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arXiv:1412.8094 · Annual review of cold atoms and molecules

FEW-BODY PHYSICS OF ULTRACOLD ATOMS AND MOLECULES WITH LONG-RANGE INTERACTIONS

Yujun Wang, Paul S. Julienne, Chris H. Greene

Published Mar 24, 2015• 12 citations
arXivHTMLPDF

Abstract

The quantum mechanical few-body problem at ultracold energies poses severe challenges to theoretical techniques, particularly when long-range interactions are present that decay only as a power-law potential. In this paper we review the techniques and progress in studies of universal few-body physics for ultracold atoms, particularly those related to long-range interactions.

DOI
10.1142/9789814667746_0002

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The quantum mechanical few-body problem at ultracold energies poses severe challenges to theoretical techniques, particularly when long-range interactions are present that decay only as a power-law potential. In this paper we review the techniques and progress in studies of universal few-body physics for ultracold atoms, particularly those related to long-range interactions.
A universal characterization of interactions in few- and many-body quantum systems is often possible without detailed description of the interaction potential, and has become a defacto assumption for cold atom research. Universality in this context is defined as the validity to fully characterize the system in terms of two-body scattering length. We discuss universality in the following three contexts: closed-channel dominated Feshbach resonance, Efimov physics near Feshbach resonances, and corrections to the mean field energy of Bose-Einstein condensates with large scattering lengths. Novel experimental tools and strategies are discussed to study universality in ultracold atomic gases: dynamic control of interactions, run-away evaporative cooling in optical traps, and preparation of few-body systems in optical lattices.
Few-body physics has played a prominent role in atomic, molecular and nuclear physics since the early days of quantum mechanics. It is now possible-thanks to tremendous progress in cooling, trapping and manipulating ultracold samples-to experimentally study few-body phenomena in trapped atomic and molecular systems with unprecedented control. This review summarizes recent studies of few-body phenomena in trapped atomic and molecular gases, with an emphasis on small trapped systems. We start by introducing the free-space scattering properties and then investigate what happens when two particles, bosons or fermions, are placed in an external confinement. Next, various three-body systems are treated analytically in limiting cases. Our current understanding of larger two-component Fermi systems and Bose systems is reviewed, and connections with the corresponding bulk systems are established. Lastly, future prospects and challenges are discussed. Throughout this review, commonalities with other systems such as nuclei or quantum dots are highlighted.
In this thesis ultracold quantum gases are studied with field theoretical methods. The quantum mechanical three-body problem is solved exactly and the recently experimentally observed universality of the three-body parameter is explained. By means of the functional renormalization group (fRG) the four-body problem is analyzed and it is shown that no additional four-body parameter has to be introduced. The second part of this thesis studies a single impurity immersed in a majority Fermi sea. We develop a new, numerical fRG technique which allows the computation of Green’s functions with full frequency and momentum dependence. Our results are in excellent agreement with recent experiments and exemplify the intricate interplay between few- and many-body physics in ultracold quantum gases.
Ultracold atomic systems have been of great theoretical and experimental interest in the past few decades.They provide ideal paradigms to study quantum phenomena, simulate condensed matter systems, and could potentially become a platform for quantum computations.This thesis focuses on the theoretical investigation of universal and non-universal properties of ultracold few-atom systems.The goal of this thesis is to answer or provide insights into several interesting open questions.First, what is the role of the non-universal three-body parameter in weakly-interacting harmonically trapped Bose gases and at which order does it kick in?Second, how large is the ground state energy of small two-component Fermi gases with infinitely strong interactions compared to their non-interacting counterparts?Lastly, what is the interplay between the spin-orbit coupling and the s-wave two-body interaction and how does it affect the energy spectrum of the two-atom system?In order to answer these questions, we develop and employ different analytical and numerical techniques.A perturbative effective field theory treatment to study the weaklyinteracting trapped Bose gas is employed.The treatment is extended to up to fourth-order perturbation theory and techniques to regularize the diverging sums are developed.A logarithmic divergence in the three-body sector is identified and the need for a non-universal three-body parameter is shown.v The explicitly correlated Gaussian method is used to calculate the ground state energy of small trapped two-component Fermi gases with up to ten particles.A code is developed from scratch and parallelized.An improved optimization scheme is developed.A novel technique to remove the finite-range dependence is proposed and tested.Our calculations serve as benchmarks for other numerical techniques.The explicitly correlated Gaussian method is extended to treat systems with periodic boundary conditions for the first time.Standard perturbation theory is used to treat the spin-orbit coupling term in trapped two-atom systems.Our treatment is based on the exact two-body zero-range solution in the trap.The interplay between the spin-orbit coupling and the two-body s-wave interaction is investigated and shown to have a great impact on the energy spectrum for certain parameter combinations.
Abstract Recent experimental developments have allowed physicists to freeze molecules' motion down to an ultracold temperature regime where quantum effects become profound. Furthermore, each molecule can be precisely prepared at chosen internal states and the mutual interactions between molecules are also highly tunable. As such, ultracold molecules have emerged as a powerful platform in multiple disciplines across physics and chemistry. Meanwhile, a grand challenge exists as to how losses of molecules depend on a quantum many‐body environment. In this article, the recent experimental and theoretical progress of exploring losses of ultracold molecules is reviewed. Since the conventional theoretical scheme of treating isolated pairs of molecules is no longer applicable to the quantum degenerate regime that has been reached in recent experiments, an alternative framework of universal relations between two‐body losses and many‐body correlations has been established. Regardless of microscopic parameters ranging from the temperature and the particle number to the interaction strength, these universal relations always hold. This approach unfolds a simple universality behind complex loss processes of many‐body systems and provides physicists and chemists with a new tool to explore ultracold molecules.
Quantum simulation, a subdiscipline of quantum computation, can provide valuable insight into difficult quantum problems in physics or chemistry. Ultracold atoms in optical lattices represent an ideal platform for simulations of quantum many-body problems. Within this setting, quantum gas microscopes enable single atom observation and manipulation in large samples. Ultracold atom-based quantum simulators have already been used to probe quantum magnetism, to realize and detect topological quantum matter, and to study quantum systems with controlled long-range interactions. Experiments on many-body systems out of equilibrium have also provided results in regimes unavailable to the most advanced supercomputers. We review recent experimental progress in this field and comment on future directions.