By Martin Suda
ISBN-10: 3540260706
ISBN-13: 9783540260707
"Quantum Interferometry in part area" is essentially enthusiastic about quantum-mechanical distribution services and their purposes in quantum optics and neutron interferometry. within the first a part of the booklet, the writer describes the phase-space illustration of quantum optical phenomena comparable to coherent and squeezed states. functions to interferometry, e.g. in beam splitters and fiber networks, also are offered. within the moment a part of the e-book, the theoretical formalism is utilized to neutron interferometry, together with the dynamical thought of diffraction, coherence houses of superposed beams, and dephasing effects.
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Extra info for Quantum interferometry in phase space: theory and applications
Example text
12. To simplify matters, for the three MZ interferometer systems Fig. 29)) are drawn in Figs. 1, which is 10 times larger than in the previous pictures. As a consequence, the sum of the four intensities has to be one for any fixed value β: Ik + Il + Io + Ip = 1. As can be seen from the figures, the quantities Ik (Io ) and Il (Ip ) have opposite phase if β takes values around the fixed parameters k0 ∆i = 50 and k0 ∆m = 50, respectively. Finally, we consider the visibility in the k beam for σ 1 and α√= 0.
This is an important result and corresponds with Sect. 2. 51), the Q-function is expressed as a Fourier transform of the corresponding characteristic function: Q(α) = 1 π2 χA (ξ)eξ ∗ α−ξα∗ 2 d ξ. 28) is used, we get, after some manipulation, a correlation between Q(α) and P (α): Q(α) = 1 π 2 P (β)e−|α−β| d2 β. 28), χA (ξ) can be expressed by χN (ξ) and we get ∗ + 2 + ∗ 2 ρe−ξ aˆ eξˆa ] = e−|ξ| T r[ˆ ρeξˆa e−ξ aˆ ] = e−|ξ| χN (ξ). 61) 2 For ρˆ = |α α| ⇒ |χA (ξ)| = e−|ξ| ≤ 1. 61), we get a relation between the three characteristic functions: 2 χN (ξ)e−|ξ| = χS (ξ)e−|ξ| 2 /2 = χA (ξ).
2). 10), the momentum wave function is a complex quantity. Therefore, |αh,g (k)|2 has to be set up. 13) where the “+” sign belongs to the h beam and the “−” sign belongs to the g beam. The momentum spectra |αh,g (k)|2 are proportional to the incoming energy distribution αa2 (k), however, they are modulated through a cos-term and thus depend on the phase difference [k(Ld −Lc )]. The transmissions Tc and Td are additional attenuators. 4 show these spectra for a certain parameter set, specified in the drawings.
Quantum interferometry in phase space: theory and applications by Martin Suda
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