By Blackburn Ch. M.
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Additional resources for An Application of the Quantum Theory of Band Spectra to the First Negative Deslandres Group of Carbon
1 of Chapter 2, the initial states of the two cavities may be expanded in terms of coherent states, ρI = ∞ n=0 = where α = √ ¯ |n n| ⊗ Πn (N) 1 4π 2 ¯ exp iθ and β = N 2π 0 √ ∞ m=0 ¯ |m m| Πm (M) 2π 0 dθdφ |α α| ⊗ |β β| , ¯ exp iφ, and Πn (µ) = µn e−µ /n! is a Poissonian M probability factor with mean µ. r! 2) where ǫ denotes the leakage parameter for both cavities and takes a value very much less than 1. ρ′ here is subnormalised and the value of the trace is the probability for the specific measurement outcome at the two detectors.
1 of chapter 2. This result assumes ancillae which are initially in the vacuum state, and for simplicity the phase shifts in the apparatus are taken to be 0. In this section a mathematical derivation of these measurement operators is presented, and in addition the effect of leakage from the cavities is fully accounted for. The action of the interference procedure on an arbitrary tensor product of Glauber coherent states is evaluated, and corresponding operators for the full evolution of the system are deduced.
Given a fixed total number of detections l + r, the localising function is progressively less well localised as the number of left counts increases, leading to a qualitative change when l and r are close in value. Specifically, for the cases when r−R(l+r) < l ≤ r, |Cl,r (∆)|2 is peaked at two values, ∆0 = ± arccos 1 (r−l) R (r+l) . Differently here from the cases of initial symmetric Fock or Poissonian states (discussed in Sec. 3 and Sec. 1 of Chapter 2), |Cl,r (∆)|2 is non-zero at ∆ = 0 and a partition of the final state into two components localised at +∆0 and −∆0 is harder to justify.