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This Defense Intelligence Reference Document from the Defense Intelligence Agency is dated 11 January 2011. It was produced in FY 2010 under the Advanced Aerospace Weapons System Applications (AAWSA) Program. It reviews negative, or sub-vacuum, energy found in squeezed light and the Casimir effect, and explains quantum optical homodyne tomography as a way to measure and map that energy in the lab. It proposes balanced homodyne detector arrays that could help detect anomalous aerospace platforms using engineered spacetime propulsion.
UNCLASSIFIED//F811. 8FFll!l*L 1!1!11! l!IIU:!Y but depends on the state of u(x,t). This state exists even if literally nothing is in the mode chosen by the observer. In this case, the light is just in the vacuum state.§ However, this "nothing" can indeed cause significant physical effects as will be discussed in later sections. To make all this more precise, we postulate that the electric field strength £ of the light field is given by £ =u*(x,t)d+u(x,t)at and that the amplitude operator fl is a bosonic** annihilation operator that obeys the quantum mechanical commutation relation [ &, tf] =I, where i/(x,r) is the complex conjugate of u(x,r) and tt is the adjoint (or conjugate) of ll called the creation operator.' 1 The hat symbol appearing over quantities denotes that they are quantum operators (or observables). Another key element of quantum-oscillator physics is the photon number operator YI, which accounts for the number of photons (quantized light particles) in the chosen u(x,r) and is given by the quantum mechanical counterpart of a classical modulus-squared amplitude: YI= cY 1 ·a. Let us now introduce a pair of operators, q and ft, called quadratures. They are defined as iJ =2 in (cit+ ii) and fa= i2 1 ,... 2 ( c/ -ci), which can be inverted to provide the additional useful definitions a= T 112 ((]+if,) and a1 • = Tu 2 ((]-if,). In optics (j and p correspond to the in-phase and the out-of-phase component of the electric field amplitude of u(x,t) (with respect to a reference phase). The bosonic commutation relation demonstrates that q and 1) are canonically conjugate observables, [ (j, ft]= ih. The quadratures q and 1) can be regarded as the position and the momentum of the quantum electromagnetic oscillator. They do not appear in real space but in the phase space spanned by the complex vibrational amplitude fl of the quantum electromagnetic oscillator, and they have nothing to do with the position and the momentum of a photon. However, the canonical commutation relation entitles us to treat q and 1) as perfect examples of position- and momentum-like quantities in quantum optics. Finally, we express the photon number operator fz in terms of the quadratures q and ft and obtain, using the bosonic commutation relation, the standard Hamiltonian (or total energy) of the quantum harmonic (electromagnetic) oscillator with unit mass and frequency: H =n+-21osc § Here we always mean by "vacuum" simply "no light" and not an evacuated system. •• Boson or bosonic refers to quantum particles that have integer quantum spin. ' In quantum mechanics, the vacuum is defined to be a state of no (or zero) particles and is denoted by the quantum state eigenvector IO). By definition a "annihilates" the vacuum state: (IIO) = 0. 6 UNCLASSIFIED/ /f81il 8fflll"'k WliEii SUlklf ( 1)
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Report, from the dia collection. The PDF is mirrored here; the original link is above. 51 pages are in the text index: search them above, or from the library's search.