Quantum stochastic resonance

Origin of photoinduced DC current and two-level population dynamics in a single molecule

Studying the photoinduced changes of materials with atomic-scale spatial resolution can provide a fundamental understanding of light-matter interaction. A long-standing impediment has been the detrimental thermal effects on the stability of the tunneling gap from intensity-modulated laser irradiation of the scanning tunneling microscope junction. Photoinduced DC current transduces photons to an electric current and is widely applied in optoelectronics as switches and signal transmission. Our results revealed the origin of the light-induced DC current and related it to the two-level population dynamics and related nonlinearity in the conductance of a single molecule. Here, we compensated for the near-visible laser-induced thermal effects to demonstrate photoinduced DC current spectroscopy and microscopy and to observe the persistent photoconductivity of a two-level pyrrolidine molecule. The methodology can be generally applied to the coupling of light to scan probes to investigate light-matter interactions at the atomic scale.

Quantum stochastic resonance of individual Fe atoms

Stochastic resonance, where noise synchronizes a system's response to an external drive, is a wide-reaching phenomenon found in noisy systems spanning from the dynamics of neurons to the periodicity of ice ages. Quantum tunneling can extend stochastic resonance to the quantum realm. We demonstrate quantum stochastic resonance for magnetic transitions in atoms by inelastic electron tunneling with a scanning tunneling microscope. Stochastic resonance is shown deep in the quantum regime, where spin-state fluctuations are driven by tunneling of the magnetization, and in a semiclassical crossover region, where thermally excited electrons drive transitions between ground and excited states. Inducing synchronization by periodically modulating transition rates provides a general mechanism to determine real-time spin dynamics ranging from milliseconds to picoseconds.

Characterizing stochastic resonance in a triple cavity

Many biological systems possess confined structures, which produce novel influences on the dynamics. Here, stochastic resonance (SR) in a triple cavity that consists of three units and is subjected to noise, periodic force and vertical constance force is studied, by calculating the spectral amplification η numerically. Meanwhile, SR in the given triple cavity and differences from other structures are explored. First, it is found that the cavity parameters can eliminate or regulate the maximum of η and the noise intensity that induces this maximum. Second, compared to a double cavity with similar maximum/minimum widths and distances between two maximum widths as the triple cavity, η in the triple one shows a larger maximum. Next, the conversion of the natural boundary in the pure potential to the reflection boundary in the triple cavity will create the necessity of a vertical force to induce SR and lead to a decrease in the maximum of η. In addition, η monotonically decreases with the increase of the vertical force and frequency of the periodic force, while it presents several trends when increasing the periodic force's amplitude for different noise intensities. Finally, our studies are extended to the impact of fractional Gaussian noise excitations. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 2)'.

Stochastic switching in the Rydberg atomic ensemble

We demonstrated stochastic switching in a bistable system implemented with the Rydberg atomic ensemble, which is realized by cascaded Rydberg excitation in a cesium vapor cell. Measurement of Rydberg state's population by means of the electromagnetically induced transparency allows us to investigate the nonlinear behavior in Rydberg atomic ensemble experimentally. The transition between the two states of the bistable system is driven by the intensity noise of the laser beams. Rydberg atomic ensemble accumulates energy in an equilibrium situation and brings the nonlinear system across the threshold, where stochastic switching occurs between the two states.

Fast Detection of a Weak Signal by a Stochastic Resonance Induced by a Coherence Resonance in an Excitable GaAs/Al_{0.45}Ga_{0.55}As Superlattice

The effect of a coherence resonance is observed experimentally in a GaAs/Al_{0.45}Ga_{0.55}As superlattice under dc bias at room temperature, which is driven by noise. For an applied voltage, for which no current self-oscillations are observed, regular current self-oscillations with a frequency of about 82 MHz are induced by exceeding a certain noise amplitude. In addition, a novel kind of a stochastic resonance is identified, which is triggered by the coherence resonance. This stochastic resonance appears when the device is driven by an external ac signal with a frequency, which is relatively close to that of the regular current self-oscillations at the coherence resonance. The intrinsic oscillation mode in the coherence resonance is found to be phase locked by an extremely weak ac signal. It is demonstrated that an excitable superlattice device can be used for the fast detection of weak signals submerged in noise. These results are very well reproduced by results using numerical simulations based on a sequential resonant tunneling model of nonlinear electron transport in semiconductor superlattices.

Large fluctuations and singular behavior of nonequilibrium systems

We present a general geometrical approach to the problem of escape from a metastable state in the presence of noise. The accompanying analysis leads to a simple condition, based on the norm of the drift field, for determining whether caustic singularities alter the escape trajectories when detailed balance is absent. We apply our methods to systems lacking detailed balance, including a nanomagnet with a biaxial magnetic anisotropy and subject to a spin-transfer torque. The approach described within allows determination of the regions of experimental parameter space that admit caustics.

