The presence of loss limits the precision of an approach to phase measurement using maximally entangled states, also referred to as NOON states. A calculation using a simple beam-splitter model of loss shows that, for all nonzero values L of the loss, phase measurement precision degrades with increasing number N of entangled photons for N sufficiently large. For L above a critical value of approximately 0.785, phase measurement precision degrades with increasing N for all values of N . For L near zero, phase measurement precision improves with increasing N down to a limiting precision of approximately 1.018L radians, attained at N approximately equal to 2.218/L, and degrades as N increases beyond this value. Phase measurement precision with multiple measurements and a fixed total number of photons N T is also examined. For L above a critical value of approximately 0.586, the ratio of phase measurement precision attainable with NOON states to that attainable by conventional methods using unentangled coherent states degrades with increasing N , the number of entangled photons employed in a single measurement, for all values of N . For L near zero this ratio is optimized by using approximately N = 1.279/L entangled photons in each measurement, yielding a precision of approximately 1.340 L/N T radians.

We describe and demonstrate sensitive room-temperature detection of terahertz (THz) radiation by nonlinearly upconverting terahertz to the near-infrared regime, relying on telecommications components. THz radiation at 700 GHz is mixed with pump light at 1550 nm in a bulk GaAs crystal to generate an idler wave at 1555.6 nm, which is separated and detected by using a commercial p-i-n diode. The THz detector operates at room temperature and has an intrinsic THz-to-optical photon conversion efficiency of 0.001%.

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We have investigated the application of near-IR reflectance spectroscopy to the determination of motor oil contamination in sandy loam. Although the present work is concerned with a specific case of contamination, we discuss the possibility of applying the method to other organic contaminants and other types of soil. The spectral region considered was 1600–1900 nm, which contains the first overtone of the CH stretch. Using a commercial Fourier transform spectrometer together with cross-validated partial least-squares data analysis, the one-sigma precision for the determination of motor oil in sandy loam was 0.17 wt % (0.13 to 0.26 wt % at the 95% confidence level). The largest contribution to the precision of the determination was sampling error, or inhomogeneity in each sample. Given the precision limit imposed by the sampling error, we found that the performance of the spectrometer could be lowered without affecting the overall precision. In a modeling exercise, adequate performance was obtained with a spectrometer having only seven spectral channels with a spectral resolution of 10 nm and a spectral noise level of 10−3 absorbance units. A design for an inexpensive miniature instrument is presented.