93 research outputs found
Pairing and pair superfluid density in one-dimensional Hubbard models
We use unbiased computational methods to elucidate the onset and properties
of pair superfluidity in two-species fermionic and bosonic systems with onsite
interspecies attraction loaded in one-dimensional optical lattice. We compare
results from quantum Monte Carlo (QMC) and density matrix renormalization group
(DMRG), emphasizing the one-to-one correspondence between the Drude weight
tensor, calculated with DMRG, and the various winding numbers extracted from
the QMC. Our results show that, for any nonvanishing attractive interaction,
pairs form and are the sole contributors to superfluidity, there are no
individual contributions due to the separate species. For weak attraction, the
pair size diverges exponentially, i.e. Bardeen-Cooper-Schrieffer (BCS) pairing
requiring huge systems to bring out the pair-only nature of the superfluid.
This crucial property is largely overlooked in many studies, thereby
misinterpreting the origin and nature of the superfluid. We compare and
contrast this with the repulsive case and show that the behavior is very
different, contradicting previous claims about drag superfluidity and the
symmetry of properties for attractive and repulsive interactions. Finally, our
results show that the situation is similar for soft core bosons: superfluidity
is due only to pairs, even for the smallest attractive interaction strength
compatible with the largest system sizes that we could attain.Comment: 5 pages, 4 figure
Superconducting Transitions in Flat Band Systems
The physics of strongly correlated quantum particles within a flat band was
originally explored as a route to itinerant ferromagnetism and, indeed, a
celebrated theorem by Lieb rigorously establishes that the ground state of the
repulsive Hubbard model on a bipartite lattice with unequal number of sites in
each sublattice must have nonzero spin S at half-filling. Recently, there has
been interest in Lieb geometries due to the possibility of novel topological
insulator, nematic, and Bose-Einstein condensed (BEC) phases. In this paper, we
extend the understanding of the attractive Hubbard model on the Lieb lattice by
using Determinant Quantum Monte Carlo to study real space charge and pair
correlation functions not addressed by the Lieb theorems
Two-photon Rabi-Hubbard and Jaynes-Cummings-Hubbard models: photon pair superradiance, Mott insulator and normal phases
We study the ground state phase diagrams of two-photon Dicke, the
one-dimensional Jaynes-Cummings-Hubbard (JCH), and Rabi-Hubbard (RH) models
using mean field, perturbation, quantum Monte Carlo (QMC), and density matrix
renormalization group (DMRG) methods. We first compare mean field predictions
for the phase diagram of the Dicke model with exact QMC results and find
excellent agreement. The phase diagram of the JCH model is then shown to
exhibit a single Mott insulator lobe with two excitons per site, a superfluid
(SF, superradiant) phase and a large region of instability where the
Hamiltonian becomes unbounded. Unlike the one-photon model, there are no higher
Mott lobes. Also unlike the one-photon case, the SF phases above and below the
Mott are surprisingly different: Below the Mott, the SF is that of photon {\it
pairs} as opposed to above the Mott where it is SF of simple photons. The mean
field phase diagram of the RH model predicts a transition from a normal to a
superradiant phase but none is found with QMC.Comment: 14 pages, 14 figure
Anyonic statistics revealed by the Hong-Ou-Mandel dip for fractional excitations
The fractional quantum Hall effect (FQHE) is known to host anyons,
quasiparticles whose statistics is intermediate between bosonic and fermionic.
