Chaotic Cavities Research Articles

Stadium and quasi-stadium laser diodes

We present theoretical and experimental studies on two-dimensional microcavity laser diodes with stadium and quasi-stadium shapes. We report a demonstration of lasing for the first time in a fully chaotic microcavity-a stadium-shaped cavity which is rigorously known to be fully chaotic. We also present systematic studies on quasi-stadium laser diodes for three types of resonator conditions: stable, marginally stable, and unstable. Morphological dependence of lasing characteristics of quasi-stadium laser diodes is elucidated. We also show examples of the application of quasi-stadium laser diodes to beam switching operation and optical signal distribution by using patterned electrodes and the phase locking phenomenon between two resonator modes.

Imaging of the scarred wave functions in chaotic quantum cavities

We numerically investigate the possibility of imaging the wave function scarring in chaotic quantum cavities using the conductance modifications induced by a scanning probe. Quantum cavities having mixed or chaotic underlying classical dynamics are examined. The modifications are shown to produce the electron probability distribution in a two-dimensional electron gas irrespective of the type of the underlying classical dynamics.

Time reversal interactive objects

Time reversal has shown to be a fruitful concept in nondestructive testing in underwater acoustic or in ultrasonic imaging. In this paper this technique is adapted in the audible range to transform every day objects into tactile sensitive interfaces. A quick historical background is presented in the ultrasonic field and specially in chaotic cavity. In all time reversal experiments, it is demonstrated that a wave field spatially and temporally recorded is able to back propagate to its source. In other words, the field contains all the information on the location of the source. In the interactive experiments, it is shown that touching an object like a window, a table or a world globe generates an acoustic field easily detectable with one or two acoustic sensors. Using the concept of time reversal, the source location is deduced in real time. Then, touching objects at specific locations (virtual switches) is used to activate devices. Such devices are for example lights, stereo volume, or computer software. From a technical point of view, all these interactive experiments just use some computation easily performed with a standard personnel computer.

3D shear wave generation in soft tissues using the time reversal kaleidoscopes

The time reversal kaleidoscope provides elegant possibilities for both temporal and spatial concentration of acoustic energy in a wide frequency band. Using such ultrasound focused beams, it is possible to generate mechanical sources radiating low frequency shear waves inside tissues. Shear waves are of great interest to investigate tissue viscoelastic properties. In most techniques relying on this concept, generation and imaging of shear waves are realized with a single ultrasonic probe, limiting the capabilities concerning the generation of the shear source. Here we propose a system able to generate and image shear waves in a full 3D volume with any kind of polarization. The focused beam is generated by the time reversal kaleidoscope. By combining the concepts of time reversal mirrors and chaotic reverberating cavities, the time reversal kaleidoscope is able to focus ultrasound beams in a large 3D volume with only some tens of transducers and presents equivalent performances than conventional 2D matrices made of thousands of transducers. The kaleidoscope is triggered by an ultrafast imaging system able to image the resulting shear waves. In vitro results in tissue mimicking phantoms are presented. Chaotic cavities of different geometries are tested and compared. [Work supported in part by NIH grant.]

Frequency scales for current statistics of mesoscopic conductors.

We calculate the third cumulant of current in a chaotic cavity with contacts of arbitrary transparency as a function of frequency. Its frequency dependence drastically differs from that of the conventional noise. In addition to a dispersion at the inverse RC time characteristic of charge relaxation, it has a low-frequency dispersion at the inverse dwell time of electrons in the cavity. This effect is suppressed if both contacts have either large or small transparencies.

Electron-electron scattering effects on the full counting statistics of mesoscopic conductors

In the hot electron regime, electron-electron scattering strongly modifies not only the shot noise but also the full counting statistics. We employ a method based on a stochastic path integral to calculate the counting statistics of two systems in which noise in the hot electron regime has been experimentally measured. We give an analytical expression for the counting statistics of a chaotic cavity and find that heating due to electron-electron scattering renders the distribution of transmitted charge symmetric in the shot noise limit. We also discuss the frequency dispersion of the third order correlation function and present numerical calculations for the statistics of diffusive wires in the hot electron regime.

Distribution of reflection eigenvalues in many-channel chaotic cavities with absorption.

