AAWSAP DIRD, High-Frequency Gravitational Wave Communications, April 2010

UNCLASSIFIED//F&R 8FFl&I.t.L 1:J&i &PIia¥ Defense Intelligence Reference Document Acquisition Threat Support 6 April 2010 ICOD: 1 December 2009 DIA-08- 1004-005 High-Frequency Gravitational Wave Communications UNCLASSIFIED/,lFOR OFFI~I\ls Wiii QNL>f UNCLASSIFIED//&O11 Oli&iliCili0 L Pl&li Qtll¥ High-Frequency Gravitational Wave Communications Prepared by: Acquisition Support Division (DW0-3) Defense Warning Office Directorate for Analysis Defense Intelligence Agency Author: AAP Person 77 Administrative Note COPYRIGHT WARNING: Further dissemination of the photographs in this publication is not authorized. This product is one in a series of advanced technology reports produced in FY 2009 under the Defense Intelligence Agency, Defense Warning Office's Advanced Aerospace Weapon System Applications (AAWSA Pro ram. Comments or uestions pertaining to this document should be addressed t AAP Person 1 AAWSA Program Manager, Defense Intelligence Agency, ATTN: CLAR/ DWO-3, Bldg 6000, Washington, DC 20340-5100. UNCLASSIFIED/ /fQB OFFICI0L 1al&li 8HLY ii UNCLASSIFIED//iiOlil OiiiilCI0L Llili QPIL¥ Contents Summary................................................................................................................. v 1.0 Introduction ..................................................................................................... 1 1.1 Introduction ................................................................................................. 1 1.2 Definition of High-Frequency Gravitational Waves ....................................... 1 2.0 HFGW Communications .................................................................................... 2 2.1 HFGW Generators (Transmitters) ................................................................. 2 2.1.1 HFGW Generator Concepts .................................................................... 2 2.1.2 Alternative Approaches ......................................................................... 6 2.1.3 Piezoelectric Approach .......................................................................... 6 2.1.4 Infrared-Excited Molecules Approach .................................................... 7 2.2 HFGW Detectors (Receivers) ...................................................................... 12 2.2.1 Alternative Approaches ....................................................................... 12 2.2.2 Concept (Li-Effect) .............................................................................. 14 2.2.3 Quantum Back-Action Limit ................................................................. 16 2.2.4 Li-Baker HFGW Detector...................................................................... 20 3.0 Operational Concerns ..................................................................................... 22 3.1 Link Budget ................................................................................................ 22 3.1.1 Signal-to-Noise Ratio .......................................................................... 22 3.1.2 Link Budget Considerations ................................................................. 23 3.2 Bandwidth .................................................................................................. 25 3.3 Frequency and Time Standard .................................................................... 25 3.3.1 Improvements Accruing from a HFGW Time Standard ......................... 27 3.3.2 Search Space Improvement Accruing From HFGW FTS ........................ 28 3.3.3 The Impact of Phase Noise Improvements on Phase Shift Encoding ... 29 3.3.4 The Impact of Frequency Noise Improvements on FDMA and FHSS..... 30 3.4 Possible Future Upgrades to the FTS Devices ............................................. 30 3.4.1 Propagating Signals From Optical Lattice Clocks for Timing ................ 31 3.4.2 In Navigating and Mapping Interplanetary Geoids .............................. 31 4.0 Future Potential ............................................................................................. 32 4.1 Developmental Roadmap............................................................................ 32 4.2 HFGW Communications Predictions to 2050 ............................................... 33 4.3 Interplanetary Navigation and Geoid Mapping to 2050 .............................. 34 4.4 Other Possible HFGW Applications ............................................................. 36 UNCLASSIFIED//FOR OiiiilCl.t.k HSI!! eflti iii UNCLASSIFIED//iiOlil OiiiilCI0L Llili QPIL¥ 4.5 2050 and Beyond ....................................................................................... 37 5.0 Acknowledgements ........................................................................................ 37 6.0 References ..................................................................................................... 37 Appendix A: Nomenclature ................................................................................... 44 Appendix B: Li-Baker HFGW Detector................................................................... 45 Appendix C: Perturbative Photon Fluxes Generated By High-Frequency Gravitational Waves and Their Physical Effects .................................... 52 Figures Figure 1. Communication Link Block Diagram ........................................................ 2 Figure 2. Change in Centrifugal Force of Orbiting Masses, Afct, Replaced by Change Figure 13. Quantum Back Action as a Mechanism for Creating the Standard Figure 15. Fractal Membrane Component of Li-Baker Detector Exhibited in Planar Figure 24. HFGW Com Space Application Development Roadmap, Estimated Figure 27. A GW Pair on Earth and on Mars for an Outer Planetary Reference in Tangential Force, '1ft, to Achieve HFGW Radiation ............................... 3 Figure 3. Circular Resonator Geometry Using Infrared Excitation .......................... 8 Figure 4. Radiation Pattern Calculated by Landau and Lifshitz (1975) ................... 8 Figure 5. GW Flux Growth Analogous to Stack of N Orbital Planes ......................... 9 Figure 6. Stack of Circular-Wave-Guide Plates With Typical Molecule Jerks, Af's ... 9 Figure 7. Omni-Directional Nature of the HFGW Radiation Pattern....................... 10 Figure 8. Predicted Relic GW Energy Density as a Function of Frequency............. 11 Figure 9. Birmingham University HFGW Detector ................................................. 13 Figure 10. INFN Genoa HFGW Detector ................................................................ 13 Figure 11. The National Astronomical Observatory of Japan 100 MHz Detector ... 14 Figure 12. Detection Photons Sent to Locations that are Less Affected by Noise.. 15 Quantum Limit..................................................................................... 17 Figure 14. Schematic of Ultra-Sensitive HFGW Detector....................................... 21 Form .................................................................................................... 21 Figure 16. Conceptual SNR Fill Factors: Signal and Noise Components ................ 23 Figure 17. A Block Diagram of a Typical Link Budget............................................ 24 Figure 18. A Proposed Near Earth Distribution of Frequency Time Standard........ 26 Figure 19. HFGW Supplemented Remote Terminal Design.................................... 