Exotic superfluid states of ultra-cold Fermi gases

This is a study of ultra-cold Fermi gases in different systems. This thesis is focused on exotic superfluid states, for an example on the three component Fermi gas and the FFLO phase in optical lattices. In the two-components case, superfluidity is studied mainly in the case of the spin population imbalanced Fermi gases and the phase diagrams are calculated from the mean-field theory. Different methods to detect different phases in optical lattices are suggested. In the three-component case, we studied also the uniform gas and harmonically trapped system. In this case, the BCS theory is generalized to three-component gases. It is also discussed how to achieve the conditions to get an SU(3)-symmetric Hamiltonian in optical lattices. The thesis is divided in chapters as follows: Chapter 1 is an introduction to the field of cold quantum gases. In chapter 2 optical lattices and their experimental characteristics are discussed. Chapter 3 deals with two-components Fermi gases in optical lattices and the paired states in lattices. In chapter 4 three-component Fermi gases with and without a harmonic trap are explored, and the pairing mechanisms are studied. In this chapter, we also discuss three-component Fermi gases in optical lattices. Chapter 5 devoted to the higher order correlations, and what they can tell about the paired states. Chapter 6 concludes the thesis.

Dependence of the large-scale vortex instability on latitude, stratification and domain size

In an earlier study, we reported on the excitation of large-scale vortices in Cartesian hydrodynamical convection models subject to rapid enough rotation. In that study, the conditions for the onset of the instability were investigated in terms of the Reynolds (Re) and Coriolis (Co) numbers in models located at the stellar North pole. In this study, we extend our investigation to varying domain sizes, increasing stratification, and place the box at different latitudes. The effect of the increasing box size is to increase the sizes of the generated structures, so that the principal vortex always fills roughly half of the computational domain. The instability becomes stronger in the sense that the temperature anomaly and change in the radial velocity are observed to be enhanced. The model with the smallest box size is found to be stable against the instability, suggesting that a sufficient scale separation between the convective eddies and the scale of the domain is required for the instability to work. The instability can be seen upto the colatitude of 30 degrees, above which value the flow becomes dominated by other types of mean flows. The instability can also be seen in a model with larger stratification. Unlike the weakly stratified cases, the temperature anomaly caused by the vortex structures is seen to depend on depth.

Ionosphere-atmosphere interaction during solar proton events

Among the most striking natural phenomena affecting ozone are solar proton events (SPE), during which high-energy protons precipitate into the middle atmosphere in the polar regions. Ionisation caused by the protons results in changes in the lower ionosphere, and in production of neutral odd nitrogen and odd hydrogen species which then destroy ozone in well-known catalytic chemical reaction chains. Large SPEs are able to decrease the ozone concentration of upper stratosphere and mesosphere, but are not expected to significantly affect the ozone layer at 15--30~km altitude. In this work we have used the Sodankylä Ion and Neutral Chemistry Model (SIC) in studies of the short-term effects caused by SPEs. The model results were found to be in a good agreement with ionospheric observations from incoherent scatter radars, riometers, and VLF radio receivers as well as with measurements from the GOMOS/Envisat satellite instrument. For the first time, GOMOS was able to observe the SPE effects on odd nitrogen and ozone in the winter polar region. Ozone observations from GOMOS were validated against those from MIPAS/Envisat instrument, and a good agreement was found throughout the middle atmosphere. For the case of the SPE of October/November 2003, long-term ozone depletion was observed in the upper stratosphere. The depletion was further enhanced by the descent of odd nitrogen from the mesosphere inside the polar vortex, until the recovery occurred in late December. During the event, substantial diurnal variation of ozone depletion was seen in the mesosphere, caused mainly by the the strong diurnal cycle of the odd hydrogen species. In the lower ionosphere, SPEs increase the electron density which is very low in normal conditions. Therefore, SPEs make radar observations easier. In the case of the SPE of October, 1989, we studied the sunset transition of negative charge from electrons to ions, a long-standing problem. The observed phenomenon, which is controlled by the amount of solar radiation, was successfully explained by considering twilight changes in both the rate of photodetachment of negative ions and concentrations of minor neutral species. Changes in the magnetic field of the Earth control the extent of SPE-affected area. For the SPE of November 2001, the results indicated that for low and middle levels of geomagnetic disturbance the estimated cosmic radio noise absorption levels based on a magnetic field model are in a good agreement with ionospheric observations. For high levels of disturbance, the model overestimates the stretching of the geomagnetic field and the geographical extent of SPE-affected area. This work shows the importance of ionosphere-atmosphere interaction for SPE studies. By using both ionospheric and atmospheric observations, we have been able to cover for the most part the whole chain of SPE-triggered processes, from proton-induced ionisation to depletion of ozone.

