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A possibility of emission of high frequency gravitational radiation from d-wave to s-wave type superconductor junctions.
Giorgio Fontana
Copyright April 1998
Faculty of Science, University of Trento, 38050 Povo, TN, Italy.
| Recent measurements on a class
of high-Tc superconductors (HTSC) have shown that Cooper-pairs binding
may be associated to a d-wave, while in another class, d
and s waves may coexist.
When d-wave Cooper-pairs are injected in a superconductor that can sustain s-wave binding, d-wave pairs decay to s-wave pairs and energy is irradiated by means of gravitons. We show that in s-wave to d-wave type superconductor (SDS) junctions in an equilibrium condition no net gravitational wave energy is emitted, on the other hand under non equilibrium conditions a net gravitational wave energy is emitted by the junction. Experiments which show a gravitational interaction between inomogeneus high-Tc superconductors, under non equilibrium conditions, and test objects may be understood by accepting a possibility of emission of gravitational radiation from SDS junctions. |
Introduction. In spite of the fact that quantum gravity is a theory currently under development (1), there are few elementary concepts that are involved in the application of some basic ideas related to the quantization of the gravitational field. For istance, it has been demonstrated (2) that gravitational waves, because of their quadrupolar nature, are carried by particles of spin 2, named gravitons. Moreover it has been suggested that atomic transitions for which the quantum number L changes by + or – 2, and for which the total quantum number J changes by 0 or + or – 2 are quadrupolar transitions and are permitted for the emission of gravitons, while the emission of photons is forbidden (2) (3).
Atomic transitions from orbitals 3d to 1s, 3d to 2s and 3d to 3s are possible candidates for transitions which may be applicable for the generation of gravitational radiation by atoms of a suitable material. The material could be pumped by photons and let decay gravitationally. The efficiency of the process depend on the half-lives of metastable states and the possibility of obtaining a population inversion , as we have in LASERs.
While looking for a natural source of high frequency gravitational radiation it has been computed that the energy of gravitons involved in some possible stellar processes are very high, 14.4 keV for 57Fe in the sun and 16.1 MeV from supernovae (2). Halpern’s work (2) (3) also defines the gravitational counterpart of the laser, called a "gaser", for which we could prefer the name GWASER, for Gravitational Wave Amplification by Stimulated Emission of Radiation.
In spite of the fact that there is a lack of substantial theoretical and experimental work in this field, we could extend the above mentioned considerations to different quantum systems, looking for a possible candidate to efficient high frequency gravitational wave generators and detectors. Our attention has been focused on superconductors, where the carriers of electric current are bound in atom-like structures composed of two electrons, the Cooper-pairs. Cooper-pairs obey to quantum rules, both individually and collectively. With superconductors we are in the very lucky situation where the collective behaviour may show the individual state of each Cooper pair, being them collectively at the ground state for the specific superconducting material.
Very recently it has been experimentally observed the existence of two different symmetries of the order parameter in high temperature superconductor, a symmetry with an s-wave component and a symmetry with a d-wave component (5), therefore we know that Cooper-pairs are in s-orbitals and d-orbitals respectively. We can also predict that when Cooper-pairs move under non equilibrium conditions, i.e. under the effect of magnetic fields, from a superconductor where the symmetry of the order parameter is of type d to a superconductor where this symmetry is of type s, the Cooper-pairs must decay loosing energy by the emission of gravitons. This working principle is similar to the photon generation mechanism in LEDs and semiconductor injection LASERs, giving the gravitational counterparts that we may call GWEDs and injection GWASERs.
Pairing states in HTSC. The symmetry of the order parameter D (k) in superconductors has been found to have an s-wave symmetry in conventional low Tc superconductors and, after an intense research both theoretical and experimental (4) (5) (6) (7), it has been found that YBCO HTSC support both an s-wave symmetry and a d-wave symmetry depending on the probe direction. The s-wave component is due to the distortion by the orthorombic symmetry and it has been found that different HTCS which do not have the orthorombic distortion are nearly pure d-wave (7). A background discussion on the symmetry of pairing states in both conventional and high Tc superconductors can be found in (4). We recall that electron pairing in low Tc superconductors is attributed to phonons, while in HTSC a strong magnetic coupling is believed to cause electron pairing, giving an inevitable d-wave symmetry and the high transition temperatures observed.
