The objective of this thesis is the design and simulation of new electromagnetic traps and guides for ultra-cold matter. The traps and guides are intended for future experiments with small amounts of alkali atoms to study the quantum-mechanical effects of condensation and coupling between trapped drops of cold matter.\n\nThe main results are with the development and simulation of new wire traps and guides based on the dressing effect realised in strong DC magnetic and RF fields of certain frequencies. Some designs are proposed using only trapping by the DC magnetic field.\n\nThe principal methodology used in the thesis is to first develop the necessary theory and design formulas to make an initial design, followed by analytical and numerical simulation of the effective trapping potential. This may be followed by optimization of the geometry and the DC driving currents to enhance the trapping performance of the structure.\n\nA wire carrying both DC and RF currents is surrounded by a cylindrical minimum potential manifold and can be used as a guide for cold atoms. Bias rings are necessary around the wire to avoid a potential minimum of zero and to move the resulting circular potential minimum up and down along the wire. The minimum potential surfaces around two crossed or two parallel wires touch each other for certain critical values of the DC currents in the two wires. The DC currents must be in opposite directions in two parallel wires. Equations are derived in Chapter 2 for the distance to the circular minimum potential manifold for a single wire, for two crossed wires and for two parallel wires. It is then explained how prospective cold atom transfer between two crossed wires can be achieved by changing the magnitudes of the RF currents in the bias rings around the wires. Electrically controlled atom transfer between two parallel wires does not seem to be practical.\n\nA four-wire cell trap made from two crossing pairs of parallel wires has been designed and optimized using a simple Matlab script. It can be used to trap both strong- and weak-field-seeking atoms and may possibly be used to study collision and entanglement between the two types of atoms. With only DC excitation the trap becomes a trap for weak-field-seeking atoms. It then unfortunately has a potential minimum of zero at its centre. A similar 3 x 3 wire dual-well trap has also been designed and optimized in Matlab. It is prospective for the study of entanglement of BEC matter placed in the two wells. A quite low potential barrier in the direction normal to the wireplanes when the two wells are merged could however entail that the trap is inadequate for this purpose or that additional bias fields are necessary.\n\nSeveral multi-wire cell-grids that may find use as part of a quantum register are also described. The cell-grids can be stacked in threedimensions and can trap both strong- and weak-field-seeking atoms. The optimization, also here performed in Matlab, showed weaknesses due to a lack of complexity. A different and better optimization technique is most likely necessary to improve the optimization further.\n\nScaling to micrometre and nanometre size is demonstrated in Chapter 3. When scaling to micrometre size thermally induced spin-flip transitions should be considered. Scaling to nanometre size demands that both thermally induced spin-flips and the effect of the Casimir-Polder force must be taken into account. The effect of the Casimir-Polder force is minimized by the use of carbon nanotubes as conductors. The minimum feasible trapping distance is expected to be no less than 100 nm from the surface of a carbon nanotube.\n\nA four micro-wire cell and a 3 x 3 micro-wire structure, both adapted for future realization on a micro-machined substrate, are given as examples of micrometre size structures. Several nanometre size structures are also demonstrated. It is shown that prospective atom transfer between two crossed nanotubes can be done essentially in the same way as for two crossed wires.\n\nA four-nanotube cell and several nanotube cell-grids are also exemplified. The depth of the trapping potential is found to be proportional to the RF frequency. If the RF frequency is increased then the DC current level must also increase to maintain the same DC current to angular frequency ratio. The depth of the trap is accordingly also proportional to the DC current level in the conductors. The depth of the trap is thus ultimately limited by the maximum conductor current.\n\nA quadrupolar trap similar to the well known Ioffe-Pritchard trap is studied in Chapter 4 with combined DC and RF current excitation of the bias rings. A non-uniform potential minimum is found around the local maximum at the centre of the trap, but this does not prevent the trap from being used to trap weak-field-seeking atoms. The potential maximum at the centre of the quadrupolar trap is more than sufficient for trapping strongfield- seeking atoms. The quadrupolar trap can therefore be used to trap both strong- and weak-field-seeking atoms if the DC bar currents are large enough. Simulations also indicate that the bias rings can be placed relatively closely together to compress clouds of cold atoms into successively smaller traps. As the gap distances become very small the B-field becomes very strong between the bias rings and there is a risk of dielectric breakdown.\n\nA metallic cylinder atom guide consisting of a cylinder with a small hole and an external wire is described analytically in Chapter 5 and simulation results from Amperes are compared favourably with the results of calculations in Matlab. It is found that there can only be a B-field zero at the centre of the hole in the cylinder when there is a second field zero further inside the cylinder. The barrier between the two field zeros typically increases in width with increasing cylinder radius and in height with decreasing cylinder radius for a given cylinder current (DC). The smallest cylinder had the highest barrier between the field zeros, but also required the highest DC current in the external wire. Bias rings around the guide must be centred on the hole in the cylinder and the DC ring currents and the spacing between the bias rings must be scaled by the same factor as the ring radius to maintain the same shape and height of the trapping potential along the centre of the hole. The cylinder guide looks promising as a hermetic guide for cold matter. Bias rings are required both to pump atoms along the guide and to remove the zero in the B-field inside the hole.
