Bound on quantum computation time: Quantum error correction in a critical environment

We obtain an upper bound on the time available for quantum computation for a given quantum computer and decohering environment with quantum error correction implemented. First, we derive an explicit quantum evolution operator for the logical qubits and show that it has the same form as that for the physical qubits but with a reduced coupling strength to the environment. Using this evolution operator, we find the trace distance between the real and ideal states of the logical qubits in two cases. For a super-Ohmic bath, the trace distance saturates, while for Ohmic or sub-Ohmic baths, there is a finite time before the trace distance exceeds a value set by the user. © 2010 The American Physical Society.

Universal quantum viscosity in a unitary Fermi gas.

A Fermi gas of atoms with resonant interactions is predicted to obey universal hydrodynamics, in which the shear viscosity and other transport coefficients are universal functions of the density and temperature. At low temperatures, the viscosity has a universal quantum scale ħ n, where n is the density and ħ is Planck's constant h divided by 2π, whereas at high temperatures the natural scale is p(T)(3)/ħ(2), where p(T) is the thermal momentum. We used breathing mode damping to measure the shear viscosity at low temperature. At high temperature T, we used anisotropic expansion of the cloud to find the viscosity, which exhibits precise T(3/2) scaling. In both experiments, universal hydrodynamic equations including friction and heating were used to extract the viscosity. We estimate the ratio of the shear viscosity to the entropy density and compare it with that of a perfect fluid.

Multimode Atomic Pattern Formation via Enhanced Light-atom Interactions

The nonlinear interaction between light and atoms is an extensive field of study with a broad range of applications in quantum information science and condensed matter physics. Nonlinear optical phenomena occurring in cold atoms are particularly interesting because such slowly moving atoms can spatially organize into density gratings, which allows for studies involving optical interactions with structured materials. In this thesis, I describe a novel nonlinear optical effect that arises when cold atoms spatially bunch in an optical lattice. I show that employing this spatial atomic bunching provides access to a unique physical regime with reduced thresholds for nonlinear optical processes and enhanced material properties. Using this method, I observe the nonlinear optical phenomenon of transverse optical pattern formation at record-low powers. These transverse optical patterns are generated by a wave- mixing process that is mediated by the cold atomic vapor. The optical patterns are highly multimode and induce rich non-equilibrium atomic dynamics. In particular, I find that there exists a synergistic interplay between the generated optical pat- terns and the atoms, wherein the scattered fields help the atoms to self-organize into new, multimode structures that are not externally imposed on the atomic sample. These self-organized structures in turn enhance the power in the optical patterns. I provide the first detailed investigation of the motional dynamics of atoms that have self-organized in a multimode geometry. I also show that the transverse optical patterns induce Sisyphus cooling in all three spatial dimensions, which is the first observation of spontaneous three-dimensional cooling. My experiment represents a unique means by which to study nonlinear optics and non-equilibrium dynamics at ultra-low required powers.

Micro-Fabricated Surface Trap and Cavity Integration for Trapped Ion Quantum Computing

Atomic ions trapped in micro-fabricated surface traps can be utilized as a physical platform with which to build a quantum computer. They possess many of the desirable qualities of such a device, including high fidelity state preparation and readout, universal logic gates, long coherence times, and can be readily entangled with each other through photonic interconnects. The use of optical cavities integrated with trapped ion qubits as a photonic interface presents the possibility for order of magnitude improvements in performance in several key areas of their use in quantum computation. The first part of this thesis describes the design and fabrication of a novel surface trap for integration with an optical cavity. The trap is custom made on a highly reflective mirror surface and includes the capability of moving the ion trap location along all three trap axes with nanometer scale precision. The second part of this thesis demonstrates the suitability of small micro-cavities formed from laser ablated fused silica substrates with radii of curvature in the 300-500 micron range for use with the mirror trap as part of an integrated ion trap cavity system. Quantum computing applications for such a system include dramatic improvements in the photonic entanglement rate up to 10 kHz, the qubit measurement time down to 1 microsecond, and the measurement error rates down to the 10e-5 range. The final part of this thesis details a performance simulator for exploring the physical resource requirements and performance demands to scale such a quantum computer to sizes capable of performing quantum algorithms beyond the limits of classical computation.