We show that current in a two-dimensional electron gas (2DEG) can trap ultracold atoms $<$1 $\ensuremath{\mu}$m away with orders of magnitude less spatial noise than a metal trapping wire. This enables the creation of hybrid systems, which integrate ultracold atoms with quantum electronic devices to give extreme sensitivity and control: For example, activating a single quantized conductance channel in the 2DEG can split a Bose-Einstein condensate (BEC) for atom interferometry. In turn, the BEC offers unique structural and functional imaging of quantum devices and transport in heterostructures and graphene.
We show that current in a two-dimensional electron gas (2DEG) can trap ultracold atoms <1 \ensuremathμm away with orders of magnitude less spatial noise than a metal trapping wire. This enables the creation of hybrid systems, which integrate ultracold atoms with quantum electronic devices to give extreme sensitivity and control: For example, activating a single quantized conductance channel in the 2DEG can split a Bose-Einstein condensate (BEC) for atom interferometry. In turn, the BEC offers unique structural and functional imaging of quantum devices and transport in heterostructures and graphene.
In this work, we consider the advantages and challenges of using free-standing two-dimensional electron gases (2DEG) as active components in atom chips for manipulating ultracold ensembles of alkali atoms. We calculate trapping parameters achievable with typical high-mobility 2DEGs in an atom chip configuration and identify advantages of this system for trapping atoms at sub-micron distances from the atom chip. We show how the sensitivity of atomic gases to magnetic field inhomogeneity can be exploited for controlling the atoms with quantum electronic devices and, conversely, using the atoms to probe the structural and transport properties of semiconductor devices.
Ultracold atomic gases have proven to be an excellent tool for research in quantum systems. A Bose gas can be trapped on an atom chip using very well defined and tunable spatially-dependent potentials. The proximity of the atoms to the chip permits the use of low currents allowing for highly accurate temporal changes. Excellent experimental apparatus is needed to achieve Bose-Einstein condensation with a sufficient atom number to study low-dimensional physics. The setup described in this document utilises a set of current-carrying structures on top of which an atom chip sits. For improved atom loading rate, a two-dimensional loading stage was added, extending the lifetime of the magnetic trap. From this loading stage to the atom chip, Bose-Einstein condensation of 105 Rubidium-87 atoms was achieved in less than 30 s, allowing for a large rate of experimental cycles. The high spatial and temporal tunability of this setup results in the ability to split the atomic cloud and quench the trapping potential geometry. Maximising the ratio between trapping frequencies for different spatial directions leads to the system presenting features of a one-dimensional gas. Manipulating the coherence dynamics of a one-dimensional Bose-Einstein condensate creates fluctuations in the phase properties of the wavefunction. These fluctuations are observed as atom density perturbations after releasing the trapping potentials, and are a tool for temperature measurements. When the cloud of atoms is positioned at a few tens of micrometres from the surface of the atom chip, corrugations in the microstructures of the chip affect the trapping potentials at very low temperatures 1 µK. This effect is simulated and quantified in the thesis, with the aim of improving future setups. Additionally, the effect is explored for microscopy purposes. The behaviour of a Bose-Einstein condensate, especially the expansion rate, has long been studied. In this thesis, the Gross-Pitaevskii Equation is introduced, finding its numerical solutions to the two-dimensional and three-dimensional forms, using the Split-Step Fourier Method. The results show very good agreement with the experimental results, as well as with other well- established theories of condensates. The creation of such a toolbox opens up the opportunity to further investigate the coherence dynamics of low-dimensional systems.
Current atom chips, conventionally made from metal wires, suffer from anumber of different problems, which we have shown can be overcome byusing graphene conductors, specifically; •Metal wires have a large Johnson noise due to the high carrier density.Graphene has a much lower charge carrier density(≈8 orders of magnitude lower), and thus, Johnson noise that is four orders of magnitude lower than metal. This leads to a corresponding major increase in the lifetime of the atom cloud above the wire. We have shown that an atom cloud trapped 1μm above a graphene wire has its lifetime increased by around 4 orders of magnitude compared to metal, i.e from 0.1 s to>10 minutes. This extends the Johnson noise limited lifetime so much that it becomes negligible as it is far beyond the limit imposed by the background gas collisions. •Metal wires exert a large Casimir-Polder attraction on atoms trapped near them, thereby limiting the minimum trapping distance to 10-100μm. Using a transfer matrix method in conjunction with the Lifshitz approach, we have demonstrated that the Casimir-Polder attraction between a graphene layer and an atom is approximately 50% that of the attraction between an atom and a thin gold layer. This enables atoms to be trapped up to 2 orders of magnitude closer to a graphene atom chip and so achieve sub-micron trapping distances. •Metal wires are spatially imperfect on 200 nm scales [1], which can lead to fragmented atom clouds. We have that shown that current lithography techniques can produce conducting paths of an arbitrary shape in graphene with roughness on only the≈10 nm scale. This leads to smoother traps and therefore smoother clouds even at sub-micron trapping distances. •Finally, we note that graphene will also allow for a greater degree of integration between all the different components of the cold atom system, trapping wires, Ultra High Vacuum (UHV) environments and optics,thus aiding the miniaturisation of the experimental set-up.
Ultracold and quantum degenerate gases held near conductive surfaces can serve as sensitive, high-resolution, and wide-area probes of electronic current flow. Previous work has imaged transport around grain boundaries in a gold wire by using ultracold and Bose-Einstein condensed atoms held microns from the surface with an atom-chip trap. We show that atom-chip microscopy may be applied to useful purpose in the context of materials exhibiting topologically protected surface transport. Current flow through lithographically tailored surface defects in topological insulators (TI), both idealized and with the band structure and conductivity typical of Bi2Se3, is numerically calculated. We propose that imaging current flow patterns enables the differentiation of an ideal TI from one with a finite bulk-to-surface conductivity ratio, and specifically, that the determination of this ratio may be possible by imaging transport around trenches etched into the TI's surface.
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.\nIn 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. \nWe 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.\nIn 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.\nCreating 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.\nFinally, in Chapter seven, we conclude and identify directions for future work emerging from this thesis.
In order to take quantum mechanical systems out of the lab and produce practical devices, a method of miniaturizing and integrating apparatus components is needed. In the context of ultracold atomic gas experiments, the ideal method of achieving this miniaturization is the implementation of atom chip technology. By depositing micro-scale current carrying wires onto planar substrates, it is possible to create a magnetic trap capable of confining a cloud of neutral atoms in sufficient proximity to the chip surface for solid state devices to interact with the cloud. This thesis presents our lab’s first steps towards creating an atom chip capable of confining a cloud of rubidium-87. The chip prototypes were developed with the intent to incorporate them into the hybrid system apparatus within our lab. The chips are intended to serve as a platform for facilitating the interaction between the atomic gas ensemble and mesoscopic solid-state devices, allowing for the hybridization of the two systems. In this work I describe the design of the trapping wire configuration and the fabrication of the first two generations of chip prototypes. Additionally, I provide numerical simulations of the produced magnetic field, from which estimates of the trap frequency and depth can be calculated. Finally, I introduce some basic characterization tests of the absolute current limitations and resistive behavior of the chip wires, and the dimensional uniformity of the fabricated wire profiles.