The objective of this thesis is the design and simulation of new electromagnetic traps and guides for ultra-cold matter. The traps and guides are intended for future experiments with small amounts of alkali atoms to study the quantum-mechanical effects of condensation and coupling between trapped drops of cold matter.\n\nThe main results are with the development and simulation of new wire traps and guides based on the dressing effect realised in strong DC magnetic and RF fields of certain frequencies. Some designs are proposed using only trapping by the DC magnetic field.\n\nThe principal methodology used in the thesis is to first develop the necessary theory and design formulas to make an initial design, followed by analytical and numerical simulation of the effective trapping potential. This may be followed by optimization of the geometry and the DC driving currents to enhance the trapping performance of the structure.\n\nA wire carrying both DC and RF currents is surrounded by a cylindrical minimum potential manifold and can be used as a guide for cold atoms. Bias rings are necessary around the wire to avoid a potential minimum of zero and to move the resulting circular potential minimum up and down along the wire. The minimum potential surfaces around two crossed or two parallel wires touch each other for certain critical values of the DC currents in the two wires. The DC currents must be in opposite directions in two parallel wires. Equations are derived in Chapter 2 for the distance to the circular minimum potential manifold for a single wire, for two crossed wires and for two parallel wires. It is then explained how prospective cold atom transfer between two crossed wires can be achieved by changing the magnitudes of the RF currents in the bias rings around the wires. Electrically controlled atom transfer between two parallel wires does not seem to be practical.\n\nA four-wire cell trap made from two crossing pairs of parallel wires has been designed and optimized using a simple Matlab script. It can be used to trap both strong- and weak-field-seeking atoms and may possibly be used to study collision and entanglement between the two types of atoms. With only DC excitation the trap becomes a trap for weak-field-seeking atoms. It then unfortunately has a potential minimum of zero at its centre. A similar 3 x 3 wire dual-well trap has also been designed and optimized in Matlab. It is prospective for the study of entanglement of BEC matter placed in the two wells. A quite low potential barrier in the direction normal to the wireplanes when the two wells are merged could however entail that the trap is inadequate for this purpose or that additional bias fields are necessary.\n\nSeveral multi-wire cell-grids that may find use as part of a quantum register are also described. The cell-grids can be stacked in threedimensions and can trap both strong- and weak-field-seeking atoms. The optimization, also here performed in Matlab, showed weaknesses due to a lack of complexity. A different and better optimization technique is most likely necessary to improve the optimization further.\n\nScaling to micrometre and nanometre size is demonstrated in Chapter 3. When scaling to micrometre size thermally induced spin-flip transitions should be considered. Scaling to nanometre size demands that both thermally induced spin-flips and the effect of the Casimir-Polder force must be taken into account. The effect of the Casimir-Polder force is minimized by the use of carbon nanotubes as conductors. The minimum feasible trapping distance is expected to be no less than 100 nm from the surface of a carbon nanotube.\n\nA four micro-wire cell and a 3 x 3 micro-wire structure, both adapted for future realization on a micro-machined substrate, are given as examples of micrometre size structures. Several nanometre size structures are also demonstrated. It is shown that prospective atom transfer between two crossed nanotubes can be done essentially in the same way as for two crossed wires.\n\nA four-nanotube cell and several nanotube cell-grids are also exemplified. The depth of the trapping potential is found to be proportional to the RF frequency. If the RF frequency is increased then the DC current level must also increase to maintain the same DC current to angular frequency ratio. The depth of the trap is accordingly also proportional to the DC current level in the conductors. The depth of the trap is thus ultimately limited by the maximum conductor current.\n\nA quadrupolar trap similar to the well known Ioffe-Pritchard trap is studied in Chapter 4 with combined DC and RF current excitation of the bias rings. A non-uniform potential minimum is found around the local maximum at the centre of the trap, but this does not prevent the trap from being used to trap weak-field-seeking atoms. The potential maximum at the centre of the quadrupolar trap is more than sufficient for trapping strongfield- seeking atoms. The quadrupolar trap can therefore be used to trap both strong- and weak-field-seeking atoms if the DC bar currents are large enough. Simulations also indicate that the bias rings can be placed relatively closely together to compress clouds of cold atoms into successively smaller traps. As the gap distances become very small the B-field becomes very strong between the bias rings and there is a risk of dielectric breakdown.\n\nA metallic cylinder atom guide consisting of a cylinder with a small hole and an external wire is described analytically in Chapter 5 and simulation results from Amperes are compared favourably with the results of calculations in Matlab. It is found that there can only be a B-field zero at the centre of the hole in the cylinder when there is a second field zero further inside the cylinder. The barrier between the two field zeros typically increases in width with increasing cylinder radius and in height with decreasing cylinder radius for a given cylinder current (DC). The smallest cylinder had the highest barrier between the field zeros, but also required the highest DC current in the external wire. Bias rings around the guide must be centred on the hole in the cylinder and the DC ring currents and the spacing between the bias rings must be scaled by the same factor as the ring radius to maintain the same shape and height of the trapping potential along the centre of the hole. The cylinder guide looks promising as a hermetic guide for cold matter. Bias rings are required both to pump atoms along the guide and to remove the zero in the B-field inside the hole.
