Neutral atoms are promising candidates to store and manipulate quantum information. In this thesis we examine several problems related to the control of neutral atoms for quantum computation and simulation. In the first problem we show how the transport of atoms in an optical lattice can be controlled through variation of the polarization of the optical lattice and the application of global microwave pulses. This type of control control is a first step in many of the schemes for quantum computation and quantum simulation. We show that with the available tools for global control, the synthesis of any unitary transformation, consistent with translational invariance, may be performed and provide an explicit method for carrying this out. In the second problem, we study a spectroscopic method for probing atomic interactions that may form the basis for two-qudit quantum logic gates. The confinement of atoms required to perform quantum computation can strongly affect how they interact. Probing the nature of those confinement-induced effects is a first step towards quantum computing with neutral atoms. Transport of the atoms to overlapping wells is achieved through microwave pulses that drive population between hyperfine levels in a lin-perp-lin polarization-gradient lattice. By measuring the amount of population transferred into certain excited states, we can detect changes in the spectrum of the two-atom system induced by the interaction. In the third problem, we consider a cloud of cold atoms driven by both microwave and radio-frequency magnetic fields. The large number of spin sublevels available in individual atoms makes them candidates for a qudit-based quantum computer. Because the applied fields that drive the system may be inhomogeneous, the collection of atoms forms an ensemble of different qudits. Borrowing ideas developed for NMR control, we show how to drive the ensemble through a given evolution. We show that even in the presence of large experimental errors, state preparation may be achieved with high fidelities. We also show that intentionally applied variations in spatial magnetic fields can be used to synthesize different states in different regions of space.
Neutral atoms are promising candidates to store and manipulate quantum information. In this thesis we examine several problems related to the control of neutral atoms for quantum computation and simulation. In the first problem we show how the transport of atoms in an optical lattice can be controlled through variation of the polarization of the optical lattice and the application of global microwave pulses. This type of control control is a first step in many of the schemes for quantum computation and quantum simulation. We show that with the available tools for global control, the synthesis of any unitary transformation, consistent with translational invariance, may be performed and provide an explicit method for carrying this out. In the second problem, we study a spectroscopic method for probing atomic interactions that may form the basis for two-qudit quantum logic gates. The confinement of atoms required to perform quantum computation can strongly affect how they interact. Probing the nature of those confinement-induced effects is a first step towards quantum computing with neutral atoms. Transport of the atoms to overlapping wells is achieved through microwave pulses that drive population between hyperfine levels in a lin-perp-lin polarization-gradient lattice. By measuring the amount of population transferred into certain excited states, we can detect changes in the spectrum of the two-atom system induced by the interaction. In the third problem, we consider a cloud of cold atoms driven by both microwave and radio-frequency magnetic fields. The large number of spin sublevels available in individual atoms makes them candidates for a qudit-based quantum computer. Because the applied fields that drive the system may be inhomogeneous, the collection of atoms forms an ensemble of different qudits. Borrowing ideas developed for NMR control, we show how to drive the ensemble through a given evolution. We show that even in the presence of large experimental errors, state preparation may be achieved with high fidelities. We also show that intentionally applied variations in spatial magnetic fields can be used to synthesize different states in different regions of space.
We study a system of neutral atoms trapped in a three-dimensional optical lattice suitable for the encoding, initialization and manipulation of atomic qubits. The qubits are manipulated by applied electromagnetic fields interacting with dipole moments of the atoms via light shifts, Raman transitions, Zeeman shifts, and microwave transitions. Our lattice is formed by three orthogonal one-dimensional lattices, which have different frequencies so that interference terms average to zero. This geometry allows considerable freedom in designing the component one-dimensional lattices, so that they provide not only confinement but also independent control in each dimension. Our atomic qubits are initialized from a laser-cooled atomic sample by Raman sideband cooling in individual lattice potential wells. We have demonstrated accurate and robust one-qubit manipulation using resonant microwave fields. In practice such control operations are always subject to errors, in our case spatial inhomogeneities in the microwave Rabi frequency and the light shifted qubit transition frequency. Observation of qubit dynamics in near real time allows us to minimize these inhomogeneities, and therefore optimize qubit logic gates. For qubits in the lattice, we infer a fidelity of 0.990(3) for a single pi-pulse. We have also explored the use of NMR-type pulse techniques in order to further reduce the effect of errors and thus improve gate robustness in the atom/lattice system. Our schemes for two-qubit quantum logic operations are based on controlled collisional interactions. We have experimented with two schemes in order to probe these collisions. The first involves manipulation of the center-of-mass wavepackets of two qubits in a geometry corresponding to two partially overlapping Mach-Zender interferometers. Unfortunately, this scheme has proven extremely sensitive to phase errors, as the wavepackets are moved by the optical lattice. The other scheme starts with two qubits in spatially separated traps, and utilizes microwaves to drive one or both qubits into a third trap in-between the two qubits. Once the wavepackets overlap, the collisions create a large energy shift which can be probed spectroscopically.
