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P M Koch

Publications and source records attributed to P M Koch.

8 recordsLinked to original sources
PubMed2006

Ghost orbit spectroscopy.

Direct periodic-orbit expansions of individual spectral eigenvalues is a new direction in quantum mechanics. Using a unitary -matrix theory, we present exact, convergent, integral-free ghost orbit expansions of spectral eigenvalues for a step potential in the tunneling regime. We suggest an experiment to extract ghost orbit information from measured spectra in the tunneling regime (ghost orbit spectroscopy). We contrast our unitary, convergent theory with a recently published nonunitary, divergent theory [Yu. Dabaghian and R. Jensen, Eur. J. Phys. 26, 423 (2005)].

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PubMed2005

Weyl formula: experimental test of ray splitting and corner corrections.

The number of resonances N(f) of a resonator below frequency f is an essential concept in physics. Smooth approximations N(f) are known as Weyl formulas. An abrupt change in the properties of the wave propagation medium in a resonator was predicted by Prange [Phys. Rev. E 53, 207 (1996)] to produce a universal ray-splitting correction to N(f). We confirm this effect experimentally. Our results with a quasi-two-dimensional dielectric-loaded microwave cavity are directly relevant to the ray-splitting correction in two-dimensional quantal ray-splitting billiards. Our experimental spectra have sufficient accuracy and extent to allow, as far as we are aware, the first experimental determination of the corner correction, which we find to agree with theory. We show that our movable-bar setup enhances non-Newtonian periodic orbits, thereby providing an experimental technique for periodic-orbit spectroscopy. This technique, differential spectroscopy, will facilitate the study of non-Newtonian classical physics.

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PubMed2001

Use of the relative phase in a bichromatic field pulse to control a quasienergy gap.

We show experimentally and theoretically how the relative phase in a short, linearly polarized microwave pulse consisting of two phase-locked frequencies is effective for strong-field quantum control of He Rydberg atoms when the frequency ratio p:q is 3:1. It is also effective when p:q = 2:1 but less effective for 3:2. Parameters in our experiment are similar to those investigating quantum control of tightly bound atoms or molecules with ultrashort pulsed lasers.

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PubMed1997

Use of four mirrors to rotate linear polarization but preserve input-output collinearity. II.

We report on the design, construction, and testing of a four-mirror reflective polarization rotator, proposed by Smith and Koch [J. Opt. Soc. Am. A 13, 2102 (1996)], that rotates by an angle phi the input linear polarization while preserving the input-output beam collinearity. We correct errors in the previous work that led to an incorrect design for a phi = pi/2 rotator. This type of pure rotator is simple and inexpensive, and it is a direct application of the concept of the nonadiabatic geometric phase to polarization rotation. We also present measurements of the polarization rotation for the case of three metallic mirrors with antiparallel input and output beams, a test of geometric phase in polarization optics not done before.

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