We use a continuous-time path integral to obtain the semiclassical propagator for minimal-spread spin coherent states. We pay particular attention to the "extra phase" discovered by Solari and Kochetov, and show that this correction is related to an anomaly in the fluctuation determinant. We show that, once this extra factor is included, the semiclassical propagator has the correct short time behaviour to O(T 2 ), and demonstrate its consistency under dissection of the path.

We present quantitative coherent measurements of scattering pulses and spectra in terahertz apertureless near-field microscopes. Broadband near-field image contrasts for both amplitude and phase spectra are measured directly from time-domain scattering signals with an unprecedentedly high single-scan signal-to-noise ratio (∼48 dB), with approach curves for both short (<200 nm) and long (up to 82 μm) ranges. By using the line dipole image method, we obtain quantitative broadband THz imaging contrasts with nanoscale resolution.

We investigated decoherence of a Josephson vortex quantum bit ͑qubit͒ in dissipative and noisy environment. As the Josephson vortex qubit ͑JVQ͒ is fabricated by using a long Josephson junction ͑LJJ͒, we use the perturbed sine-Gordon equation to describe the phase dynamics representing a two-state system and estimate the effects of quasiparticle dissipation and weakly fluctuating critical and bias currents on the relaxation time T 1 and on the dephasing time T . We show that the critical current fluctuation does not contribute to dephasing of the qubit in the lowest order approximation. Modeling the weak current variation from magnetic field fluctuations in the LJJ by using the Gaussian colored noise with long correlation time, we show that the coherence time T 2 is limited by the low frequency current noise at very low temperatures. Also, we show that a ultra-long coherence time may be obtained from the JVQ by using experimentally accessible value of physical parameters.

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