856 research outputs found
From Cavity Electromechanics to Cavity Optomechanics
We present an overview of experimental work to embed high-Q mesoscopic
mechanical oscillators in microwave and optical cavities. Based upon recent
progress, the prospect for a broad field of "cavity quantum mechanics" is very
real. These systems introduce mesoscopic mechanical oscillators as a new
quantum resource and also inherently couple their motion to photons throughout
the electromagnetic spectrum.Comment: 8 pages, 6 figures, ICAP proceedings submissio
A New Approach to Transport Coefficients in the Quantum Spin Hall Effect
We investigate some foundational issues in the quantum theory of spin transport, in the general case when the unperturbed Hamiltonian operator H does not commute with the spin operator in view of Rashba interactions, as in the typical models for the quantum spin Hall effect. A gapped periodic one-particle Hamiltonian H is perturbed by adding a constant electric field of intensity ε≪ 1 in the j-th direction, and the linear response in terms of a S-current in the i-th direction is computed, where S is a generalized spin operator. We derive a general formula for the spin conductivity that covers both the choice of the conventional and of the proper spin current operator. We investigate the independence of the spin conductivity from the choice of the fundamental cell (unit cell consistency), and we isolate a subclass of discrete periodic models where the conventional and the proper S-conductivity agree, thus showing that the controversy about the choice of the spin current operator is immaterial as far as models in this class are concerned. As a consequence of the general theory, we obtain that whenever the spin is (almost) conserved, the spin conductivity is (approximately) equal to the spin-Chern number. The method relies on the characterization of a non-equilibrium almost-stationary state (NEASS), which well approximates the physical state of the system (in the sense of space-adiabatic perturbation theory) and allows moreover to compute the response of the adiabatic S-current as the trace per unit volume of the S-current operator times the NEASS. This technique can be applied in a general framework, which includes both discrete and continuum models
Demonstration of efficient nonreciprocity in a microwave optomechanical circuit
The ability to engineer nonreciprocal interactions is an essential tool in
modern communication technology as well as a powerful resource for building
quantum networks. Aside from large reverse isolation, a nonreciprocal device
suitable for applications must also have high efficiency (low insertion loss)
and low output noise. Recent theoretical and experimental studies have shown
that nonreciprocal behavior can be achieved in optomechanical systems, but
performance in these last two attributes has been limited. Here we demonstrate
an efficient, frequency-converting microwave isolator based on the
optomechanical interactions between electromagnetic fields and a mechanically
compliant vacuum gap capacitor. We achieve simultaneous reverse isolation of
more than 20 dB and insertion loss less than 1.5 dB over a bandwidth of 5 kHz.
We characterize the nonreciprocal noise performance of the device, observing
that the residual thermal noise from the mechanical environments is routed
solely to the input of the isolator. Our measurements show quantitative
agreement with a general coupled-mode theory. Unlike conventional isolators and
circulators, these compact nonreciprocal devices do not require a static
magnetic field, and they allow for dynamic control of the direction of
isolation. With these advantages, similar devices could enable programmable,
high-efficiency connections between disparate nodes of quantum networks, even
efficiently bridging the microwave and optical domains.Comment: 9 pages, 6 figure
Effective dynamics for particles coupled to a quantized scalar field
We consider a system of N non-relativistic spinless quantum particles
(``electrons'') interacting with a quantized scalar Bose field (whose
excitations we call ``photons''). We examine the case when the velocity v of
the electrons is small with respect to the one of the photons, denoted by c
(v/c= epsilon << 1). We show that dressed particle states exist (particles
surrounded by ``virtual photons''), which, up to terms of order (v/c)^3, follow
Hamiltonian dynamics. The effective N-particle Hamiltonian contains the kinetic
energies of the particles and Coulomb-like pair potentials at order (v/c)^0 and
the velocity dependent Darwin interaction and a mass renormalization at order
(v/c)^{2}. Beyond that order the effective dynamics are expected to be
dissipative.
The main mathematical tool we use is adiabatic perturbation theory. However,
in the present case there is no eigenvalue which is separated by a gap from the
rest of the spectrum, but its role is taken by the bottom of the absolutely
continuous spectrum, which is not an eigenvalue.
Nevertheless we construct approximate dressed electrons subspaces, which are
adiabatically invariant for the dynamics up to order (v/c)\sqrt{\ln
(v/c)^{-1}}. We also give an explicit expression for the non adiabatic
transitions corresponding to emission of free photons. For the radiated energy
we obtain the quantum analogue of the Larmor formula of classical
electrodynamics.Comment: 67 pages, 2 figures, version accepted for publication in
Communications in Mathematical Physic
A Nonlinear Adiabatic Theorem for Coherent States
We consider the propagation of wave packets for a one-dimensional nonlinear
Schrodinger equation with a matrix-valued potential, in the semi-classical
limit. For an initial coherent state polarized along some eigenvector, we prove
that the nonlinear evolution preserves the separation of modes, in a scaling
such that nonlinear effects are critical (the envelope equation is nonlinear).