27 Figure 20. Acquisition Search Space Improvement Accruing From HFGW FTS ...... 28 Figure 21. The Impact of Phase Noise Improvements on Phase Shift Encoding ... 29 Figure 22. The Impact of Frequency Noise Improvements on FDMA and FHSS ..... 30 Figure 23. The Earth's Associated Lagrangian Points ........................................... 31 Timeline .............................................................................................. 32 Figure 25. A GW Pair on Earth as Used by a Lunar Mission ................................... 34 Figure 26. A GW Pair on Earth and on the Moon, as Used by a Mission to Mars .... 35 Pair...................................................................................................... 35 UNCLASSIFIED//FOR OiiiilCl.t.k HSI!! eflti iv UNCLASSIFIED//iiOlil OiiiilCI0L Llili QPIL¥ High-Frequency Gravitational Wave Communications Summary • Fourteen laboratory high-frequency gravitational wave (HFGW) generators (or transmitters) have been proposed in the past 45 years in peer-reviewed journal articles. • The most promising laboratory HFGW generators are those that utilize very large numbers of sub-microscopic radiation elements. • The Piezoelectric Approach to HFGW generation is best for the proof-of­ concept test and the proposed IR-excited Molecules Approach is best for an operational communications HFGW transmitter. • Ten different HFGW detectors (or receivers) have been proposed since 1978 and reported in peer-reviewed journal articles. • Several different HFGW receivers can be utilized for communication, but the proposed Li-Baker detector (plans & specification development in Appendix B) shows the most promise (underlying concept in Appendix C). The Li­ effect, upon which the Li-Baker detector is based, is not so new that it is untested in the literature. At least nine peer-reviewed research publications concerning the theory have appeared following the initial peer-reviewed article by Li, Tang and Zhao (1992). • Because HFGW communications are carried on an extremely narrow beam directly through the Earth, there is a very low probability of interception. • Theoretical results confirm that the Li-Baker detector is photon-signal limited, not quantum-noise limited-that is, the Standard Quantum Limit is so low that a properly designed Li-Baker detector can have sufficient sensitivity to observe HFGWs of amplitude A:::;$ 10-32 m/m. • Utilizing the IR-excited Molecules HFGW generator approach and the Li­ Baker detector, the theoretical information-transfer rate over 7,000 km of distance, beamed directly through the Earth, is about 1.9 x 106 bits per second. • A means of propagating a Frequency Time Standard may be one viable early low-bandwidth application for HFGW communications. • HFGW sources on the Earth, the Moon, and Mars may act as reference standards for interplanetary navigation, with the advantage that they cannot be shielded or shadowed by planetary masses. Plasma interference seen at planetary entry would be eliminated, and precise charting of Lagrangian points would be possible. UNCLASSIFIED//FOR OiiiilCl.t.k HSI!! eflti V UNCLASSIFIED//&Olil OiiiilCI0L Llili QPIL¥ 1.0 Introduction 1.1 INTRODUCTION Of the applications of high-frequency gravitational waves (HFGWs), communication appears to be the most important and most immediate. Gravitational waves have a very low cross section for absorption by normal matter, so high-frequency waves could, in principle, carry significant information content with effectively no absorption unlike electromagnetic (EM) waves. Multi-channel HFGW communications can be both point­ to-point (for example, to deeply submerged submarines) and point-to-multipoint, like cell phones. HFGWs pass through all ordinary material things without attenuation and represent the ultimate wireless system. One could communicate directly through the Earth from Moscow in Russia to Caracas in Venezuela-without the need for fiber optic cables, microwave relays, or satellite transponders. Antennas, cables, and phone lines would be things of the past. A timing standard alone, provided by HFGW stations around the globe, could result in a multi-billion dollar savings in conventional telecom systems over ten years, according to the recent analysis of Harper and Stephenson (2007). The communication and navigation needs of future magneto hydrodynamic (MHD) aerospace vehicles, such as the MHD aerodyne (www.mhdprospects.com), which is high in electromagnetic interference, similar to plasma interference seen at reentry, would be another possible applications area for HFGW communications. 1.2 DEFINITION OF HIGH-FREQUENCY GRAVITATIONAL WAVES Visualize the luffing of a sail as a sailboat comes about or tacks. The waves in the sail's fabric are similar in many ways to gravitational waves (GWs), but instead of sailcloth fabric, gravitational waves move through a "fabric" of space. Einstein called this fabric the "space-time continuum" in his 1915 work known as General Relativity (GR). Although his theory is very sophisticated, the concept is relatively simple. This fabric is four-dimensional: it has the three usual dimensions of space-east-west, north-south, and up-down-plus the fourth dimension of time. Here is an example: we define a location on this "fabric" (Einstein, 1916) as 5th Street and Third Avenue on the fourth floor at 9 AM. No one can see this "fabric," just as no one can see wind, sound, or gravity. Nevertheless, those elements are real, and so is this "fabric." If one could generate ripples in this space-time fabric, many applications would become available. Much like radio waves can be used to transmit information through space, gravitational waves could be used to perform analogous functions. Gravitational waves are the subject of extensive current research, which so far has focused on low frequencies. High-frequency gravitational waves, as defined by physicists Douglass and Braginsky (1979), are gravitational waves having frequencies higher than 100 kHz. Low-frequency gravitational waves (LFGWs), such as those detectable by interferometric GW detectors (for example, the Laser Interferometer Gravitational Observatory, or UGO) are not applicable to communications due to their very long wavelengths, often thousands of kilometers in length and, even more importantly, the inability to generate them effectively in the laboratory. Furthermore LFGW detectors cannot detect HFGWs (Shawhan, P. S., 2004). UNCLASSIFIED/ /FOR OiiiilCl.t.k HSI!! eflti 1 UNCLASSIFIED//iiOlil OiiiilCI0L Llili QPIL¥ 2.0 HFGW Communications Consider the case of a single point-to-point two station full duplex communication system, as is represented in Figure 1. Such a system is often characterized as a single data link, and requires two transmitters, one at each end, and two receivers, one at each end. To avoid self-interference the link in one direction often uses a frequency of radiation different than the link in the opposite direction. Full Duplex Communication Link Using Gravitational Wave Generators and Sensors Station 1 Station 2 r------------------~ r------------------~ I GW Generator I I GW Sensor ' ' I I ' Sianal 1 + Source Noise ,~ I ' I ~ <01 (01 Xmit 1 Rcvr 2 Additional Link Noise ---~ I ► -----. -----. I I I I I I I GW Sensor I GW Generator I _, Sianal 2 + Source Noise I ~, ' 'I ' {02 Xmit2 Rcvr 1 r-e+-------Additional_Link Noise ' <02 ' +-­ ' ' +-­ ' ' ' ' ' ' , ' ___________________ ' •-------------------· ' Figure 1. Communication Link Block Diagram If one were to apply the emerging technology of gravitational wave control to such a link, one would use GW generators for the transmitters on each end, and GW sensors for the receivers at each end (Stephenson, 2009a). In the example shown in Figure 1, station 1 would have a GW generator transmitting at a frequency of ro1 and a GW sensor sensitive to a frequency of CO2, without being sensitive to a frequency of co1. Likewise, station 2 would have a GW generator transmitting at a frequency of ffi2 and a GW sensor sensitive to a frequency of ro1 , without being sensitive to a frequency of co2. This is the minimum functionality required to constitute a communication link. Signal strengths of the respective GW generators would need to be sufficient to overcome link loss, coupling losses, and noises sources. Signal to noise considerations and link budgets are covered in further detail in Section 3.1. 