Dynamical processes in the stratosphere and upper troposphere and their influence on the distribution of trace gases in the polar atmosphere

Transport plays an important role in the distribution of long-lived gases such as ozone and water vapour in the atmosphere. Understanding of observed variability in these gases as well as prediction of the future changes depends therefore on our knowledge of the relevant atmospheric dynamics. This dissertation studies certain dynamical processes in the stratosphere and upper troposphere which influence the distribution of ozone and water vapour in the atmosphere. The planetary waves that originate in the troposphere drive the stratospheric circulation. They influence both the meridional transport of substances as well as parameters of the polar vortices. In turn, temperatures inside the polar vortices influence abundance of the Polar Stratospheric Clouds (PSC) and therefore the chemical ozone destruction. Wave forcing of the stratospheric circulation is not uniform during winter. The November-December averaged stratospheric eddy heat flux shows a significant anticorrelation with the January-February averaged eddy heat flux in the midlatitude stratosphere and troposphere. These intraseasonal variations are attributable to the internal stratospheric vacillations. In the period 1979-2002, the wave forcing exhibited a negative trend which was confined to the second half of winter only. In the period 1958-2002, area, strength and longevity of the Arctic polar vortices do not exhibit significant long-term changes while the area with temperatures lower than the threshold temperature for PSC formation shows statistically significant increase. However, the Arctic vortex parameters show significant decadal changes which are mirrored in the ozone variability. Monthly ozone tendencies in the Northern Hemisphere show significant correlations (|r|=0.7) with proxies of the stratospheric circulation. In the Antarctic, the springtime vortex in the lower stratosphere shows statistically significant trends in temperature, longevity and strength (but not in area) in the period 1979-2001. Analysis of the ozone and water vapour vertical distributions in the Arctic UTLS shows that layering below and above the tropopause is often associated with poleward Rossby wave-breaking. These observations together with calculations of cross-tropopause fluxes emphasize the importance of poleward Rossby wave breaking for the stratosphere-troposphere exchange in the Arctic.

Dark solitons in holographic superfluids

We construct dark soliton solutions in a holographic model of a relativistic superfluid. We study the length scales associated with the condensate and the charge density depletion, and find that the two scales differ by a non-trivial function of the chemical potential. By adjusting the chemical potential, we study the variation of the depletion of charge density at the interface.

Inhomogeneous Structures in Holographic Superfluids I

We begin an investigation of inhomogeneous structures in holographic superfluids. As a first example, we study domain wall like defects in the 3+1 dimensional Einstein-Maxwell-Higgs theory, which was developed as a dual model for a holographic superconductor. In [1], we reported on such "dark solitons" in holographic superfluids. In this work, we present an extensive numerical study of their properties, working in the probe limit. We construct dark solitons for two possible condensing operators, and find that both of them share common features with their standard superfluid counterparts. However, both are characterized by two distinct coherence length scales (one for order parameter, one for charge condensate). We study the relative charge depletion factor and find that solitons in the two different condensates have very distinct depletion characteristics. We also study quasiparticle excitations above the holographic superfluid, and find that the scale of the excitations is comparable to the soliton coherence length scales.

Holographic Superfluids and Solitons

Superfluidity is perhaps one of the most remarkable observed macroscopic quantum effect. Superfluidity appears when a macroscopic number of particles occupies a single quantum state. Using modern experimental techniques one dark solitons) and vortices. There is a large literature on theoretical work studying the properties of such solitons using semiclassical methods. This thesis describes an alternative method for the study of superfluid solitons. The method used here is a holographic duality between a class of quantum field theories and gravitational theories. The classical limit of the gravitational system maps into a strong coupling limit of the quantum field theory. We use a holographic model of superfluidity to study solitons in these systems. One particularly appealing feature of this technique is that it allows us to take into account finite temperature effects in a large range of temperatures.