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Microscopic Optical Trapping of Ultracold Neutral Atoms for Applications in Quantum Information

Michael Copley-May

Published Jan 1, 2019• 0 citations
Publisher

Abstract

In this thesis, the development of an experimental system for microscopic dipole trapping of ultracold neutral rubidium atoms is presented. The purpose of this system is to advance towards the experimental realisation of a quantum computational protocol utilising neutral atoms as qubits. It is intended that the quantum gate operations between qubits will be implemented by a scheme using Rydberg blockade, imposing a restriction on the maximum size of the dipole-trapped atom cloud; the spatial extent of the atomic ensemble contained in this trap must be smaller than the blockade radius to ensure that one single collective Rydberg state per qubit can be achieved. Therefore the experiment was designed with the intent of fulfilling these challenging requirements. This project involved the design and construction of an improved ultra-high vacuum chamber containing the optical setup for the experiment, successfully achieving pressures below 5 x 10-10 mbar. A magneto-optical trap was produced to act as a background reservoir of atoms from which to load the dipole trap. Numerous experimental measurements were done to characterise the physical properties of the trapped atoms, including the number, density and temperature of atoms, as well as the lifetime of the trap. The results of these measurements led to the conclusion that a suitable reservoir for loading the dipole trap had been produced. Significant work was carried out to set up and obtain the dipole trap in the laboratory. Measurements of the characteristic properties of the trap and the atoms confined in the trap were carried out to investigate the behaviour of the atoms and to validate our design. Ultimately a trap containing tens of atoms was achieved, with an atom cloud diameter of ~1.2 µm in two dimensions, being well within the estimated Rydberg blockade radius of ~4.4 µm for n ~ 60 as intended. The two-photon excitation laser system for the probing of Rydberg states, for future applications in Rydberg blockade-based quantum gate operations, was also developed during the course of this work. Different Rydberg states were detected experimentally by the observation of Autler-Townes splitting in a three-level atom scheme. Overall, the work presented in this thesis provides a strong groundwork for the advancement towards neutral atom-based quantum gates, including the development of the experimental system and the production of standard procedures to carry out characterisation measurements of the traps efficiently in the future. The main achievements of this work are the establishment of the experimental apparatus, the achievement of a microscopic dipole trap which conforms to the requirements of an atomic qubit, and the significant growth in the knowledge of atom trapping specific to our system.

