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Optimisation and simulation of magneto-optical traps for quantum technologies

Christopher Morley

Published Jul 24, 2020• 0 citations
OpenAlex

Abstract

The development of quantum technologies has been an important topic of research and technological development over the last few years, with numerous projects aiming to exploit cold atoms and Bose-Einstein condensates for sensing applications and probes of fundamental physics. To further develop the emerging applications of new quantum mechanical phenomena, the UK established the a national quantum tech program in 2014. The University of Nottingham, alongside university partners across the country, is currently involved in advancing quantum-based technologies for sensors and metrology applications. A key part of many experiments in this area is the Magneto-Optical Trap, or MOT, which plays a pivotal role in the initial stages of the atom cooling required to reach the nK temperatures necessary to form a condensate. Traditionally, MOTs are typically comprised of multiple pieces of specialised equipment including an ultra-high vacuum chamber, several lasers and magnetic field generating devices, all of which occupy 10's cm in linear dimensions on a laboratory bench and require mains power. As in previous quantum-enabled technologies, including MRI scanners, simulation and optimisation may prove crucial in reducing the size, weight and power requirements of such systems, and for improving their performance. Consequently, it is natural to apply such optimisation methods to emerging quantum technologies, in order to meet the restrictions on experimental size, weight and power necessary the practical cold atom-based sensing systems. As it forms a crucial part of many cold atom quantum technologies, the MOT is a natural initial target for simulation and subsequent optimisation. To develop system design capabilities, this thesis firstly presents three optimisation methods for permanent magnets. One of these builds on previous work to optimise ferromagnetic films for Ioffe-Pritchard arrays (chapter \ref{Magnetic Plate Optimisation}), the others are novel optimisation methods, drawing on more general approaches and on shimming methods frequently used in MRI. Permanent magnets were chosen for use in MOTs in order to reduce the required power and volume of current experimental equipment. While each of the three optimisation methods have different capabilities, two were particularly powerful for designing high field fidelity MOTs. One of these methods was developed specifically to design magnet systems for use with the 3D printed vacuum chamber of the Innovate UK-funded OptaMOT project, illustrating its potential to develop experimental systems. The magnetic field was generated to high accuracy by using the new optimisation algorithm, presented in chapter \ref{Spherical Harmonic Optimisation}, by using mass produced magnets, thereby offering improved practicality over designs that require, expensive, custom-made magnets. With the aim of improving the holistic design capabilities required to advance MOTs, simulation software for the dynamics of atoms in MOTs was also developed. The simulations were capable of modelling the dynamics of atom clouds in both a typical 6 beam MOT and an optical molasses arrangement. It was also used to elucidate the action of a significantly more complicated beam arrangement exploiting more advanced physical phenomena. Remarkably, the arrangement, developed by Hub partners at The University of Southampton, experimentally shows a high atom number and the potential presence of a restoring force without an applied magnetic field. The laser beam geometry also exhibits an unusual dependence of the final atom number on laser beam detuning and power. The simulations provided insights into the potential origins of this dependence (suggesting a combination of beam interference and an additional detuning from the laser fields), whilst confirming that the laser beam configuration alone creates a damping force, as with an optical molasses arrangement. However, the origins and presence of a restoring force still, unfortunately, remain unknown.

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A key element in the study of cold atoms, and their use in emerging quantum technologies, is trapping the atoms in an ultra-high vacuum (UHV) chamber. Many methods have been used to trap atoms including atom chips and magneto-optical traps (MOTs). However, the bulky apparatus, and current-carrying coils, used so far in most MOTs restrict the reduction of power and physical size, as required for quantum technology applications. The advent of 3D printing technology now offers a new route to making MOTs with current paths that can be freely shaped and shrunk to several centimetres, thereby helping to reduce the power consumption and simplify the production of the MOT itself. In this paper, we present designs for 3D printed MOTs and analyse their performance by using COMSOL simulations. We predict that the 3D-printed conductors can create magnetic fields with gradients around 15 G/cm and passing through zero, as required for atom trapping, with Joule heating as low as 0.2 W.