Emission of gravitational waves from HTSC. The efforts required for the study of the nature of pairing states in HTSC has led to many experiments where Josephson junctions have been prepared using conventional superconductors injecting a supercurrent in HTSC through an insulating barrier. While the obtained interference patterns corroborated the cited theory, we may ask about the angular momentum qauntum number of Cooper-pairs while traversing a s-wave to d-wave superconductors (SDS) junction. Experiments show that the supercurrent is not destroyed, it follows that each Cooper-pair should emit or absorb a particle carrying a spin of + or - 2, which may be identified with graviton and antigraviton respectively. In a fully superconductive circuit comprising the junction with no current, the number of Cooper-pairs that traverse the junction averages to zero, with no overall emission; on the other hand if a current flows in the superconductor, the distance between s-wave to d-wave junction and d-wave to s-wave junction along the current flow can become large enough to create two independent sources of gravitons and antigravitons which are not subjected to a local annihilation, therefore a net emission of gravitational wave could be possible, energy is subtracted from the current loop (flux vortex) which collapses and new loops are created by external fields. It is not known theoretically how much gravitational wave energy could be released by the process, as a complete theory of HTSC has not been fully developed and quantum gravity has only speculative foundations (1), nevertheless we may estimate the order of magnitude of the predicted phenomenon using some well known quantum relations.
We may estimate that the coupling energy that is released by a single decay could be a large fraction of
1) |Tcp-Tcs| kB
where Tcp is the critical temperature of the p-wave superconductor and Tcs is the critical temperature of the s-wave superconductor and kB the Boltzmann constant.
If we make the hypotesys that this fraction is a factor of one, we may write:
2) kB|Tcp-Tcs| = hf
obtaining graviton frequencies of the order of hundreds of GHz.
The maximum power emitted by the process could be found with the hypotesis of currents slightly below the critical currents of most supercondutors, and of about 10 kA/cm2, obtaining a power density of :
3) kB|Tcp-Tcs| (10kA/3.2 × 10-19) W/cm2
which is of the order of ten W/cm2.
We observe that the conditions required for the emission of gravitational radiation from a superconductor may have occured incidentally during a sequence of experiments (8) (9) where a dual layered YBCO superconducting disk had been subjected to strong e-m fields. The disk consisted in two layers, the upper part had the orthorombic phase with the c-axis parallel to the surface of the disk and a Tc of 94.2 K, the lower part had a markedly different structure, which was 40 % tetragonal, and Tc equal to 60.5 K. It is not known which was the pairing state of Cooper pairs in the lower part, nevertheles it is supposed to be pure d-wave because of the absence of the orthorombic phase. We also observe that the orthorombic layer, because of its orientation supports both d-wave and s-wave for a supercurrent traversing the junction between the two layers. It follows that a current induced by the complex coil arrangement and traversing the partially SDS junction may have generated a beam of gravitational radiation.
The observed effects were attributed to a possible gravitational shielding; this hypotesis is not corroborated by any currently accepted theory or other supporting experiments, nor the observed region of "interaction", which has exactly the shape of the superconducting disk or toroid for distances of many disk diameters from the device surface, is compatible with a static field modification. On the contrary it is compatible with a beam of millimetric or submillimetric gravitational radiation generated by the decay of Cooper-pairs. The emission is orthogonal to the plane of the junction where small domains should have emitted coherent and thus beamed gravitational radiation, these domains are associated to current fluxes that locally align Cooper-pairs and locally determine the phase of the gravitational wave radiation; we also recall that HTSC are type 2 superconductors which allow the partial penetration of magnetic field by flux vortices.
It has been already shown that gravitational radiation may transfer energy and momentum (10), because of that, the repulsive effect observed in (8) (9) could be a starightforward consequence of this property of gravitational radiation.
Conclusions. A mechanism for the efficient generation of high frequency gravitational radiation using high Tc superconductors has been proposed and discussed. The mechanism could explain a controversial experiment and clarify its essential features and construction details.
Additional experimental work and theoretical research will be required for a detailed quantitative analysis of the interaction between superconductors and gravitational radiation, nevertheless the possible existence of such a phenomenon will certainly promote the research in this field.
References.