The present work investigates the state-selective transport of single neutral cesium atoms in a one-dimensional optical lattice. It demonstrates experimental applications of this transport, including a single atom interferometer, a quantum walk and controlled two-atom collisions. The atoms are stored one by one in an optical lattice formed by a standing wave dipole trap. Their positions are determined with sub-micrometer precision, while atom pair separations are reliably inferred down to neighboring lattice sites using real-time numerical processing. Using microwave pulses in the presence of a magnetic field gradient, the internal qubit states, encoded in the hyperfine levels of the atoms, can be separately initialized and manipulated. This allows us to perform arbitrary single-qubit operations and prepare arbitrary patterns of atoms in the lattice with single-site precision. Chapter 1 presents the experimental setup for trapping a small number of cesium atoms in a one-dimensional optical lattice. Chapter 2 is devoted to fluorescence imaging of atoms, discussing the imaging setup, numeric methods and their performance in detail. Chapter 3 focuses on engineering of internal states of trapped atoms in the lattice using optical methods and microwave radiation. It provides a detailed investigation of coherence properties of our experimental system. Finally manipulation of individual atoms with almost single-site resolution and preparation of regular strings of atoms with predefined distances are presented. In Chapter 4, basic concepts, the experimental realization and the performance of the state-selective transport of neutral atoms over several lattice sites are presented and discussed in detail. Coherence properties of this transport are investigated in Chapter 5, using various two-arms single atom interferometer sequences in which atomic matter waves are split, delocalized, merged and recombined on the initial lattice site, while the interference contrast and the accumulated phase difference are measured. By delocalizing a single atom over several lattice sites, possible spatial inhomogeneities of fields along the lattice axis in the trapping region are probed. In Chapter 6, experimental realization of a discrete time quantum walk on a line with single optically trapped atoms is presented as an advanced application of multiple path quantum interference in the context of quantum information processing. Using this simple example of a quantum walk, fundamental properties of and differences between the quantum and classical regimes are investigated and discussed in detail. Finally, by combining preparation of atom strings, position-dependent manipulation of qubit states and state-selective transport, in Chapter 7, two atoms are deterministically brought together into contact, forming a starting point for investigating two-atom interactions on the most fundamental level. Future prospects and suggestions are finally presented in Chapter 8.
Neutral atoms, trapped in optical tweezers and lattices, have gained significant attention owing to advances in laser technologies, control hardware, and innovative experimental techniques. These systems offer unique advantages such as long coherence times, natural homogeneity, and scalability, while also presenting challenges related to gate speed limitations, atom loss, slow measurements, and other imperfections. Quantum control theory has emerged as a crucial tool for advancing these technologies by enabling precise manipulation of atoms. In this thesis, we review the foundational concepts in quantum control theory, outlining both analytical approaches and numerical optimization techniques, including methods to account for experimental imperfections. A concise overview of neutral atom platforms follows, covering two distinct operational regimes: Rydberg atoms in optical tweezers and fermionic atoms in optical superlattices. The core of the thesis is dedicated to our work addressing practical control problems in neutral atom systems. First, we develop a platform-independent method for estimating and compensating nonlinear pulse distortions in experimental setups and demonstrate its use numerically for Rydberg atom excitations. Next, we tackle the challenge of implementing fast and robust gates in fermionic atom systems trapped in superlattices by optimizing lattice depths. Finally, we explore the application of Rydberg-based analog quantum simulators for variational quantum eigensolvers, using Lie-algebraic tools to analyze symmetry restrictions. This work highlights the essential role of quantum control methods in enhancing the fidelity, robustness, and applicability of neutral atom quantum technologies. It also demonstrates how combining theoretical tools, numerical optimization, and experimental considerations leads to practical solutions for scalable and high-performance quantum systems. The methods and insights developed here also offer transferable strategies for other quantum hardware architectures.
Neutral atoms offer a promising platform for single- and many-body quantum control, as required for quantum information processing. This includes excellent isolation from the decohering influence of the environment, and the existence of well developed techniques for atom trapping and coherent manipulation. We present a review of our work to implement quantum control and measurement for ultra-cold atoms in far-off-resonance optical lattice traps. In recent experiments we have demonstrated coherent behavior of mesoscopic atomic spinor wavepackets in optical double-well potentials, and carried out quantum state tomography to reconstruct the full density matrix for the atomic spin degrees of freedom. This model system shares a number of important features with proposals to implement quantum logic and quantum computing in optical lattices. We present a theoretical analysis of a protocol for universal quantum logic via single qubit operations and an entangling gate based on electric dipole-dipole interactions. Detailed calculations including the full atomic hyperfine structure suggests that high-fidelity quantum gates are possible under realistic experimental conditions.
In quantum computers, the superposition of quantum states is used to perform calculations that are theoretically impossible or infeasible with classical computers, such as solving the traveling salesman problem for many nodes or conducting unstructured searches for large databases. Due to its scalable and flexible nature, neutral atoms trapped in optical tweezers are a promising technology for performing quantum computation. Here, qubit configurations are not static, allowing arbitrary geometries to be realized, and schemes where qubits are exchanged are readily available. The quantum level structure of neutral atoms is used to encode a qubit between two states, forming the basis for quantum computing. As the atoms are cooled to their electronic and motional ground states, transitions between qubit zero and qubit one can be driven with high fidelity. A multi-qubit gate is then realized when two or more atoms interact, e.g., by moving them close together, or by increasing their dipole radius when they are excited to a Rydberg state. Up to now, different qubits have been realized in neutral atoms, most notably ⁸⁷Rb, where the electronic ground state splits into two sublevels, which are used as encoding of a qubit. We describe progress on realizing a quantum computer based on ⁸⁸Sr. As a boson, its electronic ground state exhibits no hyperfine splitting, such that SPAM errors can be eliminated. The qubit is encoded in the ground state together with the highly studied, long-lived clock state, allowing for high-fidelity control of the transition. In this thesis, we present how the apparatus creates an ultra-high vacuum, as long-lived atoms are necessary for high-performance quantum algorithms. We show the main ideas behind the laser systems used for cooling, trapping, and driving the single-qubit transition. Our work demonstrates that coherently moving atoms is a feasible operation in quantum computing, allowing for the exchange of qubits, the shuttling of qubits to separate registers, or enabling additional phase gates. The results presented here establish ⁸⁸Sr as a viable candidate for quantum computing and lay the foundation for future fault-tolerant quantum systems.
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.\n\nIn 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.\n\nIn 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.