Single-shot measurement of quantum optical phase.

Although the canonical phase of light, which is defined as the complement of photon number, has been described theoretically by a variety of distinct approaches, there have been no methods proposed for its measurement. Indeed doubts have been expressed about whether or not it is measurable. Here we show how it is possible, at least in principle, to perform a single-shot measurement of the canonical phase using beam splitters, mirrors, phase shifters, and photodetectors.

Master equation for retrodiction of quantum communication signals.

We derive the master equation that governs the evolution of the measured state backwards in time in an open system. This allows us to determine probabilities for a given set of preparation events from the results of subsequent measurements, which has particular relevance to quantum communication.

Adiabatic refocusing pulse which compensates for variable rf power and off-resonance effects.

Adiabatic 180 degrees inversion rf pulses can be converted to 180 degrees refocusing pulses by inverting the effective field midway during the pulse. Suitable pulses retain insensitivity to large variations in the rf field strength and act over a reasonable spectral width. Such pulses may find application in studies utilizing surface coils.

Theory of localized polarization transfer.

Because polarization transfer from one type of nucleus to another can occur only when both types of nuclei are excited, it is possible, by using two separate rf coils for the excitation, to restrict the spatial region of the sample from which a signal can be received to a specific volume of overlap of the two inhomogeneous field patterns. In this paper we develop the theory of this method of localization in a homogeneous static field. The polarization transfer is achieved by a generalized phase-cycled DEPT sequence, in which case the method has the additional advantage of a gain in sensitivity of a 13C signal associated with the maximum polarization-transfer enhancement. Localization by means of the inverse-DEPT sequence is also studied, and off-resonance effects are calculated. Experimental confirmation of the theoretical expressions is given.

Sensitive-volume localization for in vivo NMR using heteronuclear spin-echo pulse sequences.

Heteronuclear spin-echo techniques, which require the application of an inversion pulse on the second heteronucleus, may be applied with inhomogeneous rf coils such as surface coils. There are important applications in vivo including the detection of 13C-labeled and 15N-labeled metabolites in the 1H NMR spectrum. Using a depth pulse scheme for the 1H spin-echo sequence, and particular single or composite 13C pulses, two sensitive volumes are generated by the 1H and the 13C rf coils and signal is only obtained from the region of overlap between the two sensitive volumes. This method of signal localization for in vivo applications can be extended to 1H homonuclear editing and selective polarization-transfer techniques. The off-resonance characteristics of several different composite pulses are explored.

Theoretical description of depth pulse sequences, on and off resonance, including improvements and extensions thereof.

A general mathematical description of depth pulse sequences in terms of rotation matrices permits a single matrix, known as a cycle matrix, to be written down for each phase-cycled pulse in the overall sequence, such that the result for the total phase-cycled sequence is the product of the individual cycle matrices. It is straightforward to include the effect of the tilted rf axis off resonance and obtain exact solutions. The two types of phase-cycled pulse used in a depth pulse scheme are 2 theta [+/- x] and 2 theta [+/- x, +/- y] and for the general off-resonance case, four of the off-diagonal elements in the 2 theta [+/- x] cycle matrix, and all of the off-diagonal elements in the 2 theta [+/- x, +/- y] cycle matrix, are zero. These simplifications enable important improvements of depth pulse schemes for the elimination of high-flux signals, the reduction of signals from sample regions experiencing pulse angles differing from 90 degrees, and the avoidance of deleterious off-resonance effects such as the production of dispersion signals. In all cases, the dependence of signal intensity off resonance can be easily and exactly calculated. There are important applications in in vivo spectroscopy.