Tycho Sleator

Elementary gates for quantum computation.

We show that a set of gates that consists of all one-bit quantum gates (U(2)) and the two-bit exclusive-or gate (that maps Boolean values (x,y) to (x,x ⊕y)) is universal in the sense that all unitary operations on arbitrarily many bits n (U(2 n )) can be expressed as compositions of these gates. We investigate the number of the above gates required to implement other gates, such as generalized Deutsch-Toffoli gates, that apply a specific U(2) transformation to one input bit if and only if the logical AND of all remaining input bits is satisfied. These gates play a central role in many proposed constructions of quantum computational networks. We derive upper and lower bounds on the exact number of elementary gates required to build up a variety of two- and three-bit quantum gates, the asymptotic number required for n-bit Deutsch-Toffoli gates, and make some observations about the number required for arbitrary n-bit unitary operations.

Imaging and focusing of an atomic beam with a large period standing light wave

A novel atomic lens scheme is reported. A cylindrical lens potential was created by a large period (⋍ 45 μm) standing light wave perpendicular to a beam of metastable He atoms. The lens aperture (25 μm) was centered in one antinode of the standing wave; the laser frequency was nearly resonant with the atomic transition 23S1−23P2 (λ=1.083 μm) and the interaction time was significantly shorter than the spontaneous lifetime (100 ns) of the excited state. The thickness of the lens was given by the laser beam waist (40 μm) in the direction of the atomic beam. Preliminary results are presented, where an atomic beam is focused down to a spot size of 4 μm. Also, a microfabricated grating with a period of 8 μm was imaged. We discuss the principle limitations of the spatial resolution of the lens given by spherical and chromatic aberrations as well as by diffraction. The fact that this lens is very thin offers new perspectives for deep focusing into the nm range.

Optical Nutation in Cold 85Rb Atoms

We have observed optical nutation in cold 85Rb atoms with a negligible Doppler broadening. The optical nutation of a two-level atom arranged by optical pumping has been studied as a function of detuning frequency and Rabi frequency. The change of the nutation signal caused by magnetic substate degeneracy has also been observed for σ and π excitations. This can be explained by optical nutation beatings from different transition probabilities among magnetic sublevels. Absolute transition probabilities with σ and π transitions and a branching ratio between them have been measured.

Lattice Interferometer for Laser-Cooled Atoms

We demonstrate an atom interferometer in which atoms are laser cooled into a 1D optical lattice, suddenly released, and later subjected to a pulsed optical lattice. For short pulses, a simple analytical theory predicts the signal. We investigate both short and longer pulses where the analytical theory fails. Longer pulses yield higher precision and larger signals, and we observe a coherent signal at times that can differ significantly from the expected echo time. The interferometer has potential for precision measurements of variant Plancks/m(A), and can probe the dynamics of atoms in an optical lattice.

Optical free induction decay in cold 85Rb atoms

We have observed optical free induction decay (FID) in cold 85Rb atoms. The shortening of the FID lifetime with increasing optical depth of the trap has been found. This shortening is explained by an anomalous absorption for FID propagating in a homogeneous and resonant sample. Theoretical calculations are consistent with experimental results. The Rabi oscillations of FID amplitude have been observed by increasing the pulse area.

Atom interference in pulsed standing-wave fields

We have studied suboptical wavelength atomic gratings, generated by the interference of atomic de Broglie waves in a time-domain interferometer. Three short optical standing- wave pulses, detuned from resonance with a cloud of approximately 100 (mu) K85 Rb atoms, act as phase gratings for atomic matter waves. The first two standing- wave pulses, separated by time T, produce a sequence of atomic density gratings of periods

Collisional revival of magnetic grating free-induction decay

lamda/4 at time 1.5T after the first pulse. The dependence of our signals on the time separation of the pulses is in good agreement with our theoretical predictions. As far as we know, this is the first time when the formation of a high order matter-wave diffraction grating was observed in real time. This demonstrated ability to produce sub-wavelength structures makes our techniques applicable to atomic beam lithography.

Sub-optical wavelength spatial imaging of the periodic fringes of total atomic density

Summary form only given. A ground-state coherence grating involving the magnetic sublevels of the F=3 ground state in /sup 85/Rb is created in Doppler-broadened vapor using an excitation pulse that consists of two traveling waves with orthogonally polarized wave vectors. The decay of the grating that is due to thermal motion is probed by a traveling-wave readout pulse. This results in a scattered signal magnetic grating free-induction decay (MGFID) that is detected using a heterodyne technique. In our experiment, collisional revival can be expected when the mean free path is less than the grating spacing.

Phase-space imaging of trapped atoms using magnetic sublevel coherence

Fringes of total atomic density produced in an atom interferometer consisting of two off-resonant standing wave pulses were directly imaged using an ldquooptical maskrdquo technique. Fringe periods with integer fractions of the standing-wave period were observed.

Realizable Universal Quantum Logic Gates

Experimental results on phase-space imaging of a laser- cooled atomic cloud are presented. Both position and velocity information are encoded in the frequency of the signal coherently radiated from the cloud. This encoding is achieved by application of a position-dependent magnetic field. Fourier transformation of the signal yields a projection of the phase-space density of the atoms. Since the projection direction is determined by the imposed field gradient, we can reconstruct the phase-space structure of the cloud and trace its time evolution.