311 research outputs found
Efimov trimers under strong confinement
The dimensionality of a system can fundamentally impact the behaviour of
interacting quantum particles. Classic examples range from the fractional
quantum Hall effect to high temperature superconductivity. As a general rule,
one expects confinement to favour the binding of particles. However,
attractively interacting bosons apparently defy this expectation: while three
identical bosons in three dimensions can support an infinite tower of Efimov
trimers, only two universal trimers exist in the two dimensional case. We
reveal how these two limits are connected by investigating the problem of three
identical bosons confined by a harmonic potential along one direction. We show
that the confinement breaks the discrete Efimov scaling symmetry and destroys
the weakest bound trimers. However, the deepest bound Efimov trimer persists
under strong confinement and hybridizes with the quasi-two-dimensional trimers,
yielding a superposition of trimer configurations that effectively involves
tunnelling through a short-range repulsive barrier. Our results suggest a way
to use strong confinement to engineer more stable Efimov-like trimers, which
have so far proved elusive.Comment: 8 pages, 4 figures. Typos corrected, published versio
Microscopic description of exciton-polaritons in microcavities
We investigate the microscopic description of exciton-polaritons that
involves electrons, holes and photons within a two-dimensional microcavity. We
show that in order to recover the simplified exciton-photon model that is
typically used to describe polaritons, one must correctly define the
exciton-photon detuning and exciton-photon (Rabi) coupling in terms of the bare
microscopic parameters. For the case of unscreened Coulomb interactions, we
find that the exciton-photon detuning is strongly shifted from its bare value
in a manner akin to renormalization in quantum electrodynamics. Within the
renormalized theory, we exactly solve the problem of a single exciton-polariton
for the first time and obtain the full spectral response of the microcavity. In
particular, we find that the electron-hole wave function of the polariton can
be significantly modified by the very strong Rabi couplings achieved in current
experiments. Our microscopic approach furthermore allows us to properly
determine the effective interaction between identical polaritons, which goes
beyond previous theoretical work. Our findings are thus important for
understanding and characterizing exciton-polariton systems across the whole
range of polariton densities.Comment: 14 pages, 5 figure
Three-body problem in a two-dimensional Fermi gas
We investigate the three-body properties of two identical "up" fermions and
one distinguishable "down" atom interacting in a strongly confined
two-dimensional geometry. We compute exactly the atom-dimer scattering
properties and the three-body recombination rate as a function of collision
energy and mass ratio m_up/m_down. We find that the recombination rate for
fermions is strongly energy dependent, with significant contributions from
higher partial waves at low energies. For m_up < m_down, the s-wave atom-dimer
scattering below threshold is completely described by the scattering length.
Furthermore, we examine the "up-up-down" bound states (trimers) appearing at
large m_up/m_down and find that the energy spectrum for the deepest bound
trimers resembles that of a hydrogen atom confined to two dimensions.Comment: 6 pages, 6 figure
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
Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential
A major challenge in modern physics is to accurately describe strongly
interacting quantum many-body systems. One-dimensional systems provide
fundamental insights since they are often amenable to exact methods. However,
no exact solution is known for the experimentally relevant case of external
confinement. Here, we propose a powerful ansatz for the one-dimensional Fermi
gas in a harmonic potential near the limit of infinite short-range repulsion.
For the case of a single impurity in a Fermi sea, we show that our ansatz is
indistinguishable from numerically exact results in both the few- and many-body
limits. We furthermore derive an effective Heisenberg spin-chain model
corresponding to our ansatz, valid for any spin-mixture, within which we obtain
the impurity eigenstates analytically. In particular, the classical Pascal's
triangle emerges in the expression for the ground-state wavefunction. As well
as providing an important benchmark for strongly correlated physics, our
results are relevant for emerging quantum technologies, where a precise
knowledge of one-dimensional quantum states is paramount.Comment: 13 pages, 6 figures. Published versio
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