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ENGLISH ABSTRACT: A Magneto Optical Trap (MOT) is a configuration formed by three orthogonal pairs of counterpropagating circularly polarized laser beams and a magnetic field gradient. A MOT is used to cool, capture and trap large numbers of atoms in vacuum at very low temperature in K range. In this thesis the development of an experimental setup for realising a MOT of 87Rb atoms is presented. The atomic structure of Rb and the theoretical background of laser cooling and magneto optical trapping was reviewed. The influence of rubidium background pressure in the vacuum system, the laser beam size and the power and frequency on the number of the trapped atoms were studied in literature. The trapping and repumping lasers were characterised experimentally. Six circularly polarised trapping beams with equal power were formed and properly aligned to intersect at the center of the trapping cell. Two optical setups were designed and exploited to investigate and optimise the trapping beam polarisation. The repumping laser beam was successfully aligned and colinearly combined into all the trapping beams. Three different experimental setups for saturated absorption spectroscopy were developed. Saturated absorption spectra showing the hyperfine structure of both 85Rb and 87Rb isotopes were measured and are discussed. Using two saturated absorption spectroscopy setups, the frequencies of both lasers were successfully locked to the trapping and repumping transitions of 87Rb respectively. A rectangular trapping cell was designed and attached to the vacuum system. A pressure of about 10­¯7 mbar was achieved. The magnetic field coils were characterised and affixed on both sides of the cell in an anti-Helmholtz configuration. Setups for imaging and quantification of the 87Rb atoms in the MOT were designed. Finally, the procedures for demonstrating a MOT are presented. In conclusion, the current status of the project is reported, with recommendations for the future work.

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The development of an experimental apparatus to produce Bose-Einstein condensates (BECs) of ⁸⁷Rb atoms and their application to magnetometry are discussed. Optical detection of atomic Larmor precession is a widely explored method for high-sensitivity measurements of magnetic fields. In this context, short laser/atom interaction time, atomic thermal diffusion and decoherence effects are among the main limitations. In this thesis, we overcome such problems by using spin-polarised ⁸⁷Rb ultra-cold atoms as the sensing element. After the atoms are polarised, a resonant pulse of radio-frequency excites Larmor precession, which is sensitive to external magnetic fields. By measuring the perturbations of the radio-frequency induced spin precession, information on the magnetic fields of interest. This is achieved by monitoring the polarisation plane’s rotation of a linearly polarised resonant laser probe. In the first part of this thesis, the building and optimisation of a laser-cooling set up to obtain a BEC in a hybrid trap is reported. In order to achieve the Phase Space Density (PSD) required for BEC, several different stages of trapping and cooling are necessary. Each phase has been implemented and optimised. The first step consists in the magneto-optical trap (MOT). Here a velocity dependent damping force and a spatially dependent confining force give the largest changes in PSD. Then atoms are loaded into a hybrid trap obtained by overlapping a quadrupole magnetic potential and a far detuned optical crossed dipole trap. The final stage for the condensation consists of forced evaporative cooling, both via magnetic and optical evaporation. In the second part of the thesis, a general overview of the principles of optical atomic magnetometry is provided and the advantages of using ultra-cold atoms with respect to conventional thermal vapours are discussed. The implementation, operation and a preliminary characterisation of the ultra-cold atom magnetometer are described along with the preliminary results collected. Finally, a plan for future improvements of its sensitivity is presented.

