840 research outputs found
Quantum interference from sums over closed paths for electrons on a three-dimensional lattice in a magnetic field: total energy, magnetic moment, and orbital susceptibility
We study quantum interference effects due to electron motion on a
three-dimensional cubic lattice in a continuously-tunable magnetic field of
arbitrary orientation and magnitude. These effects arise from the interference
between magnetic phase factors associated with different electron closed paths.
The sums of these phase factors, called lattice path-integrals, are
``many-loop" generalizations of the standard ``one-loop" Aharonov-Bohm-type
argument. Our lattice path integral calculation enables us to obtain various
important physical quantities through several different methods. The spirit of
our approach follows Feynman's programme: to derive physical quantities in
terms of ``sums over paths". From these lattice path-integrals we compute
analytically, for several lengths of the electron path, the half-filled
Fermi-sea ground-state energy of noninteracting spinless electrons in a cubic
lattice. Our results are valid for any strength of the applied magnetic field
in any direction. We also study in detail two experimentally important
quantities: the magnetic moment and orbital susceptibility at half-filling, as
well as the zero-field susceptibility as a function of the Fermi energy.Comment: 14 pages, RevTe
Encoding a qubit with Majorana modes in superconducting circuits
Majorana fermions are long-sought exotic particles that are their own
antiparticles. Here we propose to utilize superconducting circuits to construct
two superconducting-qubit arrays where Majorana modes can occur. A so-called
Majorana qubit is encoded by using the unpaired Majorana modes, which emerge at
the left and right ends of the chain in the Majorana-fermion representation. We
also show this Majorana qubit in the spin representation and its advantage,
over a single superconducting qubit, regarding quantum coherence. Moreover, we
propose to use four superconducting qubits as the smallest system to
demonstrate the braiding of Majorana modes and show how the states before and
after braiding Majoranas can be discriminated.Comment: 10 pages, 3 figures; an enlarged version of arXiv: 1108.3712v
Acoustic Radiation Force and Torque on Small Particles as Measures of the Canonical Momentum and Spin Densities
We examine acoustic radiation force and torque on a small (subwavelength)
absorbing isotropic particle immersed in a monochromatic (but generally
inhomogeneous) sound-wave field. We show that by introducing the monopole and
dipole polarizabilities of the particle, the problem can be treated in a way
similar to the well-studied optical forces and torques on dipole Rayleigh
particles. We derive simple analytical expressions for the acoustic force
(including both the gradient and scattering forces) and torque. Importantly,
these expressions reveal intimate relations to the fundamental field properties
introduced recently for acoustic fields: the canonical momentum and spin
angular momentum densities. We compare our analytical results with previous
calculations and exact numerical simulations. We also consider an important
example of a particle in an evanescent acoustic wave, which exhibits the
mutually-orthogonal scattering (radiation-pressure) force, gradient force, and
torque from the transverse spin of the field.Comment: 7 pages, 3 figures, Supplemental Material, to appear in Phys. Rev.
Let
Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
We analyze chiral topological edge modes in a non-Hermitian variant of the 2D
Dirac equation. Such modes appear at interfaces between media with different
"masses" and/or signs of the "non-Hermitian charge". The existence of these
edge modes is intimately related to exceptional points of the bulk
Hamiltonians, i.e., degeneracies in the bulk spectra of the media. We find that
the topological edge modes can be divided into three families
("Hermitian-like", "non-Hermitian", and "mixed"), these are characterized by
two winding numbers, describing two distinct kinds of half-integer charges
carried by the exceptional points. We show that all the above types of
topological edge modes can be realized in honeycomb lattices of ring resonators
with asymmetric or gain/loss couplings.Comment: 6 pages, 3 figures, and Supplementary Materials, to appear in Phys.
Rev. Let
Squeezed Phonon States: Modulating Quantum Fluctuations of Atomic Displacements
We study squeezed quantum states of phonons, which allow the possibility of
modulating the quantum fluctuations of atomic displacements below the
zero-point quantum noise level of coherent phonon states. We calculate the
corresponding expectation values and fluctuations of both the atomic
displacement and the lattice amplitude operators, and also investigate the
possibility of generating squeezed phonon states using a three-phonon
parametric amplification process based on phonon-phonon interactions.
Furthermore, we also propose a detection scheme based on reflectivity
measurements.Comment: 4 pages, RevTeX. The previous entry had a wrong page number in the
Journal-ref fiel
Relativistic Hall Effect
We consider the relativistic deformation of quantum waves and mechanical
bodies carrying intrinsic angular momentum (AM). When observed in a moving
reference frame, the centroid of the object undergoes an AM-dependent
transverse shift. This is the relativistic analogue of the spin Hall effect,
which occurs in free space without any external fields. Remarkably, the shifts
of the geometric and energy centroids differ by a factor of 2, and both
centroids are crucial for the correct Lorentz transformations of the AM tensor.
We examine manifestations of the relativistic Hall effect in quantum vortices,
and mechanical flywheels, and also discuss various fundamental aspects of this
phenomenon. The perfect agreement of quantum and relativistic approaches allows
applications at strikingly different scales: from elementary spinning
particles, through classical light, to rotating black-holes.Comment: 5 pages, 3 figures, to appear in Phys. Rev. Let
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