Gaussian expansion method for few-body systems

This article reviews theoretical and experimental developments for one-dimensional Fermi gases. Specifically, the experimentally realized two-component delta-function interacting Fermi gas-the Gaudin-Yang model-and its generalizations to multicomponent Fermi systems with larger spin symmetries is discussed. The exact results obtained for Bethe ansatz integrable models of this kind enable the study of the nature and microscopic origin of a wide range of quantum many-body phenomena driven by spin population imbalance, dynamical interactions, and magnetic fields. This physics includes Bardeen-Cooper-Schrieffer-like pairing, Tomonaga-Luttinger liquids, spin-charge separation, Fulde-Ferrel-Larkin-Ovchinnikov-like pair correlations, quantum criticality and scaling, polarons, and the few-body physics of the trimer state (trions). The fascinating interplay between exactly solved models and experimental developments in one dimension promises to yield further insight into the exciting and fundamental physics of interacting Fermi systems.

Fermi gases in one dimension: From Bethe ansatz to experiments

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American Mathematical Monthly

Hybrid systems of laser-cooled trapped ions and ultracold atoms combined in a single experimental setup have recently emerged as a new platform for fundamental research in quantum physics. This paper reviews the theoretical and experimental progress in research on cold hybrid ion-atom systems which aim to combine the best features of the two well-established fields. A broad overview is provided of the theoretical description of ion-atom mixtures and their applications, and a report is given on advances in experiments with ions trapped in Paul or dipole traps overlapped with a cloud of cold atoms, and with ions directly produced in a Bose-Einstein condensate. This review begins with microscopic models describing the electronic structure, interactions, and collisional physics of ion-atom systems at low and ultralow temperatures, including radiative and nonradiative charge-transfer processes and their control with magnetically tunable Feshbach resonances. Then the relevant experimental techniques and the intrinsic properties of hybrid systems are described. In particular, the impact is discussed of the micromotion of ions in Paul traps on ion-atom hybrid systems. Next, a review of recent proposals is given for using ions immersed in ultracold gases for studying cold collisions, chemistry, many-body physics, quantum simulation, and quantum computation and their experimental realizations. The last part focuses on the formation of molecular ions via spontaneous radiative association, photoassociation, magnetoassociation, and sympathetic cooling. Applications and prospects are discussed of cold molecular ions for cold controlled chemistry and precision spectroscopy.

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Cold hybrid ion-atom systems

The goal of the present article is to review the major developments that have led to the current understanding of molecule-field interactions and experimental methods for manipulating molecules with electromagnetic fields. Molecule-field interactions are at the core of several, seemingly distinct, areas of molecular physics. This is reflected in the organization of this article, which includes sections on Field control of molecular beams, External field traps for cold molecules, Control of molecular orientation and molecular alignment, Manipulation of molecules by non-conservative forces, Ultracold molecules and ultracold chemistry, Controlled many-body phenomena, Entanglement of molecules and dipole arrays, and Stability of molecular systems in high-frequency super-intense laser fields. The article contains 853 references.

Manipulation of Molecules with Electromagnetic Fields

We report on the observation of confinement-induced resonances in strongly interacting quantum-gas systems with tunable interactions for one- and two-dimensional geometry. Atom-atom scattering is substantially modified when the s-wave scattering length approaches the length scale associated with the tight transversal confinement, leading to characteristic loss and heating signatures. Upon introducing an anisotropy for the transversal confinement we observe a splitting of the confinement-induced resonance. With increasing anisotropy additional resonances appear. In the limit of a two-dimensional system we find that one resonance persists.

Confinement-Induced Resonances in Low-Dimensional Quantum Systems

The time-dependent mesh method is proposed as an efficient tool for a quantitative analysis of the Coulomb breakup of halo nuclei. The approach allows a treatment of breakup reactions in the nonperturbative regime. It avoids any multipole expansion for the Coulomb interaction between the projectile and the target. Moreover, it permits using more general trajectories allowing an estimation of postacceleration effects. This numerical technique is applied to the ${}^{11}\mathrm{Be}{+}^{208}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{Pb}}}^{10}\mathrm{Be}{+n+}^{208}\mathrm{Pb}$ breakup reaction at 72 MeV per nucleon and is compared with experiment and with a previous calculation. Corrections due to the projectile deflection from a straight-line trajectory and to the neutron spin rotation are found to be weak for the specific collision parameters.

Nonperturbative time-dependent approach to breakup of halo nuclei

Atomic effects in the determination of nuclear cross sections of astrophysical interest

We demonstrate that scattering of particles strongly interacting in three dimensions (3D) can be suppressed at low energies in a quasi-one-dimensional (1D) confinement. The underlying mechanism is the interference of the s- and p-wave scattering contributions with large s- and p-wave 3D scattering lengths being a necessary prerequisite. This low-dimensional quantum scattering effect might be useful in 'interacting' quasi-1D ultracold atomic gases, guided atom interferometry, and impurity scattering in strongly confined quantum wire-based electronic devices.

http://arxiv.org/pdf/quant-ph/0610265.pdf

Vladimir S. Melezhik

Papers

Confinement-Induced Resonances in Low-Dimensional Quantum Systems

Nonperturbative time-dependent approach to breakup of halo nuclei

Atomic effects in the determination of nuclear cross sections of astrophysical interest

Suppression of Quantum Scattering in Strongly Confined Systems

Atlas of cross sections for scattering of muonic hydrogen atoms on hydrogen isotope molecules