Defense Intelligence Reference Document Quantum Tomography Of Negative Energy States In The Vacuum

UNCLASSIFIED//509 QFFICJa ■ YEE a••b>/
(l' = 17 112
0 +(l-17)" 2
(\ from Section IIIB-2 to define the annihilation operators of the
A" 11c~, 11cA ~" 11°~, 110A A
detected light modes a 1 = 11 a 1 + (I -17) h 1 and a" = 11 -a"+ (1-17) -b2 , where b 1 and
b2 are the annihilation operators of the vacua entering the second unused ports of the
fictitious beam splitters. The annihilation operators Cl; and (J~ describe the light modes
(or fields) emerging from the 50:50 beam splitter where the signal is optically mixed
with the LO. Again, the LO is an intense field compared with the signal so it can be
treated classically. Therefore, we do some algebra to compute the difference photon
number h21 = n;-n;' = a;t a; -a;'t a~ 1 but retain only the leading terms with respect to
ULO, and obtain the final result [38]:
(12)
The symbol HC in Eq. (12) denotes the Hermitian conjugate of the other part of an
expression and i, = r 112
( b 2 -b 1). The fluctuation mode operator b corresponds to the
' '
optical mixing of the fictitious vacuum-noise modes b 1 and b 2 , and it obeys the bosonic
commutation relation [1;, [}] = 1 (e.g., see Sect. IIIB-2). Because the interference of
vacuum with vacuum yields vacuum, the fluctuation mode b can be regarded as a
bosonic mode, being in the vacuum state as well.
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