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International Journal of Modern Physics B

EFFECTIVE THEORY OF BOSONIC SUPERFLUIDS

Adriaan M. J. Schakel

Published Jul 10, 1994• 16 citations
Publisher

Abstract

We discuss the effective theory of a bosonic superfluid whose microscopic behavior is described by a nonrelativistic, weak-coupling Φ4 theory in the phase with broken particle number symmetry, both at zero temperature and in the vicinity of the phase transition. In the zero-temperature regime, the theory is governed by the gapless Goldstone mode resulting from the broken .symmetry. Although this mode is gapless, the effective theory turns out to be Gallilei invariant. The regime just below the critical temperature is approached in a high-temperature expansion which is shown to be consistent with the weak-coupling assumption of the theory. We calculate the critical temperature, the co-efficients of the Landau theory, and the finite-temperature sound velocity. A comparison with BCS theory is given.

DOI
10.1142/s021797929400083x

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We discuss the effective theory of a bosonic superfluid whose microscopic behavior is described by a nonrelativistic, weak-coupling Φ4 theory in the phase with broken particle number symmetry, both at zero temperature and in the vicinity of the phase transition. In the zero-temperature regime, the theory is governed by the gapless Goldstone mode resulting from the broken .symmetry. Although this mode is gapless, the effective theory turns out to be Gallilei invariant. The regime just below the critical temperature is approached in a high-temperature expansion which is shown to be consistent with the weak-coupling assumption of the theory. We calculate the critical temperature, the co-efficients of the Landau theory, and the finite-temperature sound velocity. A comparison with BCS theory is given.
We extend to finite temperature the time-dependent effective theory for the Goldstone field (the phase of the pair field) $\ensuremath{\theta}$ which is appropriate for a superfluid containing one species of fermions with s-wave interactions, described by the BCS Lagrangian. We show that, when Landau damping is neglected, the effective theory can be written as a local time-dependent nonlinear Schr\"odinger Lagrangian which preserves the Galilean invariance of the zero-temperature effective theory and is identified with the superfluid component. We then calculate the relevant Landau terms that are nonlocal and that destroy the Galilean invariance. We show that the retarded $\ensuremath{\theta}$ propagator (in momentum space) can be well represented by two poles in the lower-half frequency plane, describing damping with a predicted temperature, frequency, and momentum dependence. It is argued that the real parts of the Landau terms can be approximately interpreted as contributing to the normal fluid component.
Motivated by the recent experiment on ppp-orbital-band bosons in optical lattices, we study theoretically the quantum phases of Mott insulator and superfluidity in two dimensions. The system features a superfluid phase with transversely staggered orbital current at weak interaction and a Mott insulator phase with antiferro-orbital order at strong coupling and commensurate filling. We go beyond mean-field theory and derive from a microscopic model an effective action that is capable of describing both the ppp-band Mott insulating and superfluid phases in strong coupling. We further calculate the excitation spectra near the quantum critical point and find two gapless modes away from the tip of the Mott lobe but four gapless modes at the tip. Our effective theory reveals how the phase coherence peak builds up in the Mott regime when approaching the critical point. We also discuss the finite-temperature phase transition of ppp-band superfluidity.
The BCS-BEC crossover is studied in a systematic way in the broken-symmetry phase between zero temperature and the critical temperature. This study bridges two regimes where quantum and thermal fluctuations are, respectively, important. The theory is implemented on physical grounds, by adopting a fermionic self-energy in the broken-symmetry phase that represents fermions coupled to superconducting fluctuations in weak coupling and to bosons described by the Bogoliubov theory in strong coupling. This extension of the theory beyond mean field proves important at finite temperature, to connect with the results in the normal phase. The order parameter, the chemical potential, and the single-particle spectral function are calculated numerically for a wide range of coupling and temperature. This enables us to assess the quantitative importance of superconducting fluctuations in the broken-symmetry phase over the whole BCS-BEC crossover. Our results are relevant to the possible realizations of this crossover with high-temperature cuprate superconductors and with ultracold fermionic atoms in a trap.
The superfluidity of low-temperature bosons is well established in the collisional regime. In the collisionless regime, however, the presence of superfluidity is not yet fully clarified, in particular in lower spatial dimensions. Here, we compare the Vlasov-Landau equation, which does not take into account the superfluid nature of the bosonic system, with the Andreev-Khalatnikov equations, which instead explicitly contain a superfluid velocity. We show that recent experimental data of the sound mode in a two-dimensional collisionless Bose gas of 87Rb^{87}\mathrm{Rb}87Rb atoms are in good agreement with both theories, but the sound damping is better reproduced by the Andreev-Khalatnikov equations below the Berezinskii-Kosterlitz-Thouless critical temperature Tc{T}_{c}Tc​, while above Tc{T}_{c}Tc​ the Vlasov-Landau results are closer to the experimental ones. For one-dimensional bosonic fluids, where experimental data are not yet available, we find larger differences between the sound velocities predicted by the two transport theories and, also in this case, the existence of a superfluid velocity reduces the sound damping.