[Paper Review] Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics

S. I. Mistakidis, Artem G. Volosniev+6 more|arXiv (Cornell University)|Feb 22, 2022

Cold Atom Physics and Bose-Einstein Condensates992 references29 citations

TL;DR

The paper reviews theoretical progress on static and dynamical properties of few-body bosonic systems in one dimension, emphasizing strongly correlated regimes, exact solutions, and numerical methods.

ABSTRACT

Cold atomic gases have become a paradigmatic system for exploring fundamental physics, which at the same time allows for applications in quantum technologies. The accelerating developments in the field have led to a highly advanced set of engineering techniques that, for example, can tune interactions, shape the external geometry, select among a large set of atomic species with different properties, or control the number of atoms. In particular, it is possible to operate in lower dimensions and drive atomic systems into the strongly correlated regime. In this review, we discuss recent advances in few-body cold atom systems confined in low dimensions from a theoretical viewpoint. We mainly focus on bosonic systems in one dimension and provide an introduction to the static properties before we review the state-of-the-art research into quantum dynamical processes stimulated by the presence of correlations. Besides discussing the fundamental physical phenomena arising in these systems, we also provide an overview of the calculational and numerical tools and methods that are commonly used, thus delivering a balanced and comprehensive overview of the field. We conclude by giving an outlook on possible future directions that are interesting to explore in these correlated systems.

Motivation & Objective

• Motivate how cold-atom systems in one dimension serve as a controllable platform for exploring few-body and strongly correlated quantum dynamics.
• Summarize exact solutions and numerical methods used for few-body 1D bosonic systems.
• Survey static properties and dynamical processes such as quenches, transport, and pattern formation in few-body settings.
• Discuss extensions to multi-component, impurity, and spinor bosonic gases and their dynamical behavior.
• Outline future directions and experimental relevance for low-dimensional few-body quantum dynamics.

Proposed method

• Describe and connect exact solutions for few-body contact-interacting bosons, including the two- and three-particle cases and the Tonks-Girardeau limit.
• Summarize the Bethe ansatz framework and its application to Lieb-Liniger-type models and related solvable systems.
• Review numerical and computational techniques used in the field, such as DMRG, ML-MCTDHX, and spin-chain mappings.
• Discuss how confinement, resonances, and trap geometry influence effective 1D interactions via confinement-induced resonances (CIR).
• Highlight approaches to dynamics including quenches, time-dependent modulations, and driven transport in few-body settings.

Experimental results

Research questions

• RQ1 What are the exact and approximate methods to solve few-body bosonic systems with contact interactions in 1D?
• RQ2 How do confinement and interaction strength shape static properties and dynamical responses of few-body 1D Bose gases?
• RQ3 What roles do multi-component, impurity, and spinor degrees of freedom play in the dynamics of 1D bosonic systems?
• RQ4 How can experimental techniques and theoretical models bridge to understand droplets, tunneling, and collective modes in few-body regimes?
• RQ5 What computational tools are most effective for capturing beyond-mean-field correlations in these systems?

Key findings

• Exact solutions for two and three bosons with contact interactions illustrate how wave functions and energies depend on interaction strength and boundary conditions.
• The Tonks-Girardeau limit demonstrates fermionization of strongly interacting 1D bosons and validates 1D models of strongly correlated gases.
• Review of diverse dynamical phenomena including quenches, breathing modes, tunneling, and pattern formation in few-body settings.
• Overview of many-body-inspired techniques (DMRG, ML-MCTDHX, spin-chain mappings) adapted for few-body 1D bosonic systems.
• Discussion of confinement-induced resonances enabling tunable effective 1D interactions and access to different interaction regimes.
• Integration of static properties and dynamics across single-component, multi-component, impurity, and spinor bosonic gases.