We review recent theoretical work on various types of sound waves, which take place in different phases of the ultra-cold matter. These phases can be identified as the steady-state ultracold gas, the Bose Einstein condensates, and the ultra-cold Rydberg plasmas. Sound waves appear as similar but distinct manifestations of low frequency oscillations in the three phases: hybrid sound waves in the non-condensed ultra-cold gas, Bogoliubov oscillations in condensates, and ion acoustic waves in expanding ultra-cold plasmas, are successively described and compared.
We review recent theoretical work on various types of sound waves, which take place in different phases of the ultra-cold matter. These phases can be identified as the steady-state ultracold gas, the Bose Einstein condensates, and the ultra-cold Rydberg plasmas. Sound waves appear as similar but distinct manifestations of low frequency oscillations in the three phases: hybrid sound waves in the non-condensed ultra-cold gas, Bogoliubov oscillations in condensates, and ion acoustic waves in expanding ultra-cold plasmas, are successively described and compared.
Here we discuss collective processes and plasma effects that can be found in ultra‐cold matter. First, we consider the ultra‐cold atomic gas that can be produced in a magneto‐optical trap. Due to the existence of long‐range repulsive forces, new collective oscillation can take place, resembling sound waves but with a cut‐off frequency. We also examine new phenomena in Rydberg plasmas, resulting from laser ionization of the ultra‐cold gas. In these very low temperature plasmas a large amount of excited Rydberg states can exist, leading to a new dispersion relation for the electromagnetic waves. Enhanced magnetic field generation will also be considered. Finally, we discuss the collective properties of Bose Einstein condensates, showing a strong analogy with collective plasma processes. Two related examples are given as an illustration: Bogoliubov oscillations in the condensate, and two‐stream instabilities of counter‐streaming BECs.
The field of ultra-cold atomic physics allows probing of two-component quantum liquids with a hydrodynamic normal fluid accompanied by superfluid Bose-Einstein condensates (BEC’s), where the experimental results can be compared to theoretical predictions of the behavior of a weakly interacting two fluid system. Hydrodynamicity in quantum systems like BEC's can have influence on multiple aspects of the collective behavior of the system, such as on the oscillation frequency of quadrupole modes, multiple sound modes in the condensate, but also on high-order excitations which resemble standing sound waves. The hydrodynamicity and excitations of the ultra-cold atomic cloud are the main motivation for the experiments presented in this thesis. In the Utrecht experiment large BEC's up to a few hundred million atoms are produced, which are deeply in the hydrodynamic collisional regime. The macroscopic behavior of the cloud of atoms is dominated by inter-atomic collisions since the mean free path of the individual particles is much smaller than the size of the atomic sample and local equilibrium is established. The influence of the hydrodynamicity on the collective excitations can be investigated by measuring the quadrupole frequency of ultra-cold atomic clouds above the transition temperature Tc, where Bose-Einstein condensation occurs. This quadrupole frequency is determined by measuring the collective shape oscillations of the atomic cloud, where the oscillation frequency is influenced by inter-atomic collisions during the shape oscillations due to the hydrodynamicity of the atomic cloud. The hydrodynamic equations predict the existence of two sound modes in ultra-cold atomic gases below Tc. The speeds of sound are dependent on both the temperature and the chemical potential of the atomic cloud. For low enough temperatures or large enough chemical potential these two speeds of sound become comparable and reaching this regime experimentally allows measuring the speed of sound beyond this avoided crossing. An alternate method of measuring the speed of sound of ultra-cold atomic clouds is exploiting the analogy between a standing sound wave-pattern and high order excitations in BEC's, also referred to as Faraday waves. By exciting the wave-pattern with a frequency and measuring the wavenumber k of the wave-pattern, the speed of sound c can be extracted from the linear dispersion relation. In the process of exciting the standing wave-pattern, remarkable dynamics is discovered in the BECs. As a result of the excitation a large array of other modes are excited next to the wave-pattern. These modes are for example the dipole mode, the axial and radial quadrupole modes, and the scissor mode. This gives rise to complex dynamics in this hydrodynamic quantum mechanical system and although the ultra-cold sample is only excited with a very short pulsed excitation, these modes and the wave-pattern show a large degree of reproducibility during several seconds of time evolution.
We study two different subjects related to ultra-cold Bose gases. First we study the influence of the trap and the background pressure on particle loss and temperature change for trapped atom clouds. We find the number of particles to exponentially decrease over time due to the imperfect vacuum, while the rate of temperature change differs between a magnetic trap and a far off resonance optical trap. Secondly, we study the properties of a standing sound wave induced in a Bose-Einstein condensate. Phase contrast imaging is used to image the condensate in order to observe the density profile as a function of time. We find that there is coupling between the standing wave and other collective modes. There is a clear relation between the frequencies of these collective modes, and also between the frequencies of these modes and the frequency used to induce the modes. We also find that the amplitude of the standing wave decays over time.
The details of recent calculations of the expansion of ultra-cold, neutral plasmas are given. The calculations are performed at several levels. The simplest level assumes an ansatz for the form of the electron and ion density; the result is a simple, ordinary differential equation which can be easily solved. The medium level of sophistication assumes the electrons are in thermal equilibrium but does not assume a particular form for the ion density; the result is a partial differential equation which is solved numerically. For the highest level of sophistication, a Monte Carlo technique is used to solve for the electron phase space distribution and solve for the ion motion in the resulting mean field. All levels of simulation include three body recombination and electron-Rydberg scattering. This paper contains the results of our simulations and compares them to measurements made on ultra-cold plasmas. Three body recombination is found to be important at very low temperatures since it is a heating mechanism for the electron gas. The collisions between cold electrons and Rydberg atoms are another important source of electron heating and de-excitation of atoms formed in the plasma. The evolution of the distribution of atoms in the plasma is simulated and several counter-intuitive effects that have been observed can be explained. Our simulations show that the plasma coupling constant does not become larger than ∼1/5 for the reported experiments. The behavior of plasma processes are investigated, e.g., ion acoustic waves, spike formation, and electron evaporation. The evolution of a cold Rydberg gas into a plasma is also simulated but certain properties of our simulation do not agree with measurements.
We briefly review the theory of Bose-Einstein condensation in the two-dimensional trapped Bose gas and, in particular the relationship to the theory of the homogeneous two-dimensional gas and the Berezinskii-Kosterlitz-Thouless phase. We obtain a phase diagram for the trapped two-dimensional gas, finding a critical temperature above which the free energy of a state with a pair of vortices of opposite circulation is lower than that for a vortex-free Bose-Einstein condensed ground state. We identify three distinct phases which are, in order of increasing temperature, a phase coherent Bose-Einstein condensate, a vortex pair plasma with fluctuating condensate phase and a thermal Bose gas. The thermal activation of vortex-antivortex pair formation is confirmed using finite-temperature classical field simulations.
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.