# Resonance-Assisted Tunneling

@article{Brodier2002ResonanceAssistedT, title={Resonance-Assisted Tunneling}, author={O. Brodier and P. Schlagheck and D. Ullmo}, journal={Annals of Physics}, year={2002}, volume={300}, pages={88-136} }

We present evidence that tunneling processes in near-integrable systems are enhanced due to the manifestation of nonlinear resonances and their respective island chains in phase space. A semiclassical description of this \"resonance-assisted\" mechanism is given, which is based on a local perturbative description of the dynamics in the vicinity of the resonances. As underlying picture, we obtain that the quantum state is coupled, via a succession of classically forbidden transitions across… Expand

#### Figures from this paper

#### 61 Citations

On dynamical tunneling and classical resonances.

- Physics, Medicine
- The Journal of chemical physics
- 2005

It is shown that the classical phase space with its hierarchy of resonance islands completely characterizes dynamical tunneling and explicit forms of the dynamical barriers can be obtained only by identifying the key resonances. Expand

Resonance-assisted tunneling in mixed regular-chaotic systems

- Physics
- 2011

We present a comprehensive theory of resonance-assisted tunneling in quantum systems that exhibit a mixed regular-chaotic classical phase space structure. After general considerations, we… Expand

Resonance-assisted tunneling in mixed regular-chaotic systems

- Physics
- 2010

Since the early days of quantum mechanics, tunneling has been recognized as one of the hallmarks of the wave character of microscopic physics. The possibility of a quantum particle to penetrate an… Expand

Resonance- and Chaos-Assisted Tunneling

- Physics
- 2005

We consider dynamical tunneling between two symmetry-related regular islands that are separated in phase space by a chaotic sea. Such tunneling processes are dominantly governed by nonlinear… Expand

Experimental Observation of Resonance-Assisted Tunneling.

- Physics, Medicine
- Physical review letters
- 2015

We present the first experimental observation of resonance-assisted tunneling, a wave phenomenon, where regular-to-chaotic tunneling is strongly enhanced by the presence of a classical nonlinear… Expand

Semiclassical description of resonance-assisted tunneling in one-dimensional integrable models.

- Physics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2013

A semiclassical theory of the resonance-assisted tunneling process is constructed, which yields a compact analytical expression for tunnelling-induced level splittings which is found to be in very good agreement with the exactsplittings obtained through numerical diagonalization. Expand

Resonance-assisted tunneling in deformed optical microdisks with a mixed phase space.

- Physics, Medicine
- Physical review. E
- 2019

An intuitive semiclassical picture is presented that allows for an accurate prediction of decay rates of optical modes in systems with a mixed phase space and extends the perturbative description from near-integrable systems to systems with an integrable Hamiltonian. Expand

Resonance-assisted tunneling in 4D normal-form Hamiltonians

- Mathematics
- 2019

A significant enhancement of tunneling may be caused by the presence of nonlinear resonances in the corresponding classical phase space. We describe this resonance-assisted tunneling using a 4D… Expand

Resonance-assisted tunneling in four-dimensional normal-form Hamiltonians.

- Physics, Medicine
- Physical review. E
- 2019

It is demonstrated that the double resonance gives rise to a complicated tunneling peak structure in Hamiltonian systems with an at least four-dimensional phase space and the underlying mechanism of enhancement and suppression of tunneling is revealed. Expand

Tunneling of quantum particle in parametrically driven double-well system

- Physics
- 2005

Abstract We numerically study a wavepacket tunneling in one-dimensional symmetric double-well potential with a coherent perturbation. In the classical dynamics, such a system shows chaotic behavior… Expand

#### References

SHOWING 1-10 OF 51 REFERENCES

Resonance-assisted tunneling in near-integrable systems.

- Physics, Medicine
- Physical review letters
- 2001

Dynamical tunneling between symmetry related invariant tori is studied in the near-integrable regime and the exponential decay of the wave functions in the classically forbidden region is modified due to coupling processes that are mediated by classical resonances. Expand

The level splitting distribution in chaos-assisted tunnelling

- Mathematics, Physics
- 1996

A compound tunneling mechanism from one integrable region to another mediated by a delocalized state in an intermediate chaotic region of phase space was recently introduced to explain peculiar… Expand

Dynamical tunneling in mixed systems

- Physics
- 1998

We study quantum-mechanical tunneling in mixed dynamical systems between symmetry-related phase space tori separated by a chaotic layer. Considering, e.g., the annular billiard we decompose… Expand

Semiclassical quantization of slightly nonresonant systems: Avoided crossings, dynamical tunneling, and molecular spectra

- Physics
- 1986

An important problem in the spectroscopy of isolated molecules is the passage of a system through an isolated internal nonlinear resonance as the total energy is changed. The spectral signature of… Expand

Quantum dynamical tunneling in bound states

- Physics
- 1981

Tunneling involves an allowed quantum event which fails to take place classically. Dynamical tunneling is the subset of such events which do not involve a classically insurmountable potential… Expand

Fluctuations and decoherence in chaos-assisted tunneling.

- Physics, Medicine
- Physical review letters
- 2002

This work examines the dependence of the tunneling dynamics on the system parameters and indicates how the observed features provide evidence for chaos-assisted (three-state) tunneling. Expand

Semiclassical description of tunneling in mixed systems: Case of the annular billiard.

- Physics, Medicine
- Physical review letters
- 1995

This work considers the annular billiard, and uses scattering theory to relate the splitting of quasidegenerate states quantized on the two regular regions to specific paths connecting them, and gives analytical expressions for the splittings. Expand

Ionization via chaos assisted tunneling

- Physics
- 1998

A simple example of quantum transport in a classically chaotic system is studied. It consists in a single state lying on a regular island (a stable primary resonance island) that may tunnel into a… Expand

Quantum tunneling and chaotic dynamics

- Physics
- 1993

Abstract We investigate the effect of the structure of a mixed (regular and chaotic) phase-space on the process of tunneling. This is done by studying the way in which classical transport in… Expand

Dynamical tunnelling of ultracold atoms

- Physics, Medicine
- Nature
- 2001

Dynamical tunnelling of ultracold atoms from a Bose–Einstein condensate in an amplitude-modulated optical standing wave is observed, observing coherent tunneling back and forth between their initial state of oscillatory motion and the state oscillating 180° out of phase with the initial state. Expand