Quantum information processing with trapped ions

Experiments directed towards the development of a quantum computer based on trapped atomic ions are described briefly. We discuss the implementation of single qubit operations and gates between qubits. A geometric phase gate between two ion qubits is described. Limitations of the trapped-ion method such as those caused by Stark shifts and spontaneous emission are addressed. Finally, we describe a strategy to realize a large-scale device.Comment: Article submitted by D. J. Wineland ([email protected]) for proceeding of the Discussion Meeting on Practical Realisations of Quantum Information Processing, held at the Royal Society, Nov. 13,14, 200

Experimental demonstration of a technique to generate arbitrary quantum superposition states

Using a single, harmonically trapped $^9$Be$^+$ ion, we experimentally demonstrate a technique for generation of arbitrary states of a two-level particle confined by a harmonic potential. Rather than engineering a single Hamiltonian that evolves the system to a desired final sate, we implement a technique that applies a sequence of simple operations to synthesize the state

Resonant control of elastic collisions in an optically trapped Fermi gas of atoms

We have loaded an ultracold gas of fermionic atoms into a far off resonance optical dipole trap and precisely controlled the spin composition of the trapped gas. We have measured a magnetic-field Feshbach resonance between atoms in the two lowest energy spin-states, |9/2, -9/2> and |9/2, -7/2>. The resonance peaks at a magnetic field of 201.5 plus or minus 1.4 G and has a width of 8.0 plus or minus 1.1 G. Using this resonance we have changed the elastic collision cross section in the gas by nearly 3 orders of magnitude.Comment: 4 pages, 3 figure

Pauli Blocking of Collisions in a Quantum Degenerate Atomic Fermi Gas

We have produced an interacting quantum degenerate Fermi gas of atoms composed of two spin-states of magnetically trapped $^{40}$K. The relative Fermi energies are adjusted by controlling the population in each spin-state. Measurements of the thermodynamics reveal the resulting imbalance in the mean energy per particle between the two species, which is as large as a factor of 1.4 at our lowest temperature. This imbalance of energy comes from a suppression of collisions between atoms in the gas due to the Pauli exclusion principle. Through measurements of the thermal relaxation rate we have directly observed this Pauli blocking as a factor of two reduction in the effective collision cross-section in the quantum degenerate regime.Comment: 11 pages, 4 figure

Observation of p-wave Threshold Law Using Evaporatively Cooled Fermionic Atoms

We have measured independently both s-wave and p-wave cross-dimensional thermalization rates for ultracold potassium-40 atoms held in a magnetic trap. These measurements reveal that this fermionic isotope has a large positive s-wave triplet scattering length in addition to a low temperature p-wave shape resonance. We have observed directly the p-wave threshold law which, combined with the Fermi statistics, dramatically suppresses elastic collision rates at low temperatures. In addition, we present initial evaporative cooling results that make possible these collision measurements and are a precursor to achieving quantum degeneracy in this neutral, low-density Fermi system.Comment: 5 pages, 3 figures, 1 tabl

Luttinger model approach to interacting one-dimensional fermions in a harmonic trap

A model of interacting one--dimensional fermions confined to a harmonic trap is proposed. The model is treated analytically to all orders of the coupling constant by a method analogous to that used for the Luttinger model. As a first application, the particle density is evaluated and the behavior of Friedel oscillations under the influence of interactions is studied. It is found that attractive interactions tend to suppress the Friedel oscillations while strong repulsive interactions enhance the Friedel oscillations significantly. The momentum distribution function and the relation of the model interaction to realistic pair interactions are also discussed.Comment: 12 pages latex, 1 eps-figure in 1 tar file, extended Appendix, added and corrected references, new eq. (53), corrected typos, accepted for PR

Cooper Pairing in Ultracold K-40 Using Feshbach Resonances

We point out that the fermionic isotope K-40 is a likely candidate for the formation of Cooper pairs in an ultracold atomic gas. Specifically, in an optical trap that simultaneously traps the spin states |9/2,-9/2> and |9/2,-7/2>, there exists a broad magnetic field Feshbach resonance at B = 196 gauss that can provide the required strong attractive interaction between atoms. An additional resonance, at B = 191 gauss, could generate p-wave pairing between identical |9/2,-7/2> atoms. A Cooper-paired degenerate Fermi gas could thus be constructed with existing ultracold atom technology.Comment: 4 pages, 2 figs, submitted to Phys. Rev.

Rapid sympathetic cooling to Fermi degeneracy on a chip

Neutral fermions present new opportunities for testing many-body condensed matter systems, realizing precision atom interferometry, producing ultra-cold molecules, and investigating fundamental forces. However, since their first observation, quantum degenerate Fermi gases (DFGs) have continued to be challenging to produce, and have been realized in only a handful of laboratories. In this Letter, we report the production of a DFG using a simple apparatus based on a microfabricated magnetic trap. Similar approaches applied to Bose-Einstein Condensation (BEC) of 87Rb have accelerated evaporative cooling and eliminated the need for multiple vacuum chambers. We demonstrate sympathetic cooling for the first time in a microtrap, and cool 40K to Fermi degeneracy in just six seconds -- faster than has been possible in conventional magnetic traps. To understand our sympathetic cooling trajectory, we measure the temperature dependence of the 40K-87Rb cross-section and observe its Ramsauer-Townsend reduction.Comment: 5 pages, 4 figures (v3: new collision data, improved atom number calibration, revised text, improved figures.