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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.

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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

Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This review broadly covers the phenomenon of Feshbach resonances in ultracold gases and their main applications. This includes the theoretical background and models for the description of Feshbach resonances, the experimental methods to find and characterize the resonances, a discussion of the main properties of resonances in various atomic species and mixed atomic species systems, and an overview of key experiments with atomic Bose-Einstein condensates, degenerate Fermi gases, and ultracold molecules.

Feshbach resonances in ultracold gases

Rydberg atoms with principal quantum number $n⪢1$ have exaggerated atomic properties including dipole-dipole interactions that scale as ${n}^{4}$ and radiative lifetimes that scale as ${n}^{3}$. It was proposed a decade ago to take advantage of these properties to implement quantum gates between neutral atom qubits. The availability of a strong long-range interaction that can be coherently turned on and off is an enabling resource for a wide range of quantum information tasks stretching far beyond the original gate proposal. Rydberg enabled capabilities include long-range two-qubit gates, collective encoding of multiqubit registers, implementation of robust light-atom quantum interfaces, and the potential for simulating quantum many-body physics. The advances of the last decade are reviewed, covering both theoretical and experimental aspects of Rydberg-mediated quantum information processing.

Quantum information with Rydberg atoms

In the atomic Bose-Einstein condensate, the interactions that bring a binary atom system to an intermediate state molecule in the Feshbach resonance create a second condensate component of molecules. The atomic and molecular condensates coherently exchange pairs of atoms. We discuss a signature of the coherent intercondensate exchange: Josephson-like oscillations of the atomic and molecular populations in response to a sudden change of the energy detuning. The dependence of the many-body ground state energy on volume suggests that the on-resonant ground state is a dilute condensate with the liquidlike property of a self-determined density. {copyright} {ital 1999} {ital The American Physical Society}

Rarified Liquid Properties of Hybrid Atomic-Molecular Bose-Einstein Condensates

We present results from two-photon photoassociative spectroscopy of the least-bound vibrational level of the $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ state of the $^{88}\mathrm{Sr}_{2}$ dimer. Measurement of the binding energy allows us to determine the $s$-wave scattering length ${a}_{88}=\ensuremath{-}1.4(6){a}_{0}$. For the intermediate state, we use a bound level on the metastable $^{1}S_{0}\text{\ensuremath{-}}^{3}P_{1}$ potential, which provides large Franck-Condon transition factors and narrow one-photon photoassociative lines that are advantageous for observing quantum-optical effects such as Autler-Townes resonance splittings.

/pdf/two-photon-photoassociative-spectroscopy-of-ultracold-sr-88-5503s3en8g.pdf

Two-photon photoassociative spectroscopy of ultracold Sr 88

Ultracold molecules offer a broad variety of applications, ranging from metrology to quantum computing. However, forming "real" ultracold molecules, i.e., in deeply bound levels, is a very difficult proposition. Here, we show how photoassociation in the vicinity of a Feshbach resonance enhances molecular formation rates by several orders of magnitude. We illustrate this effect in heteronuclear systems, and find giant rate coefficients even in deeply bound levels. We also give a simple analytical expression for the photoassociation rate and discuss future applications of the Feshbach-optimized photoassociation technique.

Giant Formation Rates of Ultracold Molecules via Feshbach-Optimized Photoassociation

Studies of charge mobilities in an ultracold gas are reported. Calculations for the $\mathrm{Na}+{\mathrm{Na}}^{+}$ system have been carried out as a function of temperature $T$ and densities, and the conductivity of the ultracold charged gas is obtained. The total charge mobility exhibits a sharp increase as $T$ is lowered, indicating a transition from an almost insulating to a conducting system at few $\ensuremath{\mu}$K. It is shown that the nature of the charge mobility changes with temperature: at high $T$, the charges are transported by massive centers (i.e., the ions), and at low $T$, by electrons jumping from neighboring atoms onto the positive ions (the positive holes exhibit hopping conductivity). An experiment is proposed to detect this effect.

From classical mobility to hopping conductivity: charge hopping in an ultracold gas.

New experiments were proposed recently to investigate the regime of cold atomic and molecular ion-atom collision processes in a special hybrid neutral-atom-ion trap under high-vacuum conditions. We study the collisional cooling of laser precooled Ca{sup +} ions by ultracold Na atoms. Modeling this process requires knowledge of the radiative lifetime of the excited singlet A {sup 1}{sigma}{sup +} state of the (NaCa){sup +} molecular system. We calculate the rate coefficient for radiative charge transfer using a semiclassical approach. The dipole radial matrix elements between the ground and the excited states, and the potential curves were calculated using complete active space self-consistent field and Moeller-Plesset second-order perturbation theory with an extended Gaussian basis, 6-311+G (3df). The semiclassical charge-transfer rate coefficient was averaged over a thermal Maxwellian distribution. In addition, we also present elastic collision cross sections and the spin-exchange cross section. The rate coefficient for charge transfer was found to be 2.3x10{sup -16} cm{sup 3}/sec, while those for the elastic and spin-exchange cross sections were found to be several orders of magnitude higher (1.1x10{sup -8} cm{sup 3}/sec and 2.3x10{sup -9} cm{sup 3}/sec, respectively). This confirms our assumption that the milli-Kelvin regime of collisional cooling of calcium ions by sodium atoms ismore » favorable with the respect to low loss of calcium ions due to the charge transfer.« less

Robin Côté

Papers

Rarified Liquid Properties of Hybrid Atomic-Molecular Bose-Einstein Condensates

Two-photon photoassociative spectroscopy of ultracold Sr 88

Giant Formation Rates of Ultracold Molecules via Feshbach-Optimized Photoassociation

From classical mobility to hopping conductivity: charge hopping in an ultracold gas.

Radiative charge-transfer lifetime of the excited state of ( NaCa ) +