Maori economic development - Glimpses from statistical sources

This draft book chapter provide an overview of Maori economic development during the past 150 years, drawing on readily available statistical and historical sources. The path of Maori economic development that we have traced through statistical evidence is one of ongoing change and adaptation, as well as one of substantial increase in material standards of living, albeit with periods of significant setback.Maori economic development

Radiative Hydrodynamic Simulations of HD209458b: Temporal Variability

We present a new approach for simulating the atmospheric dynamics of the close-in giant planet HD209458b that allows for the decoupling of radiative and thermal energies, direct stellar heating of the interior, and the solution of the full 3D Navier Stokes equations. Simulations reveal two distinct temperature inversions (increasing temperature with decreasing pressure) at the sub-stellar point due to the combined effects of opacity and dynamical flow structure and exhibit instabilities leading to changing velocities and temperatures on the nightside for a range of viscosities. Imposed on the quasi-static background, temperature variations of up to 15% are seen near the terminators and the location of the coldest spot is seen to vary by more than 20 degrees, occasionally appearing west of the anti-solar point. Our new approach introduces four major improvements to our previous methods including simultaneously solving both the thermal energy and radiative equations in both the optical and infrared, incorporating updated opacities, including a more accurate treatment of stellar energy deposition that incorporates the opacity relevant for higher energy stellar photons, and the addition of explicit turbulent viscosity.Comment: Accepted for publication in Ap

Precision frequency measurements with interferometric weak values

We demonstrate an experiment which utilizes a Sagnac interferometer to measure a change in optical frequency of 129 kHz per root Hz with only 2 mW of continuous wave, single mode input power. We describe the measurement of a weak value and show how even higher frequency sensitivities may be obtained over a bandwidth of several nanometers. This technique has many possible applications, such as precision relative frequency measurements and laser locking without the use of atomic lines.Comment: 4 pages, 3 figures, published in PR

Ultrasensitive Beam Deflection Measurement via Interferometric Weak Value Amplification

We report on the use of an interferometric weak value technique to amplify very small transverse deflections of an optical beam. By entangling the beam's transverse degrees of freedom with the which-path states of a Sagnac interferometer, it is possible to realize an optical amplifier for polarization independent deflections. The theory for the interferometric weak value amplification method is presented along with the experimental results, which are in good agreement. Of particular interest, we measured the angular deflection of a mirror down to 560 femtoradians and the linear travel of a piezo actuator down to 20 femtometers

Optimizing the Signal to Noise Ratio of a Beam Deflection Measurement with Interferometric Weak Values

The amplification obtained using weak values is quantified through a detailed investigation of the signal to noise ratio for an optical beam deflection measurement. We show that for a given deflection, input power and beam radius, the use of interferometric weak values allows one to obtain the optimum signal to noise ratio using a coherent beam. This method has the advantage of reduced technical noise and allows for the use of detectors with a low saturation intensity. We report on an experiment which improves the signal to noise ratio for a beam deflection measurement by a factor of 54 when compared to a measurement using the same beam size and a quantum limited detector

Continuous phase amplification with a Sagnac interferometer

We describe a weak value inspired phase amplification technique in a Sagnac interferometer. We monitor the relative phase between two paths of a slightly misaligned interferometer by measuring the average position of a split-Gaussian mode in the dark port. Although we monitor only the dark port, we show that the signal varies linearly with phase and that we can obtain similar sensitivity to balanced homodyne detection. We derive the source of the amplification both with classical wave optics and as an inverse weak value.Comment: 5 pages, 4 figures, previously submitted for publicatio

Realization of an all-optical zero to π cross-phase modulation jump

We report on the experimental demonstration of an all-optical π cross-phase modulation jump. By performing a preselection, an optically induced unitary transformation, and then a postselection on the polarization degree of freedom, the phase of the output beam acquires either a zero or π phase shift (with no other possible values). The postselection results in optical loss in the output beam. An input state may be chosen near the resulting phase singularity, yielding a pi phase shift even for weak interaction strengths. The scheme is experimentally demonstrated using a coherently prepared dark state in a warm atomic cesium vapor

Interferometric weak value deflections: quantum and classical treatments

We derive the weak value deflection given in a paper by Dixon et al. (Phys. Rev. Lett. 102, 173601 (2009)) both quantum mechanically and classically. This paper is meant to cover some of the mathematical details omitted in that paper owing to space constraints

Ultrasensitive Beam Deflection Measurement via Interferometric Weak Value Amplification

We report on the use of an interferometric weak value technique to amplify very small transverse deflections of an optical beam. By entangling the beam’s transverse degrees of freedom with the which-path states of a Sagnac interferometer, it is possible to realize an optical amplifier for polarization independent deflections. The theory for the interferometric weak value amplification method is presented along with the experimental results, which are in good agreement. Of particular interest, we measured the angular deflection of a mirror down to 40

Precision Frequency Measurements with Interferometric Weak Values

We demonstrate an experiment which utilizes a Sagnac interferometer to measure a change in optical frequency of 129 ± 7 kHz/√Hz with only 2 mW of continuous-wave, single-mode input power. We describe the measurement of a weak value and show how even higher-frequency sensitivities may be obtained over a bandwidth of several nanometers. This technique has many possible applications, such as precision relative frequency measurements and laser locking without the use of atomic lines