Hydrodynamical properties of nonlinear gauge-coupled quantum fluids
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In this thesis, we investigate certain hydrodynamical properties of quantum fluids subject to a density-dependent gauge potential. Such potentials have been shown to emerge, for instance, in a weakly interacting Bose cloud of optically addressed two-level atoms. By constructing a hydrodynamic canonical formalism for the matter-field, we show that an arbitrary effective density-dependent gauge potential invariably leads to nonlinear flow terms in the wave equation for the phase. In turn, the implications for the mechanical momentum transport equation of the fluid, are two-fold, where a body-force of dilation emerges and a flow-dependent pressure term features in the stress tensor of the fluid. In order to restore the immediate lack of Galilean invariance, we derive covariant transformation laws for the nonlinear potentials, which leave the canonical field equations form invariant. We also show how density-dependent gauge potentials are physical vector potentials which may not be “gauged-away”. In a one-dimensional system, we find that attempting to do so generates the flow-dependent pressure in the Hamiltonian density of the field, which in turn leads to an additional flow term in the wave equation for the phase. Further, we study elementary excitations and derive a generalised expression relating the velocity of sound to the fluid pressure. We find that the velocity of sound is anisotropic, where the nonlinear gauge potential acts as a moving medium for sound propagation. Sound is not merely carried along with the ground state flow imparted by the gauge potential, but with an increased flow due the flow-dependent fluid pressure. To consolidate these results, we simulate the dynamics of a gauge-coupled superfluid and evaluate the velocity of sound numerically. Finally, we study the interaction of a gauge-coupled superfluid with a foreign impurity. We learn that the ground state of an inhomogenous superfluid adopts a non-trivial local phase profile due to spatial density variations. For an immobile Gaussian impurity, this leads to the formation of a canonical flow (or phase flow) dipole about the object and an asymmetrical pressure field which compresses the object along the direction of the gauge potential. Further, we drag the impurity through the superfluid and examine the mechanical flow and phase winding fields during vortex formation. By studying the phase-slip accumulation in the superfluid, we evaluate the critical velocity for vortex formation, which decreases as the orientation of the flow imparted by the gauge potential increasingly opposes the impurity. We also derive an expression for the drag force acting on the impurity and evaluate the force numerically. We find that the instantaneous drag force decays to a positive value when the impurity velocity exceeds the flow of the medium carrying sound along the direction of motion of the impurity. This latter velocity is distinct from the critical velocity for vortex formation. As such, in the case of a nonlinear gauge potential, the drag force is not a suitable quantity for estimating the critical velocity.