The proof relies on a fine geometric analysis of the role of spectral
projectors, which is compatible with the treatment of nonlinearities. We also
prove a nonlinear superposition principle for these adiabatic wave packets.Comment: 21 pages, no figur
Coupling carbon nanotube mechanics to a superconducting circuit
The quantum behaviour of mechanical resonators is a new and emerging field
driven by recent experiments reaching the quantum ground state. The high
frequency, small mass, and large quality-factor of carbon nanotube resonators
make them attractive for quantum nanomechanical applications. A common element
in experiments achieving the resonator ground state is a second quantum system,
such as coherent photons or superconducting device, coupled to the resonators
motion. For nanotubes, however, this is a challenge due to their small size.
Here, we couple a carbon nanoelectromechanical (NEMS) device to a
superconducting circuit. Suspended carbon nanotubes act as both superconducting
junctions and moving elements in a Superconducting Quantum Interference Device
(SQUID). We observe a strong modulation of the flux through the SQUID from
displacements of the nanotube. Incorporating this SQUID into superconducting
resonators and qubits should enable the detection and manipulation of nanotube
mechanical quantum states at the single-phonon level
Another proof of Gell-Mann and Low's theorem
The theorem by Gell-Mann and Low is a cornerstone in QFT and zero-temperature
many-body theory. The standard proof is based on Dyson's time-ordered expansion
of the propagator; a proof based on exact identities for the time-propagator is
here given.Comment: 5 page
Semiclassical approximations for Hamiltonians with operator-valued symbols
We consider the semiclassical limit of quantum systems with a Hamiltonian
given by the Weyl quantization of an operator valued symbol. Systems composed
of slow and fast degrees of freedom are of this form. Typically a small
dimensionless parameter controls the separation of time
scales and the limit corresponds to an adiabatic limit, in
which the slow and fast degrees of freedom decouple. At the same time
is the semiclassical limit for the slow degrees of freedom.
In this paper we show that the -dependent classical flow for the
slow degrees of freedom first discovered by Littlejohn and Flynn, coming from
an \epsi-dependent classical Hamilton function and an -dependent
symplectic form, has a concrete mathematical and physical meaning: Based on
this flow we prove a formula for equilibrium expectations, an Egorov theorem
and transport of Wigner functions, thereby approximating properties of the
quantum system up to errors of order . In the context of Bloch
electrons formal use of this classical system has triggered considerable
progress in solid state physics. Hence we discuss in some detail the
application of the general results to the Hofstadter model, which describes a
two-dimensional gas of non-interacting electrons in a constant magnetic field
in the tight-binding approximation.Comment: Final version to appear in Commun. Math. Phys. Results have been
strengthened with only minor changes to the proofs. A section on the
Hofstadter model as an application of the general theory was added and the
previous section on other applications was remove
Investigation of the 2013 Alberta Flood from Weather and Climate Perspectives
During 19–21 June 2013 a heavy precipitation event affected southern Alberta and adjoining regions, leading to severe flood damage in numerous communities and resulting in the costliest natural disaster in Canadian history. This flood was caused by a combination of meteorological and hydrological factors, which are investigated from weather and climate perspectives with the fifth generation Canadian Regional Climate Model. Results show that the contribution of orographic ascent to precipitation was important, exceeding 30% over the foothills of the Rocky Mountains. Another contributing factor was evapotranspiration from the land surface, which is found to have acted as an important moisture source and was likely enhanced by antecedent rainfall that increased soil moisture over the northern Great Plains. Event attribution analysis suggests that human induced greenhouse gas increases may also have contributed by causing evapotranspiration rates to be higher than they would have been under pre-industrial conditions. Frozen and snow-covered soils at high elevations are likely to have played an important role in generating record streamflows. Results point to a doubling of surface runoff due to the frozen conditions, while 25% of the modelled runoff originated from snowmelt. The estimated return time of the 3-day precipitation event exceeds 50 years over a large region, and an increase in the occurrence of similar extreme precipitation events is projected by the end of the 21st century. Event attribution analysis suggests that greenhouse gas increases may have increased 1-day and 3-day return levels of May–June precipitation with respect to pre-industrial climate conditions. However, no anthropogenic influence can be detected for 1-day and 3-day surface runoff, as increases in extreme precipitation in the present-day climate are offset by decreased snow cover and lower frozen water content in soils during the May–June transition months, compared to pre-industrial climate
A constant of quantum motion in two dimensions in crossed magnetic and electric fields
We consider the quantum dynamics of a single particle in the plane under the
influence of a constant perpendicular magnetic and a crossed electric potential
field. For a class of smooth and small potentials we construct a non-trivial
invariant of motion. Do to so we proof that the Hamiltonian is unitarily
equivalent to an effective Hamiltonian which commutes with the observable of
kinetic energy.Comment: 18 pages, 2 figures; the title was changed and several typos
corrected; to appear in J. Phys. A: Math. Theor. 43 (2010
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