STATISTICAL THERMODYNAMICS OF SYNTHETIC SPIN-ORBITCOUPLED QUANTUM GASES

Abstract

Spin-orbit coupling (SOC) gives rise to a large number of interesting condensed mat- ter phenomena such as spin Hall effect, topological insulators, magnetoelectric ef- fects, along with many interesting phenomena in nuclear physics and atomic physics. Ultracold gases of neutral atoms provide an ideal platform to study various such phe- nomena because of their remarkably controllable environment that can be achieved using laser light. Although a gas of neutral atoms does not possess gauge coupling to the electromagnetic eld, there has been a number of theoretical proposals for pro- ducing synthetic magnetic eld and hence synthetic SOC in neutral atoms. Only one of these, the one-dimensional (1D) equal Rashba-Dresselhaus SOC, has been realized experimentally. In this thesis we present a detailed study of the various thermody- namic properties of synthetic spin-orbit coupled quantum gases. The main purpose of this thesis is to nd out how SOC modi es the many-body effects in both uniform as well as trapped gases. This thesis comprises of six chapters. Chapter 1 is an introductory chapter containing a discussion on the thermodynamics of uniform and trapped gases. We also discuss natural SOC in atoms and solids and show how synthetic SOC can be produced in a gas of neutral atoms using atom-laser interaction. In Chapter 2, we have made a thorough study of the Weyl-coupled three-dimensional (3D) gas of free bosons and fermions. It is found that the presence of coupling induces interaction which counters \effective" attraction (repulsion) of the exchange symmetry present in zero-coupling ideal Bose (Fermi) gas. This result is further corroborated by SOC i ii dependence of the isothermal compressibility. Incipient Bose-Einstein condensation (BEC) at very weak coupling has also been reported although the system does not really go in the Bose-condensed phase. Further, our studies show that there exists a dimensional crossover from three dimensions to one dimension at large coupling strength. Study of this Weyl-coupled system after addition of harmonic trapping comprises Chapter 3 of the thesis. We have shown that the phenomenon of BEC, destroyed by the SOC in 3D Bose gas (as discussed in Ch. 2), gets restored by trapping, even in the noninteracting case. Also, we have concluded that the increase in the coupling strength makes the statistical interaction weaker and weaker in trapped gases too and that now the system undergoes dimensional crossover from three to two dimensions. Chapter 4 focuses on the study of two-dimensional (2D) gas of Rashba- coupled free bosons under harmonic trapping. We have derived expressions for the various thermodynamic quantities using Kummer's function in conjunction with the polylogarithmic function. We nd in this system, dimensional reduction takes place from two dimensions to 1.5. Chapter 5 presents our study on d-dimensional spin- orbit coupled system under power-law trapping, where we have obtained expression for density of states (DOS) for both the isotropic and anisotropic couplings in uniform as well as trapped gases. The emergence of even-odd dimensional nonequivalence evinced by SOC induced energy segmentations in the DOS has been analyzed from the point of view of the rotational symmetry. The general conditions involving the dimensionality and the power-law exponent in such systems have then been obtained for the onset of BEC. The summary of our work along with the conclusions and future directions is presented in Chapter 6.