The bistable system: an archetypal model for complex systems

Bistable systems often play the role of archetypal models to understand the dynamical behavior of complex systems. Examples range from microphysics to macrophysics, bìology, chemistry and also econophysics. Moreover the statistical mechanics is essential to study the physical properties of complex systems and to investigate stochastic systems in which the microscopic degrees of freedom behave collectively over large scales. We investigate the nonlinear relaxation in a bistable system in classical and quantum systems. (i) As a first classical system, the role of the multiplicative and additive noise in the mean life time of the metastable state of an asymmetric bistable system is investigated. Thìs model is useful to describe the dynamical behavior of an out of equilibrium Ising spin system. Nonmonotonic behavior of the average lifetime as a function of both additive and multiplicative noise source intensities ìs found. (ii) The role of a non-Gaussian Lévy noise on the nonlinear dynamics of: a) a partide moving in a metastable system, b) an ecosystem composed by two competing species interacting with the surrounding environment, and c) a short overdamped Iosephson junction is investigated. a) By using the backward fractional Fokker-Planck equation we investigate the barrier crossing event and the nonlinear relaxation time for a metastable system; b) In the ecosystem, the role of two non-Gaussian noise sources in the exclusion and coexistence regimes is analyzed. Quasiperiodic oscillations and stochastic resonance phenomenon in the dynamics of the competing specìes are found: c) In the short overdamped Iosepbson, the mean escape time of the junction is investigated considering Gaussian, Cauchy- Lorentz and Lévy-Smìrnov probability distributions of the noise signals. In these conditions we find resonant activation and the first evidence of noise enhanced stability in a metastable system in the presence of Lévy noise. For Cauchy- Lorentz noise source, trapping phenomena and power law dependence on the noise intensity are observed. (iii) Finally the dynamics of a quantum particle subject to an asymmetric bistable potential and interacting with a thermal reservoir is investigated. We obtain the time evolution of the population distributions in the position eigenstates of the particle, for dìfferent values of the coupling strength with the thermal bath. The calculation is carried out by using the Feynman-Vernon functional under the discrete variable representation

TRANSIENT DYNAMICS AND ASYMPTOTIC POPULATIONS IN A DRIVEN METASTABLE QUANTUM SYSTEM

The transient dynamics of a periodically driven metastable quantum system, interacting with a heat bath, is investigated. The time evolution of the populations, within the framework of the Feynman–Vernon influ- ence functional and in the discrete variable representation, is analyzed by varying the parameters of the external driving. The results display strong non-monotonic behaviour of the populations with respect to the driving frequency

THE BISTABLE POTENTIAL: AN ARCHETYPE FOR CLASSICAL AND QUANTUM SYSTEMS

In this work we analyze the transient dynamics of three different classical and quantum systems. First, we consider a classical Brownian particle moving in an asymmetric bistable potential, subject to a multiplicative and additive noise source. We investigate the role of these two noise sources on the life time of the metastable state. A nonmonotonic behavior of the lifetime as a function of both additive and multiplicative noise intensities is found, revealing the phenomenon of noise enhanced stability. Afterward, by using a Lotka–Volterra model, the dynamics of two competing species in the presence of Lévy noise sources is analyzed. Quasiperiodic oscillations and stochastic resonance phenomenon in the dynamics of the competing species are found. Finally the dynamics of a quantum particle subject to an asymmetric bistable potential and interacting with a thermal reservoir is investigated. We use the Caldeira–Leggett model and the approach of the Feynman–Vernon functional in discrete variable representation. We obtain the time evolution of the population distributions in energy eigenstates of the particle, for different values of the coupling strength with the thermal bath

Effect of Low-frequency Noise on Adiabatic Passage in a Superconducting Nanocircuit

Recent experiments have demonstrated coherent phenomena in three-level systems based on superconducting nanocircuits. This opens the possibility to detect Stimulated Raman Adiabatic Passage (STIRAP) in artificial atoms. Low-fequency noise (often 1/f) is one of the main sources of decoherence in these systems, and we study its effect on the transfer e±ciency. We propose a way to analyze low frequency fluctuations in terms of fictitious correlated fluctuations of external parameters. We discuss a specific implementation, namely the Quantronium setup of a Cooper-pair box, showing that optimizing the trade-off between efficient coupling and protection against noise may allow us to observe coherent population transfer in this nanodevice

High-order harmonic emission from a three-level atom in a laser field

The spectrum emitted by a three-level atom in the presence of a weak laser field is given together with the population dynamics and the phase of the Fourier transform of the acceleration. Calculations show that the spectrum can be very different from that emitted by a two-level atom. When the trapping conditions are obtained, the coupling to the third level can result in a large change in the spectrum

