Quantum networks provide opportunities and challenges across a range of intellectual and technical frontiers, including quantum computation, communication and metrology. The realization of quantum networks composed of many nodes and channels requires new scientific capabilities for generating and characterizing quantum coherence and entanglement. Fundamental to this endeavour are quantum interconnects, which convert quantum states from one physical system to those of another in a reversible manner. Such quantum connectivity in networks can be achieved by the optical interactions of single photons and atoms, allowing the distribution of entanglement across the network and the teleportation of quantum states between nodes.

The quantum internet

The phenomenon of Bose-Einstein condensation of dilute gases in traps is reviewed from a theoretical perspective. Mean-field theory provides a framework to understand the main features of the condensation and the role of interactions between particles. Various properties of these systems are discussed, including the density profiles and the energy of the ground-state configurations, the collective oscillations and the dynamics of the expansion, the condensate fraction and the thermodynamic functions. The thermodynamic limit exhibits a scaling behavior in the relevant length and energy scales. Despite the dilute nature of the gases, interactions profoundly modify the static as well as the dynamic properties of the system; the predictions of mean-field theory are in excellent agreement with available experimental results. Effects of superfluidity including the existence of quantized vortices and the reduction of the moment of inertia are discussed, as well as the consequences of coherence such as the Josephson effect and interference phenomena. The review also assesses the accuracy and limitations of the mean-field approach.

https://arxiv.org/pdf/cond-mat/9806038.pdf

Theory of Bose-Einstein condensation in trapped gases

Coherent preparation by laser light of quantum states of atoms and molecules can lead to quantum interference in the amplitudes of optical transitions. In this way the optical properties of a medium can be dramatically modified, leading to electromagnetically induced transparency and related effects, which have placed gas-phase systems at the center of recent advances in the development of media with radically new optical properties. This article reviews these advances and the new possibilities they offer for nonlinear optics and quantum information science. As a basis for the theory of electromagnetically induced transparency the authors consider the atomic dynamics and the optical response of the medium to a continuous-wave laser. They then discuss pulse propagation and the adiabatic evolution of field-coupled states and show how coherently prepared media can be used to improve frequency conversion in nonlinear optical mixing experiments. The extension of these concepts to very weak optical fields in the few-photon limit is then examined. The review concludes with a discussion of future prospects and potential new applications.

/pdf/electromagnetically-induced-transparency-optics-in-coherent-2dhges92td.pdf

Electromagnetically induced transparency : Optics in coherent media

Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

Techniques that use quantum interference effects are being actively investigated to manipulate the optical properties of quantum systems1. One such example is electromagnetically induced transparency, a quantum effect that permits the propagation of light pulses through an otherwise opaque medium2,3,4,5. Here we report an experimental demonstration of electromagnetically induced transparency in an ultracold gas of sodium atoms, in which the optical pulses propagate at twenty million times slower than the speed of light in a vacuum. The gas is cooled to nanokelvin temperatures by laser and evaporative cooling6,7,8,9,10. The quantum interference controlling the optical properties of the medium is set up by a ‘coupling’ laser beam propagating at a right angle to the pulsed ‘probe’ beam. At nanokelvin temperatures, the variation of refractive index with probe frequency can be made very steep. In conjunction with the high atomic density, this results in the exceptionally low light speeds observed. By cooling the cloud below the transition temperature for Bose–Einstein condensation11,12,13 (causing a macroscopic population of alkali atoms in the quantum ground state of the confining potential), we observe even lower pulse propagation velocities (17?m?s−1) owing to the increased atom density. We report an inferred nonlinear refractive index of 0.18?cm2?W−1 and find that the system shows exceptionally large optical nonlinearities, which are of potential fundamental and technological interest for quantum optics.

