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Three-Dimensional Manipulation of Ultracold Atoms using Optical Tweezers

C. S. Chisholm

Published Jan 1, 2018• 2 citations
OpenAlex

Abstract

This thesis describes the design and construction of a three-dimensional optical tweezer system. The three-dimensional aspects were constructed as a modular upgrade to a previously existing one-dimensional system and were characterised using 87Rb with avenues for future research using 40K in mind. The three-dimensional optical tweezer system was used to demonstrate multiple Bose-Einstein condensation in horizontal and vertical planes and gravitationally driven atomic collisions.\n\nIn order to take advantage of the three-dimensional nature of the optical tweezer system and to build capabilities with Rydberg quantum optics, vortex lattice studies and atom interferometry, a vertical imaging path was added to the existing experiment. Compared with the existing horizontal imaging path, the vertical imaging path has higher spatial resolution. A magnetic levitation scheme was implemented to prevent depth of focus issues due to atoms falling under the influence of gravity during ballistic expansion in time-of-flight. The levitation scheme was also used to increase the maximum time-of-flight using the horizontal imaging path by more than a factor of two. The improved resolution enabled observation of matter wave interference fringes for the first time in the Kjaergaard lab, which is a first step towards the study of quantum vortices.

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Abstract One of the essential requirements for atom-based technology is controlling the position and characterizing interactions between atoms and their environment. Optical tweezers are crucial for positioning atoms precisely. Typically, quantum technology research utilizes two-dimensional optical tweezers planar arrays, which are limited in manipulating atoms at different depths of field. To address this issue, three-dimensional optical tweezers can be simulated using a modulated phase mask of a Gaussian laser beam. The phase mask is computed using the direct phase addition (DPA) method with a weight factor, and the angular spectrum method (ASM) is employed to propagate a 2D intensity pattern transversely through the beam, layer by layer. Our results showed that the position of each trap can be adjusted to desire positions in 3D with a global weight factor. Furthermore, our analysis demonstrates that increasing resolution improves measurement precision. Utilizing 3D atom arrays enhances quantum simulation capabilities, providing better insights into complex phenomena. The results of this investigation will be applied to a spatial light modulator in a real setup for an ultra-cold atom trapping experiment.