2.1 HFGW GENERATORS (TRANSMITTERS) 2.1.1 HFGW Generator Concepts Several sources for HFGWs or means for their generation exist. The first generation means is the same for gravitational waves (GWs) of all frequencies and is based upon the quadrupole equation first derived by Einstein in 1918. A formulation of the quadrupole that is easily related to the orbital motion of binary stars or black holes, UNCLASSIFIED//FOR OiiiilCl.t.k 1!181!! Bfltf 2 UNCLASSIFIED//EOR OEEICI0L Llili QI\IL¥ rotating rods, laboratory HFGW generation, and so forth is based upon the "jerk" or shake of mass (time rate of change of acceleration) and is derived by Baker (2006) as P = 1.76x1Q-52 (2r.M/6t)2 W (1) where Pis the power of the GWs, W; r is the distance between two masses, m; Mis a change in force, N; over the time interval 6t, s; that is, the jerk or shake of the two masses, such as the change in centrifugal force vector with time; for example, as masses move around each other on a circular orbit. Figure 2 describes that situation. Please recognize, however, that M need NOT be a gravitational force (see Einstein, 1918; Infeld quoted by Weber 1964, p. 97; Grishchuk 1974). Electromagnetic forces are more than 1035 larger than gravitational forces and should be employed in laboratory GW generation. As Weber (1964, p. 97) points out: "The non-gravitational forces play a decisive role in methods for detection and generation of gravitational waves ... " Equation (1) is also termed "quadrupole formalism" and holds in weak gravitational fields (well over 100 g's), for speeds of the generator "components" less than the speed of light and for r less than the GW wavelength. This last restriction may not really apply. Certainly there would be GW generated for r greater than the GW wavelength, but the quadrupole formalism might not apply exactly. For very small 6t, the GW wavelength, AGw = c6t (where c ~ 3x 108 ms-1, the speed of light) is very small and the GW frequency VGw is high. As a numerical example, r is choosen to be 10 m (convenient laboratory size, though usually greater than AGw), M = 4x 108 N; for example, the force produced by a large number of piezoelectric resonators and M = 2x 10-10 s; equivalent to about a VGw = 5 GHz jerk or shake frequency so that AGw = 6 cm and P = 2.8x 10-13 W or 0.28 picowatts. Clearly a very small HFGW power is generated. GW GW A I [ A ~~----------8 ___ ! __ __._f...=Cf"---!Y fct r I I 8 I l ' I I I GW I T GW Figure 2. Change in Centrifugal Force of Orbiting Masses, dfct, Replaced by Change in Tangential Force, df,, to Achieve HFGW Radiation One of the first suggested means for the laboratory generation of HFGWs was the so­ called gaser analogous to the laser for light. Simply described (Halpern and Laurent, UNCLASSIFIED//FOR OEEICIJ.b HSI!! Dflti 3 UNCLASSIFIED//EOR OEEICI0L Llili QI\IL¥ 1964), the gaser consists of a long rod of a material and microscopic parts of which can be excited by a means, such as electromagnetic (EM) radiation, to emit HFGWs. They utilize linearized theory to treat the interaction of a gravitational field with matter: "Application is made to the emission ... of gravitons by microscopic systems such as molecules and nuclei." Grishchuk and Sazhin in early 1974 discussed the emission of gravitational waves by an electromagnetic cavity. In August of 1974 Chapline, Nuckolls and Woods suggested the generation of HFGWs by nuclear explosions. In this same regard Fontana suggested that the problem of efficient generation of HFGWs and pulses of gravitational radiation might find a reasonably simple solution by employing nuclear matter (Fontana and Baker, 2006; Fontana and Binder, 2009), especially isomers. A fissioning isomer not only rotates at extremely high frequency(~ 3.03x1024 s-1) according to the aforementioned references, but is also highly deformed in the first stages of fission (the nucleus is rotating and made asymmetric "before" fission). Thus one achieves significant impulsive forces (for example, 3.67x 108 N) acting over extremely short time spans (for example, 3.3x 10-22 s). Alternatively, a pulsed particle beam, which could include antimatter, could trigger nuclear reactions and build up a coherent GW as the particles move through a target mass. The usual difficulty with HFGWs generated by nuclear reactions is the small dimensions of their nuclear-reaction volumes-that is, the small moment of inertia and submicroscopic radii of gyration (for example, 10-16 m) of the nuclear-mass system. Such a difficulty is overcome by utilizing small clusters of nuclear material, whose nuclear reactions are in synchronization; for example, through the use of a computer controlled logic system. Such nuclear­ energized HFGW generators are currently very theoretical. Braginsky and Rudenko (1978) discussed the generation of gravitational waves in the laboratory and proposed a means utilizing small particles In 1981 Romero and Dehnen analyzed the generation of gravitational radiation in the laboratory also utilizing a linear array of piezoelectric crystals that will be analyzed in more detail in Section 2.1.3. In 1988 Pinto and Rotoli presented a paper on the laboratory generation of gravitational waves at the Italian Conference on General Relativity and Gravitational Physics. Another Italian, Giorgio Fontana (1998), suggested that the possibility of emission of high frequency gravitational radiation from junction between d-wave and s-wave superconductors. Kraus (1991) proposed that gravitational-wave communication might be possible in the IEEE Antennas & Propagation magazine. At the first HFGW Working Group Conference at the MITRE Corporation in 2003, Grishchuk analyzed electromagnetic generators and detectors of gravitational waves. At that same Conference Valentin Rudenko presented a paper on the optimization of parameters of a coupled generator-receiver for a HFGW Hertz experiment. At the second HFGW Working Group Conference in Austin, Texas, in 2007, Kolosnitsyn and Rudenko presented another paper on the generation and detection of the high-frequency gravitational radiation in a strong magnetic field. In 2007, and more recently this year, a new type of HFGW generator/detector and mirror system based on thin, type I superconducting films was proposed by R. Chiao, S. Minter, and K. Wegter-McNelly (2007; 2009a,b). Therefore it is evident that a number of devices for the laboratory generation of HFGWs have been proposed including the aforementioned gaser (as has been mentioned, was first proposed by Halpren and Laurent in 1964, some 45 years