628 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
Resonant symmetry lifting in a parametrically modulated oscillator
We study a parametrically modulated oscillator that has two stable states of
vibrations at half the modulation frequency . Fluctuations of the
oscillator lead to interstate switching. A comparatively weak additional field
can strongly affect the switching rates, because it changes the switching
activation energies. The change is linear in the field amplitude. When the
additional field frequency is , the field makes the
populations of the vibrational states different thus lifting the states
symmetry. If differs from , the field modulates the
state populations at the difference frequency, leading to fluctuation-mediated
wave mixing. For an underdamped oscillator, the change of the activation energy
displays characteristic resonant peaks as a function of frequency
Displacement Detection with a Vibrating RF SQUID: Beating the Standard Linear Limit
We study a novel configuration for displacement detection consisting of a
nanomechanical resonator coupled to both, a radio frequency superconducting
interference device (RF SQUID) and to a superconducting stripline resonator. We
employ an adiabatic approximation and rotating wave approximation and calculate
the displacement sensitivity. We study the performance of such a displacement
detector when the stripline resonator is driven into a region of nonlinear
oscillations. In this region the system exhibits noise squeezing in the output
signal when homodyne detection is employed for readout. We show that
displacement sensitivity of the device in this region may exceed the upper
bound imposed upon the sensitivity when operating in the linear region. On the
other hand, we find that the high displacement sensitivity is accompanied by a
slowing down of the response of the system, resulting in a limited bandwidth
Semiclassical theory of energy diffusive escape in a Duffing oscillator
Motivated by recent experimental progress to read out quantum bits
implemented in superconducting circuits via the phenomenon of dynamical
bifurcation, transitions between steady orbits in a driven anharmonic
oscillator, the Duffing oscillator, are analyzed. In the regime of weak
dissipation a consistent master equation in the semiclassical limit is derived
to capture the intimate relation between finite tunneling and reflection and
bath induced quantum fluctuations. From the corresponding steady state
distributions analytical expressions for the switching probabilities are
obtained. It is shown that a reduction of the transition rate due to finite
reflection at the phase-space barrier is overcompensated by an increase due to
environmental quantum fluctuations that are specific for diffusion processes
over dynamical barriers. Moreover, it is revealed that close to the bifurcation
threshold the escape dynamics enters an overdamped domain such that the quantum
mechanical energy scale associated with friction even exceeds the thermal
energy scale
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
Many-particle confinement by constructed disorder and quantum computing
Many-particle confinement (localization) is studied for a 1D system of
spinless fermions with nearest-neighbor hopping and interaction, or
equivalently, for an anisotropic Heisenberg spin-1/2 chain. This system is
frequently used to model quantum computers with perpetually coupled qubits. We
construct a bounded sequence of site energies that leads to strong
single-particle confinement of all states on individual sites. We show that
this sequence also leads to a confinement of all many-particle states in an
infinite system for a time that scales as a high power of the reciprocal
hopping integral. The confinement is achieved for strong interaction between
the particles while keeping the overall bandwidth of site energies
comparatively small. The results show viability of quantum computing with
time-independent qubit coupling.Comment: An invited paper for the topical issue of J. Opt. B on quantum
contro
Scaling in activated escape of underdamped systems
Noise-induced escape from a metastable state of a dynamical system is studied
close to a saddle-node bifurcation point, but in the region where the system
remains underdamped. The activation energy of escape scales as a power of the
distance to the bifurcation point. We find two types of scaling and the
corresponding critical exponents.Comment: 9 page
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
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