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All-microwave control of hyperfine states in ultracold spin-1 rubidium

(Georgia Institute of Technology, 2019-10-04) Boguslawski, Matthew

The manipulation of quantum spin states in a spinor Bose-Einstein condensate is critical for nearly all types of studies in these systems. State control methods are used to initialize the state of the system, apply Hamiltonian terms to modify the dynamics, and to measure properties of the quantum states. This thesis details the implementation of circularly polarized microwaves to selectively drive hyperfine transitions in the context of a spin-1 Bose-Einstein condensate of rubidium. This provides a new powerful tool for addressing specific transitions in the presence of frequency-degenerate transitions, allowing for new possibilities in state control. With this tool, we demonstrate a factor of 1/45.3 reduction in the coupling strength between polarization selected and blocked transitions by the application of a circularly polarized microwave field. This newly-developed tool is used to explore a couple of important applications. First, this polarized field is used to couple only three levels, out of all eight levels in the F=1, 2 hyperfine structure of ground-state rubidium-87, to drive an otherwise degenerate lambda system with 99.5% fidelity in state transfer from one base state of the lambda to the other. This is comparable to two-level transition fidelities measured in our system. This lambda transition has applications such as in implementing a non-adiabatic holonomic gate within the spin-1 states and could be extended to give full SU(2) control over two of the spin-1 states. Second, the circularly polarized field is applied to selectively drive hyperfine transitions in low bias fields, where the Zeeman splitting between the spin-1 states is small and comparable to the spectral linewidth of the driving field. In such low fields, microwave transitions without polarization selection scramble the state, as there are couplings between multiple levels within the hyperfine structure. This thesis demonstrates the selection of transitions using polarization control of the microwave field to solve this problem. These measurements imply the utility of circular polarization selected transitions for more rapid manipulations than otherwise possible.
Geometry, topology and control of spin-1 quantum states

(Georgia Institute of Technology, 2018-09-12) Hebbe Madhusudhana, Bharath

Non-Abelian and non-adiabatic variants of Berry's geometric phase have been pivotal in the recent advances in fault tolerant quantum computation gates, while Berry's phase itself is at the heart of the study of topological phases of matter. Here we use ultracold atoms to study the unique properties of spin-1 geometric phase. The spin vector of a spin-1 system, unlike that of a spin-1/2 system, can lie anywhere on or inside the Bloch sphere representing the phase space. This suggests a generalization of Berry's phase to include closed paths that go inside the Bloch sphere. Under this generalization, the special class of loops that pass through the center, which we refer to as\textit {singular loops}, are significant in two ways. First, their geometric phase is non-Abelian and second, their geometrical properties are qualitatively different from the nearby non-singular loops, making them akin to critical points of a quantum phase transition. Here we use coherent control of ultracold Rb atoms in an optical trap to experimentally explore the geometric phase of singular loops in a spin-1 quantum system.
Kibble-Zurek mechanism in a spin-1 Bose-Einstein condensate

(Georgia Institute of Technology, 2015-11-16) Anquez, Martin

The Kibble-Zurek mechanism (KZM) primarily characterizes scaling in the formation of topological defects when a system crosses a continuous phase transition. The KZM was first used to study the evolution of the early universe, describing the topology of cosmic domains and strings as the symmetry-breaking phase transitions acted on the vacuum fields during the initial cooling. A ferromagnetic spin-1 $^{87}$Rb Bose-Einstein condensate (BEC) exhibits a second-order gapless quantum phase transition due to a competition between the magnetic and collisional spin interaction energies. Unlike extended systems where the KZM is illustrated by topological defects, we focus our study on the temporal evolution of the spin populations and observe how the scaling of the spin dynamics depend on how fast the system is driven through the critical point. In our case, the excitations are manifest in the temporal evolution of the spin populations illustrating a Kibble-Zurek type scaling, where the dynamics of slow quenches through the critical point are predicted to exhibit universal scaling as a function of quench speed. The KZM has been studied theoretically and experimentally in a large variety of systems. There has also been a tremendous interest in the KZM in the cold atoms community in recent years. It has been observed not only in ion chains and in atomic gases in optical lattices, but also in Bose gases through the formation of vortices or solitons. The KZM in the context of crossing the quantum phase transition in a ferromagnetic BEC has been theoretically studied, but this thesis is the first experimental investigation of this phenomenon.
Quantum control of a many-body system in a spin-1 Bose-Einstein condensate

