76 research outputs found
Efimov physics from a renormalization group perspective
We discuss the physics of the Efimov effect from a renormalization group
viewpoint using the concept of limit cycles. Furthermore, we discuss recent
experiments providing evidence for the Efimov effect in ultracold gases and its
relevance for nuclear systems.Comment: 22 pages, 4 figures (invited review submitted to Phil. Trans. Roy.
Soc. A
Efimov physics beyond three particles
Efimov physics originally refers to a system of three particles. Here we
review recent theoretical progress seeking for manifestations of Efimov physics
in systems composed of more than three particles. Clusters of more than three
bosons are tied to each Efimov trimer, but no independent Efimov physics exists
there beyond three bosons. The case of a few heavy fermions interacting with a
lighter atom is also considered, where the mass ratio of the constituent
particles plays a significant role. Following Efimov's study of the (2+1)
system, the (3+1) system was shown to have its own critical mass ratio to
become Efimovian. We show that the (4+1) system becomes Efimovian at a mass
ratio which is smaller than its sub-systems thresholds, giving a pure five-body
Efimov effect. The (5+1) and (6+1) systems are also discussed, and we show the
absence of 6- and 7-body Efimov physics there
Universality of an impurity in a Bose-Einstein condensate
Universality is a powerful concept in physics, allowing one to construct
physical descriptions of systems that are independent of the precise
microscopic details or energy scales. A prime example is the Fermi gas with
unitarity limited interactions, whose universal properties are relevant to
systems ranging from atomic gases at microkelvin temperatures to the inner
crust of neutron stars. Here we address the question of whether unitary Bose
systems can possess a similar universality. We consider the simplest strongly
interacting Bose system, where we have an impurity particle ("polaron")
resonantly interacting with a Bose-Einstein condensate (BEC). Focusing on the
ground state of the equal-mass system, we use a variational wave function for
the polaron that includes up to three Bogoliubov excitations of the BEC, thus
allowing us to capture both Efimov trimers and associated tetramers. Unlike the
Fermi case, we find that the length scale associated with Efimov trimers (i.e.,
the three-body parameter) can strongly affect the polaron's behaviour, even at
boson densities where there are no well-defined Efimov states. However, by
comparing our results with recent quantum Monte Carlo calculations, we argue
that the polaron energy is a \emph{universal} function of the Efimov three-body
parameter for sufficiently low boson densities. We further support this
conclusion by showing that the energies of the deepest bound Efimov trimers and
tetramers at unitarity are universally related to one another, regardless of
the microscopic model. On the other hand, we find that the quasiparticle
residue and effective mass sensitively depend on the coherence length of
the BEC, with the residue tending to zero as diverges, in a manner akin
to the orthogonality catastrophe.Comment: 11 pages and 7 figures + supplemental materia
Universality in Four-Boson Systems
We report recent advances on the study of universal weakly bound four-boson
states from the solutions of the Faddeev-Yakubovsky equations with zero-range
two-body interactions. In particular, we present the correlation between the
energies of successive tetramers between two neighbor Efimov trimers and
compare it to recent finite range potential model calculations. We provide
further results on the large momentum structure of the tetramer wave function,
where the four-body scale, introduced in the regularization procedure of the
bound state equations in momentum space, is clearly manifested. The results we
are presenting confirm a previous conjecture on a four-body scaling behavior,
which is independent of the three-body one. We show that the correlation
between the positions of two successive resonant four-boson recombination peaks
are consistent with recent data, as well as with recent calculations close to
the unitary limit. Systematic deviations suggest the relevance of range
corrections.Comment: Accepted for publication in special issue of Few-Body Systems devoted
to the Sixth Workshop on the Critical Stability of Quantum Few-Body Systems,
October 2011, Erice, Sicily, Ital
N-body Efimov states from two-particle noise
The ground state energies of universal N-body clusters tied to Efimov
trimers, for N even, are shown to be encapsulated in the statistical
distribution of two particles interacting with a background auxiliary field at
large Euclidean time when the interaction is tuned to the unitary point.
Numerical evidence that this distribution is log-normal is presented, allowing
one to predict the ground-state energies of the N-body system.Comment: Extended discussion of results; published versio
Efimov Trimers near the Zero-crossing of a Feshbach Resonance
Near a Feshbach resonance, the two-body scattering length can assume any
value. When it approaches zero, the next-order term given by the effective
range is known to diverge. We consider the question of whether this divergence
(and the vanishing of the scattering length) is accompanied by an anomalous
solution of the three-boson Schr\"odinger equation similar to the one found at
infinite scattering length by Efimov. Within a simple zero-range model, we find
no such solutions, and conclude that higher-order terms do not support Efimov
physics.Comment: 8 pages, no figures, final versio
Universality in Three- and Four-Body Bound States of Ultracold Atoms
Under certain circumstances, three or more interacting particles may form
bound states. While the general few-body problem is not analytically solvable,
the so-called Efimov trimers appear for a system of three particles with
resonant two-body interactions. The binding energies of these trimers are
predicted to be universally connected to each other, independent of the
microscopic details of the interaction. By exploiting a Feshbach resonance to
widely tune the interactions between trapped ultracold lithium atoms, we find
evidence for two universally connected Efimov trimers and their associated
four-body bound states. A total of eleven precisely determined three- and
four-body features are found in the inelastic loss spectrum. Their relative
locations on either side of the resonance agree well with universal theory,
while a systematic deviation from universality is found when comparing features
across the resonance.Comment: 16 pages including figures and Supplementary Online Materia
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