Hydrodynamics of gases in the classical domain are examined from the perspective that the gas has a well-defined wavefunction description at all times. Specifically, the internal energy and volume exclusion of decorrelated vortex structures are included so that quantum corrections and modifications to Navier-Stokes behavior can be derived. This leads to a small deviation in rigid body rotation for a cylindrically bound gas and the internal energy changes associated with vorticity give deviations in the Reynolds' transport theorem. Some macroscopic observable features arising from this include variations in the specific heat, an anisotropic correction to thermal conductivity and a variation in optical scattering as a function of the declination from the axis of local vorticity. The improvements in magneto-optical traps suggests some interesting experiments to be done in higher temperature regimes where they are not usually employed. It is argued that the finite lifetime of observed vortices in ultracold bosonic gases is only apparent and these volume excluding structures persist in generating angular momentum and pressure in the cloud in a non-imageable form.
Hydrodynamics of gases in the classical domain are examined from the perspective that the gas has a well-defined wavefunction description at all times. Specifically, the internal energy and volume exclusion of decorrelated vortex structures are included so that quantum corrections and modifications to Navier-Stokes behavior can be derived. This leads to a small deviation in rigid body rotation for a cylindrically bound gas and the internal energy changes associated with vorticity give deviations in the Reynolds' transport theorem. Some macroscopic observable features arising from this include variations in the specific heat, an anisotropic correction to thermal conductivity and a variation in optical scattering as a function of the declination from the axis of local vorticity. The improvements in magneto-optical traps suggests some interesting experiments to be done in higher temperature regimes where they are not usually employed. It is argued that the finite lifetime of observed vortices in ultracold bosonic gases is only apparent and these volume excluding structures persist in generating angular momentum and pressure in the cloud in a non-imageable form.
Previous approaches of emergent thermalization for condensed matter based on typical wavefunctions are extended to generate an intrinsically quantum theory of gases. Gases are fundamentally quantum objects at all temperatures, by virtue of rapid delocalization of their constituents. When there is a sufficiently broad spread in the energy of eigenstates, a well-defined temperature is shown to arise by photon production when the samples are optically thick. This produces a highly accurate approximation to the Planck distribution so that thermalization arises from the initial data as a consequence of purely quantum and unitary dynamics. These results are used as a foil for some common hydrodynamic theory of ultracold gases. It is suggested here that strong history dependence typically remains in these gases and so limits the validity of thermodynamics in their description. These problems are even more profound in the extension of hydrodynamics to such gases when they are optically thin, even when their internal energy is not low. We investigate rotation of elliptically trapped gases and consistency problems with deriving a local hydrodynamic approach. The presence of vorticity that is "hidden" from order parameter approaches is discussed along with some buoyancy intrinsically associated with vorticity that gives essential quantum corrections to gases in the regimes where standard perturbation approaches to the Boltzmann equations are known to fail to converge. These results suggest that studying of trapped gases in the far from ultracold regions may yield interesting results not described by classical hydrodynamics.
In the previous companion paper, we proposed a subclass of wavefunctions to describe macroscopic solids that resolved and extended the theory quantum measurement and gave a more specific treatment of quasiparticles. Here we extend these notions to thermalization of solids and gases and to gas state hydrodynamics. This gives a modification of the thermodynamic limit to justify the canonical averages for "typical wavefunctions" without the use of ensembles. The energetic cost of vorticity is contrasted in the classical and ultracold gas limits. From this perspective, we then examine the applicability of thermo and hydro to ultracold gases and compare with the implications of pure state evolution. We illustrate how the proposed quantum limits on viscosity could be reinterpreted in terms of Schrödinger induced evolution of the one-body density function but some history dependent measurable properties should still persist.
In this dissertation, we study rotational properties of ultracold bosonic quantum gases in two trapped configurations, a quasi-two-dimensional gas in a harmonic trap and a quasi-one-dimensional gas in a toroidal trap. First, we investigate the effects of correlations on the properties of the ground state of the rotating harmonically-trapped Bose gas by adding Bogoliubov fluctuations to the mean-field ground state of an N-particle single-vortex system. We demonstrate that the fluctuation-induced correlations lower the energy compared to that of the mean-field ground state, that the vortex core is pushed slightly away from the center of the trap, and that an unstable mode with negative energy (for rotations slower than a critical frequency) emerges in the energy spectrum, thus, pointing to a better state for slow rotation. We construct mean-field ground states of 0-, 1-, and 2-vortex states as a function of rotation rate and determine the critical frequencies for transitions between these states, as well as the critical frequency for appearance of a metastable state with an off-center vortex and its image vortex in the evanescent tail of the cloud. Then, we show how the configuration-space form of the above-mentioned Bogoliubov ground-state wave function of a bosonic condensate with a single vortex in a harmonic trap can be described in terms of bosonic Jastrow correlations. We then generalize this result to study the effects of such correlations on a mean-field vortex lattice state and show that the included correlations lower the energy below that of the mean-field state. Although the reduction is relatively small, it is a precursor of the more general expected effect of correlations in describing the melting of the vortex lattice at a high angular momentum per particle. Finally, we study the stability and dynamics of an ultracold bosonic gas trapped in a toroidal geometry and driven by rotation in the absence of dissipation. We first delineate, via the Bogoliubov mode expansion, the regions of stability and the nature of instabilities of the system for both repulsive and attractive interaction strengths. To study the response of the system to variations in the rotation rate, we introduce a “disorder” potential, breaking the rotational symmetry. We demonstrate the breakdown of adiabaticity as the rotation rate is slowly varied and find forced tunneling between the eigenstates of the system. The nonadiabaticity is signaled by the appearance of a swallow-tail loop in the lowest-energy level, a general sign of hysteresis. Then, we show that this system is in one-to-one correspondence with a trapped gas in a double-well potential and thus exhibits macroscopic quantum self-trapping. Finally, we show that self-trapping is a direct manifestation of the behavior of the lowest-energy level.