(Georgia Institute of Technology, 2013-11-18) Hoang, Thai Minh

Ultracold atoms provide a powerful tool for studying quantum control of interacting many-body systems with well-characterized and controllable Hamiltonians. In this thesis, we demonstrate quantum control of a many-body system consisting of a ferromagnetic spin-1 Bose-Einstein condensate (BEC). By tuning the Hamiltonian of the system, we can generate either a phase space with an unstable hyperbolic fixed point or a phase space with an elliptical fixed point. A classical pendulum with a stable oscillation about the "down" position and an inverted pendulum with unstable non-equilibrium dynamics about the "up" position are classical analogs of the quantum spin dynamics we investigate in this thesis. In one experiment, we dynamically stabilize the system about an unstable hyperbolic fixed point, which is similar to stabilizing an inverted pendulum. In a second experiment, we parametrically excite the system by modulating the quadratic Zeeman energy. In addition, we demonstrate rectifier phase control as a new method to manipulate the quantum states of the many-body system. This is similar to parametric excitation and manipulation of the oscillation angle of a classical pendulum. These experiments demonstrate the ability to control a quantum system realized in a spinor BEC, and they also can be applied to other quantum systems. In addition, we extend our studies to atoms above the Bose-Einstein transition temperature, and we present results on thermal spin relaxation processes and equilibrium spin populations.
Production of cold barium monohalide ions

(Georgia Institute of Technology, 2013-08-20) De Palatis, Michael V.

Ion traps are an incredibly versatile tool which have many applications throughout the physical sciences, including such diverse topics as mass spectrometry, precision frequency metrology, tests of fundamental physics, and quantum computing. In this thesis, experiments are presented which involve trapping and measuring properties of Th³⁺. Th³⁺ ions are of unique interest in part because they are a promising platform for studying an unusually low-lying nuclear transition in the 229Th nucleus which could eventually be used as an exceptional optical clock. Here, experiments to measure electronic lifetimes of Th³⁺ are described. A second experimental topic explores the production of sympathetically cooled molecular ions. The study of cold molecular ions has a number of applications, some of which include spectroscopy to aid the study of astrophysical objects, precision tests of quantum electrodynamics predictions, and the study of chemical reactions in the quantum regime. The experiments presented here involve the production of barium monohalide ions, BaX⁺ (X = F, Cl, Br). This type of molecular ion proves to be particularly promising for cooling to the rovibrational ground state. The method used for producing BaX⁺ ions involves reactions between cold, trapped Ba⁺ ions and neutral gas phase reactants at room temperature. The Ba⁺ ion reaction experiments presented in this thesis characterize these reactions for producing Coulomb crystals composed of laser cooled Ba⁺ ions and sympathetically cooled BaX⁺ ions.
Dynamics of a spin-1 BEC in the regime of a quantum inverted pendulum

(Georgia Institute of Technology, 2013-04-03) Gerving, Corey Scott

The primary study of this thesis is the experimental realization of the non-equilibrium dynamics of a quantum inverted pendulum as examined in the collective spin dynamics of a spin-1 Bose-Einstein condensate. In order to compare experimental results with the simulation past the low depletion limit, current simulation techniques needed to be extended to model atomic loss. These extensions show that traditional measurements of the system evolution (e.g. measuring the mean and standard deviation of the evolving quantity) were insufficient in capturing the quantum nature of the evolution. It became necessary to look at higher order moments and cumulants of the distributions in order to capture the quantum fluctuations. Extending the implications of the loss model further, it is possible that the system evolves in a way previously unpredicted. Spin-mixing from a hyperbolic fixed point in the phase space and low noise atom counting form the core of the experiment to measure the evolution of the distributions of the spin populations. The evolution of the system is also compared to its classical analogue, the momentum-shortened inverted pendulum. The other experimental study in this thesis is mapping the mean-field phase space. The mean-field phase space consists of different energy contours that are divided into both phase-winding trajectories and closed orbits. These two regions are divided by a separatrix whose orbit has infinite period. Coherent states can be created fairly accurately within the phase space and allowed to evolve freely. The nature of their subsequent evolution provides the shape of the phase space orbit at that initial condition. From this analysis a prediction of the nature of the entire phase space is possible.
Characterizing single atom dipole traps for quantum information applications