Stochastic resonance in collective exciton-polariton excitations inside a GaAs microcavity

We report the first observation of stochastic resonance in confined exciton polaritons. We evidence this phenomena by tracking the polaritons behavior through two stochastic resonance quantifiers namely the spectral magnification factor and the signal-to-noise ratio. The evolution of the stochastic resonance in the function of the modulation amplitude of the periodic excitation signal is studied. Our experimental observations are well reproduced by numerical simulations performed in the framework of the Gross-Pitaevskii equation under stochastic perturbation.

Double resonance in the infinite-range quantum Ising model

We study quantum resonance behavior of the infinite-range kinetic Ising model at zero temperature. Numerical integration of the time-dependent Schrödinger equation in the presence of an external magnetic field in the z direction is performed at various transverse field strengths g. It is revealed that two resonance peaks occur when the energy gap matches the external driving frequency at two distinct values of g, one below and the other above the quantum phase transition. From the similar observations already made in classical systems with phase transitions, we propose that the double resonance peaks should be a generic feature of continuous transitions, for both quantum and classical many-body systems.

Classical-quantum crossover in magnetic stochastic resonance in uniaxial superparamagnets

It is shown that the signal-to-noise ratio of the magnetic moment fluctuations in the magnetic stochastic resonance of a quantum uniaxial paramagnet of arbitrary spin value S subjected to a weak probing ac field H(t) = H cos Ωt and a dc bias magnetic field H(0) displays a pronounced dependence on S. The dependence arises from the quantum dynamics of spins which differs markedly from the magnetization dynamics of classical superparamagnets. In the large spin limit, S --> ∞, the quantum solutions reduce to those for a classical uniaxial superparamagnet.

Stochastic resonance in a generalized quantum Kubo oscillator

We discuss stochastic resonance in a biased linear quantum system that is subject to multiplicative and additive noises. Starting from a microscopic system-reservoir Hamiltonian, we derive a c-number analogue of the generalized Langevin equation. The developed approach puts forth a quantum mechanical generalization of the "Kubo type" oscillator which is a linear system. Such a system is often used in the literature to study various phenomena in nonequilibrium systems via a particular interaction between system and the external noise. Our analytical results proposed here have the ability to reveal the role of external noise and vis-a-vis the mechanisms and detection of subtle underlying signatures of the stochastic resonance behavior in a linear system. In our development, we show that only when the external noise possesses a "finite correlation time" the quantum effect begins to appear. We observe that the quantum effect enhances the resonance in comparison to the classical one.

Optimal stochastic enhancement of photoionization

The effect of noise on the nonlinear photoionization of an atom due to a femtosecond pulse is investigated in the framework of the stochastic Schrödinger equation. A modest amount of white noise results in an enhancement of the net ionization yield by several orders of magnitude, giving rise to a form of quantum stochastic resonance. We demonstrate that this effect is preserved if the white noise is replaced by broadband chaotic light.

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.

Quantum stochastic synchronization

We study, within the spin-boson dynamics, the synchronization of a quantum tunneling system with an external, time-periodic driving signal. As a main result, we find that at a sufficiently large system-bath coupling strength (i.e., for a friction strength alpha > 1) the thermal noise plays a constructive role in yielding forced synchronization. This noise-induced synchronization can occur when the driving frequency is larger than the zero-temperature tunneling rate. As an application evidencing the effect, we consider the charge transfer dynamics in molecular complexes.

Ghost stochastic resonance in vertical-cavity surface-emitting lasers: experiment and theory

We study the polarization response of a vertical-cavity surface-emitting laser, driven simultaneously by noise and two (or more) weak periodic signals. In the bistable regime, we observe experimentally the occurrence of stochastic resonance at a frequency that is absent in the input driving signal. The presence of this so-called ghost resonance is confirmed theoretically.

Stochastic resonance: theory and numerics

We address the phenomenon of stochastic resonance in a noisy bistable system driven by a time-dependent periodic force (not necessarily sinusoidal) and in its two-state approximation. Even for driving forces with subthreshold amplitudes, the behavior of the system response might require a nonlinear description. We introduce analytical and numerical tools to analyze the power spectral amplification and the signal-to-noise ratio in a nonlinear regime. Our analysis shows the importance of the effects of the driving force on the system fluctuations in a nonlinear regime. These effects can be usefully exploited to achieve high quality output signals with gains larger than unity, which is impossible within a linear regime.

Modulation frequency response of a bistable system with noise

We present a method to construct a modulation frequency response curve for bistable systems in the presence of noise. To this end, a small sinusoidal modulation is applied to the system such that it switches between its two stable states. The response curve we construct yields information on the nature of the physical mechanism underlying the switching process and is furthermore comparable to the standard response curves of linear systems. Our semianalytical approach, which only needs approximate Kramer rates, is in good agreement with numerical simulations. The concept is applicable to a wide range of systems.

