Dilute gas Bose-Einstein condensates (BECs) are an example of a superfluid, and exhibit many of the same phenomena as the strongly interacting superfluid helium. However, their isolation from the environment combined with their inhomogeneous density profiles make it difficult to observe some phenomena, such as the thermo-mechanical effect, in experiments. Here we perform dynamical simulations of a finite temperature Bose-Einstein condensate coupled to spatially separated heat and particle reservoirs to observe such non-equilibrium superfluid phenomena. We analyse the resulting steady-state non-equilibrium flows in the BEC, and consider the prospect of observing sustained superfluid turbulence.
Dilute gas Bose-Einstein condensates (BECs) are an example of a superfluid, and exhibit many of the same phenomena as the strongly interacting superfluid helium. However, their isolation from the environment combined with their inhomogeneous density profiles make it difficult to observe some phenomena, such as the thermo-mechanical effect, in experiments. Here we perform dynamical simulations of a finite temperature Bose-Einstein condensate coupled to spatially separated heat and particle reservoirs to observe such non-equilibrium superfluid phenomena. We analyse the resulting steady-state non-equilibrium flows in the BEC, and consider the prospect of observing sustained superfluid turbulence.
Dilute gas Bose-Einstein condensates (BECs) are an example of a superfluid, and exhibit many of the same phenomena as the strongly interacting superfluid helium. However, their isolation from the environment combined with their inhomogeneous density profiles make it difficult to observe some phenomena, such as the thermo-mechanical effect, in experiments. Here we perform dynamical simulations of a finite temperature Bose-Einstein condensate coupled to spatially separated heat and particle reservoirs to observe such non-equilibrium superfluid phenomena. We analyse the resulting steady-state non-equilibrium flows in the BEC, and consider the prospect of observing sustained superfluid turbulence.
Quantum systems consisting of many particles are both interesting from the physics and the mathematics perspective. One aspect that makes them fascinating from the physics point of view is that they can exhibit quantum effects on macroscopic scales such as Bose-Einstein condensation. This phenomenon, first predicted 100 years ago by Bose [19] and Einstein [44], occurs when a dilute gas of bosons is cooled down to very low temperatures. Below a certain critical temperature a condensate forms, meaning that a macroscopic fraction of the particles is in the same one-particle state, and thus, quantum phenomena become relevant on length scales much larger than the individual atom. The occurrence of Bose-Einstein condensation is also related to superfluidity as suggested in [88]. Bose-Einstein condensation has been achieved experimentally independently by the groups of Cornell and Wieman [3] and Ketterle [40] earning them a Nobel prize in 2001. While Bose and Einstein analyzed theoretically the non-interacting gas, an effective theory describing weakly interacting Bose gases was proposed by Bogoliubov in 1947 with the goal of explaining the occurrence of superfluidity in liquid helium [18]. Using assumptions such as that condensation indeed occurs, his theory yields predictions for the low-energy states of the system. Seen from the mathematics perspective, describing the Bose gas is an interesting challenge due to the strong correlations between particles introduced by the interaction making this case much harder to study than the non-interacting one. In particular, a proof that Bose-Einstein condensation occurs in the thermodynamic limit for continuous systems is still out of reach. However, there has been a lot of work regarding the rigorous analysis of bosonic systems in various relevant regimes. This thesis contains three new contributions establishing rigorous results on bosonic systems in different, physically relevant settings. It is based on the articles [37, 27, 31]. The first result concerns the time-evolution of initially trapped Bose gases in the ultra-dilute Gross-Pitaevskii regime. Under some assumptions on the initial data satisfied in particular by a class of states that are expected to approximate the ground state in a trap, we derive a quasi-free approximation that is close to the true solution in L2-norm. In particular, we show that this approximate wave function is described in terms of a Bose-Einstein condensate in a one-particle state following the time-dependent Gross-Pitaevskii equation together with pair excitations with respect to this condensate. As a corollary, we establish a central limit theorem for bounded one-particle observables. The second result is a simple proof of Bose-Einstein condensation for interacting, ultra-dilute gases. More specifically, we consider scalings interpolating between the Gross-Pitaevskii regime and the thermodynamic limit. While condensation had been shown to hold in these regimes before, the advantage of the method used here is its simplicity. Lastly, the third result establishes an upper bound on the ground state energy of a dilute Bose gas in the thermodynamic limit. It captures rigorously the third order correction to the energy per unit volume for sufficiently low densities as predicted in the physics literature first by Wu and subsequently others. Full-text embargoed until: 2026-01-01
In this thesis the non-equilibrium dynamics of ultracold quantum gases is studied numerically and analytically in one, two, and three spatial dimensions. We focus on the regime of large occupation numbers, where the system can be described by an ensemble of non-linear waves. A goal of this work is to investigate the existence of non-thermal fixed points in the dynamics of ultracold Bose gases. It is shown that a two- or three-dimensional Bose gas features a non-thermal fixed point which is characterised by a dilute random distribution of vortices or vortex lines. This state is accompanied by particle and energy fluxes and decays via the formation of vortex-antivortex correlations. By making use of superfluid turbulence methods, we give a detailed analysis of the underlying vortex dynamics. Furthermore, we focus on the relevance of the non-thermal fixed point for the dynamics of phase ordering kinetics and Bose-Einstein condensation. Then, we explore the possibility of a non-thermal fixed point in a one-dimensional ultracold Bose gas as well as a two-component Bose gas in two dimensions. Finally, we discuss the realisation of a non-thermal fixed point in a relativistic scalar field theory as well as for the case of a two-component Bose gas in two dimensions. After a brief discussion of experimental prospects, we summarise our results and close with an outlook.
