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Dynamical Theory of Superfluidity in One Dimension

Oshikawa Group

Superfluidity is one of the most intriguing concepts in quantum physics, with a wide range of implications. On the other hand, importance of dimensionality has been recognized in many-body physics. While the physical space we live in is of three dimensions, construction of artificial structures with reduced dimensionality has made the effect of dimensionality relevant also in experimental studies. A fundamental question, which occurs naturally then, is the effect of dimensionality on superfluidity.

Fig. 1. (From Ref. [2]) Superfluid response for different probe frequencies, which ranges from 0.01ω0 (dark) to 100ω0 (bright), where ω0 = 2kHz [1] and parameters are chosen to match the experiment. The inset shows the dissipation (lower part), and the frequency dependence of the peak temperature of the dissipation on a log-log scale (upper part). The frequency dependence shows the essentially dynamical nature of the superfluidity in one dimension.

Superfluidity is often related to long-range ordering of quantum phase. The absence of the latter in two or lower dimensions at nonzero temperatures, which was proved mathematically, apparently implies there is no superfluidity in those dimensions. The experimental observation of superfluidity in two-dimensional 4He film contradicts this argument. In fact, the superfluidity is more directly associated to non-vanishing helicity modulus, that is rigidity against phase twist. The helicity modulus does not vanish at sufficiently low temperatures even in two dimensions, despite the lack of the long-range order. This understanding of superfluidity in two dimensions was established in 1970s.

What about one dimension? In one dimension, the helicity modulus is known to vanish in the thermodynamic limit at any nonzero temperatures. This seems to imply the absence of superfluidity. Nevertheless, a recent torsional oscillator experiment [1] on 4He confined in narrow one-dimensional channels revealed a superfluid response, calling for a new theoretical understanding.

We identify the superfluidity in one dimension as an essentially dynamical phenomenon, which is absent in strictly zero frequency limit. Peculiar nature of dynamics in one dimension however leads to an abnormally slow decay of current, which may be observed as superfluidity even at a very low frequency of torsional oscillators. Our theory reproduces main qualitative features of the experimental results, and predicts the frequency dependence of the “superfluid density” [2].


References
  • [1] J. Taniguchi, Y. Aoki, and M. Suzuki, Phys. Rev. B 82, 104509 (2010); J. Taniguchi, R. Fujii, and M. Suzuki, Phys. Rev. B 84, 134511 (2011).
  • [2] T. Eggel, M. A. Cazalilla, and M. Oshikawa, Phys. Rev. Lett. 107, 275302 (2011).
Authors
  • T. Eggel, M. A. Cazalillaa, and M. Oshikawa
  • aSpanish National Research Council and the University of the Basque Country