Photon polarization

Detect 100% of photons Photon detected as a delta function Large number of pixels Time tag for each photon Measure photon wavelength Measure photon polarization No detector noise fr Up to 99% detected fr One electron for each photon fr Over 377 million pixels 0 No - framing detectors 0 No - provided by optics 0 No - provided by optics 0 Readout noise and dark current... 

A phenomenological description of the differential cross-section for emission of photoelectrons into solid angle O in the lab frame can be written, assuming random molecular orientation and an axis of cylindrical symmetry defined by the photon polarization, as... 

By performing sequential SG experiments it can be shown that electron spin has much in common with photon polarization. In a typical arrangement the beam from the oven is first passed through an SGZ apparatus with the inhomogeneous magnetic field in the z-direction. Suppose the one (S ) component from this experiment is blocked and the second (5+), is allowed to pass into another SGZ apparatus. The beam emerging from the second device will be found to have no S component, exactly as for two parallel polaroids. 

The relationship between different components of orbital angular momentum such as Lz and Lx can be investigated by multiple SG experiments as discussed for electron spin and photon polarization before. The results are in fact no different. This is a consequence of the noncommutativity of the operators Lx and Lz. The two observables cannot be measured simultaneously. While total angular momentum is conserved, the components vary as the applied analyzing field changes. As in the case of spin or polarization, measurement of Lx, for instance, disturbs any previously known value of Lz. The structure of the wave function does not allow Lx to be made definite when Lz has an eigenvalue, and vice versa. 

Chronocoulometry and photon polarization modulation infrared reflec-tion/absorption spectroscopy have been employed [311] to study the fusion of dimyristoylphosphatidylcholine vesicles onto an Au(lll) electrode. The fusion was controlled either by the electrode potential, or charge. Film characteristics was also potential dependent. After removing the film from the electrode surface (negative potential), phospholipid molecules remained in its close proximity, in the ad-vesicle state. Several electrochemical and nonelec-trochemical methods have been applied [312, 313] to investigate the spreading of small unilamellar vesicles onto Au(lll) electrode. Vesicles fused onto the surface at > —0.5 V (versus SSCE), to form defected bilayers in contact with the metal surface. At more negative potentials, the film was removed from the electrode surface, but it still remained in its close proximity. 

Fig. 4 IPA (dashed line) and 2PA (solid line) spectra, and two-photon polarization ratio, (light dotted line) for phenylalanine, tyrosinamide, tryptophan. The abscissa corresponds to the excitation wavelength of the 2PA case. The IPA spectra are plotted at twice their excitation wavelength. The molecular structures are shown as insets in each graph. Reproduced with permission from [42]. 1993, Elsevier...

Due to the simplicity of the photon polarization operator the calculation based on the scattering approximation [8] is so straightforward that we can... 

Mgg, M g, [ = biphotonic transition, two photons polarized at right angles to each other. 

Figure 1 Angles 6 and

In this equation, the spherical angles 6 and

defined relative to the photon momentum k, photoelectron momentum p, and photon polarization vector e, as indicated in Figure 1, fi i is a dipole photoelectron angular distribution parameter, yni and Sni are nondipole photoelectron angular distribution parameters. 

The measurements were carried out using polarized-light from synchrotron radiation. The angle-resolved UPS spectra were recorded for specific directions of photon incidence, photon polarization, and electron exit, chosen in order to resolve the momentum dependence of the 7t-electron energy bands which could be observed in this experiment. Details are available elsewhere63. The UPS results are analysed not only with the help of the valence effective Hamiltonian (VEH) method, but also with the help of new quantum-chemical calculations based upon the excitation model method64. The full VEH band structure is shown in Fig. 7.32. 

When measuring absorption spectra, one records a signal that is related to the wavelength-dependent probability of making a spectroscopic transition. From the molecular point of view, this probability is proportional to the dot product jl p where (L is the molecular transition moment and p is the photon polarization direction. When the orientational distribution of the molecules is isotropic (not crystalline, liquid crystalline, or bound to a surface), its absorption spectrum represents the orientationally averaged probability of making a spectroscopic transition and the measured spectrum is independent of polarization direction. When the orientational distribution of the molecules is anisotropic, the probability of making a spectroscopic transition depends on the polarization direction, and that dependence can be exploited to deduce the direction of the transition moment relative to the laboratory frame. Because transition moments are often trivially related to the orientation of the molecule, structural information can be deduced from polarized absorption measurements on anisotropic samples. 

For angles 0 = 0°, 45° and 90°, the predictions of local realism and quantum mechanics agree. For the general case, a modification of Bell s inequality appropriate for photon polarizations was derived by Clau.ser. Horne, Shimony and Holt. The CHSH relation predicts <2, where... 

Bell s theorem is by now a well-established experimental fact. The most accurate experiments have been based on analogs of the EPR-Bohm experiment measuring photon polarizations rather than spins of massive particles. Instead of spin-up and spin-down states, photons can have right and left circular polarizations. In certain processes, two photons with correlated polarizations—one left, one right— can be emitted in opposite directions. Wheeler had proposed in 1946 that the pair of photons emitted in the annihilation of positronium (see Fig. 7.12) were entangled with opposite polarizations. This was experimentally confirmed by Wu and Shaknov in 1949. 

Together with the Faraday rotation of photon polarization (implementing singlequbit rotations) and linear phase-shift, the cphase gate is universal as it can realize arbitrary unitary transformation [Nielsen 2000],... 

Figure 3. Ancilla adding by Pumping. Photon polarization and involved sub-Zeeman levels are represented.

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