arXiv subjects

R. Ketzmerick

Publications and source records attributed to R. Ketzmerick.

At least 19 recordsLinked to original sources

arXiv2017

Pump-power-driven mode switching in a microcavity device and its relation to Bose-Einstein condensation

We investigate the switching of the coherent emission mode of a bimodal microcavity device, occurring when the pump power is varied. We compare experimental data to theoretical results and identify the underlying mechanism to be based on the competition between the effective gain on the one hand and the intermode kinetics on the other. When the pumping is ramped up, above a threshold the mode with the largest effective gain starts to emit coherent light, corresponding to lasing. In contrast, in the limit of strong pumping it is the intermode kinetics that determines which mode acquires a large occupation and shows coherent emission. We point out that this latter mechanism is akin to the equilibrium Bose-Einstein condensation of massive bosons. Thus, the mode switching in our microcavity device can be viewed as a minimal instance of Bose-Einstein condensation of photons. We, moreover, show that the switching from one cavity mode to the other occurs always via an intermediate phase where both modes are emitting coherent light and that it is associated with both superthermal intensity fluctuations and strong anticorrelations between both modes.

physics.optics↗

arXiv2015

Observing the emergence of chaos in a many-particle quantum system

Accessing the connection between classical chaos and quantum many-body systems has been a long-standing experimental challenge. Here, we investigate the onset of chaos in periodically driven two-component Bose-Einstein condensates, whose small quantum uncertainties allow for exploring the phase space with high resolution. By analyzing the uncertainties of time-evolved many-body states, we find signatures of elliptic and hyperbolic periodic orbits generated according to the Poincaré-Birkhoff theorem, and the formation of a chaotic region at increasing driving strengths. The employed fluctuation analysis allows for probing the phase-space structure by use of only short-time quantum dynamics.

quant-ph↗

arXiv2009

Nano-wires with surface disorder: Giant localization lengths and dynamical tunneling in the presence of directed chaos

We investigate electron quantum transport through nano-wires with one-sided surface roughness in the presence of a perpendicular magnetic field. Exponentially diverging localization lengths are found in the quantum-to-classical crossover regime, controlled by tunneling between regular and chaotic regions of the underlying mixed classical phase space. We show that each regular mode possesses a well-defined mode-specific localization length. We present analytic estimates of these mode localization lengths which agree well with the numerical data. The coupling between regular and chaotic regions can be determined by varying the length of the wire leading to intricate structures in the transmission probabilities. We explain these structures quantitatively by dynamical tunneling in the presence of directed chaos.

cond-mat.mes-hall↗

arXiv2008

Dynamical tunneling in mushroom billiards

We study the fundamental question of dynamical tunneling in generic two-dimensional Hamiltonian systems by considering regular-to-chaotic tunneling rates. Experimentally, we use microwave spectra to investigate a mushroom billiard with adjustable foot height. Numerically, we obtain tunneling rates from high precision eigenvalues using the improved method of particular solutions. Analytically, a prediction is given by extending an approach using a fictitious integrable system to billiards. In contrast to previous approaches for billiards, we find agreement with experimental and numerical data without any free parameter.

nlin.CD↗

arXiv2008

Regular-to-chaotic tunneling rates using a fictitious integrable system

We derive a formula predicting dynamical tunneling rates from regular states to the chaotic sea in systems with a mixed phase space. Our approach is based on the introduction of a fictitious integrable system that resembles the regular dynamics within the island. For the standard map and other kicked systems we find agreement with numerical results for all regular states in a regime where resonance-assisted tunneling is not relevant.

nlin.CD↗

arXiv2006

Nano-wires with surface disorder: Giant localization lengths and quantum-to-classical crossover

We investigate electronic quantum transport through nano-wires with one-sided surface roughness. A magnetic field perpendicular to the scattering region is shown to lead to exponentially diverging localization lengths in the quantum-to-classical crossover regime. This effect can be quantitatively accounted for by tunneling between the regular and the chaotic components of the underlying mixed classical phase space.

cond-mat.mes-hall↗

arXiv2005

Flooding of regular islands by chaotic states

We introduce a criterion for the existence of regular states in systems with a mixed phase space. If this condition is not fulfilled chaotic eigenstates substantially extend into a regular island. Wave packets started in the chaotic sea progressively flood the island. The extent of flooding by eigenstates and wave packets increases logarithmically with the size of the chaotic sea and the time, respectively. This new effect can be observed for island chains with just 10 islands.

nlin.CD↗

arXiv2002

Universal Power-law Decay in Hamiltonian Systems?

The understanding of the asymptotic decay of correlations and of the distribution of Poincaré recurrence times $P(t)$ has been a major challenge in the field of Hamiltonian chaos for more than two decades. In a recent Letter, Chirikov and Shepelyansky claimed the universal decay $P(t) \sim t^{-3}$ for Hamiltonian systems. Their reasoning is based on renormalization arguments and numerical findings for the sticking of chaotic trajectories near a critical golden torus in the standard map. We performed extensive numerics and find clear deviations from the predicted asymptotic exponent of the decay of $P(t)$. We thereby demonstrate that even in the supposedly simple case, when a critical golden torus is present, the fundamental question of asymptotic statistics in Hamiltonian systems remains unsolved.

nlin.CD↗

arXiv2001

Do Chaotic Trajectories Care About Self-Similarity?