ago) discussed by Fontana and Baker (2003); as well as an actual laser generator of HFGWs as discussed by Li and Li (2006). Finally a rather practical laboratory HFGW generator, which may be appropriate for the initial proof-of­ concept test, is one utilizing off-the-shelf components such as magnetron energized piezoelectric crystals or Film Bulk Acoustic Resonators or FBARs has been analyzed in Woods and Baker, (2005) and Baker, Woods and Li (2006). UNCLASSIFIED//FOR OEEICIJ.b HSI!! Dflti 4 UNCLASSIFIED//EOR OEEICI0L Llili QI\IL¥ The figure of merit for a HFGW generator is given explicitly by Baker, Woods and Li (2006). This Figure of merit can be extended by considering other effects since in the laboratory the force change could not even approach those of the celestial sources. It would seem that the magnitude of any laboratory generated GWs could be best increased (1) by utilizing electromagnetic forces rather than gravitational, (2) by increasing the distance between the gravitational radiators, (3) by increasing the GW frequency (that is, reducing ~t) and especially ( 4) by developing a large number of in­ phase system elements. This last effect enters as the square of the number of elements, N , as proved using General Relativity analyses by Dehnen and Romero­ Borja's analyses (Romero and Dehnen, 1981; Dehnen and Romero, 2003). Such N2 dependence also may be the key to successful laboratory generation of GWs, especially HFGWs. In that regard, recent proposal by Woods (Woods and Baker, 2009; Black and Baker, 2009)) propose the use of infrared-energized atomic nuclei, electrons and or molecules, which have a very large N, contained in a stack of N waveguide rings (Patents Pending). The distance between GW radiators may be proportional to the GW wavelength in that it may have a limit that is less than or equal to a GW wavelength. The wavelength is inversely proportional to the GW frequency. Thus given some value for the proportional constant, say unity or the distance between radiators equal to one GW wavelength, the GW frequency cancels out. As already noted it is important to take advantage of square of the number of in phase elements for useful laboratory HFGW generation. If the elements are sliced in one dimension (the dimension along the axis of HFGW generation) in order to increase the number of elements, then the change in force per element will be inversely proportional to the number of elements. For example, if the elements are sliced into one hundred separate pieces, then each piece will have one hundredth of the force of the unsliced element. Essentially, f = ma and it is assumed that the acceleration of the element was the same after the split as before. This result also follows Equation (8), page 17 in Baker, Stephenson and Li (2008b) and if there were 100 splits of an FBAR, then the power to an individual slice, P and its mass, m would be both one hundredth of their un-split value and the square root of their product would again be one hundredth. The frequency of the split elements may be a higher value -- but the attendant increase in GW power proportional to the square of the higher frequency and the decrease in power due to a smaller distance between tracks (assuming that the distance between tracks is one GW wavelength, which would be smaller) would cancel and there would be no net effect on HFGW amplitude. It is concluded, therefore, that in this particular special situation the amplitude of the generated HFGWs is proportional to the number of in-phase elements, N (not the square). In any event a large number of elements for a given HFGW-generator length can be best realized by reducing the size of the individual elements to submicroscopic size (as discussed in U. S. Patent Number 6,784,591). In the case of HFGW generation for communications applications, it is important to relate the amplitude of a GW, A, with the power, P, or more exactly with the GW flux, FGw, in wm-2 . For a viable communications link, the HFGW amplitude, A, must be large enough to be detected at the HFGW receiver. From Appendix B of Baker, Woods and Li (2006), A= 1.28x10-18 ( FGw/VGw) 112 m/m (2) where A has the dimensionless value of spacetime strain or m/m and VGw is the GW frequency s-1. Following the proceeding numerical example we will concentrate the HFGW on a diffraction-limited area of 4x 10-3 m2 or 0.004 m2 for a HFGW flux of UNCLASSIFIED//FOR OEEICIJ.b HSI!! Dflti 5 UNCLASSIFIED//&Olil OiiiilCI0L Llili QPIL¥ (2.8x1Q·13)/(4x1Q· 3 ) = 7x10· 11 wm· 2 . Thus A= 2x1Q·33 It is an extremely small . HFGW amplitude, but possibly a detectable signal. 2.1.2 Alternative Approaches There are several alternative approaches to the laboratory generation of HFGWs developed over the past 45 years as discussed in the preceding Section 2.1.1. They can be categorized as EM-cavity generated, nuclear-energy generated, superconductor­ generated, laser-impact generated and energized microscopic & submicroscopic-particle generated HFGWs. Of these categories the last category appears to be the most promising for early deployment in HFGW communications systems. Furthermore, one embodiment of that category: the Magnetron-energized FBARs generator, utilizing off­ the-shelf equipment, would seem the most useful for proof-of-concept tests. For a practical, operational communications system HFGW generator (transmitter) the strong dependence of HFGW generator's power on the number of radiating elements, N, recommends a system utilizing molecular elements as suggested by Braginsky and Rudenko (1978) or using Infrared (IR)-energized pentane molecules in a stack of circular waveguides as proposed by Woods and Baker (2009). The Magnetron-energized FBARs and the IR-energized pentane will be considered in the next-following sections. 2.1.3 Piezoelectric Approach Let us consider the l.8x 108 cell-phone film bulk acoustic resonators or FBARs, 10,000 Microwave-Magnetron, proof-of-concept laboratory HFGW generator. Assuming a 10 µm distance or margin between the 100 µm square conventional FBARs, the overall length of the laboratory generator will be 110 x (10· 6 m) x (l.8x 10 8 elements) = 19.8 km. It will have a total HFGW power of 0.066 W and for a distance out from the last in-line, in­ phase FBAR element of one HFGW wavelength (6 .1 cm) it will have a flux of 3.53 wm·2 , yielding a HFGW amplitude there of A= 4.9x 10-28 m/m. By the way, the inline set of FBAR elements also produces a more needlelike radiation pattern of HFGWs so that the flux and resulting A may even be larger. Although the frequencies may be different analyses (2003), one can extrapolate approximately from the results of Dehnen and Romero-Borja's analyses in which the angle of the needle-like radiation pattern is inversely proportional to the square root of the product of the distance between the radiators (the width between FBAR bands or tracks) and N. The distance for the system discussed here is 6.1 cm and for Dehne n's system 0.00001 m, for a factor of 6,100 and N differs by (1.8x 108)/(5x 107) = 3.6 for a product of 2.2x 104 and the inverse of the square root is 6.7xl0·3. Using the result from Dehnen's paper (Equation (4.51), page 12) of a needle half angle of 1.7 degrees we would extrapolate to 0.0115 degrees or very approximately 2x10·4 radians. Since there is no longer the constraint to the use of rudimentary off-the-shelf components as there was for the proof-of-concept apparatus, the specially designed submicroscopic elements