DOW-UAP-D153, AAWSAP DIRD, Quantum Tomography of Negative Energy States in the Vacuum, January 2011

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Quantum Tomography of Negative Energy States in the The Defense Intelligence Reference Document provides non-substantive but authoritative reference information related to intelligence topics or methodologies. Prepared by: Technology Warning Division (DW0-4) Defense Warning Office Directorate for Analysis Defense Intelligence Agency AAP Person 58 COPYRIGHT WARNING: Further dissemination of the photographs in this publication is not authorized. This product is one of a series of advanced technology reports produced in FY 2010 under the Defense Intelligence Agency, Defense Warning Office's Advanced Aerospace Weapons System Applications AAWSA Pro ram. Comments or questions pertaining to this document should be addressed to MP Person 1 AAWSA Program Manager, Defense Intelligence Agency, ATTN: JUIAF -

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REVIEW OF NEGATIVE (or SUB-VACUUM) ENERGY................................................. 3 Examples of Negative (Sub-Vacuum) Energy Found in Nature ....................... 4 Basic Notions of the Quantum Field Theory of Light ................................... 5 Basic Notions on the Origin of the Quantum Vacuum Zero-Point Negative (Sub-Vacuum) Energy in Squeezed Light .................................... 8 Negative (Sub-Vacuum) Energy in the Casimir Effect................................13 QUANTUM OPTICAL HOMODYNE TOMOGRAPHY .................................................... 15 Observing Negative Energy in the Lab.......................................................... 15 Basic Notions of Quantum Optical Homodyne Tomography .......................... 16 Beam Splitters.......................................................................................... 24 Balanced Homodyne Detection ................................................................. 27 Outline of Experimental Procedure........................................................... 32 BALANCED HOMODYNE SYSTEMS FOR MEASURING NEGATIVE Time-Domain Balanced Homodyne System .................................................. 33 Balanced Homodyne System for Casimir Cavities ......................................... 36 UNCLASSIFIED// FOR OFFICIAL U:!I! fJHLY

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Figure 1. Illustration of a Squeezed State of Light ............................................... 13 Figure 2. Schematic of the Casimir Effect ............................................................. 14 Figure 3. Illustration of Quantum Optical Homodyne Tomography ....................... 16 Figure 4. Wigner Function for a Vacuum and for a Coherent State ....................... 19 Figure 5. Wigner Function of a Squeezed Vacuum ................................................ 20 Figure 6. Wigner Function of a Single Photon....................................................... 21 Figure 7. Quantum Tomography of Schrodinger-Cat States.................................. 22 Figure 8. Schematic of an Ideal Lossless Beam Splitter........................................ 25 Figure 9. Illustration of a Fictitious Beam Splitter................................................ 26 Figure 10. Schematic of a Balanced Homodyne Detector...................................... 29 Figure 11. Balanced Homodyne Detector Using Fictitious Beam Splitters............. 31 Figure 12. Balanced Homodyne Detector Using A Single Effective Fictitious Beam Figure 13. Time-Domain Balanced Homodyne Detector........................................ 34 Figure 14. Experimentally Measured Squeezed State ........................................... 35 Figure 15. Balanced Homodyne Detector with a Local Oscillator .......................... 38 Figure 16. Diagram of Casimir Cavity with BHD Photodiodes ............................... 40 Figure 17. Experimental Setup of BHD Photodiodes and LO Field ......................... 40 Figure 18. Detailed Schematic of Experimental BHD Apparatus ........................... 41 Figure 19. Predicted Casimir Spectral Density...................................................... 41 Figure 20. Predicted Suppression of Vacuum Fluctuations in dB.......................... 42

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Quantum Tomography of Negative Energy States in the Future aerospace vehicles could have an advanced propulsion system that uses negative quantum vacuum energy to modify the spacetime geometry in the immediate vicinity surrounding the vehicle in order to induce faster-than-light motion via traversable wormholes or warp drives, or even levitation via antigravity [1, 2]. These exotic propulsion concepts are well-known in mainstream general relativity and quantum field theory research. The notion of a physical state with negative energy is not familiar in the realm of classical physics. However, it is not rare in quantum field theory to have quantum states with negative energy density or a negative energy flux. Even for a quantum scalar field in the flat Minkowski spacetime, it can be proved that the existence of quantum states with negative energy density is inevitable [3]. Although all known forms of classical matter have non-negative energy density, it is not so in quantum field theory. A general quantum state can be a superposition of particle number eigenstates and may have a negative expectation value of energy density in certain spacetime regions due to quantum coherence effects [3]. These considerations remain true even for quantum fields in a curved spacetime where the effects of gravitational fields, or equivalently, accelerations, can be observed due to the mass of astronomical bodies or the motions of astronomical bodies. There are two key examples of specially prepared quantum vacuum states that are known to produce small amounts of negative energy density in the laboratory. These are the well-known Casimir effect and the squeezed vacuum states of the electromagnetic field. The former is a static quantum vacuum effect wh ile the latter is a time-domain quantum vacuum effect. There are several other examples of special quantum vacuum or particle states that produce negative energy density, but they are beyond the scope of this report because they remain mathematical curiosities or are not practicable to im plement in the laboratory in the foreseeable future. We already make small amounts of negative energy in the laboratory via the Casimir effect and squeezed electromagnetic vacuum states, but we do not yet know if we can access larger amounts for extended periods of time over extended spatial distributions for the purpose of modifying spacetime for aerospace propulsion applications. It will be necessary to first explore the quantum nature of the Casimir effect and squeezed electromagnetic vacuum states to determine whether we can measure and spatially map their negative energy density. This is a necessary first step to take before beginning any study on producing large quantities of negative energy because we will first need to know how to measure and spatially map negative energy in order to properly control it after producing it. This is the motivation for this report. We need to firm up our understanding of how lab detectors will respond to negative energy in situ. A first step in this direction was already taken by Hansen et al. [4] in 2001 for the time-domain negative energy pulses in squeezed electromagnetic vacuum states, and more recently Marecki [5, 6] generalized the analysis of the output of balanced homodyne detectors (BHDs) for the case of static negative energy states

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inside Casimir cavities. The most important feature of these devices is their ability to quantify the quantum vacuum fluctuations of the electric field because the output of BHDs provides information on the one- and two-point functions of arbitrary states of