[Paper Review] Heavy-Light Few Fermion Clusters at Unitarity

Stefano Gandolfi, J. Carlson|arXiv (Cornell University)|Jun 27, 2010

Cold Atom Physics and Bose-Einstein Condensates3 citations

TL;DR

This paper investigates few-body fermionic clusters composed of one light fermion and up to four heavy fermions at unitarity using quantum Monte Carlo methods. It finds that four- and five-body bound states can collapse at lower mass ratios than the established two-heavy-one-light system, revealing a richer non-universal few-body structure with potential for exotic many-body phases in ultracold atomic gases.

ABSTRACT

We examine the physics of two, three, and four heavy fermions interacting with a single light fermion via short-range interactions. Four-particle bosonic Efimov states have proven important experimentally and also been the subject of significant theoretical effort. Similar fermionic systems are just now being investigated. We find that with some simple interactions the four- and five-particle states collapse to the interaction range at smaller mass ratios than the three-body state, and also before larger clusters can collapse. These states and their excitations can be studied in cold atom experiments, providing unique insights into the role of few-body systems in many-body physics.

Motivation & Objective

• To investigate the existence and stability of few-body bound states in heterogeneous Fermi mixtures with one light and multiple heavy fermions at unitarity.
• To determine whether four- and five-body resonances can form at lower mass ratios than the established two-heavy-one-light (2H1L) system.
• To assess the role of non-universal three-body interactions in stabilizing or destabilizing these clusters.
• To explore the implications of these few-body states for strongly correlated many-body systems, including potential exotic superfluid phases.
• To examine the possibility of bound excited states and scaling behaviors in these systems using variational and quantum Monte Carlo techniques.

Proposed method

• Uses a model Hamiltonian with short-range two- and three-body interactions between one light fermion (mass $m$) and $N$ heavy fermions (mass $M$), tuned to unitarity via effective range and scattering length.
• Employs P"oschl-Teller and Gaussian two-body potentials with adjustable strength to simulate unitary interactions, ensuring consistent effective range $r_{\text{eff}}$.
• Applies a three-body interaction of the form $V_3 \propto \cosh^{-2}(\lambda r)\cosh^{-2}(\lambda r')$ to model three-body correlations with the same range as two-body forces.
• Utilizes variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) techniques with a trial wave function $\Psi_T = \phi_L \Phi_H$, where $\phi_L$ describes the light particle and $\Phi_H$ an antisymmetric state of the heavy particles.
• Implements center-of-mass removal to avoid spurious center-of-mass motion and ensures nodal surfaces are physically meaningful for fermionic statistics.
• Performs systematic calculations for 2H1L, 3H1L, and 4H1L systems, analyzing binding energy, root-mean-square radii, and single-particle densities.

Experimental results

Research questions

• RQ1 Can four- and five-body bound states form in heavy-light Fermi mixtures at unitarity, and at what mass ratios do they collapse?
• RQ2 How do three-body interactions influence the binding and stability of these clusters, and what is their role in non-universal few-body physics?
• RQ3 Do the 4H1L and 5H1L systems exhibit bound states at lower mass ratios than the 2H1L system, and what does this imply for cluster formation?
• RQ4 Can a single three-body interaction parameter describe the binding of multiple cluster types (2H1L, 3H1L, 4H1L), as in universal systems like nuclei or bosonic Efimov states?
• RQ5 What is the spatial structure of these clusters, particularly the density distribution of light vs. heavy fermions, and how does it relate to nodal structure and symmetry?

Key findings

• Four- and five-body bound states collapse at mass ratios $M/m \approx 10.25$ and below, which is lower than the critical value of $M/m \approx 13.6$ for the 2H1L system.
• For the 4H1L system, the light particle's root-mean-square radius is approximately 0.30 $r_{\text{eff}}$ in QMC, while the heavy particle radius is 0.24 $r_{\text{eff}}$, indicating a more compact configuration than in smaller systems.
• The 2H1L system shows a light-particle rms radius of about 1.14 $r_{\text{eff}}$ in QMC, significantly larger than the heavy particle radius, consistent with the light particle occupying the center of mass.
• Three-body interactions shift the binding energy threshold for collapse significantly; even small repulsive three-body forces ($V_3 \sim 1$) can unbind the system, confirming the non-universal nature of the regime.
• The light fermion exhibits maximum density at the center of mass, while heavy fermions have near-zero density there due to nodal structure, reflecting their antisymmetrized spatial wave function.
• Different two-body potentials with the same effective range yield different binding energies and intercepts at zero binding, further confirming the non-universality of the few-body physics in this regime.