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

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As discussed in the previous subsection, we can use balanced homodyne detection to
precisely measure the quadratures C/ 0 of a spatial-temporal mode. As was also
discussed in the previous subsection, the angle 0 is defined by the phase of the local
oscillator with respect to the signal. The phase O can be varied using a piezo-electric
translator. To measure the quadrature distributions, one may fix O and perform a
series of homodyne measurements at this particular phase to build up a quadrature
histogram. Then the LO phase should be changed in order to repeat the procedure at a
new phase, and so on. Another possibility is to monitor the phase while it drifts or to
sweep it in a known way. In any case, the homodyne measurement must be repeated
many times on identically prepared light modes (or on a continuous wave field) to gain
sufficient statistical information about the quadrature values at a certain number of
reference phases. Finally, the Wigner function is tomographically reconstructed from
the experimental data.
It is beyond the scope of this report to summarize the entire subject of experimental
quantum tomography, its mathematical basis and procedures of quantum state
sampling, and the corresponding algorithms and numerical recipes. The reader should
see Reference [58] for the excruciating details.
Balanced homodyne detectors with local oscillators are amplifiers capable of detecting
and quantifying vacuum and sub-vacuum fluctuations. This is the subject of the two
experimental approaches that will be discussed in the next section.
BALANCED HOMODYNE SYSTEMS FOR MEASURING
NEGATIVE (SUB-VACUUM) ENERGY
Time-Domain Balanced Homodyne System
Squeezed states of light, which are "darker than vacuum," have regions with sub-
vacuum fluctuations. Slusher and collaborators [40, 41] and Robinson [42, 43] were
the first to experimentally observe these sub-vacuum regions. Numerous other
experiments followed, which employed variations on the experimental devices and
techniques used to generate squeezed light and measure its sub-vacuum fluctuation
pulses. Those early experimental devices later gave way to the development and use
of balanced homodyne detectors.
For example, Schneider et al. [59] describe their compact and efficient source of
amplitude-squeezed light. Their experiment used a semi-monolithic degenerate
MgO:LiNbQ3 optical parametric amplifier pumped by a frequency-doubled Nd:YAG laser
at 532 nm. They employed injection-seeding of the amplifier by a 1064 nm wave to
provide active stabilization of the cavity length and stable operation. At a pump power
of 380 mW, their device detected a maximum noise reduction of 6.5 dB in the
amplitude fluctuations of the 0.2 mW 1064 nm wave, while the average detected noise
reduction in continuous operation over 14 minutes was 6.2 dB. They reported a
squeezing of 7.2 dB in the emitted wave.
However, most of these early and more recent series of balanced homodyne detector
(BHD) measurements have been performed in the frequency domain. A significant
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