Dynamics of a quantum particle interacting with a thermal bath and subject to an oscillating asymmetric bistable potential

Exploiting the approach of the Feynman-Vernon influence functional [1] within the framework of the discrete variable representation (DVR) [2], we consider a quantum particle described by the Caldeira-Leggett model [3]. The particle, “moving” in an asymmetric bistable potential and subject to a periodical driving, interacts with a thermal bath of harmonic oscillators. In this conditions we study the dynamics of the particle by analyzing the time evolution of the populations in the DVR. Specifically we focalize on the position eigenstate located in the shallower well, i.e. metastable state, finding a non-monotonic behaviour of the corresponding population as a function of the frequency. Moreover, for different values of the coupling strength with the thermal bath, we obtain the equilibrium energy of the particle as a function both of the amplitude and frequency of the driving force

Effect of broadband noise on adiabatic passage in superconducting nanocircuits

With the rapid technological progress in quantum-state engineering in superconducting devices there is an increasing demand for techniques of quantum control. Stimulated Raman adiabatic passage (STIRAP) is a powerful method in quantum optics which has remained largely unknown to solid-state physicists. It is used to achieve highly efficient and controlled population transfer in (discrete) multilevel quantum systems[1]. Apart from other potential applications in solid-state physics, adiabatic passage offers interesting possibilities to manipulate qubit circuits, in particular for the generation of nonclassical states in nanomechanical or electromagnetic resonators[2]. In this contribution, we study in detail a possible implementation of the STIRAP protocol in the Quantronium, a superconducting nanocircuit based on Josephson junctions in the so called charge-phase regime. Il has been proposed[2] that this devices is a good candidate for observing coherent adiabatic population transfer for its characteristics of low decoherence and efficient addressability by external AC electromagnetic fields. In particular we present a detailed analysis of the efect of broadband charge noise, which is the main source of decoherence for this device, extending to a three level system the theory proposed in Ref.[3]. It is shown that the effect of high-frequency noise is similar to the quantum optical case. The main problem in solid state devices comes from low-frequency noise, which has the 1/f form. In this case it may produce stray two-photon detunings which prevent the device to evolve adiabaticaly towards the correct target state. However inducing Zener tunneling between Autler-Townes states it is shown to increase the population transfer efficiency, minimizing the effect of low-frequency noise

Quantum Relaxation Time in Asymmetric Bistable Potential

Quantum tunneling effect occurs often in condensed matter physics, examples are JJs, heteronanostructures, etc.. The tunneling effect plays an important role in the nonlinear relaxation time from a metastable state in an open quantum system, interacting with a thermal bath. Symmetrical and asymmetric bistable systems are good quantum model systems for analysis of the "superconducting quantum bits" and decoherence phenomena. To obtain very long coherence times in the presence of interaction between the qubit and the noisy environment is one of the greatest challenges of physics. The inf1uence of the environment in quantum tunneling has been in the focus of intense research over the last years [1]-[4]. The environment is commonly described as an ensemble of harmonic oscillators (thermal bath) at thermal equilibrium at temperature T, with a bilinear coupling between the quantum system and the thermal bath. By this kind of coupling between system and environment the quantum mechanical analogue of the generalized Langevin equation can be derived [1]. Time dependent driving fields, such as laser beams, have most interesting implications for quantum systems. These time-dependent fields give rise to interesting effects, such as the coherent destruction of tunneling[5], the effect of quantum stochastic resonance[6], and the control and reduction of decoherence in open quantum systems[7]. In this work we analyze a timedependent asynmmetric bistable potential by using the approach of the Feynman-Vemon functional[8] in discrete variable representation (DVR)[9,10]. We calculate the quantum relaxation time for different values of the asymmetry parameter of the potential profile and different temperatures

RELAXATION PHENOMENA IN CLASSICAL AND QUANTUM SYSTEMS

Relaxation phenomena in three different classical and quantum systems are investigated. First, the role of multiplicative and additive noise in a classical metastable system is analyzed. The mean lifetime of the metastable state shows a nonmonotonicbehavior with a maximum as a function of both the additive and multiplicative noise intensities. In the second system, the simultaneous action of thermal and non-Gaussian noise on the dynamics of an overdamped point Josephson junction is studied. The effect of a Lévy noise generated by a Cauchy–Lorentz distribution on the mean lifetime of the superconductive metastable state, in the presence of a periodic driving, is investigated. We find resonant activation and noise enhanced stability in the presence of Lévy noise. Finally, the time evolution of a quantum particle moving in a metastable potential and interacting with a thermal reservoir is analyzed. Within the Caldeira-Legget model and the Feynman–Vernon functional approach, we obtain the time evolution of the population distributions in the position eigenstates of the particle, for different values of the thermal bath coupling strength