can be manipulated. First, they will be staggered into two bands or tracks of 100 rows each or 110 x 100 µm = 1.1 cm wide bands of FBARs a wavelength or 6.1 cm apart. The rows will be staggered by displacing adjacent rows in the bands by 1.1 µm. Thus the overall length will be reduced to 198 m. Second, the 100 µm length of each FBAR element can be sliced, along the direction of travel of the HFGW build up, into one-hundred 1 µm wide slices (exhibiting 0.1 µm margins). The staggered row displacements are now reduced to 11 nm. The overall length will be reduced to about 198 cm. Concentrating the 10 MW power to each of these 1.1 cm wide bands may prove to be difficult. Thus, as an example, the continuous-wave Magnetrons will be replaced by a pulsed microwave source having UNCLASSIFIED//FOR OiiiilCl.t.k HSI!! eflti 6 UNCLASSIFIED//iiOR OiiiilCI OL lallili QPIL¥ one-microsecond-long pulses one second apart. The required average power for each FBAR band will now be 10 W. As a practical nanotechnology limit, the slice width can be reduced by two orders of magnitude to 10 nm. This would also require that the row displacements would be 110 pm (we are now into atomic if not sub-atomic dimensional changes). The overall length could be reduced to about 2 cm or the amplitude of the HFGWs could be increased to A= 4.9x10-26 . In this latter case the average energizing microwave power applied to each band would need to be increased to 1 kW. A preferred compromise in this apparent nano-technology limit might be to reduce the HFGWs generator's length to about 20 cm and increase the HFGW amplitude A to 4x 10-27 m/m. The complementary approach to optimizing a practical HFGW generator is to increase the force produced by each element without increasing the required power (that is, increasing element efficiency). This was initially done using the modern light-weight piezoelectric FBARs rather than the heavy 10-gram crystals considered by Dehnen and Romero-Borja that were of 1981 vintage. Special designs of FBAR-like elements for optimum force-generation efficiency will improve the HFGW generator performance beyond that for the usual cell-phone FBAR designs. Another approach to element design is to utilize nano-size lasers whose targets are the force-generating elements (Li and Li, 2006). Utilization of myriads of nano-size lasers would generate high-frequency HFGW pulses as noted in U. S. Patent Number 6,784,591. Thus there are a number of opportunities to enhance HFGW generation performance, utilizing special element designs, either by reducing the generator size or increasing the generated HFGW amplitude or both. 2.1.4 Infrared-Excited Molecules Approach The very theoretical IR-generated HFGWs suggested by Woods and Baker (2009) have significant promise. If one has a standing wave in a waveguide ring and excites it properly, then one will have a GW source at its center, as shown in Figure 3. The GW flux produced at its center is proportional to the n submicroscopic particle pairs (in this case pentane molecule pairs) in each ring. There is no n2buildup, but there is an n buildup. If one has a stack of N plates of rings, which are excited in sequence at light speed as a generated, growing as a GW passes by, then one has an nN2 buildup in GW flux. UNCLASSIFIED//FOR OiiiilCl.t.k HSI!! eflti 7 UNCLASSIFIED//&OR Oii&ICI0L Ll&li QPIL¥ Position of focused GW generated IR monomode waveguide formed by active material High power IR source Figure 3. Circular Resonator Geometry Using Infrared Excitation Analogous to Figure 2, we see in Figure 4 the radiation pattern for a pair of orbiting masses. GW I .1 GW ' Figure 4. Radiation Pattern Calculated by Landau and Lifshitz (1975) Next consider a number N of such orbit planes stacked one on top of another with the gravitational-wave (GW) radiation growing flux (Wm-2) proportional to N2 as the GW moves up the axis of the N orbit planes as in Figure 5. UNCLASSIFIED//FOP OiiiilCl.t.k l!ISI!!! l>flti 8 UNCLASSIFIED//&Olil OiiiilCI0L Llili QPIL¥ The stack of orbital planes are no replaced by a stack of N plates each containing n molecules in each waveguide ring as exhibited in Figure 6. Now there is a HFGW wave moving up the axis of the rings (or normal to the waveguide plates) and increasing in strength according to the product nN2 . GW GW Figure 5. GW Flux Growth Analogous to Stack of N Figure 6. Stack of Circular-Wave-Guide Plates Orbital Planes With Typical Molecule Jerks, df's One should consider the IR rings in more detail. As calculated, the IR wavelength is about 2.Sx10· 6 m. The IR waveguide has a cross-sectional area radius of A/4 in order for it to be a monomode (lowest order mode) so that the phase doesn't change across the waveguide. Thus the cross-sectional area of each IR ring is n x (2.Sx10·6 m/4)2 = l.23x 10-12 m2 and its diameter is 1.25xl0-6 m. The volume of each 100-m radius nano­ size toroidal ring is 2n x (100) x (1.23x 10-12) = 7. 7x 10-12 m3 . The mass density of pentane is divided by its molecular mass and that gives the density of jerkable masses of 6.3x1028 m·3. Thus the number of jerkable mass pairs, n, in a 100 m radius circular wave guide 2n = (6.3xl028) x ( 7.7x 10-12) = 4.85x1017 submicroscopic "particles" or potentially jerkable masses or n = 2.45 x 1017 mass pairs. According to Table 1 of Woods and Baker (2009) for pentane A= 4.62x 10-16 W. Thus the flux at one meter distance for all of the mass pairs in a single ring from Equation (8) of Black and Baker (2009) is n x (0.01146) x P; = 1.29 wm-2• It should be recognized that the axes of the opposite pentane molecules jerk (in response to the EM wave) may not be anti-parallel and tangential to the circular waveguides. On the other hand, the radiation pattern for the HFGW exhibits some omni-directional form, as shown in Figure 7, so significant HFGW radiation will be directed along the axis of the stack of circular waveguides (normal to the plates) and the HFGW will build up. UNCLASSIFIED//FOR OiiiilCl.t.k HSI!! eflti 9 UNCLASSIFIED//&Olil OiiiilCI0L Llili QPIL¥ G Figure 7. Omni-Directional Nature of the HFGW Radiation Pattern Next consider a more convenient laboratory arrangement for the rings. The ring radius is reduced to one meter, but set up 100 rings, concentrically (side by side concentric rings in the same plane or plate) with an average radius of the one meter. The reduced radius drops the Pi by (100) 2 to 4.62x 10-20, but because of the 100 concentric rings the n = 4.85x1017/2 remains the same. Thus the flux for a single "plate" of concentric rings is only reduced by 104 to 1.29x 10-4 Wm·2. Now stack some 106 of these 1.25x 10-6 m thick plates on top of one another. Thus a 1.25 m high stack, barrel or cylinder as described in Baker (2001) is created. In this case, as shown in Figure 6, N = 106 and the N2 law can be applied. Thus a HFGW total flux of 1.29x 108 wm-2 in a very narrow beam will be generated by the stack. Of course (as pointed out in Woods and Baker (2009)) caution needs to be taken on how much power is fed to each ring. One possible arrangement is to feed the output of one ring to the input of the next. The problem here is that the source won't have a long enough coherence length, even if the attenuation of the IR doesn't kill the power after a ring or two. To avoid this, from one source the available energizing power could be divided equally between all the rings and fed to them up the stack or cylinder at the speed of light. The practical difficulties