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

This document is a Defense Intelligence Reference Document (DIRD), a technical reference format used by the Defense Intelligence Agency (DIA) to capture baseline knowledge on a specific topic for later analytic use. DIRDs are best understood as reference and synthesis products rather than as original research. It is one of 38 DIRDs produced under the Advanced Aerospace Weapon System Applications Program (AAWSAP) between 2009 and 2011. Because AAWSAP’s scope permitted a broad range of supporting topics, not every DIRD in the series directly concerns aerospace systems or future threat assessment. The following summary reflects the DIRD’s scope and framing at the time of writing and should not be read as implying current validation of the concepts discussed. This DIRD examines how negative-energy, or “sub-vacuum,” states in quantum fields might be detected and mapped. Its practical scope is limited to the laboratory-scale measurement of minute quantum effects, though it extrapolates from those effects to consider theoretical relevance to concepts such as warp drives, wormholes, or gravitational control. By reviewing previously identified laboratory examples such as the Casimir effect and squeezed light states, the report identifies the core technical challenge as mapping their spatial and temporal structures reliably. To address this, it proposes quantum optical homodyne tomography as a method to reconstruct and quantify the vacuum fluctuations associated with these states. The document acknowledges that only microscopic, transient negative-energy effects have been realized in laboratory settings. It remains unknown whether larger or longer-lived distributions of such effects can be generated or stabilized, particularly given the experimentally unresolved constraints imposed by quantum inequalities. Overall, this DIRD functions as a measurement- and diagnostics-oriented review intended to lay experimental groundwork for a far more ambitious, highly speculative negative-energy research agenda.

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Defense
Intelligence
Reference
Document
Defense Futures
11 January 2011
!COD: 10 August 2010
DIA-08-1102-007
Quantum Tomography of
Negative Energy States in
the Vacuum
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Quantum Tomography of Negative Energy States in the
Vacuum
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
Author:
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 -
ashington D.C. 20340-5100.
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Contents
Introduction ........................................................................................................... 1
REVIEW OF NEGATIVE (or SUB-VACUUM) ENERGY................................................. 3
Overview........................................................................................................ 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
Fluctuations ............................................................................................... 7
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
Wigner Functions ..................................................................................... 17
Beam Splitters.......................................................................................... 24
Photodiodes ............................................................................................. 27
Balanced Homodyne Detection ................................................................. 27
Outline of Experimental Procedure........................................................... 32
BALANCED HOMODYNE SYSTEMS FOR MEASURING NEGATIVE
(SUB-VACUUM) ENERGY ....................................................................................... 33
Time-Domain Balanced Homodyne System .................................................. 33
Balanced Homodyne System for Casimir Cavities ......................................... 36
CONCLUSION........................................................................................................ 43
ACKNOWLEDGEMENTS ......................................................................................... 45
REFERENCES ........................................................................................................ 46
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Figures
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
Splitter ................................................................................................................. 32
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
Vacuum
Introduction
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
quantum fields. Marecki computed the two-point function and the associated spectral
density for the ground state of the quantum electric field in Casimir geometries, and
predicts a position- and frequency-dependent pattern of BHD responses if a device of
this type is placed inside a Casimir cavity. The proposed device allows for the direct
detection of quantum vacuum fluctuations and provides a spatial mapping of the
negative energy contained inside the cavity, which will be summarized in this report.
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REVIEW OF NEGATIVE (or SUB-VACUUM) ENERGY
Overview
The implementation of faster-than-light (FTL) interstellar travel via traversable
wormholes or warp drives or other antigravity forces for propulsion, generally requires
the engineering of spacetime into very specialized local geometries surrounding the
immediate vicinity of the aerospace vehicle undergoing this type of motion. The
analysis of these via the general relativistic field equation plus the resultant source
matter equations of state demonstrates that such geometries require the use of
"exotic" matter in order to produce the requisite FTL or antigravity spacetime
modification. Exotic matter is generally defined by general relativity physics to be
matter that possesses (renormalized) negative energy density (sometimes negative
=
stress-tension outward pressure, a.k.a. gravitational repulsion or antigravity), and
this is a very misunderstood and misapplied term by the non-general relativity
community. We clear up this misconception by defining what negative energy is, where
it can be found in nature, and we also review the two primary experimental concepts
that are known to produce negative energy in the laboratory. Also, it has been claimed
that FTL and antigravity spacetimes are not plausible because exotic matter violates the
general relativistic energy conditions. However, it has been shown that this is a
spurious issue. The identification, magnitude, and production of exotic matter is seen
to be a key technical challenge, however. FTL and antigravity spacetimes also possess
features that challenge the notions of causality and there are alleged constraints placed
upon them by quantum effects. Reference [1] reviews and summarizes these issues
with an assessment on the present state of their resolution.
What exactly is "exotic" matter? In classical physics the energy density of all observed
forms of matter (fields) is non-negative. What is exotic about the type of matter that
must be used to produce traversable wormhole, warp drive, or antigravity spacetimes is
that it must have negative energy density and/or negative flux [7]. The energy density
is "negative" in the sense that the configuration of matter fields we must deploy to
produce a traversable wormhole, warp drive, or antigravity effect must have an energy
density, PE (= pc2, where pis the rest-mass density), that is less than or equal to its
pressures/tensions, pi [8, 9].* In many cases, these equations of state are also known
to possess an energy density that is algebraically negative, i.e., the energy density and
flux are less than zero. It is on the basis of these conditions that we call this material
property "exotic." The condition for ordinary, classical (non-exotic) forms of matter
that we are all familiar with in nature is that PE> pi and/or PE;:::,: 0. These conditions
represent two examples of what are variously called the "standard" energy conditions
which are computed from the trace of the matter stress-energy tensort : Weak Energy
Condition (WEC: PE;:::,: 0, PE+ Pi;:::,: 0), Null Energy Condition (NEC: PE+ Pi;:::,: 0),
Dominant Energy Condition (DEC), and Strong Energy Condition (SEC). These energy
conditions forbid negative energy density between material objects to occur in nature,
but they are mere hypotheses. Hawking and Ellis [10] formulated the energy conditions
in order to establish a series of mathematical hypotheses governing the behavior of
• From this point forward, all Latin letters (e.g., i, j, k = 1...3) that appear as indices on physical quantities denote
the usual 3-dimensional space coordinates, x•. ..x3, indicating the spatial components of vector or tensor quantities.
t The stress-energy-momentum tensor is a matrix quantity that encodes the density and flux of energy and
momentum for any type of matter under study.
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collapsed-matter singularities in their study of cosmology and black hole physics. More
specifically, classical general relativity allows one to prove lots of general theorems
about the behavior of matter in gravitational fields.
However, real physical matter is not "reasonable" because the energy conditions are in
general violated by semiclassical quantum effects ( occurring at order Tl) [9].* More
specifically, quantum effects generically violate the average NEC (ANEC). Furthermore,
it was discovered in 1965 that quantum field theory has the remarkable property of
allowing states of matter containing local regions of negative energy density or negative
fluxes [3]. This violates the WEC, which postulates that the local energy density is non­
negative for all observers. And there are also general theorems of differential geometry
that guarantee that there must be a violation of one, some, or all of the energy
conditions (meaning exotic matter is present) for all FTL and antigravity spacetimes.
Howe