We show here that Hong-Ou-Mandel (HOM) interferences between excitations
created by narrow voltage pulses on the edge states of a FQHE system at low
temperature show a direct signature of anyonic statistics. The width of the HOM
dip is universally fixed by the thermal time scale, independently of the
intrinsic width of the excited fractional wavepackets. This universal width can
be related to the anyonic braiding of the incoming excitations with thermal
fluctuations created at the quantum point contact. We show that this effect
could be realistically observed with periodic trains of narrow voltage pulses
using current experimental techniques
Designer Flat Bands: Topology and Enhancement of Superconductivity
We construct quasi one-dimensional topological and non-topological three-band
lattices with tunable band gap and winding number of the flat band. Using mean
field (MF) and exact density matrix renormalization group (DMRG) calculations,
we show explicitly how the band gap affects pairing and superconductivity (SC)
in a Hubbard model with attractive interactions. We show excellent agreement
between MF and DMRG. When a phase twist is applied on the system, a phase
difference appears between pairing order parameters on different sublattices,
and this plays a very important role in the SC density. The SC weight, ,
on the gapped topological, , flat band increases linearly with
interaction strength, , for low values, and with a slope that depends on the
details of the compact localized state at . As for the gapped
non-topological flat band (), decays with a power law faster than
quadratic but slower than exponential. This indicates that isolated
non-topological flat bands are less beneficial to SC. In the gapless case (flat
band touching the band above it), we find at low (both for and ) that with contrary to the behavior reported in the literature. In other words,
increases faster than linearly for low thus favoring SC at weak interaction
more than the gapped case. For systems with touching bands, we observe that the
one-body correlation length, , diverges as a power law as ,
while for the isolated flat band is a constant smaller than one
lattice spacing. Both behaviors are distinct from the exponential divergence of
in the dispersive case. Our results re-establish that the BCS mean field
and quantum metric alone are insufficient to characterize SC at weak coupling
Coherent Backscattering of Light with Nonlinear Atomic Scatterers
We study coherent backscattering of a monochromatic laser by a dilute gas of
cold two-level atoms in the weakly nonlinear regime. The nonlinear response of
the atoms results in a modification of both the average field propagation
(nonlinear refractive index) and the scattering events. Using a perturbative
approach, the nonlinear effects arise from inelastic two-photon scattering
processes. We present a detailed diagrammatic derivation of the elastic and
inelastic components of the backscattering signal both for scalar and vectorial
photons. Especially, we show that the coherent backscattering phenomenon
originates in some cases from the interference between three different
scattering amplitudes. This is in marked contrast with the linear regime where
it is due to the interference between two different scattering amplitudes. In
particular we show that, if elastically scattered photons are filtered out from
the photo-detection signal, the nonlinear backscattering enhancement factor
exceeds the linear barrier two, consistently with a three-amplitude
interference effect.Comment: 18 pages, 13 figures, submitted to Phys. Rev.
Negative delta- noise in the Fractional Quantum Hall effect
We study the current correlations of fractional quantum Hall edges at the
output of a quantum point contact (QPC) subjected to a temperature gradient.
This out-of-equilibrium situation gives rise to a form of temperature-activated
shot noise, dubbed delta- noise. We show that the tunneling of Laughlin
quasiparticles leads to a negative delta- noise, in stark contrast with
electron tunneling. Moreover, varying the transmission of the QPC or applying a
voltage bias across the Hall bar may flip the sign of this noise contribution,
yielding signatures which can be accessed experimentally.Comment: 6+8 pages, 3 figure
Nonlinear two-photon Rabi-Hubbard model: superradiance and photon/photon-pair Bose-Einstein condensate
We study the ground state phase diagram of a nonlinear two-photon
Rabi-Hubbard (RH) model in one dimension using quantum Monte Carlo (QMC)
simulations and density matrix renormalization group (DMRG) calculations. Our
model includes a nonlinear photon-photon interaction term. Absent this term,
the RH model has only one phase, the normal disordered phase, and suffers from
spectral collapse at larger values of the photon-qubit interaction or
inter-cavity photon hopping. The photon-photon interaction, no matter how
small, stabilizes the system which now exhibits {\it two} quantum phase
transitions: Normal phase to {\it photon pair} superfluid (PSF) transition and
PSF to single particle superfluid (SPSF). The discrete symmetry of the
Hamiltonian spontaneously breaks in two stages: First it breaks partially as
the system enters the PSF and then completely breaks when the system finally
enters the SPSF phase. We show detailed numerical results supporting this, and
map out the ground state phase diagram.Comment: 9 pages, 11 figure
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