100 research outputs found
Noise-Induced Linearisation and Delinearisation
It is demonstrated, by means of analogue electronic simulation and
theoretically, that external noise can markedly change the character of the
response of a nonlinear system to a low-frequency periodic field. In general,
noise of sufficient intensity {\it linearises} the response. For certain
parameter ranges in particular cases, however, an increase in the noise
intensity can sometime have the opposite effect and is shown to {\it
delinearise} the response. The physical origins of these contrary behaviours
are discussed.Comment: 17 pages. No special macros. Figures on reques
Dephasing with strings attached
Motivated by the existence of mobile low-energy excitations like domain walls
in one dimension or gauge-charged fractionalized particles in higher
dimensions, we compare quantum dynamics in the presence of weak Markovian
dephasing for a particle hopping on a chain and for an Ising domain wall whose
motion leaves behind a string of flipped spins. Exact solutions show that the
two models have near identical transport responses in the bulk. On the other
hand, in finite-length chains, the broadening of discrete spectral lines is
much more noticeable in the case of a domain wall. These results may be of
relevance to a broad class of systems including quasi-1D antiferromagnets,
polymer chains, and even retinal systems
The Geometry of Most Probable Trajectories in Noise-Driven Dynamical Systems
This paper presents a heuristic derivation of a geometric minimum action
method that can be used to determine most-probable transition paths in
noise-driven dynamical systems. Particular attention is focused on systems that
violate detailed balance, and the role of the stochastic vorticity tensor is
emphasized. The general method is explored through a detailed study of a
two-dimensional quadratic shear flow which exhibits bifurcating most-probable
transition pathways.Comment: 8 pages, 7 figure
On the Energy Transfer Performance of Mechanical Nanoresonators Coupled with Electromagnetic Fields
We study the energy transfer performance in electrically and magnetically
coupled mechanical nanoresonators. Using the resonant scattering theory, we
show that magnetically coupled resonators can achieve the same energy transfer
performance as for their electrically coupled counterparts, or even outperform
them within the scale of interest. Magnetic and electric coupling are compared
in the Nanotube Radio, a realistic example of a nano-scale mechanical
resonator. The energy transfer performance is also discussed for a newly
proposed bio-nanoresonator composed of a magnetosomes coated with a net of
protein fibers.Comment: 9 Pages, 3 Figure
Single-shot qubit readout in circuit Quantum Electrodynamics
The future development of quantum information using superconducting circuits
requires Josephson qubits [1] with long coherence times combined to a
high-fidelity readout. Major progress in the control of coherence has recently
been achieved using circuit quantum electrodynamics (cQED) architectures [2,
3], where the qubit is embedded in a coplanar waveguide resonator (CPWR) which
both provides a well controlled electromagnetic environment and serves as qubit
readout. In particular a new qubit design, the transmon, yields reproducibly
long coherence times [4, 5]. However, a high-fidelity single-shot readout of
the transmon, highly desirable for running simple quantum algorithms or measur-
ing quantum correlations in multi-qubit experiments, is still lacking. In this
work, we demonstrate a new transmon circuit where the CPWR is turned into a
sample-and-hold detector, namely a Josephson Bifurcation Amplifer (JBA) [6, 7],
which allows both fast measurement and single-shot discrimination of the qubit
states. We report Rabi oscillations with a high visibility of 94% together with
dephasing and relaxation times longer than 0:5 \mu\s. By performing two
subsequent measurements, we also demonstrate that this new readout does not
induce extra qubit relaxation.Comment: 14 pages including 4 figures, preprint forma
Finite-size and correlation-induced effects in Mean-field Dynamics
The brain's activity is characterized by the interaction of a very large
number of neurons that are strongly affected by noise. However, signals often
arise at macroscopic scales integrating the effect of many neurons into a
reliable pattern of activity. In order to study such large neuronal assemblies,
one is often led to derive mean-field limits summarizing the effect of the
interaction of a large number of neurons into an effective signal. Classical
mean-field approaches consider the evolution of a deterministic variable, the
mean activity, thus neglecting the stochastic nature of neural behavior. In
this article, we build upon two recent approaches that include correlations and
higher order moments in mean-field equations, and study how these stochastic
effects influence the solutions of the mean-field equations, both in the limit
of an infinite number of neurons and for large yet finite networks. We
introduce a new model, the infinite model, which arises from both equations by
a rescaling of the variables and, which is invertible for finite-size networks,
and hence, provides equivalent equations to those previously derived models.
