Resonant activation of a Brownian particle out of a potential well: Microwave-enhanced escape from the zero-voltage state of a Josephson junction

Barrier crossing in a viscoelastic medium under active noise: Predictions of Kramers' flux-over-population method

The biochemical activity inside a cell has recently been suggested to act as a source of hydrodynamic fluctuations that can speed up or slow down enzyme catalysis [Tripathi et al., Commun. Phys. 5, 101 (2022).] The idea has been tested against and largely corroborated by simulations of activated barrier crossing in a simple fluid in the presence of thermal and athermal noise. The present paper attempts a wholly analytic solution to the same noise-driven barrier crossing problem but generalizes it to include viscoelastic memory effects of the kind likely to be present in cellular interiors. A calculation of the model's barrier crossing rate, using Kramers' flux-over-population formalism, reveals that in relation to the case where athermal noise is absent, athermal noise always accelerates barrier crossing, though the extent of enhancement depends on the duration τ0 over which the noise acts. More importantly, there exists a critical τ0-determined by the properties of the medium-at which Kramers' theory breaks down and, on approach to which, the rate grows significantly. The possibility of such a giant enhancement is potentially open to experimental validation using optically trapped nanoparticles in viscoelastic media that are acted on by externally imposed colored noise.

Josephson radiation threshold detector

A Josephson radiation threshold detector (JRTD) that is based on the threshold behaviour of a current bias Josephson junction (CBJJ) is designed and fabricated for infrared radiation (IR@1550nm) detection at low temperatures. To achieve the optimal performance, we develop a binary hypothesis detection method to calibrate Josephson threshold behaviours (i.e. the switching current distributions of the CBJJ with the Al/AlOx/Al junction) in the absence and presence of radiation. In the absence of IR radiation, the junction transitioned with a measurable voltage drop across the junction, and this signal was treated as the events of hypothesis H0. The events of junction transition observed in the presence of the IR radiation served as hypothesis H1. Considering the usual Gaussian noise and based on statistical decision theory, the accumulated data of the measured switching current distributions are processed, and the threshold sensitivity of the demonstrated JRTD device is estimated. The minimum detectable IR radiation power of the proposed detector is approximately 0.74 pW, which corresponds to the photon rate of 5.692 × 106 photons/second. Further optimisation of JRTDs to implement the desired binary detection of a single photon is still a subject of argument, at least theoretically.

Faster and More Accurate Geometrical-Optics Optical Force Calculation Using Neural Networks

Optical forces are often calculated by discretizing the trapping light beam into a set of rays and using geometrical optics to compute the exchange of momentum. However, the number of rays sets a trade-off between calculation speed and accuracy. Here, we show that using neural networks permits overcoming this limitation, obtaining not only faster but also more accurate simulations. We demonstrate this using an optically trapped spherical particle for which we obtain an analytical solution to use as ground truth. Then, we take advantage of the acceleration provided by neural networks to study the dynamics of ellipsoidal particles in a double trap, which would be computationally impossible otherwise.

Solution to the Kramers barrier crossing problem caused by two noises: Thermal noise and Poisson white noise

We consider the escape of a particle trapped in a metastable potential well and acted upon by two noises. One of the noises is thermal and the other is Poisson white noise, which is non-Gaussian. Using path integral techniques, we find an analytic solution to this generalization of the classic Kramers barrier crossing problem. Using the "barrier climbing" path, we calculate the activation exponent. We also derive an approximate expression for the prefactor. The calculated results are compared with the simulations, and a good agreement between the two is found. Our results show that, unlike in the case of thermal noise, the rate depends not just on the barrier height but also on the shape of the whole barrier. A comparison between the simulations and the theory also shows that a better approximation for the prefactor is needed for agreement for all values of the parameters.

Detection of signals in presence of noise through Josephson junction switching currents

Josephson junctions can be employed to reveal a sinusoidal signal in presence of Gaussian noise. To mimic realistic setups, the detection is performed linearly ramping the bias current until a switch to the finite voltage occurs; the analysis of the resulting switching currents can be exploited to decide about the presence of the harmonic drive. The signal is applied in two conditions: with an unknown initial phase (incoherent strategy) and with a known initial phase (coherent strategy). In both conditions, the analysis of the efficiency of the detection, performed through the signal-to-noise ratio, as estimated by the Kumar-Carrol index, shows that the dependence upon the Josephson junction ramp rate is beneficial, especially for relatively fast speed. One can conclude that the collection of the switching currents is a robust technique, and thus it is possible to exploit the advantages of a predetermined finite time to collect the data.

