# Bistability and chaos at low levels of quanta.

@article{Gevorgyan2013BistabilityAC, title={Bistability and chaos at low levels of quanta.}, author={Tigran V. Gevorgyan and Anna R. Shahinyan and Lock Yue Chew and G. Y. Kryuchkyan}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2013}, volume={88 2}, pages={ 022910 } }

We study nonlinear phenomena of bistability and chaos at a level of few quanta. For this purpose, we consider a single-mode dissipative oscillator with strong Kerr nonlinearity with respect to the dissipation rate driven by a monochromatic force as well as by a train of Gaussian pulses. The quantum effects and decoherence in the oscillatory mode are investigated in the framework of the purity of states and the Wigner functions calculated from the master equation. We demonstrate the quantum…

## Topics from this paper

## 12 Citations

Quantum properties of a strongly driven Josephson junction

- PhysicsPhysical Review B
- 2019

A Josephson junction embedded in a dissipative circuit can be externally driven to induce nonlinear dynamics of its phase. Classically, under sufficiently strong driving and weak damping, dynamic…

Bistability in a hyperchaotic system with a line equilibrium

- Physics
- 2014

A hyperchaotic system with an infinite line of equilibrium points is described. A criterion is proposed for quantifying the hyperchaos, and the position in the three-dimensional parameter space where…

Selective excitations of a Kerr-nonlinear resonator: exactly solvable approach

- Physics
- 2015

Abstract
We study Kerr nonlinear resonators (KNR) driven by a continuous wave field in quantum
regimes where strong Kerr interactions give rise to selective resonant excitations of
oscillatory modes.…

Nonlinear coupler operating on Werner-like states—entanglement creation, its enhancement, and preservation

- Physics
- 2014

We discuss a model of two nonlinear Kerr-like oscillators, mutually coupled and excited by parametric process. We show that the system’s evolution, starting from Werner-like states, remains closed…

Excitations of photon-number states in Kerr nonlinear resonator at finite temperatures

- Physics
- 2014

AbstractWe investigate temperature reservoir effects in a lossy Kerr nonlinear resonator considering selective excitation of ooscillatory mode driven by a sequence of Gaussian pulses. In this way, we…

Simplified P-representation operator correspondence applied to quantum systems with generalized Kerr nonlinearity

- PhysicsModern Physics Letters B
- 2019

A simplified operator correspondence scheme is derived to address nonlinear quantum systems within the framework of the [Formula: see text]-representation. The simplified method is applied to a…

Two proposals of quantum chaos indicators related to the mean number of photons: pulsed Kerr-like oscillator case

- Physics, EngineeringPolish-Slovak-Czech Optical Conference on Wave and Quantum Aspects of Contemporary Optics
- 2016

We propose two parameters which are mutually related to the fidelity between two states1-4 and mean number of photons. We discuss them for situations corresponding to the regular and chaotic behavior…

Ground-state entanglement of spin-1 bosons undergoing superexchange interactions in optical superlattices

- Physics
- 2014

We will discuss a model with ultracold atoms confined in optical superlattices. In particular, we will study the ground-state properties of two spin-1 bosons trapped in a double-well potential.…

Born's rule and measurement

- Computer Science, Physics
- 2019

This paper gives a self-contained, deductive introduction to quantum measurement and Born's rule, in its generalized form that applies to the results of measurements described by POVMs.

Quantum mechanics via quantum tomography

- Physics
- 2021

Starting from a new basic principle inspired by quantum tomography rather than from Born’s rule, this paper gives an elementary, and self-contained deductive approach to quantum mechanics and quantum…

## References

SHOWING 1-10 OF 67 REFERENCES

Dissipative Chaos in Quantum Distributions

- Physics
- 2010

We discuss some problems of dissipative chaos for open quantum systemsin the framework of semiclassical and quantum distributions. For this goal,we propose a driven nonlinear oscillator with…

Chaos and time-series analysis

- Mathematics
- 2001

Preface 1. Introduction 2. One-dimensional maps 3. Nonchaotic multidimensional flows 4. Dynamical systems theory 5. Lyapunov exponents 6. Strange attractors 7. Bifurcations 8. Hamiltonian chaos 9.…

Progress in optics

- PhysicsIEEE Journal of Quantum Electronics
- 1980

Have you ever felt that the very title, Progress in Optics, conjured an image in your mind? Don’t you see a row of handsomely printed books, bearing the editorial stamp of one of the most brilliant…

Quantum State Diffusion

- Physics
- 1998

1. Introduction 2. Brownian motion and Ito calculus 3. Open quantum systems 4. Quantum state diffusion 5. Localisation 6. Numerical methods and examples 7. Quantum foundations 8. Primary state…

"J."

- 1890

however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)…

A Review of Scientific Instruments

- EngineeringNature
- 1952

Journal of Scientific InstrumentsEditor: Dr. H. R. Lang. Vol. 28 and Supplement No. 1, 1951. Pp. xvi + 388 + iii + 80. (London: Institute of Physics, 1951.) Bound, £3 12s.; unbound, £3.

24

- 2002

We study the relation between the number of firms and market power in experimental oligopolies. Price competition under decreasing returns involves a wide interval of pure strategy equilibrium…

Phys

- Rev. Lett. 81, 1203 (1998); 82, 241
- 1999

A: Math

- Gen. 13, 725
- 1980

Nature (London) 430

- 329 (2004). 022910-8 BISTABILITY AND CHAOS AT LOW LEVELS OF QUANTA PHYSICAL REVIEW E 88, 022910
- 2013