Stochastic resonance in vertical-cavity surface-emitting lasers based on a multiple time-scale analysis

We provide analytical evidence of stochastic resonance in polarization switching vertical-cavity surface-emitting lasers (VCSELs). We describe the VCSEL by a two-mode stochastic rate equation model and apply a multiple time-scale analysis. We were able to reduce the dynamical description to a single stochastic differential equation, which is the starting point of the analytical study of stochastic resonance. We confront our results with numerical simulations on the original rate equations, validating the use of a multiple time-scale analysis on stochastic equations as an analytical tool.

Brillouin propagation modes in optical lattices: interpretation in terms of nonconventional stochastic resonance

We report the first direct observation of Brillouin-like propagation modes in a dissipative periodic optical lattice. This has been done by observing a resonant behavior of the spatial diffusion coefficient in the direction corresponding to the propagation mode with the phase velocity of the moving intensity modulation used to excite these propagation modes. Furthermore, we show theoretically that the amplitude of the Brillouin mode is a nonmonotonic function of the strength of the noise corresponding to the optical pumping, and discuss this behavior in terms of nonconventional stochastic resonance.

Quantum-fluctuation-induced spatial stochastic resonance at zero temperature

We consider a model in which the quantum fluctuation can be controlled and show that the system responds to a spatially periodic external field at zero temperature. This signifies the occurrence of spatial stochastic resonance where the fluctuations are purely quantum in nature. Various features of the phenomenon are discussed.

Phase diffusion as a model for coherent suppression of tunneling in the presence of noise

We study the stabilization of coherent suppression of tunneling in a driven double-well system subject to random periodic delta-function "kicks." We model dissipation due to this stochastic process as a phase diffusion process for an effective two-level system, and derive a corresponding set of Bloch equations with phase damping terms that agree with the periodically kicked system at discrete times. We demonstrate that the ability of noise to localize the system on either side of the double-well potential arises from overdamping of the phase of oscillation, and not from any cooperative effect between the noise and the driving field. The model is investigated with a square wave drive, which has qualitatively similar features to the widely studied cosinusoidal drive, but has the additional advantage of allowing one to derive exact analytic expressions.

Stochastic resonance and nonlinear response using NMR spectroscopy

We revisit the phenomenon of quantum stochastic resonance in the regime of validity of the Bloch equations. We find that a stochastic resonance behavior in the steady-state response of the system is present whenever the noise-induced relaxation dynamics can be characterized via a single relaxation time scale. The picture is validated by a simple nuclear magnetic resonance experiment on water.

Cooperativity and resonances in periodically driven spin-boson systems

We present an analytical recursive formulation for the quantum transport in symmetric two-level systems under the influence of both dissipation and periodic driving. The rate-matching condition for quantum stochastic resonance despite its different appearance is found to be physically the same as that in the classical case. Analyzed are also the Rabi resonance and its implication to quantum stochastic resonance. We demonstrate that no matter how weak the driving field is, transport can involve about 70% population in the vicinities of the third-harmonic as well as the fundamental-harmonic Rabi resonance. Recovered is also an adiabatic passage condition in which the transport carries a nearly 100% population in the low frequency and strong driving limit.

Stochastic resonance in the coherence of a quantum system

We demonstrate the noise-induced amplification of a weak periodic signal inscribed in the coherence of a two-level atom, interacting with a single mode of the quantized radiation field coupled to a dissipative environment.

Stochastic resonance in vertical cavity surface emitting lasers

We report a detailed experimental investigation of stochastic resonance (SR) in the polarized emission of a pump-modulated vertical cavity surface emitting laser. We characterize SR in the time and frequency domains, with a quantitative agreement with existing theories. We further report a statistical analysis of SR in terms of residence-time probability distributions exhibiting alternative features which are fully explained here. By using an accurate choice of the indicator, we are also able to give clear evidence of bona fide resonance.

Markov analysis of stochastic resonance in a periodically driven integrate-and-fire neuron

We model the dynamics of the leaky integrate-and-fire neuron under periodic stimulation as a Markov process with respect to the stimulus phase. This avoids the unrealistic assumption of a stimulus reset after each spike made in earlier papers and thus solves the long-standing reset problem. The neuron exhibits stochastic resonance, both with respect to input noise intensity and stimulus frequency. The latter resonance arises by matching the stimulus frequency to the refractory time of the neuron. The Markov approach can be generalized to other periodically driven stochastic processes containing a reset mechanism.

Quantum stochastic resonance in symmetric systems

We investigate the low-temperature quantum stochastic resonance (QSR) phenomenon in a two-level system (TLS) which is coupled to an Ohmic heat bath. In contrast to common belief we find that QSR occurs also for symmetric (i.e., unbiased) TLS's if the viscous friction parameter alpha exceeds a critical value: We demonstrate that with respect to the spectral power amplification measure QSR always occurs for alpha>1; in contrast, the output signal-to-noise ratio exhibits an amplification only for alpha>3/2.

Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs

Noise in dynamical systems is usually considered a nuisance. But in certain nonlinear systems, including electronic circuits and biological sensory apparatus, the presence of noise can in fact enhance the detection of weak signals. This phenomenon, called stochastic resonance, may find useful application in physical, technological and biomedical contexts.