Noise-induced current switching in semiconductor superlattices: observation of nonexponential kinetics in a high-dimensional system

We report on measurements of first-passage-time distributions associated with current switching in weakly coupled GaAs/AlAs superlattices driven by shot noise, a system that is both far from equilibrium and high dimensional. Static current-voltage (I-V) characteristics exhibit multiple current branches and bistability; precision, high-bandwidth current switching data are collected in response to steps in the applied voltage to final voltages V1 near the end of a current branch. For a range of V1 values, the measured switching times vary stochastically. At short times (≲10  μs), the switching time distributions decay exponentially, while at longer times the distributions develop nonexponential tails that follow an approximate power law over several decades. The power law decay behavior is attributed to the presence of multiple switching pathways, which may arise from small spatial variations in the superlattice growth parameters.

Characterization of escape times of Josephson junctions for signal detection

The measurement of the escape time of a Josephson junction might be used to detect the presence of a sinusoidal signal embedded in noise when use of standard signal processing tools can be prohibitive due to the extreme weakness of the source or to the huge amount of data. In this paper we show that the prescriptions for the experimental setup and some physical behaviors depend on the detection strategy. More specifically, by exploitation of the sample mean of escape times to perform detection, two resonant regions are identified. At low frequencies there is a stochastic resonance or activation phenomenon, while near the plasma frequency a geometric resonance appears. Furthermore, detection performance in the geometric resonance region is maximized at the prescribed value of the bias current. The naive sample mean detector is outperformed, in terms of error probability, by the optimal likelihood ratio test. The latter exhibits only geometric resonance, showing monotonically increasing performance as the bias current approaches the junction critical current. In this regime the escape times are vanishingly small and therefore performance is essentially limited by measurement electronics. The behavior of the likelihood ratio and sample mean detector for different values of incoming signal to noise ratio is discussed, and a relationship with the error probability is found. Detectors based on the likelihood ratio test could be employed also to estimate unknown parameters in the applied input signal. As a prototypical example we study the phase estimation problem of a sinusoidal current, which is accomplished by using the filter bank approach. Finally we show that for a physically feasible detector the performances are found to be very close to the Cramer-Rao theoretical bound. Applications might be found, for example, in some astronomical detection problems (where the all-sky gravitational and/or radio wave search for pulsars requires the analysis of nearly sinusoidal long-lived waveforms at very low signal-to-noise ratio) or to analyze weak signals in the subterahertz range (where the traditional electronics counterpart is difficult to implement).

Detection of noise-corrupted sinusoidal signals with Josephson junctions

We investigate the possibility of exploiting the speed and low noise features of Josephson junctions for detecting sinusoidal signals masked by Gaussian noise. We show that the escape time from the static locked state of a Josephson junction is very sensitive to a small periodic signal embedded in the noise, and therefore the analysis of the escape times can be employed to reveal the presence of the sinusoidal component. We propose and characterize two detection strategies: in the first, the initial phase is supposedly unknown (incoherent strategy), while in the second, the signal phase remains unknown but is fixed (coherent strategy). Our proposals are both suboptimal, with the linear filter being the optimal detection strategy, but they present some remarkable features, such as resonant activation, that make detection through Josephson junctions appealing in some special cases.

Poisson-noise-induced escape from a metastable state

We provide a complete solution of the problems of the probability distribution and the escape rate in Poisson-noise driven systems. It includes both the exponents and the prefactors. The analysis refers to an overdamped particle in a potential well. The results apply for an arbitrary average rate of noise pulses, from slow pulse rates, where the noise acts on the system as strongly non-Gaussian, to high pulse rates, where the noise acts as effectively Gaussian.

Switching exponent scaling near bifurcation points for non-Gaussian noise

We study noise-induced switching of a system close to bifurcation parameter values where the number of stable states changes. For non-Gaussian noise, the switching exponent, which gives the logarithm of the switching rate, displays a non-power-law dependence on the distance to the bifurcation point. This dependence is found for Poisson noise. Even weak additional Gaussian noise dominates switching sufficiently close to the bifurcation point, leading to a crossover in the behavior of the switching exponent.

Noise-induced escape from bifurcating attractors: Symplectic approach in the weak-noise limit

The effect of noise is studied in one-dimensional maps undergoing transcritical, tangent, and pitchfork bifurcations. The attractors of the noiseless map become metastable states in the presence of noise. In the weak-noise limit, a symplectic two-dimensional map is associated with the original one-dimensional map. The consequences of their noninvertibility on the phase-space structures are discussed. Heteroclinic orbits are identified which play a key role in the determination of the escape rates from the metastable states. Near bifurcations, the critical slowing down justifies the use of a continuous-time approximation replacing maps by flows, which allows the analytic calculation of the escape rates. This method provides the universal scaling behavior of the escape rates at the bifurcations.