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This thesis describes the design and construction of a three-dimensional optical tweezer system. The three-dimensional aspects were constructed as a modular upgrade to a previously existing one-dimensional system and were characterised using 87Rb with avenues for future research using 40K in mind. The three-dimensional optical tweezer system was used to demonstrate multiple Bose-Einstein condensation in horizontal and vertical planes and gravitationally driven atomic collisions.\n\nIn order to take advantage of the three-dimensional nature of the optical tweezer system and to build capabilities with Rydberg quantum optics, vortex lattice studies and atom interferometry, a vertical imaging path was added to the existing experiment. Compared with the existing horizontal imaging path, the vertical imaging path has higher spatial resolution. A magnetic levitation scheme was implemented to prevent depth of focus issues due to atoms falling under the influence of gravity during ballistic expansion in time-of-flight. The levitation scheme was also used to increase the maximum time-of-flight using the horizontal imaging path by more than a factor of two. The improved resolution enabled observation of matter wave interference fringes for the first time in the Kjaergaard lab, which is a first step towards the study of quantum vortices.
Since the experimental achievement of Bose-Einstein condensation (BEC) in dilute gases, ultra-cold atom systems have proven to be an unparalleled test bed for condensed matter phenomena. With this in mind, our laboratory set out to build an apparatus for the study of the effects of disorder on condensed matter phase transitions using a BEC loaded into one, two, and three-dimensional lattices. My thesis is divided into two main sections. In the first section I describe in detail the design and construction of our apparatus. Our system is designed to form <super>87<\super>Rb condensates of approximately 10<super>5<\super> atoms. We have three possible experimental science chambers. 1. One can perform 1D lattice experiments in the chamber where the condensate is formed. There is a mirror located in vacuum, which is suitable for this purpose. 2. In a glass chamber one can do 1D, 2D, or 3D lattice experiments. Atoms are loaded into a dipole trap (optical tweezer) prior to condensation and transported approximately 20 cm to the glass cell where optical evaporation is performed to form a BEC. 3. One can transfer, using the same techniques as (2), to a chamber with a multi-channel plate detector for Rydberg atom experiments. The experimental results described in my thesis pertain to situation (1). However, I describe some details of (2) in the construction section. The first experiment presented in my thesis demonstrates the effect of disorder on the time-dependent dynamics of lattice systems. We observe that a small perturbation produces a dramatic change in the adiabaticity criteria for loading a BEC into one-dimensional optical lattice. I conclude with experiments that we expect to perform on this apparatus.
This thesis presents work towards the realisation of dark solitons in a two-dimensional Bose-Einstein condensate. \nThe technical redesign of two sets of coils, necessary for magnetic trapping of the atom cloud in order to \ncreate a condensate, is reported. Two different types of coil technology are presented, discussed, and used. \nThe fabrication of the coils is described, and each set of coils is characterised. Both sets of coils have been installed on the main experiment and are fully operational. \nA key aspect of this thesis is the development of an optical system capable of achieving resolution on the micrometer scale, which can be used for manipulation of a two-dimensional condensate by the method of phase imprinting. The optical system demagnifes the image on a spatial light modulator and focuses the image on the atom plane. Characterisation of the resolution of the optical system shows that a resolution of 3 µm is achieved. The optical system has successfully been implemented on the main experiment and has been used to manipulate the condensate. \nA two-dimensional BEC of \\(^{87}\\)Rb with 31000 atoms and a temperature of 88 nK is realised in a dipole trap of frequencies ω\\(_x\\) = 2π∙5.8 Hz, ω\\(_y\\)= 2π∙19.1 Hz, ω\\(_z\\)= 2π∙269.4 Hz, with gravity being in the z-direction. The method of phase imprinting is used to create the first observed soliton in a 2D BEC. Preliminary analysis of the soliton velocity, width and curvature is presented.
Ultracold atoms in optical lattices can be used to model condensed matter systems. They provide a clean, tuneable system which can be engineered to reach parameter regimes that are not accessible in condensed matter systems. Furthermore, they provide different techniques for probing the properties of these systems.This thesis presents an experimental and theoretical study of ultracold atoms in optical lattices for quantum simulation of two-dimensional systems.The first part of this thesis describes an experiment with a Bose-Einstein condensate of 87Rb loaded into a two-dimensional optical lattice. The beams that generate the optical lattice are controlled by acousto-optic deflection to provide a flexible optical lattice potential. The use of a dynamic ‘accordion’ lattice with ultracold atoms, where the spacing of the lattice is increased in both directions from 2.2 to 5.5 μm, is described. This technique allows an experiment such as quantum simulations to be performed with a lattice spacing smaller than the resolution limit of the imaging system, while allowing imaging of the atoms at individual lattice sites by subsequent expansion of the optical lattice. The optical lattice can also be rotated, generating an artificial magnetic field. Previous experiments with the rotating optical lattice are summarised, and steps to reaching the strongly correlated regime are discussed.The second part of this thesis details numerical techniques that can be used to describe strongly correlated two-dimensional systems. These systems are challenging to simulate numerically, as the exponential growth in the size of the Hilbert space with the number of particles means that they can only be solved exactly for very small systems. Recently proposed correlator product states [Phys. Rev. B 80, 245116 (2009)] provide a numerically efficient description which can be used to simulate large two-dimensional systems. In this thesis we apply this method to the two-dimensional quantum Ising model, and the Bose-Hubbard model subject to an artificial magnetic field in the regime where fractional quantum Hall states are predicted to occur.
Ultracold atoms in optical lattices can be used to model condensed matter systems. They provide a clean, tuneable system which can be engineered to reach parameter regimes that are not accessible in condensed matter systems. Furthermore, they provide different techniques for probing the properties of these systems.This thesis presents an experimental and theoretical study of ultracold atoms in optical lattices for quantum simulation of two-dimensional systems.The first part of this thesis describes an experiment with a Bose-Einstein condensate of 87Rb loaded into a two-dimensional optical lattice. The beams that generate the optical lattice are controlled by acousto-optic deflection to provide a flexible optical lattice potential. The use of a dynamic ‘accordion’ lattice with ultracold atoms, where the spacing of the lattice is increased in both directions from 2.2 to 5.5 μm, is described. This technique allows an experiment such as quantum simulations to be performed with a lattice spacing smaller than the resolution limit of the imaging system, while allowing imaging of the atoms at individual lattice sites by subsequent expansion of the optical lattice. The optical lattice can also be rotated, generating an artificial magnetic field. Previous experiments with the rotating optical lattice are summarised, and steps to reaching the strongly correlated regime are discussed.The second part of this thesis details numerical techniques that can be used to describe strongly correlated two-dimensional systems. These systems are challenging to simulate numerically, as the exponential growth in the size of the Hilbert space with the number of particles means that they can only be solved exactly for very small systems. Recently proposed correlator product states [Phys. Rev. B 80, 245116 (2009)] provide a numerically efficient description which can be used to simulate large two-dimensional systems. In this thesis we apply this method to the two-dimensional quantum Ising model, and the Bose-Hubbard model subject to an artificial magnetic field in the regime where fractional quantum Hall states are predicted to occur.
Abstract One of the essential requirements for atom-based technology is controlling the position and characterizing interactions between atoms and their environment. Optical tweezers are crucial for positioning atoms precisely. Typically, quantum technology research utilizes two-dimensional optical tweezers planar arrays, which are limited in manipulating atoms at different depths of field. To address this issue, three-dimensional optical tweezers can be simulated using a modulated phase mask of a Gaussian laser beam. The phase mask is computed using the direct phase addition (DPA) method with a weight factor, and the angular spectrum method (ASM) is employed to propagate a 2D intensity pattern transversely through the beam, layer by layer. Our results showed that the position of each trap can be adjusted to desire positions in 3D with a global weight factor. Furthermore, our analysis demonstrates that increasing resolution improves measurement precision. Utilizing 3D atom arrays enhances quantum simulation capabilities, providing better insights into complex phenomena. The results of this investigation will be applied to a spatial light modulator in a real setup for an ultra-cold atom trapping experiment.