Ultracold fermionic few-body systems in reduced dimensions: Static and dynamic properties

Andrew Marcum

Rui Lin, Paolo Molignini, Luca Papariello +6 more

Abstract We introduce and describe the multiconfigurational time-depenent Hartree for indistinguishable particles (MCTDH-X) software, which is hosted, documented, and distributed at http://ultracold.org . This powerful tool allows the investigation of ground state properties and dynamics of interacting quantum many-body systems in different spatial dimensions. The MCTDH-X software is a set of programs and scripts to compute, analyze, and visualize solutions for the time-dependent and time-independent many-body Schrödinger equation for indistinguishable quantum particles. As the MCTDH-X software represents a general solver for the Schrödinger equation, it is applicable to a wide range of problems in the fields of atomic, optical, molecular physics, and condensed matter systems. In particular, it can be used to study light–matter interactions, correlated dynamics of electrons in the solid state as well as some aspects related to quantum information and computing. The MCTDH-X software solves a set of nonlinear coupled working equations based on the application of the time-dependent variational principle to the Schrödinger equation. These equations are obtained by using an ansatz for the many-body wavefunction that is a expansion in a set of time-dependent, fully symmetrized bosonic (X = B) or fully anti-symmetrized fermionic (X = F) many-body basis states. It is the time-dependence of the basis set that enables MCTDH-X to deal with quantum dynamics at a superior accuracy as compared to, for instance, exact diagonalization approaches with a static basis, where the number of basis states necessary to capture the dynamics of the wavefunction typically grows rapidly with time. Herein, we give an introduction to the MCTDH-X software via an easy-to-follow tutorial with a focus on accessibility. The illustrated exemplary problems are hosted at http://ultracold.org/tutorial and consider the physics of a few interacting bosons or fermions in a double-well potential. We explore computationally the position-space and momentum-space density, the one-body reduced density matrix, Glauber correlation functions, phases, (dynamical) phase transitions, and the imaging of the quantum systems in single-shot images. Although a few particles in a double well potential represent a minimal model system, we are able to demonstrate a rich variety of phenomena with it. We use the double well to illustrate the fermionization of bosonic particles, the crystallization of fermionic particles, characteristics of the superfluid and Mott-insulator quantum phases in Hubbard models, and even dynamical phase transitions. We provide a complete set of input files and scripts to redo all computations in this paper at http://ultracold.org/data/tutorial_input_files.zip , accompanied by tutorial videos at https://tinyurl.com/tjx35sq . Our tutorial should guide the potential users to apply the MCTDH-X software also to more complex systems.

Selim Jochim

Selim Jochim

Chen Zhang

In this dissertation, we study the few-body ultracold Bose-Fermi mixture and quasi-1D scattering at ultracold temperature. Degenerate quantum gases have attracted enormous attentions during the past two decades. They have opened new platforms of quantum simulation, precision measurement and quantum chemistry. The scattering properties of degenerate quantum gases are the first things to study in order to gain insight into various novel phenomena at ultracold temperatures.\nTo address the role of quantum statistics at ultracold temperature, we study the spectrum and dynamics of a few-body Bose-Fermi mixtures. In particular, we focus the dynamical evolution of a few-body Bose-Fermi mixture and concentrate on its universal behavior at large inter-particle scattering length. We predict the molecule formation efficiency in many-body Bose-Fermi mixtures by mapping this critical observable in few-body calculations. We also propose that a the quantum beat experiment could be used to measure the energy of the lowest Efimov trimer at unitarity.\nTo address the role of dimensionality, we study confinement induced resonances and similar phenomena in general transverse confining potentials. Well-separated energy scales in different dimensions allow the creation of reduced dimensional systems at ultracold temperatures. We develop a general framework to regularize the low-energy quasi-1D scattering phase shift associated with a zero range interaction.\nLastly, we discuss future prospects for the study of an ultracold Bose-Fermi mixture, and scattering in reduced dimensional systems of a more general topology.

Mingyuan He, Chenwei Lv, Qi Zhou

Physical systems in reduced dimensions exhibit intriguing properties. For instance, the dependences of two-body and many-body physics on scattering lengths are distinct from their counterparts in three dimensions. Whereas many studies of ultracold atoms and molecules in reduced dimensions have been focusing on closed systems, two-body losses may occur in such systems. Here, we show that the two-body inelastic loss rate in reduced dimensions can be expressed in universal relations that are governed by contacts. These universal relations correlate the two-body decay rate with other physical observables at zero and finite temperatures and generic interaction strengths. Our results will provide experimentalists with a new protocol to study inelastic scatterings in both few- and many-body systems in reduced dimensions.