In this letter, the results on the development and simulation of new three-dimensional nanotraps for cold dressed atoms are considered. The traps are the multi-cell structures built by crossed non-touching carbon nanotubes. The trapping effect is tuned by the DC and RF currents to confine the strong- or low-potential seeking atoms far enough from the areas of strong Casimir-Polder and spin-flip forces. It is supposed that the developed and simulated multi-cell structures are pertinent for catching the Bose-Einstein condensates to demonstrate the Josephson effect, and to enable the study of the entanglement of confined clouds in three-dimensional nano-cells.
This thesis presents the first demonstration of a guide for cold atoms based on a miniature structure of four current-carrying wires. The four wires are embedded within a hollow silica fibre. Atoms are guided along the centre of a fifth hole on the axis of the fibre by the Stern-Gerlach force. A vapour cell Magneto Optical Trap (MOT), formed 1 cm above the mouth of the waveguide is the source of cold "8"5Rb atoms. After cooling the atoms to 25 #mu#K in optical molasses they fall under the influence of gravity through a magnetic funnel into the waveguide. After propagating for 2 cm, the atoms are reflected by the field of a small pinch coil wound around the base of the guide. The atoms then travel back up the fibre and out into the funnel, where they can be imaged either in fluorescence or by recapturing in the MOT. A video sequence of atoms falling into the guide and re-emerging after reflection from the pinch coil graphically illustrates the operation of the guide. The coupling efficiency and transverse temperature of the atoms is measured experimentally and in a Monte-Carlo simulation. We find an optimum coupling efficiency of 12% and we measure the spatial extent of the cloud within the fibre to be of order 100 #mu#m. We find good agreement between experimental data and results from the numerical simulation. We have also been able to observe different thresholds for the reflection of different positive m_F levels. In another experiment we are able to trap the atoms in an elongated Ioffe trap for up to two seconds, increasing the distance over which the atoms are guided. We are able to guide the atoms over distances of 40 cm with a loss rate indistinguishable from the free space loss rate. (author)
In this letter, the results on the development and simulation of new three-dimensional nanotraps for cold dressed atoms are considered. The traps are the multi-cell structures built by crossed non-touching carbon or metallic nanotubes. The trapping effect is tuned by the DC and RF currents to confine the strong- or low-potential seeking atoms far enough from the areas of strong Casimir–Polder and spin-flip forces. It is supposed that the developed and simulated multi-cell structures are pertinent for catching the Bose–Einstein condensates to demonstrate the Josephson effect, and to enable the study of the entanglement of confined clouds in three-dimensional nano-cells.
Abstract We propose two novel schemes for guiding cold, neutral atoms using static magnetic fields generated by several cylindrical arrays of current‐carrying wires or a few different‐shaped (V‐, or U‐shaped, etc.) current‐carrying conductors, and calculate the corresponding magnetic‐field contours and their trapping potentials. Our study shows that some guiding schemes can be used to form an atomic funnel, or an atomic beam‐splitter, or even construct an atomic interferometer, and some guiding schemes can be used to realize a single‐mode wave guide of ultracold atoms (or coherent matter waves, BEC) under certain conditions. We also propose a few new schemes to microscopically trap neutral atoms by using various planar arrays of current‐carrying wires and calculate the spatial distribution of the magnetic fields. Our research shows that these microtrap arrays can be used to form 1D, 2D or 3D atomic magnetic lattices, and then to prepare 1D, 2D or 3D photonic crystals, even to realize a 1D, 2D or 3D array of magnetically‐trapped BECs or Bose Clusters.