The study of this model allows us to understand qualitative behavior of such
large-scale networks. We show that, though the solutions of the deterministic
mean-field equation constitute uncorrelated solutions of the new mean-field
equations, the stability properties of limit cycles are modified by the
presence of correlations, and additional non-trivial behaviors including
periodic orbits appear when there were none in the mean field. The origin of
all these behaviors is then explored in finite-size networks where interesting
mesoscopic scale effects appear. This study leads us to show that the
infinite-size system appears as a singular limit of the network equations, and
for any finite network, the system will differ from the infinite system
Resolving photon number states in a superconducting circuit
Electromagnetic signals are always composed of photons, though in the circuit
domain those signals are carried as voltages and currents on wires, and the
discreteness of the photon's energy is usually not evident. However, by
coupling a superconducting qubit to signals on a microwave transmission line,
it is possible to construct an integrated circuit where the presence or absence
of even a single photon can have a dramatic effect. This system is called
circuit quantum electrodynamics (QED) because it is the circuit equivalent of
the atom-photon interaction in cavity QED. Previously, circuit QED devices were
shown to reach the resonant strong coupling regime, where a single qubit can
absorb and re-emit a single photon many times. Here, we report a circuit QED
experiment which achieves the strong dispersive limit, a new regime of cavity
QED in which a single photon has a large effect on the qubit or atom without
ever being absorbed. The hallmark of this strong dispersive regime is that the
qubit transition can be resolved into a separate spectral line for each photon
number state of the microwave field. The strength of each line is a measure of
the probability to find the corresponding photon number in the cavity. This
effect has been used to distinguish between coherent and thermal fields and
could be used to create a photon statistics analyzer. Since no photons are
absorbed by this process, one should be able to generate non-classical states
of light by measurement and perform qubit-photon conditional logic, the basis
of a logic bus for a quantum computer.Comment: 6 pages, 4 figures, hi-res version at
http://www.eng.yale.edu/rslab/papers/numbersplitting_hires.pd
Evolution of opinions on social networks in the presence of competing committed groups
Public opinion is often affected by the presence of committed groups of
individuals dedicated to competing points of view. Using a model of pairwise
social influence, we study how the presence of such groups within social
networks affects the outcome and the speed of evolution of the overall opinion
on the network. Earlier work indicated that a single committed group within a
dense social network can cause the entire network to quickly adopt the group's
opinion (in times scaling logarithmically with the network size), so long as
the committed group constitutes more than about 10% of the population (with the
findings being qualitatively similar for sparse networks as well). Here we
study the more general case of opinion evolution when two groups committed to
distinct, competing opinions and , and constituting fractions and
of the total population respectively, are present in the network. We show
for stylized social networks (including Erd\H{o}s-R\'enyi random graphs and
Barab\'asi-Albert scale-free networks) that the phase diagram of this system in
parameter space consists of two regions, one where two stable
steady-states coexist, and the remaining where only a single stable
steady-state exists. These two regions are separated by two fold-bifurcation
(spinodal) lines which meet tangentially and terminate at a cusp (critical
point). We provide further insights to the phase diagram and to the nature of
the underlying phase transitions by investigating the model on infinite
(mean-field limit), finite complete graphs and finite sparse networks. For the
latter case, we also derive the scaling exponent associated with the
exponential growth of switching times as a function of the distance from the
critical point.Comment: 23 pages: 15 pages + 7 figures (main text), 8 pages + 1 figure + 1
table (supplementary info
Motional Averaging in a Superconducting Qubit
Superconducting circuits with Josephson junctions are promising candidates
for developing future quantum technologies. Of particular interest is to use
these circuits to study effects that typically occur in complex
condensed-matter systems. Here, we employ a superconducting quantum bit
(qubit),a transmon, to carry out an analog simulation of motional averaging, a
phenomenon initially observed in nuclear magnetic resonance (NMR) spectroscopy.
To realize this effect, the flux bias of the transmon is modulated by a
controllable pseudo-random telegraph noise, resulting in stochastic jumping of
the energy separation between two discrete values. When the jumping is faster
than a dynamical threshold set by the frequency displacement of the levels, the
two separated spectral lines merge into a single narrow-width,
motional-averaged line. With sinusoidal modulation a complex pattern of
additional sidebands is observed. We demonstrate experimentally that the
modulated system remains quantum coherent, with modified transition
frequencies, Rabi couplings, and dephasing rates. These results represent the
first steps towards more advanced quantum simulations using artificial atoms.Comment: Main text (5 pages and 4 figures) and Supplementary Information (11
pages and 5 figures
Quantum non-demolition measurement of a superconducting two-level system
In quantum mechanics, the process of measurement is a subtle interplay
between extraction of information and disturbance of the state of the quantum
system. A quantum non-demolition (QND) measurement minimizes this disturbance
by using a particular system - detector interaction which preserves the
eigenstates of a suitable operator of the quantum system. This leads to an
ideal projective measurement. We present experiments in which we perform two
consecutive measurements on a quantum two -level system, a superconducting flux
qubit, by probing the hysteretic behaviour of a coupled nonlinear resonator.
The large correlation between the results of the two measurements demonstrates
the QND nature of the readout method. The fact that a QND measurement is
possible for superconducting qubits strengthens the notion that these
fabricated mesoscopic systems are to be regarded as fundamental quantum
objects. Our results are also relevant for quantum information processing,
where projective measurements are used for protocols like state preparation and
error correction.Comment: 14 pages, 4 figure
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