Exploring the few- to many-body crossover using cold atoms in one dimension

Abstract

Abstract. Cold atomic gases have provided us with a great number of opportunities for studying various physical systems under controlled conditions that are seldom offered in other fields. We are thus at the point where one can truly do quantum simulation of models that are relevant for instance in condensed-matter or high-energy physics, i.e. we are on the verge of a 'cool' quantum simulator as envisioned by Feynman. One of the avenues under exploration is the physics of one-dimensional systems. Until recently this was mostly in the many-body limit but now experiments can be performed with controllable particle numbers all the way down to the few-body regime. After a brief introduction to some of the relevant experiments, I will review recent theoretical work on one-dimensional quantum systems containing bosons, fermions, or mixtures of the two, with a particular emphasis on the case where the particles are held by an external trap.

Flow equations for cold Bose gases

“…Hence,  is unitarily equivalent to H 0 ( ). We emphasize that s h ( ) is given from the beginning for every s and not obtained dynamically as before.The operator  can be written as ) is obtained from the truncated flow and H a satisfies the equation Note that the operator H a is generated by W, which is the part of(20) that is neglected in our truncation scheme. Therefore, we postulate that our approximation is…”

Dynamical properties of a few mass-imbalanced ultra-cold fermions confined in a double-well potential

“…The dynamical scenario of the particle imbalanced system can be thought as the dynamics of an impurity atom (lighter or heavier) in contact with a fermionic bath. The unpaired initial states are denoted as |ini 7…”

Exactly solvable model of two interacting Rydberg-dressed atoms confined in a two-dimensional harmonic trap

“…Radial density distribution F(ρ) of the relative motion in bosonic (n, ) = (0, 0) and fermionic (n, ) = (0, 1) ground states for a = 1 and different strengths of interaction V . Thick solid lines represent distributions obtained in the simplified model of interactions (3) while thin dotted lines represent results in the realistic model(2). Note that in the case of fermionic particles, due to the Pauli exclusion principle, the radial density distribution F(ρ) must necessarily vanish at ρ = 0.…”