DOI
10.21954/ou.ro.0000ec37

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In this thesis, the development of an experimental system for microscopic dipole trapping of ultracold neutral rubidium atoms is presented. The purpose of this system is to advance towards the experimental realisation of a quantum computational protocol utilising neutral atoms as qubits. It is intended that the quantum gate operations between qubits will be implemented by a scheme using Rydberg blockade, imposing a restriction on the maximum size of the dipole-trapped atom cloud; the spatial extent of the atomic ensemble contained in this trap must be smaller than the blockade radius to ensure that one single collective Rydberg state per qubit can be achieved. Therefore the experiment was designed with the intent of fulfilling these challenging requirements. This project involved the design and construction of an improved ultra-high vacuum chamber containing the optical setup for the experiment, successfully achieving pressures below 5 x 10-10 mbar. A magneto-optical trap was produced to act as a background reservoir of atoms from which to load the dipole trap. Numerous experimental measurements were done to characterise the physical properties of the trapped atoms, including the number, density and temperature of atoms, as well as the lifetime of the trap. The results of these measurements led to the conclusion that a suitable reservoir for loading the dipole trap had been produced. Significant work was carried out to set up and obtain the dipole trap in the laboratory. Measurements of the characteristic properties of the trap and the atoms confined in the trap were carried out to investigate the behaviour of the atoms and to validate our design. Ultimately a trap containing tens of atoms was achieved, with an atom cloud diameter of ~1.2 µm in two dimensions, being well within the estimated Rydberg blockade radius of ~4.4 µm for n ~ 60 as intended. The two-photon excitation laser system for the probing of Rydberg states, for future applications in Rydberg blockade-based quantum gate operations, was also developed during the course of this work. Different Rydberg states were detected experimentally by the observation of Autler-Townes splitting in a three-level atom scheme. Overall, the work presented in this thesis provides a strong groundwork for the advancement towards neutral atom-based quantum gates, including the development of the experimental system and the production of standard procedures to carry out characterisation measurements of the traps efficiently in the future. The main achievements of this work are the establishment of the experimental apparatus, the achievement of a microscopic dipole trap which conforms to the requirements of an atomic qubit, and the significant growth in the knowledge of atom trapping specific to our system.
In this work we report on the development progress of a cold atoms platform to demonstrate a model of quantum computation known as deterministic Quantum computing with One Clean Qubit (DQC1). This is a novel class of algorithms where interactions between qubits enable nonclassical correlations other than entanglement, namely discord. We aim to demonstrate the DQC1 protocol using a scheme in which the information processing is realized on cold neutral rubidium atoms through the cNOT gate based on a Rydberg blockade. The implementation of this protocol imposes very stringent requirements on the cloud of atoms: to realise the cNOT gate with high fidelity it is required that a full Rydberg blockade is operating throughout the extent of the ensemble. This means that a cloud of atoms needs to have a radius below approximately 5 μm (for Rydberg states of atoms n = 43). A dipole trap system was designed and implemented during the course of this PhD with the aim of satisfying these experimental constraints. In our setup, a vapour of 87Rb is first trapped in a Magneto-Optical Trap (MOT) and cooled to sub-Doppler temperatures. The atoms are then subsequently trapped in the dipole trap. Our dipole trapping setup is based on a high numerical aperture lens (NA=0.53) to achieve a sub-micron trapping potential and simultaneously observe trapped atoms with a micrometre resolution. According to the design and the optical tests, the system is capable of creating the trapping potential with about 1 μm waist and 4 μm Rayleigh length. The aim of this work was to examine and optimise experimental conditions under which the dipole trap should be operated, so that the sufficiently small trap for the DQC1 algorithm can be obtained in the future. For characterisation, a trap of a bigger volume (about 6 μm waist and 28 μm length) was setup instead of using the full capacity of the system. This enhanced the atom loading procedure and provided more convenient conditions for experiments. The temperature of atoms was typically around 250 μK, and the trap lifetime (2.5 s) was limited by the background collisions, which indicates that the vacuum was maintained on the expected level. The key findings of the thesis are that the properties of the atoms reservoir (MOT temperature and density), and the loading processes (intensity of MOT beams), need to be optimised to be able to load a micrometre size trap. These findings are instrumental for the future implementation of the DQC1 protocol and also have implications for other protocols founded on the use of a Rydberg blockade.
During the course of this PhD an experimental set-up has been designed and implemented to confine neutral atoms in microscopic dipole traps and to manipulate their internal states by laser excitation to Rydberg states. A lot of effort was devoted to the stabilization of the laser sources for two-photon excitation to the Rydberg states, using techniques based on modulation transfer spectroscopy and electromagnetically induced transparency (EIT). Taking advantage of the EIT spectroscopy scheme, we have measured for the first time the electric dipole moments for the transitions between the first excited 5P3/2 and Rydberg nDS/2 level of rubidium. These measurements provided benchmarking of existing theoretical models to calculate the reduced matrix elements and have helped us to identify the D'yachkov Pankratov method as a particularly reliable one. Therefore we made use of the existing code to calculate the relative radial matrix elements for bound-bound, bound-free and free-free transitions between arbitrary states of alkali atoms. Our results allowed us to identify many features of interest and several Cooper minima have been revealed for the first time. The preparation of a new apparatus required ultra-high vacuum for efficient laser cooling and trapping experiments. A unique 4-beam magneto-optical trap has been designed and implemented in our new system. The tetrahedral MOT operating at a very acute beams angle has been demonstrated for the first time. The characterisation of the basic properties of our MOT has highlighted. some interesting new cooling mechanisms that do not fully match existing theoretical models and will require further investigation. It has been demonstrated that our tetrahedral MOT is suitable to prepare cold, diluted reservoirs of atoms and therefore efficiently load our microscopic dipole trap.
This thesis presents a new experimental facility that has been developed in the course of the PhD of the author together with the experimental measurements of the dipole moments for transitions between 5P3/2 and nD5/2 states in Rb atoms, where 20 ≤ n ≤ 48. A laser cooling setup for rubidium atoms was designed and built that allows to produce 3 x 10 atoms at temperature of few microkelvins. A laser system for coherent excitation to Rydberg states was realised that exploits a two-photon ladder excitation scheme. Such setup allowed to directly measure transition dipole moments from the first excited state to high n Rydberg states. The electromagnetically induced transparency and Autler-Townes splitting phenomena were exploited in order to obtain the values of the dipole moments, which were found to be in an excellent agreement with the theoretical values calculated using the quasiclassical approach by our collaborators in Novosibirsk. To the author's knowledge, these are the first direct measurements of such dipole moments. The data shown in the thesis proves the reliability of the measurement method. The obtained results are extremely useful to validate theoretical models and gain insight in the physics of the interactions that will be an object of subsequent studies. The methods presented in the dissertation will be used in the future to detect in a non-destructive way Rydberg-Rydberg interactions within mesoscopic samples.
