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.

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