The reflection matrix R=S(dagger)S, with S being the scattering matrix, differs from the unit matrix when absorption is finite. Using the random matrix approach, we calculate analytically the distribution function of its eigenvalues in the limit of a large number of propagating modes in the leads attached to a chaotic cavity. The obtained result is independent of the presence of time-reversal symmetry in the system, being valid at finite absorption and arbitrary openness of the system. The particular cases of perfectly and weakly open cavities are considered in detail. An application of our results to the problem of thermal emission from random media is briefly discussed.

Fluctuations of radiation from a chaotic laser below threshold

Radiation from a chaotic cavity filled with gain medium is considered. A set of coupled equations describing the photon density and the population of gain medium is proposed and solved. The spectral distribution and fluctuations of the radiation are found. The full noise is a result of a competition between positive correlations of photons with equal frequencies (due to stimulated emission and chaotic scattering) which increase fluctuations, and a suppression due to interaction with a gain medium which leads to negative correlations between photons. The latter effect is responsible for a pronounced suppression of the photonic noise as compared to the linear theory predictions.

Electron dwell time in weakly-open chaotic quantum cavity and periodic orbits

The dwell time is defined as the ratio of the number of particles inside the quantum cavity to the incident flux. It is calculated semiclassically, showing that for a large weakly open chaotic quantum dot, this quantity can be expressed as a summation over periodic orbits that are well coupled to the entrance tunneling barrier.

Time reversed wave propagation experiments in chaotic micro-structured cavities

The elastic wave propagation in strongly scattering solid-state cavity consisting of a thin micro-patterned silicon wafer is studied experimentally. The chaotic behavior is induced by the irregular boundary of the cavity and/or by fabricating patterns of small holes in the wafer by laser machining. The pattern and hole size are designed with length scales matching the wavelength ⩽1 MHz and induce multiple scattering within the wafer bounds. Regular patterns of holes add phononic band like dispersion properties to the system. Elastic waves obey under very general conditions time reversal and reciprocity symmetry. In the cavity system the strong mode mixing in the wafer between shear and compression waves, the strong anisotropy of silicon, and even small dissipation is not destroying the time reversal and reciprocity symmetry in the system. We present a systematic study of the quality of the time-reversal signal as function of the chosen time interval and the position in the recorded signal. Also the influence of time dilatation, i.e. stretching and compressing the time scale of the re-emitted signal, is studied.

Ehrenfest-time-dependent suppression of weak localization

The Ehrenfest time dependence of the suppression of the weak localization correction to the conductance of a {\em clean} chaotic cavity is calculated. Unlike in earlier work, no impurity scattering is invoked to imitate diffraction effects. The calculation extends the semiclassical theory of K. Richter and M. Sieber [Phys. Rev. Lett. {\bf 89}, 206801 (2002)] to include the effect of a finite Ehrenfest time.

Distribution of reflection coefficients in absorbing chaotic microwave cavities.

The distribution of reflection coefficients P(R) for chaotic microwave cavities with time-reversal symmetry is investigated in different absorption and antenna coupling regimes. For all regimes the agreement between experimental distributions and random-matrix theory predictions is very good, provided both the antenna coupling T(a) and the wall absorption strength T(w) are taken into account in an appropriate way. These parameters are determined by independent experimental quantities.

Shot noise in chaotic cavities from action correlations.

We consider universal shot noise in ballistic chaotic cavities from a semiclassical point of view and show that it is due to action correlations within certain groups of classical trajectories. Using quantum graphs as a model system, we sum these trajectories analytically and find agreement with random-matrix theory. Unlike all action correlations which have been considered before, the correlations relevant for shot noise involve four trajectories and do not depend on the presence of any symmetry.

Delay times and reflection in chaotic cavities with absorption.