Coherent Control of Quantum Dynamics with Sequences of Unitary Phase-Kick Pulses

Coherent-optical-control schemes exploit the coherence of laser pulses to change the phases of interfering dynamical pathways and manipulate dynamical processes. These active control methods are closely related to dynamical decoupling techniques, popularized in the field of quantum information. Inspired by nuclear magnetic resonance spectroscopy, dynamical decoupling methods apply sequences of unitary operations to modify the interference phenomena responsible for the system dynamics thus also belonging to the general class of coherent-control techniques. This article reviews related developments in the fields of coherent optical control and dynamical decoupling, emphasizing the control of tunneling and decoherence in general model systems. Considering recent experimental breakthroughs in the demonstration of active control of a variety of systems, we anticipate that the reviewed coherent-control scenarios and dynamical-decoupling methods should raise significant experimental interest.

Phase dynamics of ferromagnetic Josephson junctions

We have investigated the classical phase dynamics of underdamped ferromagnetic Josephson junctions by measuring the switching probability in both the stationary and nonstationary regimes down to 350 mK. We found the escape temperature to be the bath temperature, with no evidence of additional spin noise. In the nonstationary regime, we have performed a pump-probe experiment on the Josephson phase by increasing the frequency of the junction current bias. We show that an incomplete energy relaxation leads to dynamical phase bifurcation. Bifurcation manifests itself as premature switching, resulting in a bimodal switching distribution. We directly measure the phase relaxation time tau_{phi} by following the evolution of the bimodal switching distribution when varying the bias frequency. Numerical simulations account for the experimental values of tau_{phi}.

Detecting charge noise with a Josephson junction: a problem of thermal escape in presence of non-Gaussian fluctuations

Motivated by several experimental activities to detect charge noise produced by a mesoscopic conductor with a Josephson junction as on-chip detector, the switching rate out of its zero-voltage state is studied. This process is related to the problem of thermal escape in presence of non-Gaussian fluctuations. In the relevant case of weak higher than second order cumulants, an effective Fokker-Planck equation is derived, which is then used to obtain an explicit expression for the escape rate. Specific results for the rate asymmetry due to the third moment of current noise allow to analyze experimental data and to optimize detection circuits.

Resonant symmetry lifting in a parametrically modulated oscillator

We study a parametrically modulated oscillator that has two stable states of vibration at half the modulation frequency omega{F}. 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 omega{d} is omega{F}2 , the field makes the populations of the vibrational states different, thus lifting the states symmetry. If omega{d} differs from omega{F}2 , 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.

Pathways of activated escape in periodically modulated systems

We investigate dynamics of activated escape in periodically modulated systems. The trajectories followed in escape form diffusion-broadened tubes, which are periodically repeated in time. We show that these tubes can be directly observed and find their shape. Quantitatively, the tubes are characterized by the distribution of trajectories that, after escape, pass through a given point in phase space for a given modulation phase. This distribution may display several peaks separated by the modulation period. Analytical results agree with the results of simulations of a Brownian particle in a model modulated potential.

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.

Noise-induced escape of periodically modulated systems: from weak to strong modulation

Noise-induced escape from a metastable state is studied for an overdamped periodically modulated system. We develop an asymptotic technique that gives both the instantaneous and period-average escape rates, including the prefactor, for an arbitrary modulation amplitude A . We find the parameter range where escape is strongly synchronized and the instantaneous escape rate displays sharp peaks. The peaks vary with increasing modulation frequency or amplitude from Gaussian to strongly asymmetric. The prefactor nu in the period-average escape rate depends on A nonmonotonically. Near the bifurcation amplitude A(c) it scales as nu approximately (A(c) - A)(zeta). We identify three scaling regimes, with zeta = 1/4, -1, and 1/2.

Resonant activation in a nonadiabatically driven optical lattice

We demonstrate the phenomenon of resonant activation in a nonadiabatically driven dissipative optical lattice with broken time symmetry. The resonant activation results in a resonance as a function of the driving frequency in the current of atoms through the periodic potential. We demonstrate that the resonance is produced by the interplay between deterministic driving and fluctuations, and we also show that by changing the frequency of the driving it is possible to control the direction of the diffusion.