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The development of quantum technologies has been an important topic of research and technological development over the last few years, with numerous projects aiming to exploit cold atoms and Bose-Einstein condensates for sensing applications and probes of fundamental physics. To further develop the emerging applications of new quantum mechanical phenomena, the UK established the a national quantum tech program in 2014. The University of Nottingham, alongside university partners across the country, is currently involved in advancing quantum-based technologies for sensors and metrology applications. A key part of many experiments in this area is the Magneto-Optical Trap, or MOT, which plays a pivotal role in the initial stages of the atom cooling required to reach the nK temperatures necessary to form a condensate. Traditionally, MOTs are typically comprised of multiple pieces of specialised equipment including an ultra-high vacuum chamber, several lasers and magnetic field generating devices, all of which occupy 10's cm in linear dimensions on a laboratory bench and require mains power. As in previous quantum-enabled technologies, including MRI scanners, simulation and optimisation may prove crucial in reducing the size, weight and power requirements of such systems, and for improving their performance. Consequently, it is natural to apply such optimisation methods to emerging quantum technologies, in order to meet the restrictions on experimental size, weight and power necessary the practical cold atom-based sensing systems. As it forms a crucial part of many cold atom quantum technologies, the MOT is a natural initial target for simulation and subsequent optimisation. To develop system design capabilities, this thesis firstly presents three optimisation methods for permanent magnets. One of these builds on previous work to optimise ferromagnetic films for Ioffe-Pritchard arrays (chapter \ref{Magnetic Plate Optimisation}), the others are novel optimisation methods, drawing on more general approaches and on shimming methods frequently used in MRI. Permanent magnets were chosen for use in MOTs in order to reduce the required power and volume of current experimental equipment. While each of the three optimisation methods have different capabilities, two were particularly powerful for designing high field fidelity MOTs. One of these methods was developed specifically to design magnet systems for use with the 3D printed vacuum chamber of the Innovate UK-funded OptaMOT project, illustrating its potential to develop experimental systems. The magnetic field was generated to high accuracy by using the new optimisation algorithm, presented in chapter \ref{Spherical Harmonic Optimisation}, by using mass produced magnets, thereby offering improved practicality over designs that require, expensive, custom-made magnets. With the aim of improving the holistic design capabilities required to advance MOTs, simulation software for the dynamics of atoms in MOTs was also developed. The simulations were capable of modelling the dynamics of atom clouds in both a typical 6 beam MOT and an optical molasses arrangement. It was also used to elucidate the action of a significantly more complicated beam arrangement exploiting more advanced physical phenomena. Remarkably, the arrangement, developed by Hub partners at The University of Southampton, experimentally shows a high atom number and the potential presence of a restoring force without an applied magnetic field. The laser beam geometry also exhibits an unusual dependence of the final atom number on laser beam detuning and power. The simulations provided insights into the potential origins of this dependence (suggesting a combination of beam interference and an additional detuning from the laser fields), whilst confirming that the laser beam configuration alone creates a damping force, as with an optical molasses arrangement. However, the origins and presence of a restoring force still, unfortunately, remain unknown.
A key element in the study of cold atoms, and their use in emerging quantum technologies, is trapping the atoms in an ultra-high vacuum (UHV) chamber. Many methods have been used to trap atoms including atom chips and magneto-optical traps (MOTs). However, the bulky apparatus, and current-carrying coils, used so far in most MOTs restrict the reduction of power and physical size, as required for quantum technology applications. The advent of 3D printing technology now offers a new route to making MOTs with current paths that can be freely shaped and shrunk to several centimetres, thereby helping to reduce the power consumption and simplify the production of the MOT itself. In this paper, we present designs for 3D printed MOTs and analyse their performance by using COMSOL simulations. We predict that the 3D-printed conductors can create magnetic fields with gradients around 15 G/cm and passing through zero, as required for atom trapping, with Joule heating as low as 0.2 W.
