Volume 24A, number 1 PHYSICS LETTERS 2 January 1967

DETECTION OF INERTIAL EFFECTS WITH SUPERCONDUCTING INTERFEROMETERS

G. PAPINI Division of Natural Sciences, Department of Physics,

University of Saskatchewan Regina Campus, Regina, Sask., Canada

Received 6 December 1966

Superconducting interferometers hay be useful indetecting inertial effects and in accurate rotation rate measurements.

In a recent paper [l] we have pointed out the connection between London [2] moment of rotat- ing superconductors and Lense-Thirring fields [3] of general relativity. On the basis of this re- lationship it is easy to predict the behavior of rotating superconducting interferometers [4]. These consist essentially of two Josephson junc- tions [5] connected in parallel by superconduct- ing links. For simplicity we consider a circular interferometer. If we rotate masses about the symmetry axis through the center and normal to the plane of the interferometer, then the rotation causes a difference in the quantum phase. This can be seen from the Hamiltonian for the en- semble of free electrons inside a superconductor

PI

H=Cj ~[Pj-~cho(rj)- zA(rj)12+V(rj) +VI (1) 1 i

where

V(q) = -3 mck,, -; A,

and VI contains the usual interaction of the BCS theory [+I]. A, and A are the electromagnetic potentials and ho0 andho = (kol,k&ko3) repre- sent the Lense-Thirring field corresponding to the given distribution of rotating matter. For a rotating sphere the components of the field of interest to us are

h ~4 GIM R2,., 0 __ 5 c3,3

(2)

where 111 and R are mass and radius of the sphere, w its angular velocity and G the gravitational constant. In the absence of magnetic fields we obtain for the phase difference

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AS =$%$h,.dl

where the integration is over the closed path des- cribed by the superelectrons, and for the total supercurrent flow through the pair of junctions

IT = 1, sin 6, cos (4A.S). (4)

Eqs. (2), (3) and (4) may be used, in principle, to test the general theory of relativity [8].

Lest us now accept the Machian view that iner- tia depends on a mutual action of matter. Then rotation of the interferometer with respect to matter also generates a phase difference in the wave function of the superelectrons. If we assume the interaction to be again represented by (2), where w now is the angular velocity of the appa- ratus relative to matter, then we find

(5)

with a radius of the apparatus and N order of multiplicity of the connected region between the Josephson ‘unctions. When a - 50 cm, N - 103 and w - 10 b cps, we find for AS due to sun, earth and galaxy the values 4 X 10-5, 2 and lo3 radians respectively, if the quantum phase re- mains coherent on the required distances. For the same values of the parameters a rotation of the apparatus relative to the fixed stars gives AS - 2 x log radians. It should therefore be pos- sible to choose suitable values of a, Nor LJ to make IT sensitive to the different values of the masses. The best candidates for a measurement of the described effects appear to be earth and galaxy. A rotation of the apparatus in a direc- tion perpendicular to the radius of the earth or the axis of the galaxy would result in a vanishing

Volume 24A, number 1 PHYSICS LETTERS 2 January1967

AS. The apparatus should also be screened ac- curately from any magnetic field. In fact it is easy to see that the magnetic fields - lo-11 G al- ready contribute a phase shift comparable with the values previously calculated. This may re- quire the development of refined techniques of measurement along the lines discussed by Blackett [ 91.

Finally, we wish to point out that rotating superconducting interferometers may be used for accurate rotation rate measurements, particu- larly when the conditions of the problem do not allow the use of external references. In this case AS is given by

ma2 Nw AS=ti

and IT has maxima whenever

mwa2 =mNii (6)

where n is an integer. Notice that when N is one, eq. (6) represents

the Bohr-Sommerfeld quantum rule for the area1 velocity of the interferometer. Experiments of

this type have an analog in the classical one per- formed by Michelson and Gale [lo] who studied the effects of rotation on the propagation of light by means of an optical interferometer. With superconducting interferometers, however, the interference is essentially a quantum mechanical phenomenon.

References 1. G.Papini, N. Cim. 45B (1966) 66. 2. F. London, Super-fluids, Vol. I (J. Wiley and Sons,

Inc., New York, 1950) p. 78. 3. H.Thirring, Physik. 2. 19 (1918) 33;

J. Lense and H. Thirring, Physik. 2. 19 (1918) 156. 4. R.C.JakIevic, J.Lambe, A.H.Silver and J.E.

Mercereau, Phys. Rev. Letters 12 (1964) 159. 5. B.D.Josephson. Phys. Letters 1 (1962) 251. 6. B.S.De Witt, Phys. Rev. Letters 16 (1966) 1092. 7. J. Bardeen, L. N. Cooper and J.R. Schrieffer,

Phys. Rev. 108 (1957) 1175. 8. See also G.Papini, Physics Letters, to be published. 9. P.M.S.Blackett, Phil. Trans. A245 (1952) 309.

10. A.A.Michelson and H.G.Gale, Astrophys. J. 61 (1925) 140.

LOW TEMPERATURE SPECIFIC HEAT OF DILUTE MAGNETIC ALLOYS

S . NAKAJIMA* Theoretical Physics Institute, University of Alberta, Edmonton, Alberta, Canada

Received 26 November 1966

The electronic specific heat due to the second order sd exchange interaction with ordered impurity spins is proportional to T log T, when the vanishing molecular field acting on the impurity spin has a finite probability.

In Cu + Mn alloys, when the concentration of to the system of impurity spins. Since the low Mn is not too low, there appears at low tempera- temperature specific heat arises from those tures a spin ordering of Mn atoms. Well below spins which happen to exist in weak molecular the transition temperature, the specific heat is field, it was essential to assume that the proba- T-linear and the proportionality factor is indepen- bility distribution p(Q) of the impurity spin Zee- dent of the Mn concentration. man energy Q has a finite value at Q = 0.

To obtain this anomalous T-linear specific heat, Marshall [l] applied the Ising spin model together with the molecular field approximation

On the other hand, in analogy with the elec- tron-phonon coupling, Kondo [2] obtained a mass enhancement of the conduction electron by the sd exchange coupling with impurity spins, as- suming an “Einstein” type p(Q).

With use of the same model as was used in dis * Now returned to: Institute for Solid State Physics,

University of Tokyo, Azabu, Tokyo.

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