/pdf/light-speed-reduction-to-17-metres-per-second-in-an-5echiu51el.pdf

Light speed reduction to 17 metres per second in an ultracold atomic gas

Electromagnetically induced transparency1,2,3 is a quantum interference effect that permits the propagation of light through an otherwise opaque atomic medium; a ‘coupling’ laser is used to create the interference necessary to allow the transmission of resonant pulses from a ‘probe’ laser. This technique has been used4,5,6 to slow and spatially compress light pulses by seven orders of magnitude, resulting in their complete localization and containment within an atomic cloud4. Here we use electromagnetically induced transparency to bring laser pulses to a complete stop in a magnetically trapped, cold cloud of sodium atoms. Within the spatially localized pulse region, the atoms are in a superposition state determined by the amplitudes and phases of the coupling and probe laser fields. Upon sudden turn-off of the coupling laser, the compressed probe pulse is effectively stopped; coherent information initially contained in the laser fields is ‘frozen’ in the atomic medium for up to 1 ms. The coupling laser is turned back on at a later time and the probe pulse is regenerated: the stored coherence is read out and transferred back into the radiation field. We present a theoretical model that reveals that the system is self-adjusting to minimize dissipative loss during the ‘read’ and ‘write’ operations. We anticipate applications of this phenomenon for quantum information processing.

Observation of coherent optical information storage in an atomic medium using halted light pulses

We present quantitative measurements of the spatial density profile of Bose-Einstein condensates of sodium atoms confined in a 4-Dee magnetic bottle. The condensates are imaged in transmission with near-resonant laser light. We demonstrate that the Thomas-Fermi surface of a condensate can be determined to better than 1%. More generally, we obtain excellent agreement with mean-field theory. We conclude that precision measurements of atomic scattering lengths and interactions between phase-separated cold atoms in a harmonic trap can be performed with high precision using this method. @S1050-2947~98!51707-6# PACS number~s!: 03.75.Fi Recently Bose-Einstein condensates ~BECs! have been created from dilute, ultracold atomic clouds of Rb, Li, and Na @1‐5# through a combination of laser @6# and evaporative cooling @7#. Evidence for condensation in Refs. @1# and @3‐5# rely on time-of-flight measurements on atomic clouds after release from the magnetic traps in which they are initially confined; valuable information on condensate dynamics has been obtained from studying such release data @8#. Alternatively, it is possible to probe confined condensates directly without the transformations associated with release processes. This has been done with dark-field and phase-contrast imaging @9‐11#. In this Rapid Communication, we describe such a capability obtained with near-resonant absorption imaging in a BEC setup based on a 4-Dee magnetic bottle in which we routinely create multimillion atom condensates of sodium atoms. The name ‘‘4-Dee’’ stems from the fact that the shape of each of the four coils needed to create the confining field for spin aligned atoms resembles the letter‘‘D.’’ Figure 1~b! shows the configuration of these coils. We present quantitative in situ spatial images of the condensate surface region and perform detailed comparisons of density profile measurements on pure condensates ~no visible noncondensate component! to ground-state mean-field calculations. These condensates, confined in a harmonic trap and with large numbers of atoms ~Thomas-Fermi limit @12#!, have sharply defined boundaries that can be determined with high precision with near-resonant imaging. Combined with an in

/pdf/near-resonant-spatial-images-of-confined-bose-einstein-2gxsfzibr6.pdf

Near-Resonant Spatial Images of Confined Bose-Einstein Condensates in a 4-Dee Magnetic Bottle

High coverage phases of Pb on the Si(111) surface: structures and phase transitions

X-ray bound states trapped on a curved surface are realized by coupling subangstrom photons at grazing angles into a bent silicon wafer with adjustable radius. At small radii of curvature the usual ray approximation breaks down and new phenomena associated with wave optical behavior of x-ray surface eigenmodes are revealed. For such samples, tunneling is shown to extinguish all but the ground state surface eigenmode, whose presence may be detected after extremely long distances of propagation along the surface.

/pdf/surface-trapped-x-rays-whispering-gallery-modes-at-l-0-7-a-420zn9gauz.pdf

Chien Liu

Papers

Observation of coherent optical information storage in an atomic medium using halted light pulses

Near-Resonant Spatial Images of Confined Bose-Einstein Condensates in a 4-Dee Magnetic Bottle

High coverage phases of Pb on the Si(111) surface: structures and phase transitions

Surface Trapped X Rays: Whispering-Gallery Modes at λ = 0.7 Å

Soft incommensurate reconstruction on Pb/Si(111): Structure, stress modulation, and phase transition