Quantum field theories with a complex action suffer from a sign problem in stochastic nonperturbative treatments, making many systems of great interest – such as polarized or mass-imbalanced fermions and QCD at finite baryon density – extremely challenging to treat numerically. Another such system is that of bosons at finite angular momentum; experimentalists have successfully achieved vortex formation in supercooled bosonic atoms, and have measured quantities of interest such as the moment of inertia. However, the rotation results in a complex action, making the usual numerical treatments of the theory unusable. This thesis treats systems of nonrelativistic bosons with finite angular momentum using two approaches. One approach is to determine the virial coefficients using a semi-classical lattice approximation (SCLA). Through this approach, we are able to compute the thermodynamic equation of state of the bosons for finite trapping frequency, rotation, and inter-particle interaction. The second approach uses the complex Langevin (CL) method – a method which employs an extension of the Langevin equation to complex space and circumvents the sign problem to compute the full quantum behavior of a low energy system of interacting, trapped, and rotating bosons. We examine the density and angular momentum of the system using all three methods, but the CL method in principal allows us to compute properties unique to rotating superfluids, in particular to show the formation of density singularities (so-called vortex lattices) and compute the circulation of the fluid around those vortices. This work advances our understanding of the quantum effects of rotation on ultracold bosonic gases in two different limits.
At temperatures near the absolut zero, a gas, here atomic sodium vapour, with high enough density cannot be described as tiny balls moving around as in classical physics. Since the temperature is low, the atoms are so slow that the matterwave of each atom starts to extend over the size of the atom and even over the interatomic distance. Therefore, they start to interfere like waves. Quantum mechanics start to dominate the physics in this regime. Further, depending on the sort of atoms (bosons or fermions) the atoms prefer to be in the same state or avoid to be in the same state. In the case of bosons as in the thesis, if the temperature is lowered to sub micro Kelvin temperature, a new state of matter appears after a phase transition - a macroscopic, standing wave, the Bose-Einstein condensate. This leads to a new phenomena: superfluidity - frictionless flow, second sound, vorticity and coherent scattering effects to name a few. The atoms are trapped in a elongated trap as in most of the experiments in ultra cold gasses. Usually experiments are done in a regime where the atoms seldomly collide with each other while travelling from one end to the other end of the cloud. In this experiment, however, the atoms collide many times with each other when they oscillate in the trap. This means that the cloud is hydrodynamic and leads to a very different behaviour. Two different sound waves (first and second sound), heat conduction, and collisional dominated transport can be observed in this case. The fact that the gas is weakly interacting allows comparison with current theory. At very low temperatures as in the experiments described in the thesis, the Bose character strongly alters the collisions of the atoms. The outcome of the collision does not only depend on the colliding atoms, but also on the atoms near by in phase space. The experiments outlined in this thesis cover some aspects of physics involved. Vortices have been created and observed in the Bose-Einstein condensate that rested in a weak trap. Both sound modes first and second sound have been observed with slight local heating. In the regime considered, first sound, that has not been observed in a dilute Bose-Einstein condensate before, is mainly a modulation in local temperature and not density. In another experiment a particular effect is observed when the cloud is only axially hydrodynamic. When the trap is suddenly axially relaxed, the cloud creats a strip pattern that is in the radial direction and moving outward. The analysis of this experiment suggests that this is only the case when the cloud is indeed only axially hydrodynamic. The last chapter describs a spin drag experiment. In this experiment two spin species of atoms are prepared and on one of them a force is applied. Through collisions, the other species is dragged along. This effect is Bose enhanced at temperatures approaching the transition temperature to a Bose-Einstein condensate which is observed and matches recent theory.
At low temperature Quantum Physics can manifest itself at the macroscopic scale in many spectacular ways. Some of its most remarkable features occur when a fluid is stirred. Indeed, as a consequence of the existence of a macroscopic wave-function describing the system, a quantum fluid cannot sustain rigid body rotation by contrast with a classical fluid. Rather, the stirring generates quantized vortices. The recent observation of novel quantum fluids formed by ultra-cold atomic gases allows us to revisit the properties of vortex systems, and to address pending questions of condensed matter physics.