Activated escape of periodically modulated systems

The rate of noise-induced escape from a metastable state of a periodically modulated overdamped system is found for an arbitrary modulation amplitude A. The instantaneous escape rate displays peaks that vary with the modulation from Gaussian to strongly asymmetric. The prefactor nu in the period-averaged escape rate depends on A nonmonotonically. Near the bifurcation amplitude A(c) it scales as nu proportional, variant(A(c) - A)(zeta). We identify three scaling regimes, with zeta = 1/4, -1, and 1/2.

Direct observation of dynamical bifurcation between two driven oscillation states of a Josephson junction

We performed a novel phase-sensitive microwave reflection experiment which directly probes the dynamics of the Josephson plasma resonance in both the linear and the nonlinear regime. When the junction was driven below the plasma frequency into the nonlinear regime, we observed for the first time the transition between two different dynamical states predicted for nonlinear systems. In our experiment, this transition appears as an abrupt change in the reflected signal phase at a critical excitation power. This controlled dynamical switching can form the basis of a sensitive amplifier, in particular, for the readout of superconducting qubits.

Escaping from nonhyperbolic chaotic attractors

The noise-induced escape process from a nonhyperbolic chaotic attractor is of physical and fundamental importance. We address this problem by uncovering the general mechanism of escape in the relevant low noise limit using the Hamiltonian theory of large fluctuations and by establishing the crucial role of the primary homoclinic tangency closest to the basin boundary in the dynamical process. In order to demonstrate that, we provide an unambiguous solution of the variational equations from the Hamiltonian theory. Our results are substantiated with the help of physical and dynamical paradigms, such as the Hénon and the Ikeda maps. It is further pointed out that our findings should be valid for driven flow systems and for experimental data.

Scaling and crossovers in activated escape near a bifurcation point

Near a bifurcation point a system experiences a critical slowdown. This leads to scaling behavior of fluctuations. We find that a periodically driven system may display three scaling regimes and scaling crossovers near a saddle-node bifurcation where a metastable state disappears. The rate of activated escape W scales with the driving field amplitude A as ln W proportional, variant ( A(c) -A)(xi), where A(c) is the bifurcational value of A. With increasing field frequency the critical exponent xi changes from xi=3/2 for stationary systems to a dynamical value xi=2 and then again to xi=3/2. The analytical results are in agreement with the results of asymptotic calculations in the scaling region. Numerical calculations and simulations for a model system support the theory.

Critical exponent crossovers in escape near a bifurcation point

In periodically driven systems, near a bifurcation (critical) point the period-averaged escape rate Wmacr; scales with the field amplitude A as |ln(Wmacr;| proportional, variant (A(c)-A)(xi), where A(c) is a critical amplitude. We find three scaling regions. With increasing field frequency or decreasing |A(c)-A|, the critical exponent xi changes from xi=3/2 for a stationary system to a dynamical value xi=2 and then again to xi=3/2. Monte Carlo simulations agree with the scaling theory.

Asymptotic distributions of periodically driven stochastic systems

We study the large-time behavior of Brownian particles moving through a viscous medium in a confined potential, and which are further subjected to position-dependent driving forces that are periodic in time. We focus on the case where these driving forces are rapidly oscillating with an amplitude that is not necessarily small. We develop a perturbative method for the high-frequency regime to find the large-time behavior of periodically driven stochastic systems. The asymptotic distribution of Brownian particles is then determined to second order. To first order, these particles are found to execute small-amplitude oscillations around an effective static potential that can have interesting forms.

Simple approximation of the singular probability distribution in a nonadiabatically driven system

Singular behavior and the formation of plateaus in the probability distribution in a nonadiabatically driven system are investigated numerically in the weak noise limit. A simple extension of the recently introduced logarithmic susceptibility theory is proposed to construct an approximation of the nonequilibrium potential that is valid throughout whole of the phase space.

Strong enhancement of noise-induced escape by nonadiabatic periodic driving due to transient chaos

We have found a mechanism by which a moderately weak nonadiabatic periodic driving may significantly facilitate noise-induced interwell transitions in an underdamped multiwell system. The mechanism is associated with the onset of a homoclinic tangle in the noise-free system: if the ratio of the driving amplitude A to the damping gamma exceeds a critical value approximately 1, then the basins of attraction of the linear responses related to different wells are mixed in a complex manner in some layer associated with the separatrix of the undriven nondissipative system, and the minimal energy in such layer is lower than the top of the barrier. Thus the energy to which the system needs to be activated by the noise, to be able to make a transition, is lower than the top of the barrier.