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

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H,i,r_, 111 =ex' ®E;(x,t) • g(t)where e is the electron charge and g(t) is a smooth test
(or smearing) function that is equal to 1 during the measurement and smoothly
vanishing elsewhere. Using first-order time-dependent perturbation theory, Marecki [5,
6] derived the probability of excitation:
r J+x •• ( • r • r )
Pex,(g,x)= -wdrdsg(r)g(s)G'l(r-s) E;(x,r)E/x,s) s' (14)
where Gii(r-s)= fdq(Olx;(r)l&)(&lx\s)IO) is the electronic two-point function, rand
s are dummy time and integration variables, and fdrdsg(r)g(s) is the temporal
sensitivity in the measurement process.
The balanced homodyne detector consists of an arrangement of two photodiodes,
whose outputs are subtracted, and illuminated with an auxiliary coherent state of the
radiation field (i.e., the local oscillator, LO; see Figure 15). Per the discussion in
Section IIIB-4, the LO is used as a tool to investigate the properties of a certain state S
of the quantum radiation field under study, and so on a BHD the state Sis optically
mixed with the coherent LO state (see References [SJ or [6] for further details). The
quantum field S de-balances the detector (stochastic process of measurement). The
expectation value of the observable corresponding to the electronic charge collected at
the point Pin Figure 15 (i.e., the BHD current) is the difference of excitation
' 'probabilities of the two photodiodes [S, 6]: ( J \- = P,,x.:CK, x) - P,,xc (g, y), where positions
X and } correspond to the positions :! and y in Figure 15. Further calculations and
other theoretical considerations lead to the following final result for (.!)_1
. [5, 6]:
(1) 5 =a,,,• £~0 • ( £, (f,1 11 ) + £J}·,t0 ) )s where ae, depends on the electronic structure
of the PIN semiconductor in the photodiode, E/.o is the electric field of the LO
(corresponding to Fin Figure 15), to is the LO phase that can easily be varied in
. r
experiments, and all field operators E 1(x,t) are restricted to the frequency ffi of the LO.
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