would be how to drive them all in correct phase, but it is a challenge for future research in the IR-ring approach. For an operational so,oooA infrared (IR), 12.5 meter long, 10-meter radius (104 concentric rings per plate so Pi = 1.29x 102 wm-2 and 107 plates) cylindrical HFGW generator (Woods and Baker, 2009), the flux at a one-meter distance from the generator is, according to Table 1 of Black and Baker (2009) for N = 107, (1.146x 1012) x (1.29x 102) = 1.48x 1014 wm·2 (very large, but with a very narrow 2.3x 10-4 radian half-power-point needle beam). The required generator power can be reduced by utilizing pulsed HFGWs. Suppose that the distance between the generating or transmitting device and the detecting or receiving device is a little more than an Earth's equatorial radius, or~ 7x 106 meters. At this distance, 7,000 km, the flux of the UNCLASSIFIED//FOR OiiiilCl.t.k HSI!! eflti 10 UNCLASSIFIED/ /iiOR OiiiilCI O L lallili QPIL¥ received signal, S, is (1.48x1014)/(7x106) 2 = 3 wm·2, more than adequate for an effective communication system. With this configuration, the width of the needle-like, narrow HFGW beam at the receive end is (2.3x 10·4 ) x (7x 106) = 1.6 km, and multiple HFGW carrier frequencies can be used, so the signal is very difficult to intercept, and is therefore useful as a low­ probability-of-intercept (LPI) signal, even with widespread adoption of the technology. From Equation (2) the amplitude A of the HFGW at 7,000 km with the HFGW frequency (twice the IR frequency of VGw = 1.2x 1014 s·1) given by: A = 1.28x 10-18 (S/vGw )V2 = 1.8x 10-32 (in dimensionless units or m/m), which would be detectable by the currently designed Li-Baker HFGW detector. Since the exact frequency and phase of the HFGW signal is known (unlike the stochastic relic HFGWs, for which the Li-Baker detector was designed), a much more sensitive, optimized HFGW detector will likely be developed. As shown in Figure 8, from Grishchuk (2008), there will be negligible relic HFGW noise at the IR HFGW generator's frequency of 1.2x 1014 s·1 and no other cosmic sources at these frequencies are currently hypothesized. Prior to the proof-of-concept test, one can assume a noise figure at the Li-Baker detector of 10·8 Wm·2. C 0 10·2 1a N .,,j "'0 ci. C. E -td 104 0 ... - "' <I) :, ~1'! ID 8_ :;;E - ► :: 1o·6 U$ en a -= 1 o•B 1 o.10 10 •12 \ "'············•"·' , ......., ..... , ........ ....... .QW...... ~ ................ : ......... ~ ...... ....... ,r ··•~ ............. , 10•14 I ! I I I t I I ,I t I t I I 1 I I f I I I I • I • I <I> ~ ::i I Q. I ,::, I C I 0 I '-' I G> 1 .!!! • = e .,. ~~ "' a, I -9 f§ I Q> ,._ : ['5 : (11 £ I I I ' I I I I I I I ' ' I I • I ' I A ! ,~ §' 0 , r\ =1 .0 : ! : l /' : -20 10·10 10·5 10° 10 Frequency v, Hz Figure 8. Predicted Relic GW Energy Density as a Function of Frequency UNCLASSIFIED/ /FOR CiiiilCl.t..k 1!191!!! tJfltf 11 UNCLASSIFIED//iiOlil OiiiilCI0L Llili QPIL¥ 2.2 HFGW DETECTORS (RECEIVERS) 2.2.1 Alternative Approaches One of the first suggested means for the detection of HFGWs concerns electromagnetic detectors (Braginsky, et al. 1974 and Braginsky and Rudenko, V, 1978). Then Pegoraro, et al. (1978) suggested the use of tuned resonant chamber HFGW detectors. Rudenko and Sazhin in 1980 proposed a Laser interferometer as a gravitational wave detector (somewhat similar to the current Japanese approach). In 1995 Tobar characterized multi-mode resonant-mass HFGW detectors and three years later in 1998 (Ottaway, et al.) proposed a compact injection-locked Nd :YAG laser for HFGW detection. And in 1999 Tobar suggested, microwave parametric transducers for the next generation of resonant-mass gravitational wave HFGW detectors. In the past few years, HFGW detectors have been fabricated at Birmingham University, England, INFN Genoa, Italy and in Japan. These types of detectors may be promising for the detection of the HFGWs in the GHz band (MHz band for the Japanese) in the future, but currently, their sensitivities are orders of magnitude less than what is required for the detection of high-frequency relic gravitational waves (HFRGWs) from the big bang. Such a detection capability is to be expected, utilizing the Li-Baker detector (please see Appendix B for Plans & Specifications development). Nevertheless, all four candidate detectors; plus, possibly, the use of superconductors (Li and Baker, 2007) should be analyzed for possible military applications. The Li-Baker HFGW detector was invented by R. M L Baker, Jr. of Transportation Sciences Corporation, California and patented in P. R. China (Baker, 2001). Based upon the theory of Li, Tang and Zhao (1992) termed the Li-effect, the detector was proposed by Baker during the period 1999-2000, a patent for it was filed in 2001, subsequently granted (Baker, 2001), and preliminary details were published later by Baker, Stephenson and Li (2008a). This detector was conceived to be sensitive to relic HFGWs (HFRGWs) having amplitudes as small as 10-32 to 10-30 . The Birmingham University HFGW detector measures changes in the polarization state of a microwave beam (indicating the presence of a GW) moving in a waveguide about one meter across (see Figure 9). Also see Cruise (2000), Ingley and Cruise (2001) and Cruise and Ingley (2005). It is expected to be sensitive to HFGWs having spacetime strains of A ~ 2 x 10-13 (Hz)·½, where Hz is the GW frequency, and as usual A is a measure of the strain or fractional deformation in the spacetime continuum (dimensionless m/m). UNCLASSIFIED//FOR OiiiilCl.t.k HSI!! eflti 12 UNCLASSIFIED//&OR Oii&ICI0L Ll&li QPIL¥ Figure 9. Birmingham University HFGW Detector The INFN Genoa HFGW resonant antenna consists of two coupled, superconducting, spherical, harmonic oscillators a few centimeters in diameter (see Figure 10). The oscillators are designed to have (when uncoupled) almost equal resonant frequencies. In theory, the system is expected to have a sensitivity to HFGWs with size (fractional deformations) of about ~ 2x 10·17 (Hz)·½ with an expectation to reach a sensitivity of~ 2x 10-20 (Hz)·½ (Bernard, Gemme, Parodi, and Picasso (2001); Chincarini and Gemme. (2003)). As of this date, however, there is no further development of the INFN Genoa HFGW detector. Figure 10. INFN Genoa HFGW Detector The Kawamura 100 MHz HFGW detector has been built by the Astronomical Observatory ofJapan. It consists of two synchronous interferometers exhibiting an arms length of 75 cm. Please see Figure 11. Its sensitivity is now about 10-16 (Hz)·½ UNCLASSIFIED//FOP OiiiilCl.t.k l!ISI!!! l>flti 13 UNCLASSIFIED//&Olil OiiiilCI0L Llili QPIL¥ According to Cruise (2008) of Birmingham University its frequency is limited to 100 MHz and at higher frequencies its sensitivity diminishes. In the case of the Infrared-excited molecules approach, on might employ a variant of the Robinson Gravitational Wave Background Telescope for the receiver or detector (Yoon, et al., 2006). It is a bolometric large angular scale Cosmic Microwave Background (CMB) polarimeter, but might possibly be modifiable for direct HFGW detection. Development of 100MHz GW detectors at National Astronomical Observatory of Japan Two synchronous recycling interferometers were built! S ynchronous recycling Interferometer (Concept: Drever 1983) Figure 11. The National Astronomical Observatory of Japan 100 MHz Detector 2.2.2 Concept (Li-Effect) The Li-Effect was first published in 1992 and subsequently, some nine peer-reviewed papers have been