18,892 research outputs found
Low-energy doublons in the ac-driven two-species Hubbard model
The hopping dynamics of two fermionic species with different effective masses
in the one-dimensional Hubbard model driven by an external field is
theoretically investigated. A multiple-time-scale asymptotic analysis of the
driven asymmetric Hubbard model shows that a high-frequency bichromatic
external field can sustain a new kind of low-energy particle bound state
(doublon), in which two fermions of different species occupy nearest neighbor
sites and co-tunnel along the lattice. The predictions of the asymptotic
analysis are confirmed by direct numerical simulations of the two-particle
Hubbard Hamiltonian.Comment: 4 figure
Absence of Floquet scattering in oscillating non-Hermitian potential wells
Scattering of a quantum particle from an oscillating barrier or well does not
generally conserve the particle energy owing to energy exchange with the photon
field, and an incoming particle-free state is scattered into a set of outgoing
(transmitted and reflected) free states according to Floquet scattering theory.
Here we introduce two families of oscillating non-Hermitian potential wells in
which Floquet scattering is fully suppressed for any energy of the incident
particle. The scattering-free oscillating potentials are synthesized by
application of the Darboux transformation to the time-dependent Schr\"{o}dinger
equation. For one of the two families of scattering-free potentials, the
oscillating potential turns out to be fully invisible.Comment: 5 figure
Coherent perfect absorbers for transient, periodic or chaotic optical fields: time-reversed lasers beyond threshold
Recent works [Y.D. Chong {\it et al.}, Phys. Rev. Lett. {\bf 105}, 053901
(2010); W. Wan {\it et al.}, Science {\bf 331}, 889 (2011)] have shown that the
time-reversed process of lasing at threshold realizes a coherent perfect
absorber (CPA). In a CPA, a lossy medium in an optical cavity with a specific
degree of dissipation, equal in modulus to the gain of the lasing medium, can
perfectly absorb coherent optical waves at discrete frequencies that are the
time-reversed counterpart of the lasing modes. Here the concepts of
time-reversal of lasing and CPA are extended for optical radiation emitted by a
laser operated in an arbitrary (and generally highly-nonlinear) regime, i.e.
for transient, chaotic or periodic coherent optical fields. We prove that any
electromagnetic signal generated by a laser system \textbf{S} operated
in an arbitrary regime can be perfectly absorbed by a CPA device
which is simply realized by placing inside \textbf{S} a broadband linear
absorber (attenuator) of appropriate transmittance. As examples, we discuss CPA
devices that perfectly absorb a chaotic laser signal and a frequency-modulated
optical wave.Comment: 9 pages, 3 figure; to appear in Phys. Rev.
Transparency at the interface between two isospectral crystals
Reflection at an interface separating two different media is a rather
universal phenomenon which arises because of wave mismatching at the interface.
By means of supersymmetric quantum mechanics methods, it is shown that a fully
transparent interface can be realized, connecting two isospectral but different
one-dimensional crystals. An example of reflectionless interface is presented
for the sinusoidal (Mathieu) crystal connected to a non-sinusoidal potential by
a transparent domain wall.Comment: 4 figures, to appear in EP
Invisible defects in complex crystals
We show that invisible localized defects, i.e. defects that can not be
detected by an outside observer, can be realized in a crystal with an
engineered imaginary potential at the defect site. The invisible defects are
synthesized by means of supersymmetric (Darboux) transformations of an ordinary
crystal using band-edge wave functions to construct the superpotential. The
complex crystal has an entire real-valued energy spectrum and Bragg scattering
is not influenced by the defects. An example of complex crystal synthesis is
presented for the Mathieu potential
Non-Hermitian time-dependent perturbation theory: asymmetric transitions and transitionless interactions
The ordinary time-dependent perturbation theory of quantum mechanics, that
describes the interaction of a stationary system with a time-dependent
perturbation, predicts that the transition probabilities induced by the
perturbation are symmetric with respect to the initial an final states. Here we
extend time-dependent perturbation theory into the non-Hermitian realm and
consider the transitions in a stationary Hermitian system, described by a
self-adjoint Hamiltonian , induced by a time-dependent non-Hermitian
interaction . In the weak interaction (perturbative) limit, the
transition probabilities generally turn out to be {\it asymmetric} for exchange
of initial and final states. In particular, for a temporal shape of the
perturbation with one-sided Fourier spectrum, i.e. with only positive (or
negative) frequency components, transitions are fully unidirectional, a result
that holds even in the strong interaction regime. Interestingly, we show that
non-Hermitian perturbations can be tailored to be transitionless, i.e. the
perturbation leaves the system unchanged as if the interaction had not occurred
at all, regardless the form of and . As an application of
the results, we discuss asymmetric (chiral) behavior of dynamical encircling of
an exceptional point in a two- and three-level system.Comment: final version, to appear in Annals of Physic
Klein tunneling of two correlated bosons
Reflection of two strongly interacting bosons with long-rage interaction
hopping on a one-dimensional lattice scattered off by a potential step is
theoretically investigated in the framework of the extended Hubbard model. The
analysis shows that, in the presence of unbalanced on-site and nearest-neighbor
site interaction, two strongly correlated bosons forming a bound particle state
can penetrate a high barrier, despite the single particle can not. Such a
phenomenon is analogous to one-dimensional Klein tunneling of a relativistic
massive Dirac particle across a potential step.Comment: 10 pages; Spring select paper; highlighted in: Science Daily, 29 May
2013 and in phys.org May 29, 201
Optical lattices with exceptional points in the continuum
The spectral, dynamical and topological properties of physical systems
described by non-Hermitian (including -symmetric) Hamiltonians
are deeply modified by the appearance of exceptional points and spectral
singularities. Here we show that exceptional points in the continuum can arise
in non-Hermitian (yet admitting and entirely real-valued energy spectrum)
optical lattices with engineered defects. At an exceptional point, the lattice
sustains a bound state with an energy embedded in the spectrum of scattered
states, similar to the von-Neumann Wigner bound states in the continuum of
Hermitian lattices. However, the dynamical and scattering properties of the
bound state at an exceptional point are deeply different from those of ordinary
von-Neumann Wigner bound states in an Hermitian system. In particular, the
bound state in the continuum at an exceptional point is an unstable state that
can secularly grow by an infinitesimal perturbation. Such properties are
discussed in details for transport of discretized light in a
-symmetric array of coupled optical waveguides, which could
provide an experimentally accessible system to observe exceptional points in
the continuum.Comment: 11 pages, 4 figures, slightly revised revision (corrected misprints
in caption of Figs.2 and 4 from published version
A polarisation modulation scheme for measuring vacuum magnetic birefringence with static fields
A novel polarisation modulation scheme for polarimeters based on Fabry-Perot
cavities is presented. The application to the proposed HERA-X experiment aiming
to measuring the magnetic birefringence of vacuum with the HERA superconducting
magnets is discussed
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