Absorption yields an additional exponential decay in open quantum systems which can be described by shifting the (scattering) energy E along the imaginary axis, E+i variant Planck's over 2pi /2tau(a). Using the random-matrix approach, we calculate analytically the distribution of proper delay times (eigenvalues of the time-delay matrix) in chaotic systems with broken time-reversal symmetry that is valid for an arbitrary number of generally nonequivalent channels and an arbitrary absorption rate tau(-1)(a). The relation between the average delay time and the "norm-leakage" decay function is found. Fluctuations above the average at large values of delay times are strongly suppressed by absorption. The relation of the time-delay matrix to the reflection matrix S dagger S is established at arbitrary absorption that gives us the distribution of reflection eigenvalues. The particular case of single-channel scattering is explicitly considered in detail.

Smoothed Coulomb blockade peak height fluctuations in a chaotic quantum cavity: Semiclassical approach

We show semiclassically that the leading term of the fluctuations of smoothed Coulomb blockade peak heights in chaotic quantum dots is given by the summation over periodic orbits that bounce at the tunneling barriers and therefore they are nonuniversal, unique to the systems under consideration. We then show that for a weakly open quantum cavity with symmetrically placed leads, the frequencies of the fluctuations are the same as the frequencies of scar recurrence of periodic orbits that are well coupled to the entrance tunneling barrier.

Statistics of charge fluctuations in chaotic cavities

We consider the zero-frequency fluctuations of the charge inside a mesoscopic conductor in the large capacitance limit. In analogy to current counting statistics, we derive the characteristic function of charge fluctuations in terms of the scattering matrix of the conductor. Using random matrix theory, we evaluate the characteristic function semianalytically for chaotic cavities. Our result is universal in the sense that it describes not only the fluctuations of the charge but of any observable quantity inside the cavity. We discuss equilibrium and nonequilibrium fluctuations and extend our theory to the case of contacts with arbitrary transparency. Finally, we investigate the suppression of fluctuations in the small capacitance limit due to charge screening.

Noiseless scattering states in a chaotic cavity

Shot noise in a chaotic cavity (Lyapunov exponent $\lambda$, level spacing $\delta$, linear dimension $L$), coupled by two $N$-mode point contacts to electron reservoirs, is studied as a measure of the crossover from stochastic quantum transport to deterministic classical transport. The transition proceeds through the formation of {\em fully} transmitted or reflected scattering states, which we construct explicitly. The fully transmitted states contribute to the mean current $\bar{I}$, but not to the shot-noise power $S$. We find that these noiseless transmission channels do not exist for $N\alt\sqrt{k_{F}L}$, where we expect the random-matrix result $S/2e\bar{I}=1/4$. For $N\agt\sqrt{k_{F}L}$ we predict a suppression of the noise $\propto (k_{F}L/N^{2})^{N\delta/\pi\hbar\lambda}$. This nonlinear contact dependence of the noise could help to distinguish ballistic chaotic scattering from random impurity scattering in quantum transport.

Stochastic Path Integral Formulation of Full Counting Statistics

We derive a stochastic path integral representation of counting statistics in semiclassical systems. The formalism is introduced on the simple case of a single chaotic cavity with two quantum point contacts, and then further generalized to find the propagator for charge distributions with an arbitrary number of counting fields and generalized charges. The counting statistics is given by the saddle-point approximation to the path integral, and fluctuations around the saddle point are suppressed in the semiclassical approximation. We use this approach to derive the current cumulants of a chaotic cavity in the hot-electron regime.

Synchronisation regimes in chaotic optical communication systems

A careful comparison is made between experimental results and two models describing optical synchronisation of chaotic external cavity semiconductor lasers. It is demonstrated that optical synchronisation regimes for chaotic semiconductor lasers in a master-slave configuration are dependent both on the frequency detuning between the master and slave lasers and also on the slave laser output power.

Adiabatic quantization of Andreev quantum billiard levels.

We identify the time T between Andreev reflections as a classical adiabatic invariant in a ballistic chaotic cavity (Lyapunov exponent lambda), coupled to a superconductor by an N-mode constriction. Quantization of the adiabatically invariant torus in phase space gives a discrete set of periods T(n), which in turn generate a ladder of excited states epsilon (nm)=(m+1/2)pi(h) /T(n). The largest quantized period is the Ehrenfest time T(0)=lambda(-1)ln(N). Projection of the invariant torus onto the coordinate plane shows that the wave functions inside the cavity are squeezed to a transverse dimension W/sqrt[N], much below the width W of the constriction.