387 research outputs found
Efimov Trimers in a Harmonic Potential
We study the Efimov effect in a harmonic oscillator in the hyperspherical
formulation, and show how a reduced model allows for a description that is a
generalization of the Efimov effect in free space and leads to results that are
easily interpreted. Efimov physics may be observed by varying the value of the
scattering length, since in the regime where the trimers have a mixed harmonic
oscillator and Efimov character, the inelastic properties of these states are
still manageable. The model also allows for the study of non-universal Efimov
trimers by including the effective range scattering parameter. While we find
that in a certain regime the effective range parameter can take over the role
of the three-body parameter, interestingly, we obtain a numerical relationship
between these two parameters different from what was found in other models.Comment: 15 pages, 9 figure
Feshbach resonances in ultracold gases
In this chapter, we describe scattering resonance phenomena in general, and
focus on the mechanism of Feshbach resonances, for which a multi-channel
treatment is required. We derive the dependence of the scattering phase shift
on magnetic field and collision energy. From this, the scattering length and
effective range coefficient can be extracted, expressions which are
particularly useful for ultracold gases.Comment: 23 pages, 3 figures. This article will be published as Chapter 4 in
"Quantum gas experiments - exploring many-body states", edited by P.
T\"orm\"a and K. Sengstock, Imperial College Press, London, to be published
201
Total control over ultracold interactions via electric and magnetic fields
The scattering length is commonly used to characterize the strength of
ultracold atomic interactions, since it is the leading parameter in the
low-energy expansion of the scattering phase shift. Its value can be modified
via a magnetic field, by using a Feshbach resonance. However, the effective
range term, which is the second parameter in the phase shift expansion,
determines the width of the resonance and gives rise to important properties of
ultracold gases. Independent control over this parameter is not possible by
using a magnetic field only. We demonstrate that a combination of magnetic and
electric fields can be used to get independent control over both parameters,
which leads to full control over elastic ultracold interactions.Comment: 4 pages, 3 figure
Trapped electrons in the quantum degenerate regime
A full strength Coulomb interaction between trapped electrons can be felt
only in absence of a neutralizing background. In order to study quantum
degenerate electrons without such a background, an external trap is needed to
compensate for the strong electronic repulsion. As a basic model for such a
system, we study a trapped electron pair in a harmonic trap with an explicit
inclusion of its Coulomb interaction. We find the eigenenergy of the ground
state, confirming earlier work in the context of harmonium. We extend this to a
complete set of properly scaled energies for any value of the trapping
strength, including the excited states. The problem is solved either
numerically or by making harmonic approximations to the potential. As function
of the trapping strength a crossover can be made from the strongly to the
weakly-coupled regime, and we show that in both regimes perturbative methods
based on a pair-wise electron description would be effective for a
many-particle trapped electron system, which resembles a Wigner crystal in the
ground state of the strongly coupled limit.Comment: 6 pages, 3 figure
Finite range effects in two-body and three-body interactions
Efimov physics in ultracold gases is described very well by the universal scaling laws, based on the scattering length and van der Waals length. The first can be tuned magnetically via a Feshbach resonance, the second is constant and connected to the radial range of the potential.However, experimental hints at non-universal behavior, when going away from resonance, are quite badly understood. The next leading coefficient in the scattering phase shift, the effective range parameter, gives an indication of this non-universality, but at the same time it can also be strongly dependent on the magnetic field. Moreover, higher-order terms take over quickly when increasing the collision energy. We show how the finite range corrections can be understood by making the connection to more fundamental parameters of the two-body physics, and use this description to derive a better criterion for entering the non-universal regime
Three-body recombination at vanishing scattering lengths in an ultracold Bose gas
We report on measurements of three-body recombination rates in an ultracold
gas of Li atoms in the extremely nonuniversal regime where the two-body
scattering length vanishes. We show that the rate is well defined and can be
described by two-body parameters only: the scattering length and the
effective range . We find the rate to be energy independent, and, by
connecting our results with previously reported measurements in the universal
limit, we cover the behavior of the three-body recombination in the whole range
from weak to strong two-body interactions. We identify a nontrivial magnetic
field value in the nonuniversal regime where the rate should be strongly
reduced.Comment: Version with enhanced supplemental material
Ramsey fringes in a Bose-Einstein condensate between atoms and molecules
In a recent experiment, a Feshbach scattering resonance was exploited to
observe Ramsey fringes in a Rb Bose-Einstein condensate. The oscillation
frequency corresponded to the binding energy of the molecular state. We show
that the observations are remarkably consistent with predictions of a resonance
field theory in which the fringes arise from oscillations between atoms and
molecules.Comment: 5 pages, 5 figure
Wireless network control of interacting Rydberg atoms
We identify a relation between the dynamics of ultracold Rydberg gases in
which atoms experience a strong dipole blockade and spontaneous emission, and a
stochastic process that models certain wireless random-access networks. We then
transfer insights and techniques initially developed for these wireless
networks to the realm of Rydberg gases, and explain how the Rydberg gas can be
driven into crystal formations using our understanding of wireless networks.
Finally, we propose a method to determine Rabi frequencies (laser intensities)
such that particles in the Rydberg gas are excited with specified target
excitation probabilities, providing control over mixed-state populations.Comment: 6 pages, 7 figures; includes corrections and improvements from the
peer-review proces
Nuclear-spin-independent short-range three-body physics in ultracold atoms
We investigate three-body recombination loss across a Feshbach resonance in a
gas of ultracold 7Li atoms prepared in the absolute ground state and perform a
comparison with previously reported results of a different nuclear-spin state
[N. Gross et.al., Phys. Rev. Lett. 103 163202, (2009)]. We extend the
previously reported universality in three-body recombination loss across a
Feshbach resonance to the absolute ground state. We show that the positions and
widths of recombination minima and Efimov resonances are identical for both
states which indicates that the short-range physics is nuclear-spin
independent.Comment: 4 pages, 2 figure
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