View the related article [J. Phys.Soc. Jpn. 77 (2008) 013601]

Localized Bose-Einstein Condensation near Quantum Phase Transition [January 16, 2008]
Osamu Ishikawa
(Graduate School of Science, Osaka City University)

   Phase transitions are a very common phenomenon in condensed matter physics; these include the magnetic phase transitions in ferromagnetic and anti-magnetic materials, liquid-solid and liquid-vapor transitions, superfluid-(normal)fluid transitions, superconductor-metal transition, etc. Usually, phase transitions are observed at a finite temperature and are considered to be classical even if the system is described by quantum mechanics, as in the case of superfluid helium and superconductors. Near the critical point, a classical thermal fluctuation is important at the longer length scale. The long-scale fluctuation governs the critical behavior at the finite temperature [1]. At zero temperature, classical thermal fluctuations are frozen out, while quantum fluctuations can induce macroscopic phase transitions called quantum phase transitions (QPTs).

Fig. 1. The P-T phase diagram of 4HE in the 2.5-nm nanoporous glass.(Figure is taken from [5])

  QPTs occur by changing some parameter in the Hamiltonian, where the quantum ground state changes. Such QPTs have been carefully studied in several situations: doping in a high-Tc superconductor destroys the anti-ferromagnetic order, disorder in a metal controls the metal-insulator transition, and the periodic potential in ultracold atoms controls the Bose-Einstein condensate (BEC)-Mott insulator transition [2]. In disordered Bose systems such as 4He in a random potential, the long-range order correlation can compete with the random potential. Both the BEC and superfluidity are suppressed and may disappear. The theoretical study shows three phases, namely, the superfluid phase, Mott insulating phase, and Bose glass phase in disordered Bose systems, accompanying the presence of QPTs between them [3].

  K. Yamamoto et al. observed the superfluid transition of 4HE confined in a nanoporous Gelsil glass with a pore diameter of 2.5 nm using a torsional oscillator (TO) [4]. Such a nanoporous medium acts as a random potential and the density of 4HE is a parameter for the phase transitions. The TO is a good experimental device for detecting a very small change in the moment of inertia. When a porous medium is filled with normal liquid 4HE, the liquid oscillates with the TO due to its viscosity. A superfluid has a component with no viscosity and the oscillating period changes with the onset of superfluidity. Recently, by the precise measurement of pressure P(T) with warming and cooling under constant volumes, K. Yamamoto et al. determined the phase boundary between the solid and liquid states of 4HE confined in the same nanoporous Gelsil glass and obtained the total phase diagram, as shown in Fig.1 [5]. Increasing the pressure reduces the superfluid transition temperature and above the critical pressure of 3.4 MPa, the superfluidity disappears. The finding of a liquid state between the superfluid state and the solid phase is a significant feature of their results. This nonsuperfluid state (NSF) exists at zero temperature and at finite temperatures. Applying the Clapeyron-Clausius relation to the phase boundary between the NSF state and the solid phase, the entropy of the NSF state is found to be as small as that of the solid. The fact that the solid entropy is very small near the zero temperature suggests that the NSF may be a new ordered state. It should be noted that the pore size of their Gelsil glass is very suitable for observing the NSF state because the solidification of 4HE must occur in a pore-like bulk liquid and no liquid state is observed near the zero temperature if the pore size is larger than that of this Gelsil glass.

  K. Yamamoto et al. proposed that the low entropy NSF state is the localized BEC state (LBEC). In the LBEC state, the condensate is not completely destroyed by the random potential. However, it is localized to some regions in the nanopores and does not contribute to the superfluidity on account of the combination of the random potential and the interaction. The BEC state has a global coherence over the sample but the LBEC has no global coherence. A recent theoretical study on a strongly correlated Bose fluid in a confined potential showed that the superfluidity disappeared above a pressure of 4.2 MPa, which supports the LBEC in Fig.1 [6].

  This QPT between the superfluid phase and the LBEC is similar to that of the BEC-Mott insulator in ultracold atoms and of the superconductor-insulator in Josephson-junction arrays. Further studies using different pore sizes or disorder potentials will help us to understand the general QPT phenomena for many other materials.

References
[1] S. L. Sondhi et al.: Rev. Mod. Phys. 69 (1997) 315.
[2] M. Greiner et al.: Nature 415 (2002) 39.
[3] M. P. A. Fisher et al.: Phys. Rev. B 40 (1989) 546.
[4] K. Yamamoto et al.: Phys. Rev. Lett. 93 (2004) 075302.
[5] K. Yamamoto et al.: J. Phys. Soc. Jpn. 77 (2008) 013601.
[6] M. Kobayashi and M. Tsubota: cond-mat/0510335

The above article should be referred as “O. Ishikawa: JPSJ Online-News and Comments [Jan 16, 2008]” when citing.

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