Session B2: Solid Helium

Observation of superfluidity in solid helium and solid hydrogen

A torsional oscillator technique is used to search for non-classical rotational inertia of solid helium$^{1}$ and solid hydrogen. Several important experimental details already observed will be reviewed for both systems. Some of these include the transition temperature, supersolid fraction, and dependencies on oscillation speed and impurities. Comparisons will be made in order to demonstrate the similarities and/or differences between helium and hydrogen. With further work currently underway, we will also report on recent experimental progress. This work is done in collaboration with Eunseong Kim, Xi Lin and Moses Chan and is supported by the NSF under grant 0207071. [1] E. Kim and M. H. W. Chan, \textit{Nature} \textbf{427}, 225 (2004); \textit{Science} \textbf{305}, 1941(2004); \textit{J. Low Temp. Phys}. \textbf{138}, 859 (2005).   

Pressure-driven Flow of Solid Helium

Recent torsional oscillator measurements by Moses Chan's Penn State group showed evidence of ``non-classical rotational inertia'' for solid helium at temperatures below 200 mK. This discovery followed decades of theoretical speculation and experimental searches for ``supersolidity'' in helium. The experiments generated a great deal of interest but the origin and properties of such a state are still unclear. It would be very interesting to know whether supersolids share any of the other unusual properties of superfluids: persistent currents, second sound and quantized vortices. We have studied the response of solid helium to pressure changes in order to look for unusual flow properties that might be associated with supersolidity. The measurements involved both helium confined in the nanometer pores of Vycor glass and bulk solid helium, at temperatures as low as 30 mK. Pressure changes were generated with piezoelectrically driven diaphragm and flow was monitored with sensitive capacitive techniques. Near melting, solid helium flows very easily but we did not see any evidence of superflow at low temperatures. If helium does become a supersolid at low temperatures then its response to pressure gradients must be very different from that of liquid helium.   

Theory for supersolid 4He: Vacancy condensation facilitated by a low-energy bound state

Although both vacancies and interstitials have relatively high activation energies in the normal solid, we propose that a lower energy bound state of a vacancy and an interstitial may facilitate vacancy condensation to give supersolidity in 4He. We use a phenomenological two-band boson lattice model to demonstrate this new mechanism and discuss the possible relevance to the recently observed superfluidlike, nonclassical rotational inertial experiments of Kim and Chan in solid 4He. Some of our results may also be applicable to trapped bosons in optical lattices.   

Off diagonal long range order in solid 4He

The presence both of long range order (LRO) and of off diagonal long range order (ODLRO) in solid 4He is discussed on the basis of an accurate variational theory (shadow wave function, SWF) and of an exact projection method (shadow path integral ground state, SPIGS). If the solid is incommensurate (e.g. solid with a vacancy: number of atoms different from number of equilibrium sites) both SWF and SPIGS give ODLRO and close to melting density there is a BEC of about 0.3 He atoms per vacancy. For a commensurate solid (number of atoms equal to number of sites) SWF gives ODLRO with a condensate of about one part per thousand. Preliminary evidence indicates that also SPIGS gives a finite BEC. The key process is the spontaneous formation of unbound vacancy-interstitial pairs. These results support the presence of supersolidity in bulk solid 4He. As a final point we address the question if the exact ground state of bulk solid 4He is commensurate or incommensurate and conclude that there is not yet a definite answer to this question from microscopic theory.   

Path Integral Simulations of Solid $^4$He

Kim and Chan have found indications that solid $^4$He is a supersolid by measuring the period of a torsional oscillator. To understand the state of solid $^4$He at low temperature, we [1] have calculated tunnelling frequencies for ring exchanges in bulk solid helium with Path Integral Monte Carlo by finding the free energy of a path that begins with the atoms in one configuration and ends with a permutation of those positions. The exchange frequencies are found to be described by a lattice model which does not show superfluid behavior. However, simulations [2] of $^4$He absorbed in Vycor find that $^4$He forms a layered structure with the first layer solid-like and highly localized, the second layer disordered with some atoms delocalized and possibly superfluid. This persistent liquid layer mechanism can only be relevant for bulk $^4$He in a very disordered crystal. New calculations [3] of the single particle density matrix, (the fourier transform of the momentum distribution) to measure ODLRA will also be discussed. \newline \newline [1] D. M. Ceperley and B. Bernu, Phys. Rev. Letts. 93, 155303(2004).\newline [2] S. A. Khairallah and D. M. Ceperley, Phys. Rev. Letts. 95, 185301 (2005). \newline [3] B. Clark and D. M. Ceperley, unpublished.