# Quantum versus classical effects in the chirped-drive discrete nonlinear Schrödinger equation

@article{Armon2019QuantumVC, title={Quantum versus classical effects in the chirped-drive discrete nonlinear Schr{\"o}dinger equation}, author={Tsafrir Armon and Lazar Friedland}, journal={Physical Review A}, year={2019} }

A chirped parametrically driven discrete nonlinear Schrodinger equation is discussed. It is shown that the system allows two resonant excitation mechanisms, i.e., successive two-level transitions (ladder climbing) or a continuous classical-like nonlinear phase-locking (autoresonance). Two-level arguments are used to study the ladder-climbing process, and semiclassical theory describes the autoresonance effect. The regimes of efficient excitation in the problem are identified and characterized…

## 2 Citations

### Quantum versus classical chirps in a Rydberg atom

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- 2020

The interplay between quantum-mechanical and classical evolutions in a chirped driven Rydberg atom is discussed. It is shown that the system allows two continuing resonant excitation mechanisms,…

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We observed vanishing of the transition dipole moment, interrupting vibrational ladder climbing (VLC) in molecular systems. We clarified the mechanism of this phenomenon and present a method to use…

## References

SHOWING 1-10 OF 70 REFERENCES

### Quantum and classical chirps in an anharmonic oscillator.

- PhysicsPhysical review letters
- 2012

The state dynamics of a tunable anharmonic quantum system, the Josephson phase circuit, is measured under the excitation of a frequency-chirped drive to report exponentially enhanced lifetimes of highly excited states, held by the drive.

### Quantum versus classical phase-locking transition in a frequency-chirped nonlinear oscillator

- Physics
- 2011

sionless parameters P1 = "/ √ 2m~!0� and P2 = (3~�)/(4m √ �) (", �, � and !0 being the driving amplitude, the frequency chirp rate, the nonlinearity parameter and the linear frequency of the…

### Autoresonant excitation of Bose-Einstein condensates.

- PhysicsPhysical review. E
- 2018

Controlling the state of a Bose-Einstein condensate driven by a chirped frequency perturbation in a one-dimensional anharmonic trapping potential is discussed and the transition thresholds on the driving parameter P_{1} and their width in P{1} in both the AR and LC regimes are discussed.

### Ladder Climbing and Autoresonant Acceleration of Plasma Waves.

- PhysicsPhysical review letters
- 2015

By formulating the wave dynamics within a universal Lagrangian framework, similar ladder climbing and autoresonance effects are predicted to be achievable with general linear waves in both plasma and other media.

### Anderson localization and nonlinearity in one-dimensional disordered photonic lattices.

- PhysicsPhysical review letters
- 2008

An intermediate regime is found in which the ballistic and localized components coexist while diffusive dynamics is absent and evidence is found for a faster transition into localization under nonlinear conditions.

### From quantum ladder climbing to classical autoresonance

- Physics
- 2004

The autoresonance phenomenon allows excitation of a classical, oscillatory nonlinear system to high energies by using a weak, chirped frequency forcing. Ladder climbing is its counterpart in quantum…

### Quantum versus classical dynamics in the optical centrifuge

- Physics
- 2017

The interplay between classical and quantum mechanical evolution in the optical centrifuge (OC) is discussed. The analysis is based on the quantum mechanical formalism starting from either the ground…

### Spatial autoresonance: Enhancement of mode conversion due to nonlinear phase locking

- Physics
- 1992

It is shown that the inclusion of weak nonlinearities may have a profound effect on the conservative linear mode conversion in inhomogeneous media. The phenomenon is demonstrated by adding a…

### Dynamical control of matter-wave tunneling in periodic potentials.

- PhysicsPhysical review letters
- 2007

Measurements of dynamical suppression of interwell tunneling of a Bose-Einstein condensate (BEC) in a strongly driven optical lattice show that the strong shaking does not destroy the phase coherence of the BEC, opening up the possibility of realizing quantum phase transitions by using the shaking strength as the control parameter.

### Time-dependent tunneling of Bose-Einstein condensates

- Physics
- 2000

The influence of atomic interactions on time-dependent tunneling processes of Bose-Einstein condensates is investigated. In a variety of contexts the relevant condensate dynamics can be described by…