This NSF award will support the development of general methods to control and measure physical systems whose behavior is governed by quantum mechanics. As a concrete physical testbed the project will use cold atoms and optical lattices (spatially periodic potential wells formed by interfering laser beams used to trap cold atoms). This system provides access to a broad range of quantum phenomena, and is considered one of the leading platforms for quantum information science such as quantum computation. The immediate goal is to develop robust and flexible control tools to manipulate quantum information encoded in finite sets of atomic ground states (qudits). By correlating the state of an atom with its position in an optical lattice, it becomes possible to control the quantum mechanical motion of atoms on a grid. Simultaneous quantum control of the internal and motional quantum states of atoms will be essential if the atom-lattice system is to be used for quantum computation and quantum simulation of condensed-matter physics, both of which are grand challenges pursued by research groups across the world.
When physical devices are used to perform real world tasks, the process can be understood abstractly in terms of a system moving through a sequence of configurations (states) in response to external commands (controls). In practice, control of the device must be accurate and reliable even in the presence of errors and imperfections. This is a non-trivial challenge even for systems governed by classical mechanics, and has historically given rise to an entire engineering discipline known as Control Science. Modern advances in nanoscience is pushing technology into the quantum realm, and an analogous new field of Quantum Control must therefore be established. This NSF award will contribute substantially to the knowledge base of Quantum Control and Quantum Information Science. Notably, the tools and techniques developed for the cold atoms and optical lattice platform will be broadly applicable because a single set of mathematical principles underlie the design of controls for any quantum system, be it atomic, molecular, optical or condensed matter. All aspects of the research will involve graduate students, and will occur within the framework of the Center for Quantum Information and Control (CQuIC), a newly established joint venture involving principal investigators at the University of New Mexico and the University of Arizona. The award will thus contribute to the training of future scientists and researchers in Quantum Control and Quantum Information Science.
Quantum computing, quantum simulation, and other types of quantum information processing (QIP) are, at the most fundamental level, based on quantum control and measurement of complex quantum systems. Physical implementation of QIP is now explored on a variety of physical platforms, and though technical details differ greatly, it is becoming clear that the underlying ideas, concepts and protocols for control and measurement are largely system independent. As a result, many of the tools developed on one platform can be applied to another. Perhaps the best example is nuclear magnetic resonance (NMR) spectroscopy in molecular physics, which has been the primary platform for the development of composite pulses and other tools for robust control that are now applied to many types of physical qubits. The principal goal of this project has been to replicate this success by developing analogous tools for quantum systems that go beyond qubits. The first part of the project focused on quantum control and quantum tomography in the 16-dimensional state space formed by the hyperfine structure of the electronic ground state in atomic Cesium. By driving this atomic system entirely with radio frequency (rf) and microwave (µw) magnetic fields, accurate control of its time evolution was implemented in a manner that allows universal control, without the detrimental effects of light scattering that plagues approaches that rely on lasers. Optimal control and computer optimized phase modulation techniques were used to show that one arbitrarily chosen quantum state can be transformed into another with a fidelity (probability of success) well in excess of 99%. This represents an improvement over current state of the art by a factor 5-10. Accurate measurements of such high fidelities were enabled by a novel benchmarking protocol that is itself a valuable addition to the general toolbox for QIP. New techniques for quantum state tomography were developed and tested, based on time-continuous spectroscopic measurement of the atomic spin while driving the system in a known manner with rf and µw fields. The resulting measurement record was used to estimate the initial unknown quantum state, using both standard analysis and a novel algorithm based on compressed sensing. Surprisingly, both approaches were able to reconstruct nearly-pure quantum states from far less measurement data than one would naively expect. This experiment has opened the door for further use of advanced compressed-sensing type algorithms that may greatly reduce the experimental challenge posed by quantum tomography. The second part of the project focused on quantum control of atomic qubits trapped in optical lattices (arrays of microtraps formed by interfering laser beams). The atom/lattice system lends itself naturally to quantum simulation of many body physics, and provides one possible path towards a scalable quantum computer. The power of such schemes, however, is greatly enhanced when atoms at individual lattice sites can be accessed for measurement and control. This project developed a technique similar to magnetic resonance imaging (MRI), based on microwave pulses and frequency shifts in laser fields, to image atoms in an optical lattice with a resolution of ~50nm, far below the resolving power of any optical microscope. This same technique was used to perform either spin flips or complete quantum gates on target atoms, with no significant cross talk to atoms at neighboring lattice sites 500nm away. By adapting NMR techniques for inhomogeneous control, these quantum gates were made highly robust to small but unavoidable misalignment between the targeted atoms and the laser field used to address them. As a result, gate fidelities of ~95% were achieved with virtually no cross talk between sites. Other work on the atom/lattice system included theoretical and experimental studies of microwave driven quantum motion of atoms in optical lattices. Significant results from the project were disseminated through peer reviewed publications and presentations at scientific conferences and workshops, thus contributing to the knowledge base and technology toolbox available to the QIP community. Three UA graduate students directly involved with the research received PhD degrees, and two are now postdocs at NSF Physics Frontiers Centers and the third has a permanent R&D position at HRL Laboratories. The project served as a cornerstone for the NSF-funded Center for Quantum Information and Control (CQuIC), thereby contributing to the education and training of a much larger group of PhD students and postdocs at the University of Arizona and the University of New Mexico.
