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7 Gravitomagnetic London Moment in Rotating 0 0 Supersolid He4 2 n a ∗ J C. J. de Matos 5 February 6, 2008 ] n o c - r p Abstract u s . NonclassicalrotationalinertiaobservedinrotatingsupersolidHe4 t a can be accounted for by a gravitomagnetic London moment similar to m the one recently reported in rotating superconductive rings. - d n Non Classical Rotational Inertia (NCRI) was predicted by London 50 o years ago [1]. It was eventually verified experimentally by Hess and Fairbank c [ [2], who set Helium in a suspended bucket into rotation above the critical 1 temperature Tc at which superfluidity sets in, and then cooled it (with the v bucket still rotating at angular velocity ω) through T . They found that, c 0 provided ω is less than a critical value ω , the apparent moment of inertia of 1 c 1 the helium - that is, the ratio of its angular momentum to ω - is not given 1 by the classical value I but rather by 0 classical 7 0 L / I(T) = = I 1−f (T) (1) at ω classical" s # m ∗ - where fs(T) = ρ /ρ is the superfluid fraction. In liquid helium, fs(T) tends d ∗ to 1 in the zero-temperature limit and to zero when T = T , ρ and ρ being n c o respectively the mass density of superfluid helium, and the mass density of c normal helium. : v 4 NCRI has recently been observed in rotating supersolid He by Kim and i X Chan [3]. They measured the resonance frequency of a torsional oscilla- r tor that contains an annulus of solid He4. Below 230mK, the frequency a experiences a relative increase that depends on the temperature and drive ∗ESA-HQ, EuropeanSpace Agency, 8-10rue Mario Nikis, 75015Paris,France, e-mail: [email protected] 1 5 amplitude and reaches a maximum of about four parts in 10 . Having ex- cluded by various control experiments, other explanations, they conclude that the data indicate a change in the moment of inertia of the supersolid, which according to Equ.(1), corresponds to a maximum supersolid fraction ∗ (fs(T) = ρsupersolidHe4/ρnormalsolidHe4) of 0.017 (see figure 1). Figure 1: Signs of supersolidity. The supersolid fraction f (T) inferred from s the data in [3] as interpreted by Eq.(1), as a function of temperature for dif- ferent values of the maximum velocity of the walls. The pressure is 41Bars. [Adapted from [3]] Tajmar and the author recently [4] [5] [6] observed a gravitomagnetic London moment, B [Rad/s], in rotating superconductive rings. g B = 2ωf (T) (2) g s ∗ Where ω is the angular velocity of the ring, and f (T) = ρ /ρ is the Cooper s ∗ pairs fraction, ρ being the Cooper pairs mass density and ρ the superconductor’s bulk density. 4 Assuming that a rotating supersolid He crystal also exhibits a gravitomagnetic London moment, B proportional to the supersolid fraction, its g angular momentum would be given by 1 L = I ω − B (3) classical g " 2 # Doing Equ.(2) into Equ.(3) we find back Equ.(1)! 4 Thereforewe conclude thattherotationofsupersolid He exhibits agrav- itomagnetic London moment similar to the one observed in rotating superconductive rings, which can account for the observed NCRI in this physical system. Kim and Chan’s experiment would tend to confirm the existence of the gravitomagnetic London moment in rotating quantum materials. 2 References [1] London, F., ”Superfluids”, wiley New York 1954, Vol II, P. 144 [2] Hess, G. B., Fairbank, W. M., Phys. Rev. Lett., 19 216 (1967) [3] Kim, E., Chan, W., Science, 305, 1941 (2004) [4] Tajmar, M., Plesescu, F., Marhold, K., de Matos, C.J., ”Exper- imental Detection of the Gravitomagentic London Moment”, 2006, gr-qc/0603033 [5] de Matos, C. J., ”Gravitoelectromagnetism and Dark Energy in Super- conductors”, to appear in Int. J. Mod. Phys. D, (2007). (also available gr-qc:/0607004) [6] Tajmar, M., Plesescu, F., Marhold, K. ”Measurement of Gravitoma- gentic and acceleration fields around a rotating superconductor”, 2006, gr-qc/0610015 3 This figure "Chan.JPG" is available in "JPG"(cid:10) format from: http://arXiv.org/ps/cond-mat/0701110v1