A mesoscopic superposition of quantum states involving radiation fields with classically distinct phases was created and its progressive decoherence observed. The experiment involved Rydberg atoms interacting one at a time few photon coherent field trapped in high $Q$ microwave cavity. the equivalent an `` $\mathrm{atom}+\mathrm{measuring}\mathrm{apparatus}$'' system which ``meter'' pointing simultaneously towards two different directions---a ``Schr\"odinger cat.'' phenomenon transforming...

Quantum phase engineering is demonstrated with two techniques that allow the spatial distribution of a Bose-Einstein condensate (BEC) to be written and read out. A quantum state was designed produced by optically imprinting pattern onto BEC sodium atoms, matter-wave interferometry spatially resolved imaging used analyze resultant distribution. An appropriate imprint created solitons, first experimental realization this nonlinear phenomenon in BEC. The subsequent evolution these excitations...

We have observed the Rabi oscillation of circular Rydberg atoms in vacuum and small coherent fields stored a high Q cavity. The signal exhibits discrete Fourier components at frequencies proportional to square root successive integers. This provides direct evidence field quantization weights yield photon number distribution field. investigation excited levels atom-cavity system reveals nonlinear quantum features extremely low strengths.

Pairs of atoms have been prepared in an entangled state the Einstein-Podolsky-Rosen (EPR) type. They were produced by exchange a single photon between high $Q$ cavity. The atoms, superposition involving two different circular Rydberg states, separated distance order 1 cm. At variance with most previous EPR experiments, this one involves massive particles. It can be generalized to three or more and opens way new tests nonlocality mesoscopic quantum systems.

We have observed Bragg diffraction of a Bose-Einstein condensate sodium atoms by moving, periodic, optical potential. The coherent process produced splitting the with unidirectional momentum transfer. Using selectivity process, we separated component width narrower than that original condensate. By repeatedly pulsing potential while were trapped, trajectory split atomic wave packets in confining magnetic

The quantum information carried by a two-level atom was transferred to high- $Q$ cavity and, after delay, another atom. We realized in this way memory made of field superposition 0 and 1 photon Fock states. measured the ``holding time'' corresponding decay intensity or amplitude at single level. This experiment implements step essential for processing operations.

We analyze and experimentally demonstrate a new (temporal) Talbot effect, where pulsed phase grating is applied to cloud of cold atoms (Bose-Einstein condensate). In contrast the usual (spatial) our gain kinetic energy when diffracted by grating. The matter-wave-dispersion relation result in an exact (no paraxial approximation) effect initial wave front reconstructed at multiples ``Talbot time'' ${T}_{\mathrm{T}}$. applying second after variable delay. When this even (odd)...

We present experimental and theoretical studies of the coherence properties a Bose-Einstein condensate (BEC) using an interference technique. Two optical standing wave pulses duration 100 ns separation $\ensuremath{\Delta}t$ are applied to condensate. Each phase grating makes small copies displaced in momentum space. The quantum mechanical amplitudes each copy interfere, depending on spatial variations across find that behavior trapped BEC is consistent with uniform phase. A released BEC,...

Phase-coherent matter-wave amplification was demonstrated using Bose- Einstein–condensed rubidium-87 atoms. A small seed matter wave created with coherent optical Bragg diffraction. Amplification of this achieved by the initial condensate as a gain medium through superradiance effect. The coherence properties amplified wave, studied interferometer, were shown to be locked those wave. active device here has great potential in fields atom optics, lithography, and precision measurements.

We propose a scheme to achieve multiparty entanglement with perfectly efficient, ultraslow, multichannel pairwise four-wave mixing (FWM). A cold atomic medium is illuminated an $N$-mode continuous-wave (cw) control laser produce coherent mixtures of excited states. An ultraslowly propagating, single-photon quantum probe field completes multichannel, FWM, creating depth dependent $N$ Fock show explicitly that this can be utilized realize $N$-party entangled state propagating quantized fields....

We show that by strongly modifying the dispersion properties of a four-level system, non-existing wave mixing channels can be opened and significantly enhanced. Specifically, we coherent optical four-wave with pump mediated electromagnetically induced transparency (thereby propagating an extremely slow group velocity) will lead to many orders magnitude enhancement in amplitude generated wave. Contrary common belief, large window, which causes propagation velocity, actually diminishes...