Atom optics has been a highly active field of research with many scientific breakthroughs over the past two decades, largely due to successful advances in laser technology, microfabrication techniques, and the development of laser cooling and trapping of neutral atoms. This dissertation details several atom optics experiments with the motivation to develop tools and techniques for precision atom wave interferometry. It provides background information about atom optics and the fundamentals behind laser cooling and trapping, including basic techniques for cold gas thermometry and absorptive detection of atoms. A brief overview of magnetic trapping and guiding in tight wire-based traps is also provided before the experimental details are presented. ❧ We developed a novel laser source of 780 nm light using frequency-doubled 1560 nm fiber amplifier. This laser system provided up to a Watt of tunable frequency stabilized light for two Rb laser cooling and trapping experiments. One system generates Bose-Einstein condensates in an optical trap while the second is based on atom chip magnetic traps. The atom chip system, detailed in this thesis, was designed and built to develop the tools necessary for transport and loading large numbers of cold atoms and explore the potential for guided atom interferometry. Techniques and results from this experiment are presented, including an efficient magnetic transport and loading method to deliver cold atom to atom chip traps. We also developed a modeling tool for the magnetic fields formed by coiled wire geometries, as well as planar wire patterns. These models helped us design traps and determine adiabatic transportation of cold atoms between macro-scale traps and micro-traps formed on atom chips. Having achieved near unity transfer efficiency, we demonstrated that this approach promises to be a consistent method for loading large numbers of atoms into micro-traps. Furthermore, we discuss an in situ imaging technique to investigate magnetic field contours of the traps and the dynamics of atoms within those confining potentials. We also controlled the propagation along the atom chip guides by accelerating atoms with longitudinal magnetic gradients, and investigated an atom focusing scheme. ❧ While the atom chip wire guides perform a role analogous to optical fibers guiding light waves, ""free space"" cold atoms offer great opportunity for precision interferometry. We describe a second on-going atom optics experiment that measures gravity gradients using a pair of atom fountain interferometers separated by one meter. We have demonstrated Gravity Gradiometer resolution down to 4x10⁻⁹ g/m using a 40 kg test mass. The atomic physics subsystem is described in detail, including the vacuum, cold atom source, optics, magnetic coils and shields, and vibration isolation and compensation. The system is designed to be a compact, robust, transportable instrument, taking strides towards future gravity gradient measurements in the field. In the realm of space applications, there has been interest for micro-gravity science experiments aboard the International Space Station, along with instrument development for gravity mapping of Earth and planetary bodies with satellite-based instruments. Furthermore, there are ground-based applications for gravity imaging of local density distributions, precision measurement of gravity, as well as proposals for redefining the kilogram, detecting gravitational waves and determining the Gravitational constant.
Ultracold atomic gases can be utilised as extremely sensitive probes of their surrounding environment. In particular, samples of ultracold atoms confined using chip-based microtraps are an ideal tool for mapping electric and magnetic field landscapes. Over the course of this thesis, a new experiment capable of performing surface microscopy using magnetically trapped clouds of cold rubidium-87 atoms has been built. The focus of the work is on the design and construction of the experimental system, which must incorporate many different aspects for manipulating thermal atomic gases, with a view to positioning them at sub-micron distances from special surfaces. This reduced atom-surface separation is necessary for implementing a high resolution, high sensitivity magnetic field sensor with cold atoms. Although current microfabrication techniques easily enable trapping at distances on the order of micrometres, several distance-dependent surface effects - such as the Casimir-Polder force, Johnson-Nyquist noise, and stray potentials - eventually impede magnetic trapping at the sub-micron level. These surface effects can greatly modify the confining potentials, which reduces the trap depth and consequently leads to an additional loss rate of atoms from the trap. We have explored the possibility of using special surfaces such as nano-membranes of silicon nitride and graphene, which have reduced atom- surface interactions, to enable trapping distances at the sub-micron level. A multilayer printed circuit board chip has been designed to form an initial magnetic trap and then transport the cloud of atoms to a desired location over the samples. This chip, along with various samples, is mounted on a custom-made electrical feedthrough designed to make connections to all conductor that are inside the vacuum chamber. The initial cloud of cold atoms can then be prepared in the central region of the chip and delivered to the location of the samples on either side. The experimental system is able to routinely capture over 10^8 rubidium-87 atoms at a temperature of 80 micro-Kelvin in a magneto-optical trap using a novel scheme of five laser beams. A method is demonstrated for enhancing the atom number in the magneto-optical traps by a factor of two by using laser beams with two slightly different frequencies. Atoms from the magneto-optical trap are then transferred to a purely magnetic trap formed by the wires on the printed circuit board chip. Time-dependent currents in the chip wires then create a dynamic potential, which is shown to successfully transport the atomic sample over a distance of 12 millimetre with minimal atom loss. This thesis describes the development of the apparatus in detail, along with careful characterisation of the cold cloud at various stages of the experimental sequence. Initial results on the long distance atom transport are presented. Finally, the experimental results of the two frequency magneto-optical trap for atom number improvement are discussed.