We investigate the relation between the chaotic dynamics and the hierarchical phase-space structure of generic Hamiltonian systems. We demonstrate that even in ideal situations when the phase space is dominated by an exactly self-similar structure, the long-time dynamics is {\it not} dominated by this structure. This has consequences for the power-law decay of correlations and Poincaré recurrences.

nlin.CD↗

arXiv2001

Superballistic spreading of wave packets

We demonstrate for various systems that the variance of a wave packet $M(t)\propto t^ν$, can show a {\it superballistic} increase with $2<ν\le3$, for parametrically large time intervals. A model is constructed which explains this phenomenon and its predictions are verified numerically for various disordered and quasi-periodic systems.

cond-mat.dis-nn↗

arXiv2000

Conductance Fluctuations of Generic Billiards: Fractal or Isolated?

We study the signatures of a classical mixed phase space for open quantum systems. We find the scaling of the break time up to which quantum mechanics mimics the classical staying probability and derive the distribution of resonance widths. Based on these results we explain why for mixed systems two types of conductance fluctuat ions were found: quantum mechanics divides the hierarchically structured chaotic component of phase space into two parts - one yields fractal conductance fluctuations while the other causes isolated resonances. In general, both types appear together, but on different energy scales.

cond-mat.mes-hall↗

arXiv2000

Metal-insulator transitions in cyclotron resonance of periodic nanostructures due to avoided band crossings

A recently found metal-insulator transition in a model for cyclotron resonance in a two-dimensional periodic potential is investigated by means of spectral properties of the time evolution operator. The previously found dynamical signatures of the transition are explained in terms of avoided band crossings due to the change of the external electric field. The occurrence of a cross-like transport is predicted and numerically confirmed.

cond-mat.mes-hall↗

arXiv2000

New Class of Eigenstates in Generic Hamiltonian Systems

In mixed systems, besides regular and chaotic states, there are states supported by the chaotic region mainly living in the vicinity of the hierarchy of regular islands. We show that the fraction of these hierarchical states scales as $\hbar^{-α}$ and relate the exponent $α=1-1/γ$ to the decay of the classical staying probability $P(t)\sim t^{-γ}$. This is numerically confirmed for the kicked rotor by studying the influence of hierarchical states on eigenfunction and level statistics.

nlin.CD↗

arXiv2000

Bloch Electrons in a Magnetic Field - Why Does Chaos Send Electrons the Hard Way?

We find that a 2D periodic potential with different modulation amplitudes in x- and y-direction and a perpendicular magnetic field may lead to a transition to electron transport along the direction of stronger modulation and to localization in the direction of weaker modulation. In the experimentally accessible regime we relate this new quantum transport phenomenon to avoided band crossing due to classical chaos.

cond-mat.mes-hall↗

arXiv1998

A covering property of Hofstadter's butterfly

Based on a thorough numerical analysis of the spectrum of Harper's operator, which describes, e.g., an electron on a two-dimensional lattice subjected to a magnetic field perpendicular to the lattice plane, we make the following conjecture: For any value of the incommensurability parameter sigma of the operator its spectrum can be covered by the bands of the spectrum for every rational approximant of sigma after stretching them by factors with a common upper bound. We show that this conjecture has the following important consequences: For all irrational values of sigma the spectrum is (i) a zero measure Cantor set and has (ii) a Hausdorff dimension less or equal to 1/2. We propose that our numerical approach may be a guide in finding a rigorous proof of these results.

cond-mat.mes-hall↗

arXiv1998

Efficient Diagonalization of Kicked Quantum Systems

We show that the time evolution operator of kicked quantum systems, although a full matrix of size NxN, can be diagonalized with the help of a new method based on a suitable combination of fast Fourier transform and Lanczos algorithm in just N^2 ln(N) operations. It allows the diagonalization of matrizes of sizes up to N\approx 10^6 going far beyond the possibilities of standard diagonalization techniques which need O(N^3) operations. We have applied this method to the kicked Harper model revealing its intricate spectral properties.

cond-mat↗

arXiv1997

Fractal Conductance Fluctuations in a Soft Wall Stadium and a Sinai Billiard

Conductance fluctuations have been studied in a soft wall stadium and a Sinai billiard defined by electrostatic gates on a high mobility semiconductor heterojunction. These reproducible magnetoconductance fluctuations are found to be fractal confirming recent theoretical predictions of quantum signatures in classically mixed (regular and chaotic) systems. The fractal character of the fluctuations provides direct evidence for a hierarchical phase space structure at the boundary between regular and chaotic motion.

cond-mat.mes-hall↗

arXiv1997

Avoided Band Crossings: Tuning Metal-Insulator Transitions in Chaotic Systems

We show that avoided crossings of energy bands may give rise to a variety of phenomena such as transitions from metal to insulator and vice versa, changes in localization lengths, and changes in the fractal dimension of energy spectra. We explain the occurrence of these phenomena in the kicked Harper model under classically chaotic conditions and predict them to occur in other systems.

cond-mat↗