We construct a Mach-Zehnder interferometer using Bose-Einstein condensed rubidium atoms and optical Bragg diffraction. In contrast to interferometers based on normal diffraction, where only small percentage of the contribute signal, our diffraction uses all condensate atoms. The coherence properties high phase-space density result in an interference pattern nearly 100% contrast. two arms may be completely separated space, making it ideal tool that can used detect vortices or other topological phases.

We have demonstrated the exchange of sifted quantum cryptographic key over a 730 meter free-space link at rates up to 1.0 Mbps, two orders magnitude faster than previously reported results. A classical channel 1550 nm operates in parallel with 845 nm. Clock recovery techniques on 1.25 Gbps enable transmission clock rate. System performance is currently limited by timing resolution our silicon avalanche photodiode detectors. With improved detector resolution, technique will yield another...

We demonstrate a spatially resolved autocorrelation measurement with Bose-Einstein condensate and measure the evolution of spatial profile its quantum mechanical phase. Upon release from magnetic trap, phase develops form that we to be quadratic in coordinate. Our experiments also reveal effects repulsive interaction between two overlapping wave packets small momentum they impart each other.

The 2${\mathit{S}}_{1/2\mathrm{\ensuremath{-}}}$2${\mathit{P}}_{3/2}$ interval in hydrogen has been measured using a fast atomic beam and separated oscillatory field technique at energy of 96.5 keV standard X-band waveguides as interaction regions. experimental value for the fine structure is 9911.200(12) MHz. This implies Lamb shift 1057.839(12) MHz, fair agreement with theoretical 1057.866(5) MHz that was calculated smaller two discrepant values proton radius literature.

We analyze a lifetime-broadened four-state four-wave-mixing (FWM) scheme in the ultraslow propagation regime and show that generated FWM field can acquire same group velocity pulse shape as those of an pump field. new type induced transparency resulted from multiphoton destructive interference significantly reduced loss. Such based on multphoton may have important applications other nonlinear optical processes.

We investigate an efficient scheme for generating ultraviolet single-photons $(\ensuremath{\sim}300\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$. The combines the highly single-photon four-wave mixing and fast developing quantum dot on demand source technology. show that near maximum, entanglement between two well matched ultraslowly propagating wave packets can be achieved. This study may lead to research development opportunities in schemes using photons of very large frequency difference,...

Propagation of a light pulse through high-Q optical microcavity containing few cold atoms (N<10) in its cavity mode is investigated experimentally. With less than ten rubidium launched into an microcavity, up to 170 ns propagation lead time ("superluminal"), and 440 delay (subluminal) are observed. Comparison the experimental data with numerical simulations as well future experiments discussed.

We demonstrate a fast Kerr phase gate in room-temperature (85)Rb vapor using Raman gain method where the probe wave travels "superluminally". Continuously variable, zero to π radian nonlinear shifts of relative reference have been observed at 333 K. show rapid manipulation digitally encoded waves phase-control light field, demonstrating capability system information science and telecommunication applications.

We investigate the simultaneous formation and stable propagation of ultraslow optical soliton pairs in a lifetime broadened four-state atomic system under double-Lambda excitation with large one- two-photon detunings. show that detrimental probe field distortions due to strong dispersion effects weak driving conditions can be well balanced by self- cross-phase modulation effects, leading pair temporal, group velocity, amplitude matched solitons different frequencies.

Exotic nonlinear optical single-crystal microstructures have unique guided-wave and efficient frequency-doubling properties.

We report on experimental investigation of optical-pulse group-velocity reduction and probe-pulse ``regeneration'' using a Raman scheme. This scheme, which does not rely the commonly used on-one-photon-resonance electromagnetically induced transparency (EIT) process, has many advantages over conventional method that critically relies window created by an EIT process. demonstrate significant group velocity, less probe-field loss, reduced distortion, high regeneration efficiency.

We demonstrate matter-wave self-imaging resulting from atomic center-of-mass motion-based interference. show that non-negligible motion and an instantaneous Doppler shift can drastically change the condensate momentum distribution, in a periodic collapse recurrence of diffraction probability as function stationary light-field pulsing time. The observed is characterized by induced population amplitude interference presence light field simultaneously minimizes all high (n>or=1) orders...

We present a small-signal wave propagation theory on matter-wave superradiant scattering. show, in longitudinally excited condensate, that the backward-propagating, superradiantly generated optical field propagates with ultraslow group velocity and gain profile has Bragg resonance. further show unidirectional suppression of scattering, explain why superradiance can occur only when pump laser is red detuned. This first analytical all experiments to date used single-frequency, long-pulse,...