617 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
Flux-Across-Surfaces Theorem for a Dirac Particle
We consider the asymptotic evolution of a relativistic spin-1/2-particle.
i.e. a particle whose wavefunction satisfies the Dirac equation with external
static potential. We prove that the probability for the particle crossing a
(detector) surface converges to the probability, that the direction of the
momentum of the particle lies within the solid angle defined by the (detector)
surface, as the distance of the surface goes to infinity. This generalizes
earlier non relativistic results, known as flux across surfaces theorems, to
the relativistic regime
High Fidelity Adiabatic Quantum Computation via Dynamical Decoupling
We introduce high-order dynamical decoupling strategies for open system
adiabatic quantum computation. Our numerical results demonstrate that a
judicious choice of high-order dynamical decoupling method, in conjunction with
an encoding which allows computation to proceed alongside decoupling, can
dramatically enhance the fidelity of adiabatic quantum computation in spite of
decoherence.Comment: 5 pages, 4 figure
Necessary Condition for the Quantum Adiabatic Approximation
A gapped quantum system that is adiabatically perturbed remains approximately
in its eigenstate after the evolution. We prove that, for constant gap, general
quantum processes that approximately prepare the final eigenstate require a
minimum time proportional to the ratio of the length of the eigenstate path to
the gap. Thus, no rigorous adiabatic condition can yield a smaller cost. We
also give a necessary condition for the adiabatic approximation that depends on
local properties of the path, which is appropriate when the gap varies.Comment: 5 pages, 1 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
Adiabatic quantum algorithm for search engine ranking
We propose an adiabatic quantum algorithm for generating a quantum pure state
encoding of the PageRank vector, the most widely used tool in ranking the
relative importance of internet pages. We present extensive numerical
simulations which provide evidence that this algorithm can prepare the quantum
PageRank state in a time which, on average, scales polylogarithmically in the
number of webpages. We argue that the main topological feature of the
underlying web graph allowing for such a scaling is the out-degree
distribution. The top ranked entries of the quantum PageRank state
can then be estimated with a polynomial quantum speedup. Moreover, the quantum
PageRank state can be used in "q-sampling" protocols for testing properties of
distributions, which require exponentially fewer measurements than all
classical schemes designed for the same task. This can be used to decide
whether to run a classical update of the PageRank.Comment: 7 pages, 5 figures; closer to published versio
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
Control of microwave signals using circuit nano-electromechanics
Waveguide resonators are crucial elements in sensitive astrophysical
detectors [1] and circuit quantum electrodynamics (cQED) [2]. Coupled to
artificial atoms in the form of superconducting qubits [3, 4], they now provide
a technologically promising and scalable platform for quantum information
processing tasks [2, 5-8]. Coupling these circuits, in situ, to other quantum
systems, such as molecules [9, 10], spin ensembles [11, 12], quantum dots [13]
or mechanical oscillators [14, 15] has been explored to realize hybrid systems
with extended functionality. Here, we couple a superconducting coplanar
waveguide resonator to a nano-coshmechanical oscillator, and demonstrate
all-microwave field controlled slowing, advancing and switching of microwave
signals. This is enabled by utilizing electromechanically induced transparency
[16-18], an effect analogous to electromagnetically induced transparency (EIT)
in atomic physics [19]. The exquisite temporal control gained over this
phenomenon provides a route towards realizing advanced protocols for storage of
both classical and quantum microwave signals [20-22], extending the toolbox of
control techniques of the microwave field.Comment: 9 figure
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