published concerning it including a capstone paper, Li, et al. (2008) included as Appendix C. The Li-Effect is very different from the classical (inverse) Gertsenshtein-Effect. With the Li-Effect, a gravitational wave transfers energy to a separately generated electromagnetic (EM) wave in the presence of a static magnetic field. That EM wave has the same frequency as the GW and moves in the same direction. This is the "synchro-resonance condition," in which the EM and GW waves are synchronized (move in the same direction and have the same frequency) and is unlike the Gertsenshtein- Effect. The result of the intersection of the parallel and superimposed EM and GW beams, according to the Li-Effect, is new EM photons moving off in a direction perpendicular to the beams and the magnetic field directions. Thus, these new photons occupy a separate region of space (see Figure 12) that can be made essentially noise-free and the synchro-resonance EM beam itself (in this case a Gaussian beam) is not sensed there, so it does not interfere with detection of the photons. This Li-Effect was utilized by Baker (2001) in the design of the Li-Baker HFGW detector and Chinese Patent (Baker, 2000) of a device to detect HFGWs, the innovative Li-Baker HFGW Detector. UNCLASSIFIED//FOR OiiiilCl.t.k HSI!! eflti 14 UNCLASSIFIED//&Olil OiiiilCI0L Llili QPIL¥ :z Signal (PPF) and Noise (BPF) have very different physical behavior PPF > BPF at this end of x-axis Very Noisy (BPF) / Poynting Vector or Detection Photons (PP ) / / Poynting Vector or -✓-----------► Y S Detection X otons (P F) .. Signal (PPF) and Noise (BPF) have very different physical behavior PPF > BPF at this end of x-axis GW&E Synchro-Resonant Figure 12. Detection Photons Sent to Locations That are Less Affected by Noise The synchro-resonance solution of Einstein's field equations [Li et al. (2008), pp. 411 to 413] is radically different from the Gertsenshtein (1962) effect. The newer Li-Effect solution utilizes a coupling between EM and gravitational waves (Li, Tang and Zhao, 1992) that arises according to the theory of relativity. And a strong static magnetic field in the y-direction, B, is superimposed upon a GW propagating in the z-direction, as in the inverse Gertsenshtein effect. However, with the Li-Effect, there is an additional focused microwave beam ("Gaussian beam") at the expected frequency, phase and bandwidth of the HFGWs in the same direction (z) as the GW (as shown in Figure 12). Unlike the Gertsenshtein effect, a first-order perturbative photon flux (PPF), comprising the detection photons, will be generated in the x-direction. Since there is a 90 degree shift in direction, there is little crosstalk between the PPF and the superimposed EM wave (Gaussian beam), so the PPF signal can be isolated and distinguished from the effects of the Gaussian beam, enabling detection of the GW. Here's how it works: The perturbative photon flux (PPF), which signals the detection of a passing gravitational wave (GW), is generated when the two waves (EM and GW) have the UNCLASSIFIED//FOR OiiiilCl.t.k HSI!! eflti 15 UNCLASSIFIED/ /iiOR OiiiilCI O L lallili QPIL¥ same frequency, direction and phase. This situation is termed "synchro-resonance." These PPF detection photons a are generated as the EM wave propagates along its z­ axis path, which is also the path of the GWs, as shown in Figure 12. The magnetic field is in the y-direction. According to the Li-Effect, the PPF detection photon flux (also called the "Poynting Vector") moves out along the x-axis in both directions. The signal (the PPF) and the noise, or background photon flux (BPF) from the Gaussian beam have very different physical behaviors. The BPF (background noise photons) are from the synchro-resonant EM Gaussian beam and move in the z-direction, whereas the PPF (signal photons) move out in the x-direction along the x-axis. The PPF signal can be intercepted by electromagnetic-interference-shielded microwave receivers located on the x-axis (isolated from the synchro-resonance Gaussian EM field, which is along the z-axis). In addition, isolation is further improved by cooling the microwave receiver apparatus to greatly reduce thermal noise background (Baker, Stephenson and Li, 2008a). The resultant efficiency of detection of HFGWs is very much greater than from the inverse Gertsenshtein effect, which has been exploited in some previously proposed HFGW detectors and found to have insufficient sensitivity to HFGWs (Eardley, et al., 2008). The amplitude of the PPF has space accumulation dependence-that is, it is proportional to the length of the wave overlap. This is because the GWs (gravitons) and EM waves (photons) have identical propagation velocities, so that the two waves overlap synchronously and coherently throughout and their interaction is cumulative (Boccaletti et al., 1970; Delogi and Mickelson, 1977). This is the synchro-resonant condition or Li-effect. This means that for maximum signal, the interaction overlap coupling must be as long as possible. It should be noted that the identification of this coupling or Li-effect, upon which the Li-Baker HFGW detector is based, is not so new that it is untested in the literature. At least nine peer-reviewed research publications concerning the theory have appeared following Li, Tang and Zhao (1992), including those by Li and Tang (1997), Li et al. (2000), Li, Tang and Shi (2003), Li and Yang (2004), Li and Li (2006), Li and Baker (2007), Li, Baker and Fang (2007), Baker, Stephenson and Li (2008a), and Li et al. (2008). 2.2.3 Quantum Back-Action Limit The Standard Quantum Limit (SQL) will be introduced and reviewed in this section (Stephenson, 2009b), and design of the Li-Baker HFGW Detection System will also be reviewed to understand how the SQL might limit the sensitivity of this new type of GW detector. Review of the Standard Quantum Limit The Standard Quantum Limit (SQL) is often defined as "The limit on measurement accuracy at quantum scales due to back-action effects." But what is "back-action"? (See Kippenberg and Vahala, 2008.) From Clerk (2008) the Heisenberg Uncertainty Principle is (&') X (Lip) > fl/2 (3) UNCLASSIFIED/ /FOR CiiiilCl.t..k 1!191!!! tJfltf 16 UNCLASSIFIED/ /iiOR OiiiilCI O L lallili QPIL¥ where L1x is the position uncertainty, LJp is the momentum uncertainty, and n is Planck's reduced constant. Thus measuring x disturbs p, which in turn disturbs future measurements of x Llx(dt) = Llx(O) + dt[L1p(O)/m] (4) where Llx(O) is the initial position uncertainty is, Llp(O) is the initial momentum uncertainty, dt is the time of the future measurement, and m is the mass of the system under measurement. E/c2 may be substituted for mass in an energy only system. This is depicted in Figure 13. To summarize, the quantum effects of measurements on future measurements is quantum back action. Therefore the Standard Quantum Limit defines the lower sensitivity limit for all measurement instruments, including gravitational-wave detectors, according to the Heisenberg uncertainty principle. Detectors cannot avoid quantum back action, however the use of higher energies in the detection process can change the relative scale and impact of back action, and the use of squeezed states can shift the relative distribution of back action into states not involved in measurement. TIME t= 0 "A---+----,'• : I I ' ' ~ ~ Ap(O) > li/2 Al((O) A~(qt) =ox(dt) + Slt[Ap(O) / m] Measurement of x drives down All.