This thesis details the advances made in the use of additive manufacturing to produce magnetic field generating devices and vacuum components for atomic quantum technologies. Cold atomic clouds are used across a suite of quantum sensors including magnetometers, gravimeters and navigational interferometers; as these sensors approach industrial use, they must be translated from laboratory systems to portable devices. The discussion focuses on a number of devices that demonstrate the benefits provided by this approach. Specifically, the devices discussed are a current carrying cylinder trapping device, an ultra-high vacuum (UHV) chamber and a hollow-core coil mount device. This thesis also covers a range of auxiliary developments that have been made alongside the main body of work including a microprocessor-based control system and a pre-cooling stage for cold atom experiments. To begin this thesis reviews the underlying physical phenomena which are exploited when trapping neutral atoms. In particular, it is important to understand the details of the specific case when working with rubidium-87, including the relevant energy levels diagrams and corresponding laser frequencies. This allows for the discussion of the key forces that are used in magneto-optical trapping (MOT) and magnetic trapping including the origin of the magnetic fields generated by these devices using the Biot-Savart law. The key results that are presented in this thesis centre on the efficacy of these devices as atom traps for quantum technologies and atomic experiments. The atom trap cylinder is capable of trapping 108 rubidium atoms at a temperature of 20 µK, demonstrating the feasibility of this approach. The hollow coil mount device presents a viable route for magnetic trapping. Lastly, the UHV chamber operates in the range of 10-10 mbar as necessary for atomic physics experiments. In addition, this thesis reviews the design of a pre-cooling stage for complex atomic experiments and a simplified experimental control system. These are addressed in a systematic approach to the experimental constituents with a comparison between complex fundamental physics experiments and the developments made towards a portable quantum technology device.
The ongoing drive to transfer quantum technologies from research laboratories to practical, portable devices requires the development of multiple key enabling technologies. The field of cold atoms, which includes high-precision metrology and quantum simulation, has various real-world applications including time-keeping and navigation. A crucial component in these systems is a cold-atom source that generates a flux of low-velocity atoms suitable for subsequent capture. A large flux enables fast repetition rates, high duty cycles, long measurement times, and resistance to long-term performance degradation with a good signal-to-noise ratio, all of which are essential to produce cold-atom devices and technologies that are capable of out-performing the classical alternatives. This thesis presents the design, fabrication and characterisation of a novel cold-atom source using a compact pyramidal magneto-optical trap (MOT) with a unique adjustable-aperture mechanism. This allowed an investigation of the dependence of the flux characteristics on the aperture size, a parameter space that has not previously been explored. The measurements showed a strong dependence of the flux on the aperture size, with a negligible flux below 0.4mm, then an approximately linear increase up to 1.0mm, at which point the relationship showed possible signs of saturation. Using 87Rb, a flux of 1.18×1010 atoms/s was produced using a 1.27mm aperture, for which the mean velocity of the atoms was 21.6(3) m/s with a FWHM of 11.2(2) m/s, and the FWHM divergence of the beam was 86(2) mrad. This is the highest recorded flux from a pyramid or 2D+-MOT source, and amongst the highest reported fluxes from any MOT sources, and avenues for improvement still remain. This work fulfils the aim of demonstrating a compact and robust cold-atom source generating a high flux of laser-cooled atoms for real-world quantum technology applications.
This thesis describes the progress achieved towards two goals. One is the construction of a compact magneto-optical trap (MOT) apparatus, used both as a standalone undergraduate laboratory experiment and as part of a public engagement demonstration of cold atom physics. The setup, which utilises a dichroic atomic vapour laser lock (DAVLL) system plus homemade sideband generation electronics, is capable of trapping and cooling up to 8x10⁷ ⁸⁵Rb atoms in a standard six-beam laser cooling scheme. The second goal is the loading of an ultracold ensemble of ⁸⁷Rb atoms into novel optical trap geometries using a phase-only liquid crystal spatial light modulator (LC SLM) for applications to atomtronics and quantum simulation. Details of a double vacuum chamber apparatus, designed to produce the first Bose-Einstein condensates (BECs) at St Andrews, are provided. The setup incorporates a hybrid trap evaporative cooling scheme towards quantum degeneracy and reliably produces BECs of 1.9 10⁵ ⁸⁷Rb atoms. Two computational techniques, developed during the course of this project, are presented with the aim of creating flexible, smooth holographic optical traps. The first method illuminates a single SLM with overlapped, co-propagating light beams of different wavelengths to create a composite optical pattern for atom manipulation. The second uses conjugate gradient minimisation to create exceptionally high fidelity light patterns in both amplitude and phase for light in the output plane. These techniques, combined with the implementation of a light sheet into the experimental setup, are used to trap atoms in both a ring profile and in a set of narrow waveguides connected with a tunnelling barrier.