(Georgia Institute of Technology, 2013-03-27) Shih, Chung-Yu

Ultracold neutral atoms confined in optical dipole traps have important applications in quantum computation and information processing, quantum simulators of interacting-many-body systems and atomic frequency metrology. While optical dipole traps are powerful tools for cold atom experiments, the energy level structures of the trapped atoms are shifted by the trapping field, and it is important to characterize these shifts in order to accurately manipulate and control the quantum state of the system. In order to measure the light shifts, we have designed a system that allows us to reliably trap individual 87Rb atoms. A non-destructive detection technique is employed so that the trapped atoms can be continuously observed for over 100 seconds. Single atom spectroscopy, trap frequency measurements, and temperature measurements are performed on single atoms in a single focus trap and small number of atoms in a 1D optical lattice in order to characterize the trapping environment, the perturbed energy level structures, and the probe-induced heating. In the second part of the thesis, we demonstrate deterministic delivery of an array of individual atoms to an optical cavity and selective addressability of individual atoms in a 1D optical conveyor, which serves as a potential candidate for scalable quantum information processing. The experiment is extended to a dual lattice system coupled to a single cavity with the capability of independent lattice control and addressability. The mutual interactions of atoms in different lattices mediated by a common cavity field are demonstrated. A semi-classical model in the many-atom regime based on the Jaynes-Cummings model is developed to describe the system that is in good qualitative agreement with the data. This work provides a foundation for developing multi-qubit quantum information experiments with a dual lattice cavity system.
Spin-nematic squeezing in a spin-1 Bose-Einstein condensate

(Georgia Institute of Technology, 2012-01-17) Hamley, Christopher David

The primary study of this thesis is spin-nematic squeezing in a spin-1 condensate. The measurement of spin-nematic squeezing builds on the success of previous experiments of spin-mixing together with advances in low noise atom counting. The major contributions of this thesis are linking theoretical models to experimental results and the development of the intuition and tools to address the squeezed subspaces. Understanding how spin-nematic squeezing is generated and how to measure it has required a review of several theoretical models of spin-mixing as well as extending these existing models. This extension reveals that the squeezing is between quadratures of a spin moment and a nematic (quadrapole) moment in abstract subspaces of the SU(3) symmetry group of the spin-1 system. The identification of the subspaces within the SU(3) symmetry allowed the development of techniques using RF and microwave oscillating magnetic fields to manipulate the phase space in order to measure the spin-nematic squeezing. Spin-mixing from a classically meta-stable state, the phase space manipulation, and low noise atom counting form the core of the experiment to measure spin-nematic squeezing. Spin-nematic squeezing is also compared to its quantum optics analogue, two-mode squeezing generated by four-wave mixing. The other experimental study in this thesis is performing spin-dependent photo-association spectroscopy. Spin-mixing is known to depend on the difference of the strengths of the scattering channels of the atoms. Optical Feshbach resonances have been shown to be able to alter these scattering lengths but with prohibitive losses of atoms near the resonance. The possibility of using multiple nearby resonances from different scattering channels has been proposed to overcome this limitation. However there was no spectroscopy in the literature which analyzes for the different scattering channels of atoms for the same initial states. Through analysis of the initial atomic states, this thesis studies how the spin state of the atoms affects what photo-association resonances are available to the colliding atoms based on their scattering channel and how this affects the optical Feshbach resonances. From this analysis a prediction is made for the extent of alteration of spin-mixing achievable as well as the impact on the atom loss rate.
Robust, reusable qubits for quantum information applications

(Georgia Institute of Technology, 2011-01-21) Gibbons, Michael J.

Most neutral atom quantum computing experiments rely on destructive state detection techniques that eject the detected qubits from the trap. These techniques limit the repetition rate of these experiments due to the necessity of reloading a new quantum register for each operation. We address this problem by developing reusable neutral atom qubits. Individual Rubidium 87 atoms are trapped in an optical lattice and are held for upwards of 300 s. Each atom is prepared in an initial quantum state and then the state is subsequently detected with 95% fidelity with less than a 1% probability of losing it from the trap. This combination of long storage times and nondestructive state detection will facilitate the development of faster and more complex quantum systems that will enable future advancements in the field of quantum information.
Relative number squeezing in a Spin-1 Bose-Einstein condensate

(Georgia Institute of Technology, 2010-11-15) Bookjans, Eva M.

The quantum properties of matter waves, in particular quantum correlations and entanglement are an important frontier in atom optics with applications in quantum metrology and quantum information. In this thesis, we report the first observation of sub-Poissonian fluctuations in the magnetization of a spinor 87Rb condensate. The fluctuations in the magnetization are reduced up to 10 dB below the classical shot noise limit. This relative number squeezing is indicative of the predicted pair-correlations in a spinor condensate and lay the foundation for future experiments involving spin-squeezing and entanglement measurements. We have investigated the limits of the imaging techniques used in our lab, absorption and fluorescence imaging, and have developed the capability to measure atoms numbers with an uncertainly < 10 atoms. Condensates as small as ≈ 10 atoms were imaged and the measured fluctuations agree well with the theoretical predictions. Furthermore, we implement a reliable calibration method of our imaging system based on quantum projection noise measurements. We have resolved the individual lattice sites of a standing-wave potential created by a CO2 laser, which has a lattice spacing of 5.3 µm. Using microwaves, we site-selectively address and manipulate the condensate and therefore demonstrate the ability to perturb the lattice condensate of a local level. Interference between condensates in adjacent lattice sites and lattice sites separated by a lattice site are observed.