{0) Therefore ApjO) drives up Ax(£1t) which drives up Ap(O) Quantum Back Action: x dt) measurement affected l1Y, earlier x(O) measurement \ \ I I I I I I ox dt) ---.: ~ I I TIME t= dt Figure 13. Quantum Back Action as a Mechanism for Creating the Standard Quantum Limit Calculating the Standard Quantum Limit (SOU A method for calculating the Standard Quantum Limit (SQL) is introduced in this section. The calculation of coherent versus stochastic SQL is compared and contrasted. Important terms of the SQL calculation are described, including the impact of contained energy levels within the detector on SQL, and the sources of Quality Factor and its effect on SQL. Calculating the Standard Quantum Limit (SQL) UNCLASSIFIED/ /FOR OiiiilCl,.k 1!191!!! tJflti 17 UNCLASSIFIED//EOR OEEICI0L Llili QI\IL¥ Coherent Versus Stochastic SOL The question under consideration in this paper is whether or not the Li-Baker detector, Figure 14, is quantum-limited when detecting relic HFGW. In other words, does the standard quantum limit (SQL) interfere with the sensitivity of the Li-Baker detector design? The answer will be negative if the SQL is less than 10-32 m/m. Grishchuk (1977, 2007) has calculated the SQL for GW detectors in general, which for a coherent GW is hdet = (1/Q)(nwJE/12 (5) and for a stochastic GW is: (6) where hdet is the metric (strain) detection limit in m/m, w is the frequency of sensed gravitational waves (typically around 10 GHz in the Li-Baker detector), Eis the effective energy contained within the detector cavity summed over the detection averaging time, and Q is the quality factor or selectivity of the signal over noise. The SQL depends on the values of these parameters. For the remainder of this paper, we will consider the SQL of only the stochastic signal detection case. In the following subsections the best possible value of the SQL using current technology will be estimated to determine the fundamental limitations of the Li-Baker detector as now envisioned. Impact of Contained Energy Levels on SOL First attempt to estimate a realistic best case for the energy contained within the detection process, E. Typically it is expected that for a refrigerated microwave resonant cavity the best possible electrical quality factor will be around 2nx105. Assuming a "best efforts" value of 1000 W for the power of the Gaussian beam in a laboratory installation, the effective total RF energy stored in the microwave resonant cavity of the Li-Baker detector, summed over the system averaging time, is estimated to be given by (Grishchuk, 2007): ERF = (103 W) x (1000s) x (21tx105/21t) = 1011] (7) over a typical 1000 s averaging time. Both the Li-Baker detector and a detector using the Gertsenshtein effect use a large static magnetic field B. For the present suggested outline design for the Li-Baker detector, the nominal value of B = 3 T, so that the magnetic energy density is given by (8) The interaction volume in a practical laboratory-based detector is likely to be a maximum of around 1 m3 • So, the effective total stored energy from the Gaussian UNCLASSIFIED//FOR OEEICIJ.b HSI!! Dflti 18 UNCLASSIFIED//EOR OEEICI0L Llili QI\IL¥ beam is much greater than the stored magnetic field energy, and it follows that E::; ERF = 1011 J to a reasonable approximation. Sources of Quality Factor and Effect on SOL To calculate the SQL, hdet, we also need the value of the detector quality factor Q (not the same as the cavity quality factor). Anything that concentrates or enhances the signal preferentially over noise, in any measurement dimension, can be considered a contributor to the quality factor Q. The quality factor can therefore be understood as the "signal selectivity" in each dimension, so that Qtot = (Qspatial) (Qt) = QrQsolid angle Qt . (9) The temporal quality factor in the Li-Baker detector arises from averaging the signal over time, so that at 10 GHz, Qt= nt;nt = (10x109 Hz) x 1000s = 1013. There is a contribution to Q arising from the fractal membranes that focus and concentrate the signal photon energy - but not the background photons - along the radial dimension. The radial selectivity arising from the general relativity solution, in conjunction with fractal membranes, is calculated by Li et al. (2008). Their table III gives Qr= SNRrr=J7cmJ/SNRrr=J.scmJ = 3.4x1021 . This is mostly due to the effective Q contribution arising from the synchro-resonance solution to the Einstein field equations that limit the PPF signal to a radiation pattern in certain directions, whereas noise is distributed uniformly. By utilizing directional antennas, the Li-Baker detector can capitalize upon this gain due to the focusing power of fractal membranes as a contribution to Q in angular space as well. This is calculated in detail, octant by octant, by Li et al. (2008). Page 24 of Li et al. summarizes this in terms of angular concentration onto the detector. A non-directional antenna corresponds roughly to solid angle 21r steradians (one hemisphere), so that the effective antenna gain is estimated as (Qsolidangle) = 2n sr/10-4sr = 6.3x104 . Therefore, the predicted maximum quality factor will be Qtotal = QrQsolidang1eQt = 2.1x1039 . This finally gives the Standard Quantum Limit (SQL) for stochastic GW detection at 10 GHz: hdet = (1/Q) 112cncv/E) 112 = 1.Sxl0-37 m/m . (10) Comparison of SOL With Predicted Sensitivity As noted in the previous section, hdet = 1.Sxl0-37 m/m represents the lowest possible GW amplitude detectable by each RF receiver in the Li-Baker HFGW detector, limited by quantum back-action. An additional (1/ ✓ 2) factor applies if the separate outputs from the two RF receivers are averaged, rather than used independently for false alarm reduction, resulting in a minimum hdet = 1.2x10-37 . Since the predicted best sensitivity of the Li-Baker detector in its currently proposed configuration is A = 10-32 m/m, these results confirm that the Li-Baker Detector is photon-signal limited, not quantum noise limited; that is, the Standard Quantum Limit is so low that a properly designed Li-Baker detector can have sufficient sensitivity to observe HFRGW of amplitude A ~ 10-32 m/m. UNCLASSIFIED//FOR OEEICIJ.b HSI!! Dflti 19 UNCLASSIFIED//iiOlil OiiiilCI0L Llili QPIL¥ 2.2.4 Li-Baker HFGW Detector The detector, shown in Figure 14, has five major components: 1. A Gaussian (focused, with minimal side lobes) microwave beam (GB) is aimed along the +z-axis at the same frequency as the intended HFGW signal to be detected (Yariv, 1975), typically in the GHz band, and also aligned in the same direction as the HFGW to be detected. The microwave transmitter's horn antenna is not shown, but would be located on the -z-axis. 2. A static magnetic field B, generated by two powerful magnets, typically using powerful superconductor magnets such as those found in a conventional MRI medical body scanner, is directed along the y-axis. 3. Two paraboloid-shaped reflectors, which are formed from "fractal membranes" (Wen eta/., 2002; Zhou eta/., 2003; Hou eta/., 2005), are located in the y-z plane at the origin of the coordinate system to aim and focus the detection photons at diffraction­ limited spot antennas connected to two microwave receivers. These reflectors, shown in planer form in Figure 15, are segmented (similar to a Fresnel lens) and located back-to­ back in the y-z plane. They are thin enough (less than a centimeter thick in the x­ direction) to not block the z-directed Gaussian beam. These microwave reflectors reflect the x-directed detection pho