SILVIA: STUDI SUL GAS DI BOSE

https://journals.aps.org/pra/abstract/10.1103/PhysRevA.100.013612

Pair formation in quenched unitary Bose gases
S. Musolino, V. E. Colussi, and S. J. J. M. F. Kokkelmans
Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
(Dated: April 2, 2019)

We study a degenerate Bose gas quenched to unitarity by solving a many-body model including
three-body losses and correlations up to second order. As the gas evolves in this strongly-interacting
regime, the buildup of correlations leads to the formation of extended pairs bound purely by manybody e ects, analogous to the phenomenon of Cooper pairing in the BCS regime of the Fermi gas.
Through fast sweeps away from unitarity, we detail how the correlation growth and formation of
bound pairs emerge in the fraction of unbound atoms remaining post sweep, nding quantitative
agreement with experiment. We comment on the possible role of higher-order e ects in explaining
the deviation of our theoretical results from experiment for slower sweeps and longer times spent in
the unitary regime.

I. INTRODUCTION
In ultracold quantum gases, precision control of
magnetically-tunable Feshbach resonances makes it possible
to tune the e ective interaction strength, characterized
by the s-wave scattering length a [1]. As a becomes
much larger than the interparticle spacing n􀀀1=3, where
n is the atomic density, the gas enters the unitary regime
(njaj3 1). At unitarity (jaj ! 1) interactions between
atoms in the gas are as strong as allowed by quantum mechanics.
The insensitivity of unitary quantum gases to
diverging microscopic scales makes them paradigmatic
for other strongly-correlated systems including the inner
crust of neutron stars and the quark-gluon plasma [2, 3].
The universality of the unitary Fermi gas is both theoretically
and experimentally well-established over the
last two decades [4]. Under the universality hypothesis,
the unitary Bose gas is also expected to behave
similarly, with thermodynamic properties and relations
that scale continuously solely with the \Fermi"scales constructed
from powers of n, including the Fermi wave number
kn = (6 2n)1=3, energy En = ~2k2n
=2m, and time
tn = ~=En where m is the atomic mass [5].
Unlike their fermionic counterparts, at unitarity three
bosons may form an in nite series of bound E mov
trimers [6] with characteristic nite size set by the threebody
parameter [7{9]. Whereas Pauli-repulsion suppresses
three-body losses for fermions, the E mov effect
leads to a catastrophic a4 scaling of three-body
losses near unitarity, and therefore the unitary Bose gas
is inherently unstable. In Refs. [10{13], this barrier
was overcome through a fast quench from the weaklyinteracting
to the unitary regime, where the establishment
of a steady-state was observed before heating dominates.
Time-resolved studies of the single-particle momentum
distribution in Ref. [13] revealed that the theoretically
predicted prethermal state [14{16] transitions
to steady-state prior to being overcome by heating. Although
these ndings, combined with studies of loss dy-
s.musolino@tue.nl

FIG. 1. Schematic representation of the experimental protocol
used in Refs. [10{13]. First, the magnetic eld, B, is
ramped suddenly towards the resonant value B0, taking the
system from the weakly-interacting (na3 < 1) to the unitary
regime na3 & 1 (shaded region). In the second stage, the system
evolves at unitarity for a variable time thold. In the third
and nal step, a fast sweep of the magnetic eld away from
resonance returns the system back to the weakly-interacting
regime where measurements are made.
namics in Refs. [10{12], are consistent with the universality
hypothesis, a macroscopic population of E mov
trimers was observed in Ref. [11]. Understanding the
role of the E mov e ect [17, 18] and dynamics of higherorder
correlations [19{21] in the quenched unitary Bose
gas remains however an ongoing pursuit in the community.
The di culties of probing the system at unitarity require
that experiments return to the more stable and
better-understood weakly-interacting regime. During the
course of the experiment, we have to distinguish di erent
types of atomic pairs: (i) pairs of atoms with opposite
momentum, analogous to Cooper pairs in Fermi
gases, (ii) embedded dimers at unitarity whose size is dearXiv:
1904.00908v1  ...