ENGLISH ABSTRACT: A Magneto Optical Trap (MOT) is a configuration formed by three orthogonal pairs of counterpropagating circularly polarized laser beams and a magnetic field gradient. A MOT is used to cool, capture and trap large numbers of atoms in vacuum at very low temperature in K range. In this thesis the development of an experimental setup for realising a MOT of 87Rb atoms is presented. The atomic structure of Rb and the theoretical background of laser cooling and magneto optical trapping was reviewed. The influence of rubidium background pressure in the vacuum system, the laser beam size and the power and frequency on the number of the trapped atoms were studied in literature. The trapping and repumping lasers were characterised experimentally. Six circularly polarised trapping beams with equal power were formed and properly aligned to intersect at the center of the trapping cell. Two optical setups were designed and exploited to investigate and optimise the trapping beam polarisation. The repumping laser beam was successfully aligned and colinearly combined into all the trapping beams. Three different experimental setups for saturated absorption spectroscopy were developed. Saturated absorption spectra showing the hyperfine structure of both 85Rb and 87Rb isotopes were measured and are discussed. Using two saturated absorption spectroscopy setups, the frequencies of both lasers were successfully locked to the trapping and repumping transitions of 87Rb respectively. A rectangular trapping cell was designed and attached to the vacuum system. A pressure of about 10­¯7 mbar was achieved. The magnetic field coils were characterised and affixed on both sides of the cell in an anti-Helmholtz configuration. Setups for imaging and quantification of the 87Rb atoms in the MOT were designed. Finally, the procedures for demonstrating a MOT are presented. In conclusion, the current status of the project is reported, with recommendations for the future work.
The development of an experimental apparatus to produce Bose-Einstein condensates (BECs) of ⁸⁷Rb atoms and their application to magnetometry are discussed. Optical detection of atomic Larmor precession is a widely explored method for high-sensitivity measurements of magnetic fields. In this context, short laser/atom interaction time, atomic thermal diffusion and decoherence effects are among the main limitations. In this thesis, we overcome such problems by using spin-polarised ⁸⁷Rb ultra-cold atoms as the sensing element. After the atoms are polarised, a resonant pulse of radio-frequency excites Larmor precession, which is sensitive to external magnetic fields. By measuring the perturbations of the radio-frequency induced spin precession, information on the magnetic fields of interest. This is achieved by monitoring the polarisation plane’s rotation of a linearly polarised resonant laser probe. In the first part of this thesis, the building and optimisation of a laser-cooling set up to obtain a BEC in a hybrid trap is reported. In order to achieve the Phase Space Density (PSD) required for BEC, several different stages of trapping and cooling are necessary. Each phase has been implemented and optimised. The first step consists in the magneto-optical trap (MOT). Here a velocity dependent damping force and a spatially dependent confining force give the largest changes in PSD. Then atoms are loaded into a hybrid trap obtained by overlapping a quadrupole magnetic potential and a far detuned optical crossed dipole trap. The final stage for the condensation consists of forced evaporative cooling, both via magnetic and optical evaporation. In the second part of the thesis, a general overview of the principles of optical atomic magnetometry is provided and the advantages of using ultra-cold atoms with respect to conventional thermal vapours are discussed. The implementation, operation and a preliminary characterisation of the ultra-cold atom magnetometer are described along with the preliminary results collected. Finally, a plan for future improvements of its sensitivity is presented.