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.
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.
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 thesis, I describe a proposal for experiments with dense ensembles of ultracold Rubidium atoms optically excited to highlying electronic states known as Rydberg states. The proposed experiment is designed to implement a model of quantum computation known as deterministic quantum computation with one qubit (DQC1). My proposal is novel among other proposals for Rydberg atoms because it employs mixed states and could provide insights into the source of the enhancements of quantum technology over classical technology. I demonstrate that ultracold atoms and Rydberg interactions offer new perspectives for exploring the DQC1 model. This is mainly due to the large strength, long range and controllability of Rydberg interactions. My specific contributions include: a proposal that solves one of the main issues with implementing quantum logic gates between ensembles of atoms; numerical simulations of the proposed cold atom implementation of a DQC1 protocol; and the design and laboratory implementation of a high-performance optical system for imaging ultracold atoms. These contributions bring the experimental exploration of the DQC1 model closer to realisation.
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.
Single atoms are a promising candidate for the creation of a scalable quantum computer. Neutral atoms trapped by optical fields are especially encouraging due to the full controllability of the trap potential. Single neutral atoms trapped within a fibre-fibre cavity allow us to strongly couple atoms and photons. This creates an efficient atom-photon interface which can compensate for the short state transfer distance inherent of neutral atoms. A spatial light modulator allows for the creation and manipulation of an array of these single atom traps.\n\nIn this research we create a setup to cool and trap neutral rubidium-87 atoms by a combination of a magneto-optical trap (MOT) and a dipole trap. The dipole trap uses a strongly focused, far red-detuned laser, which enables us to trap single atoms via the collisional blockade regime. These traps are realised within a novel glass cell, allowing for great optical access.\n\nThe MOT in this setup is able to trap (4.27 +/- 0.10) * 10^3 atoms with a density of (7.89 +/- 0.56) * 10^9 atoms cm^-3 . The MOT temperature is in the order of 100 μK. We also show the manipulation of these properties, allowing us to tailor the MOT. The dipole trap is created with a trap waist of 37 μm, allowing us to trap a cloud of atoms. With the dipole trap we achieve a lifetime of atoms of (34.8 +/- 2.0) ms.
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.
Qubits encoded in the electronic states of single atoms trapped in arrays of optical tweezers are a promising platform for a universal quantum computer. These qubits can be prepared in a well-defined quantum state, coherently manipulated using a nearresonant driving field, and their state detected with high fidelity. The most promising aspect of this platform is the large scalability, with arrays of up to 6100 qubits demonstrated[62].We present our progress in developing such a system with an array of single 85Rbatoms. We provide an overview of the experimental setup constructed for this purpose. Typically 50 atoms are loaded from a MOT into a 10×10 array of optical tweezers with sub-micrometer waists, with only a single atom present in a tweezer. The occupation of the tweezers is determined using a fluorescence image. We provide a characterisation of the trapping potentials experienced by the atoms. This characterisation is performed by measuring properties of the atoms in the tweezers, allowing for an in situ characterisation. In particular, the trap depth and trap frequencies were characterised. The temperature of the atoms after the initial fluorescence image was determined using the release and recapture technique [101] and the trapping lifetime of the atom was measured. With the ability to prepare, manipulate, and read out the electronic state of the atoms, an array of hyperfine qubits has been created. The qubits are encoded in the hyperfine clock states as |0⟩ := 52S1/2 |F = 2,mF = 0⟩ and |1⟩ := 52S1/2 |F = 3,mF = 0⟩. These long-lived first-order Zeeman shift insensitive states exhibit good coherence times, which we have characterized as T1=205 ± 3 ms , T2* = 2.01 ± 0.02 ms, andT2 echo = 67.1 ± 0.1 ms. State preparation is achieved by repetitions of optical and microwave pulses, to which the |0⟩ state is dark, allowing for population to accumulate in this state. The coherent evolution of the qubits have been performed using 3.035 GHz microwave radiation. The antenna used to produce this radiation is a home-built fullwave loop antenna. The antenna has allowed for addressing the qubits with Rabi frequencies up to Ω/2π ≈ 160 kHz. We have implemented the single-qubit Clifford gates using the global microwave drive. We determine using randomized benchmarking an166 Summary average gate fidelity of 0.99949(3), limited by Rabi frequency inhomogeneity over the array. To combat this fidelity limitation, we repeated the randomized benchmarking using the pulse length error robust SCROFULOUS pulses [135], which resulted in an increased gate fidelity of 0.999653(5). As a further extension of the capabilities of the system, we demonstrated a preliminary implementation of addressing a single atom int he array by applying a local Rz rotation to the selected qubit using a Stark shifting laser. The high level of control of the microwave radiation has allowed for an experimental verification of control noise-fidelity relations proposed by [115]. We have found good agreement between the experimentally measured fidelities and the proposed analytical relations developed using the stochastic Schrödinger equation. As a preliminary step towards implementing a two-qubit gate, we have performed coherent excitation of the |1⟩ state to the |r ⟩ :=602S1/2 |mJ = −1/2> Rydberg state using an off-resonant two-photon excitation. The low contrast of the Rabi oscillations on the |1⟩↔|r ⟩ transition was investigated using a simple Lindblad master equation based model. The largest contributors to the reduced contrast is SPAM error, intermediate state scattering and laser phase noise. Since Rydberg atoms interact via the van der Waals interaction, the spacing between atoms must be deterministically controlled. For this purpose, we have used an additional optical tweezer which can be dynamically moved using an acousto-optic deflector to rearrange the stochastically filled array into a desired configuration. By placing 2 atoms a distance ≈ 5 μm apart, we have demonstrated the p2 enhancement of the Rabi oscillation on the |1⟩↔|r ⟩ transition, a required first step towards implementing an entangling gate between the hyperfine qubits. To extend the temperature-limited T2* coherence time, we have implemented Λ-enhanced gray molasses cooling. We have opted to perform this cooling on the D2line as it is experimentally convenient to use this transition. Because using this transition for this purpose has not been reported in this isotope of Rb, we studied the efficacy of this cooling scheme under these circumstances. The reduced excited state hyperfine splitting of 85Rb compared to 87Rb has allowed for the study of the efficacy of this technique in the presence of additional transitions that may inhibit the cooling performance. Despite the challenges of the smaller hyperfine splitting, we have cooled the atoms to4.0±0.2 μK. This additional cooling is partially negated by the heating from the qubit state preparation procedure, but the additional cooling has allowed for the average T2*to be extended from ⟨T2*⟩ = 3.4 ± 0.1 ms to ⟨T2*⟩ = 5.3 ± 0.2 ms.