We describe several novel techniques for the optical trapping of ultracold atoms and for the production of wavelength-stabilised, coherent light at the frequencies required for use in atomic physics experiments. The greater part of this thesis deals with work towards the creation of regular arrays of microscopic optical dipole traps formed at the foci of truncated spherical cavities in a metallic film, in which the inter-site spacing can be set anywhere between one and several hundred micrometers. Arrays of such cavities are synthesised and structurally characterised via optical and electron microscopy, and numerical simulations of the light intensity distribution near the foci of such cavities under normal illumination are used to confirm their suitability for dipole trap production. A method for the construction of arrays of magneto-optical traps based on such structures is proposed and theoretically examined, and some preliminary experimental work towards the synthesis of the required microstructures is also described. Possible approaches to the loading of such traps and the imaging of the atoms contained therein are discussed - experimental work towards ballistic atom transfer from a specialised form of magneto-optical trap that can be formed close to a microstructured surface is carried out, and the efficacy of wavelength-selective fluorescence imaging as a means of reducing the effects of background scatter from the surface is experimentally demonstrated. Further work described herein includes the proposal and experimental demonstration of two novel techniques for the removal of the carrier wave from a phase-modulated laser beam, one of which is based on a fiber-optic Mach-Zehnder interferometer that is shown to be an effective device for splitting or combining beams of nearly equal frequencies. A spontaneous-force based atom trapping mechanism that does not rely on the use of a magnetic field, but rather on spatially-dependent optical pumping between different metastable atomic states, is also proposed, and a proof of principle experiment is carried out to demonstrate the validity of the suggested mechanism. We find that this trapping scheme allows the spatial dependence of the trapping force to be tailored with a greater degree of flexibility than is usually possible with magneto-optical trapping, and that it is also capable of producing traps with stronger spring constants than are typically achievable with magneto-optical trapping under realistic experimental constraints.
High optical nonlinearities can be achieved at the single photon level by coupling the photon states to strongly interacting Rydberg excitations under the conditions of electromagnetically induced transparency. The nonlinear response in Rydberg quantum optics comes as a direct result of the long range dipole-dipole interactions via Rydberg blockade and interaction induced dephasing. In this thesis, Rydberg quantum optics experiments are performed with two spatially separated mediums with a nonlinear response at the single photon level. Two ultracold rubidium atomic clouds are tightly confined by a pair of in-vacuo aspheric lenses such that only a few Rydberg excitations can exist in each one of the clouds simultaneously. The long range character of the dipole-dipole interactions leads to the generation of quantum states of light. The effective photon-photon interactions are directly observed as an anti-correlation in the simultaneous photon retrieval as a result of the non resonant van der Waals interactions. The collective Rydberg excitations, stored in the non-overlapping mediums, experience an additional spatial non-uniform phase. In addition, we experimentally characterize the cooperative optical response of a cold atomic medium at a single photon level. This aims to exploit the enhancement of the spontaneous emissions decay rate (superradiance) as a dependence of the number of atoms involved in the ensemble. The observed atomic response in two different regimes gives a further understanding of the system dynamics and unlocks a promising potential route towards the implementation in scalable, multichannel quantum optical devices.
Neutral atoms trapped and manipulated by laser light provide experimentally well accessible quantum systems allowing for a high degree of control over external and internal degrees of freedom. Arrays of dipole traps in which the atoms are confined individually in a configurable geometry constitute a versatile platform for quantum simulation and information applications. By exciting these atoms into Rydberg states, interactions of variable strength and range can be introduced into the system, allowing for the implementation of entangling gate operations or spin Hamiltonians. A crucial requirement for these schemes to function in a reliable way is the ability to create defect-free arrays of single atoms. This is generally a challenge in these types of systems, as common atom loading schemes are limited to roughly 50% probability of filling each site. In this work, a technique for the rearrangement of atoms within a scalable architecture based on micro-optical lens arrays was developed and implemented, resulting in the creation of uniformly filled regions containing more than 100 atoms, which represent the largest defect-free structures realized so far in systems of this kind. This was accomplished by filling the empty traps in a pre-defined pattern with an atom one by one using an optical tweezer. Thus, structures with up to 5 x 5 atoms could be rendered defect-free in more than 99% of attempts. Although the success rate drops below unity for larger clusters, a value of 3.1% for a 100-atom structure is still viable for experiments working with post-selection methods. The filling fraction of even the largest examined structures was observed to be higher than 88%, surpassing common loading schemes by a significant margin. The measurements presented in this thesis build on a region of the array containing 361 sites, being limited by available laser power. In contrast, the addressable range of the optical tweezer includes more than 1500 sites and microlens arrays with up to a million lenses are commercially available. By implementing coherent Rydberg excitation of this assembled atom array, significant progress toward a universal quantum computer or flexible quantum simulator has been made. Using a two-photon excitation scheme, coherent dynamics between the ground and Rydberg state could be observed simultaneously in a 5 x 5 region of the array, with two-photon Rabi frequencies on the order of Omega = 2Pi x 500kHz measured for a Rydberg laser beam waist of w_0,B = 18.7(10) µm. The choice of an appropriate Rydberg state and interatomic spacing led to the presence of strong nearest-neighbor interactions and allowed for the demonstration of the Rydberg blockade effect by observing a collective enhancement of the Rabi frequency consistent with the expected scaling ~ sqrt(N) as well as the suppression of multiple excitations. This mechanism represents the fundamental constituent of a two-qubit gate operation. The architecture introduced in this work offers a scalability unique among quantum simulation platforms and the presented results underpin its potential to propel the atom-optical approach for quantum information processing beyond the threshold of quantum supremacy. Different approaches for scaling up the system have been explored, indicating that defect-free structures of more than 1000 atoms are within range with feasible experimental improvements. Through a detailed analysis of the factors limiting the coherence of the observed dynamics, strategies for future experimental improvements have been developed. Among these, increasing the coupling strength to the Rydberg state into the megahertz regime by increasing laser power and implementing single-site addressing represents the most straight-forward and promising approach.