements. We identify previously published solutions to some of the flaws.Comment: To be published in Physical Review

Quantum phase estimation with lossy interferometers

We give a detailed discussion of optimal quantum states for optical two-mode interferometry in the presence of photon losses. We derive analytical formulae for the precision of phase estimation obtainable using quantum states of light with a definite photon number and prove that maximization of the precision is a convex optimization problem. The corresponding optimal precision, i.e. the lowest possible uncertainty, is shown to beat the standard quantum limit thus outperforming classical interferometry. Furthermore, we discuss more general inputs: states with indefinite photon number and states with photons distributed between distinguishable time bins. We prove that neither of these is helpful in improving phase estimation precision.Comment: 12 pages, 5 figure