Quantum properties of Bose-Einstein condensates coupled to semiconductor heterojunctions

Abstract

In this thesis, we present a theoretical study of the effects that a current-carrying Two-Dimensional Electron Gas (2DEG) produce on a neighbouring magnetically trapped Bose-Einstein Condensate of alkali atoms (BEC). We suggest that technology used for magnetic micro-controlling of cold gases could be improved by replacing or combining the metallic wires used in such structures with 2DEG-based conductors or quantum electronic devices. All calculations presented in this thesis consider parameters attainable with present technology, suggesting that experimental realization of the scenarios proposed here is already feasible. In Chapter one we present the general context in which this thesis is developed. It includes a definition of the Bose-Einstein condensate state, a description of the principles of magnetic trapping and a brief review of the developments in the area of micromanipulation of atomic BECs. Chapter two is devoted to describe the characteristics of the heterojunction considered in the thesis, and a simple model used to evaluate the electron flow in the 2DEG it contains. Chapter three shows in detail the properties of magnetic trapping configurations considered afterwards. We study two simple applications that can be developed by bringing a BEC near to a current carrying 2DEG. Firstly, in Chapter four, we demonstrate the feasibility of creating magnetic trapping potentials using a current-carrying 2DEG and an external magnetic field. We identify the advantages of such a 2DEG-based trap over traditional metal-based traps and the conditions needed for operability. Recently developed techniques of magnetic field microscopy with BECs motivate our second considered application, namely, using a Bose-Einstein Condensate to probe the electron transport in 2DEGs and structural characteristics of the heterojunction. In Chapter five, we demonstrate how the quantization of conductance occurring in Quantum Point Contacts (QPC) fabricated from the heterojunction in the 2DEG, can be detected through a localized depletion of the BEC caused by a small inhomogeneity of the magnetic field that originates from a current through the QPC. In addition, we show that the electron density fluctuations in the 2DEG can be measured by detecting the corresponding inhomogeneous magnetic field produced when current flows, via modulation of the BEC’s density. We establish the conditions under which a sensitive response of the BEC to the magnetic field is possible. We also derive a general relation between the modulation of the magnetic field affecting the BEC and the distribution of ionized donors in the heterojunction. Creating semiconductor-cold-atom hybrid systems, where electrons in the semiconductor and atoms in the BEC are coupled to each other, requires a full understanding of the properties of both systems. Since typical micro-traps have an elongated geometry, in Chapter six we present a study of phase correlations of BECs in such geometries. To do this, we use a recently proposed effective one-dimensional equation that takes into account the 3D character of the BEC. Finally, in Chapter seven, we conclude and identify directions for future work emerging from this thesis