696 research outputs found
Poisson noise induced switching in driven micromechanical resonators
We study Poisson-noise induced switching between coexisting vibrational
states in driven nonlinear micromechanical resonators. In contrast to Gaussian
noise induced switching, the measured logarithm of the switching rate is
proportional not to the reciprocal noise intensity, but to its logarithm, for
fixed pulse area. We also find that the switching rate logarithm varies as a
square root of the distance to the bifurcation point, instead of the
conventional scaling with exponent 3/2.Comment: accepted by PR
Spectrum of an oscillator with jumping frequency and the interference of partial susceptibilities
We study an underdamped oscillator with shot-noise frequency fluctuations.
The oscillator spectrum is determined by the interference of the
susceptibilities for different eigenfrequencies. Depending on the parameters,
it has a fine structure or displays a single asymmetric peak. For
nano-mechanical resonators with a fluctuating number of attached molecules, the
spectrum is found in a simple analytical form. The results bear on various
types of systems where the reciprocal correlation time of frequency
fluctuations can be comparable to the typical frequency jumps
Exponential peak and scaling of work fluctuations in modulated systems
We extend the stationary-state work fluctuation theorem to periodically
modulated nonlinear systems. Such systems often have coexisting stable periodic
states. We show that work fluctuations sharply increase near a kinetic phase
transition where the state populations are close to each other. The work
variance is proportional here to the reciprocal rate of interstate switching.
We also show that the variance displays scaling with the distance to a
bifurcation point and find the critical exponent for a saddle-node bifurcation
Laser-like Instabilities in Quantum Nano-electromechanical Systems
We discuss negative damping regimes in quantum nano-electromechanical systems
formed by coupling a mechanical oscillator to a single-electron transistor
(normal or superconducting). Using an analogy to a laser with a tunable
atom-field coupling, we demonstrate how these effects scale with system
parameters. We also discuss the fluctuation physics of both the oscillator and
the single-electron transistor in this regime, and the degree to which the
oscillator motion is coherent.Comment: 4+ pages, 1 figure; reference to the work of Dykman and Krivoglaz
adde
Cooling and squeezing via quadratic optomechanical coupling
We explore the physics of optomechanical systems in which an optical cavity
mode is coupled parametrically to the square of the position of a mechanical
oscillator. We derive an effective master equation describing two-phonon
cooling of the mechanical oscillator. We show that for high temperatures and
weak coupling, the steady-state phonon number distribution is non-thermal
(Gaussian) and that even for strong cooling the mean phonon number remains
finite. Moreover, we demonstrate how to achieve mechanical squeezing by driving
the cavity with two beams. Finally, we calculate the optical output and
squeezing spectra. Implications for optomechanics experiments with the
membrane-in-the-middle geometry or ultracold atoms in optical resonators are
discussed.Comment: 4 pages, 3 figure
Quasienergy description of the driven Jaynes-Cummings model
We analyze the driven resonantly coupled Jaynes-Cummings model in terms of a
quasienergy approach by switching to a frame rotating with the external
modulation frequency and by using the dressed atom picture. A quasienergy
surface in phase space emerges whose level spacing is governed by a rescaled
effective Planck constant. Moreover, the well-known multiphoton transitions can
be reinterpreted as resonant tunneling transitions from the local maximum of
the quasienergy surface. Most importantly, the driving defines a quasienergy
well which is nonperturbative in nature. The quantum mechanical quasienergy
state localized at its bottom is squeezed. In the Purcell limited regime, the
potential well is metastable and the effective local temperature close to its
minimum is uniquely determined by the squeezing factor. The activation occurs
in this case via dressed spin flip transitions rather than via quantum
activation as in other driven nonlinear quantum systems such as the quantum
Duffing oscillator. The local maximum is in general stable. However, in
presence of resonant coherent or dissipative tunneling transitions the system
can escape from it and a stationary state arises as a statistical mixture of
quasienergy states being localized in the two basins of attraction. This gives
rise to a resonant or an antiresonant nonlinear response of the cavity at
multiphoton transitions. The model finds direct application in recent
experiments with a driven superconducting circuit QED setup.Comment: 13 pages, 8 fi
Foundations for Cooperating with Control Noise in the Manipulation of Quantum Dynamics
This paper develops the theoretical foundations for the ability of a control
field to cooperate with noise in the manipulation of quantum dynamics. The
noise enters as run-to-run variations in the control amplitudes, phases and
frequencies with the observation being an ensemble average over many runs as is
commonly done in the laboratory. Weak field perturbation theory is developed to
show that noise in the amplitude and frequency components of the control field
can enhance the process of population transfer in a multilevel ladder system.
The analytical results in this paper support the point that under suitable
conditions an optimal field can cooperate with noise to improve the control
outcome.Comment: submitted to Phys. Rev.
Dynamical multistability in high-finesse micromechanical optical cavities
We analyze the nonlinear dynamics of a high-finesse optical cavity in which
one mirror is mounted on a flexible mechanical element. We find that this
system is governed by an array of dynamical attractors, which arise from
phase-locking between the mechanical oscillations of the mirror and the ringing
of the light intensity in the cavity. We describe an analytical approximation
to map out the diagram of attractors in parameter space, derive the slow
amplitude dynamics of the system, including thermally activated hopping between
different attractors, and suggest a scheme for exploiting the dynamical
multistability in the measurement of small displacements.Comment: 5 pages, 4 figure
Momentum average approximation for models with electron-phonon coupling dependent on the phonon momentum
We generalize the momentum average (MA) approximation to study the properties
of models with momentum-dependent electron-phonon coupling. As in the case of
the application of the original MA to the Holstein model, the results are
analytical, numerically trivial to evaluate, exact for both zero bandwidth and
for zero electron-phonon coupling, and are accurate everywhere in parameter
space. Comparison with available numerical data confirms this accuracy. We then
show that further improvements can be obtained based on variational
considerations, using the one-dimensional breathing-mode Hamiltonian as a
specific example. For example, by using this variational MA, we obtain ground
state energies within at most 0.3% error of the numerical data.Comment: 15 pages, 10 figure
- …