Nonthermal fixed points of the dynamics of a dilute degenerate Bose gas far from thermal equilibrium are analyzed in two and three spatial dimensions. Universal power-law distributions, previously found within a nonperturbative quantum-field theoretical approach and recently shown to be related to vortical dynamics and superfluid turbulence [Phys. Rev. B 84, 020506(R) (2011)], are studied in detail. The results imply an interpretation of the scaling behavior in terms of independent vortex excitations of the superfluid and show that the statistics of topological excitations can be described in the framework of wave turbulence. The particular scaling exponents observed in the single-particle momentum distributions are found to be consistent with irreversibility as well as conservation laws obeyed by the wave interactions. Moreover, long-wavelength acoustic excitations of the vortex-bearing condensate, driven by vortex annihilations, are found to follow a nonthermal power law. Considering vortex correlations in a statistical model, the long-time departure from the nonthermal fixed point is related to vortex-antivortex pairing. The studied nonthermal fixed points are accessible in cold-gas experiments. The results shed light on fundamental aspects of superfluid turbulence and have strong potential implications for related phenomena, for example, in early universe inflation or quark-gluon plasma dynamics.
The field of Bose-Einstein condensation (BEC) in dilute atomic gases provides a fruitful playground to test well-developed theories of quantum fluids. Research using BECs can address open questions relating to the many-body aspects of two-component quantum liquids, namely the interaction between the hydrodynamic normal and the superfluid component at finite temperatures. After the first realization of BEC some pilot experiments have been carried out, but detailed experiments are missing. This has to be compared to the case of liquid helium II, where many experiments since the 1950s have added to our understanding of novel phenomena in quantum liquids, like collective excitations, first and second sound, and others. One of the drawbacks of liquid helium is that the interactions are so strong that a clear distinction between the two components is difficult and the interpretation of the phenomena remains ambiguous. Most experimental studies of dilute Bose-Einstein condensed gases use clouds, which are in the collisionless regime. The reason for the lack of detailed experiments in BECs to study quantum liquids and in particular the hydrodynamical aspects of it, is the limited number of atoms (typically 1--10 million) in the experiments leaving the thermal atoms virtually collisionless. Efforts to decrease the mean free path by increasing the confinement limits the lifetime of the sample, since the density is limited by three-body decay. Experiments on dilute clouds of cold atoms are generally conducted in highly asymmetric traps. In these elongated, cigar-shaped geometries the mean free path of the atoms can become much shorter than the size of the cloud in the long, axial direction, but at the same time exceeds the size in the other, radial directions. In this so-called hydrodynamic-collisionless regime the system can be considered radially collisionless and axially hydrodynamic. In our setup we have created BECs containing up to 300 million sodium atoms by evaporation of atoms in an axially strongly decompressed trap with an aspect ratio of 1:65. Hot atoms created in three-body collisions are able to leave the sample in this highly asymmetric trap, before they can heat other atoms in an avalanche. The sample is axially hydrodynamic, but due to the large aspect ratio collisionless in the radial direction. Such samples are ideal for the observation of the interaction between the superfluid and normal fluid component of the cloud. In this thesis we describe the setup which is used to reach the hydrodynamic regime and we describe a novel implementation of the well-known phase contrast imaging technique. Next, we study collective excitations in the crossover from the collisionless toward the hydrodynamic regime, we determine the heat conduction in a cold, hydrodynamic thermal cloud and observe the propagation of a thermal wave in the two-fluid regime. Furthermore, we study the friction between the superfluid and normal fluid component of the cloud. In the final chapters of this thesis we study the propagation of second sound, as well as the formation and propagation of shock waves.
This thesis describes a collection of experiments that explore interacting ultracold Bose gases, both in and out of equilibrium. Our experiments are performed using a gas of 39K or 87Rb confined in the uniform potential of an optical box trap, a novel testbed for quantum many-body phenomena. Our work focuses on weakly interacting non-equilibrium systems, moderately interacting systems that are still in equilibrium, and the unitary Bose gas which is both strongly interacting and eludes equilibrium. We begin with studies of weakly-interacting gases far from equilibrium, which feature ties to nonlinear wave phenomena. Highlights of our experiments include the direct measurement of turbulent-cascade fluxes, which (alongside realizing a tuneable dissipation scale) allow us to demonstrate the zeroth law of turbulence, and the first observation of weak collapse, a general type of nonlinear wave collapse predicted over 40 years ago. We then turn to moderately strong interactions, confronting existing theories of interacting quantum fluids. One of our most important results is the first quantitative measurement of the quantum depletion of a Bose–Einstein condensate, confirming a 70-year-old theory first developed to describe liquid helium. The culmination of our work explores the unitary Bose gas, where interparticle interactions are as strong as allowed by the laws of quantum mechanics. This strongly-correlated state promises tantalizing possibilities, including emergent universal behavior set solely by the gas density and novel forms of superfluidity. However, the strong interactions also lead to a complex interplay between coherent and dissipative dynamics. By disentangling these two processes, we have caught a glimpse of the promises that the unitary Bose gas holds. In particular, we observe the emergence of universal behavior, and find that the gas features a well defined quasi-equilibrium state, with a non-zero condensed fraction.