Chirality of wave functions for three coalescing levels

The coalescence of three levels has particular attractive features. Even though it may be difficult to realise such event in the laboratory (three additional real parameters must be adjusted), to take up the challenge seems worthwhile. In the same way as the chiral behaviour of a usual EP can give a direction on a line, the state vectors in the vicinity of an EP3 provide an orientation in the plane. The distinction between left and right handedness depends on the distribution of the widths of the three levels in the vicinity of the point of coalescence.Comment: Manuscript has been discussed in June 2007 with the experimental group under Professor Achim Richter at the TU Darmstadt. It has been presented at the 6th International Workshop on Pseudo Hermitian Hamiltonians, London, 16-18 July 2007. An expanded version is being prepared for publication. 3 Figures, 11 page

Instabilities, nonhermiticity and exceptional points in the cranking model

A cranking harmonic oscillator model, widely used for the physics of fast rotating nuclei and Bose-Einstein condensates, is re-investigated in the context of PT-symmetry. The instability points of the model are identified as exceptional points. It is argued that - even though the Hamiltonian appears hermitian at first glance - it actually is not hermitian within the region of instability.Comment: 4 pages, 1 figur

A Simple Shell Model for Quantum Dots in a Tilted Magnetic Field

A model for quantum dots is proposed, in which the motion of a few electrons in a three-dimensional harmonic oscillator potential under the influence of a homogeneous magnetic field of arbitrary direction is studied. The spectrum and the wave functions are obtained by solving the classical problem. The ground state of the Fermi-system is obtained by minimizing the total energy with regard to the confining frequencies. From this a dependence of the equilibrium shape of the quantum dot on the electron number, the magnetic field parameters and the slab thickness is found.Comment: 15 pages (Latex), 3 epsi figures, to appear in PhysRev B, 55 Nr. 20 (1997

Shell Structures and Chaos in Deformed Nuclei and Large Metallic Clusters

A reflection-asymmetric deformed oscillator potential is analysed from the classical and quantum mechanical point of view. The connection between occurrence of shell structures and classical periodic orbits is studied using the ''removal of resonances method'' in a classical analysis. In this approximation, the effective single particle potential becomes separable and the frequencies of the classical trajectories are easily determined. It turns out that the winding numbers calculated in this way are in good agreement with the ones found from the corresponding quantum mechanical spectrum using the particle number dependence of the fluctuating part of the total energy. When the octupole term is switched on it is found that prolate shapes are stable against chaos whereas spherical and oblate cases become chaotic. An attempt is made to explain this difference in the quantum mechanical context by looking at the distribution of exceptional points which results from the matrix structure of the respective Hamiltonians. In a similar way we analyse the modified Nilsson model and discuss its consequences for nuclei and metallic clusters.Comment: to appear in Physica Scripta., CNLS-94-02, a talk given at the Nobel sponsored conference SELMA 94 "New Nuclear Phenomena in the Vicinity of Closed Shell" (Stockholm and Uppsala, 29 Aug.- 3 Sept. 1994

Probing spin relaxation in an individual InGaAs quantum dot using a single electron optical spin memory device

We demonstrate all optical electron spin initialization, storage and readout in a single self-assembled InGaAs quantum dot. Using a single dot charge storage device we monitor the relaxation of a single electron over long timescales exceeding 40{\mu}s. The selective generation of a single electron in the quantum dot is performed by resonant optical excitation and subsequent partial exciton ionization; the hole is removed from the quantum dot whilst the electron remains stored. When subject to a magnetic field applied in Faraday geometry, we show how the spin of the electron can be prepared with a polarization up to 65% simply by controlling the voltage applied to the gate electrode. After generation, the electron spin is stored in the quantum dot before being read out using an all optical implementation of spin to charge conversion technique, whereby the spin projection of the electron is mapped onto the more robust charge state of the quantum dot. After spin to charge conversion, the charge state of the dot is repeatedly tested by pumping a luminescence recycling transition to obtain strong readout signals. In combination with spin manipulation using fast optical pulses or microwave pulses, this provides an ideal basis for probing spin coherence in single self-assembled quantum dots over long timescales and developing optimal methods for coherent spin control

Phase transitions in open quantum systems

We consider the behaviour of open quantum systems in dependence on the coupling to one decay channel by introducing the coupling parameter $\alpha$ being proportional to the average degree of overlapping. Under critical conditions, a reorganization of the spectrum takes place which creates a bifurcation of the time scales with respect to the lifetimes of the resonance states. We derive analytically the conditions under which the reorganization process can be understood as a second-order phase transition and illustrate our results by numerical investigations. The conditions are fulfilled e.g. for a picket fence with equal coupling of the states to the continuum. Energy dependencies within the system are included. We consider also the generic case of an unfolded Gaussian Orthogonal Ensemble. In all these cases, the reorganization of the spectrum occurs at the critical value $\alpha_{crit}$ of the control parameter globally over the whole energy range of the spectrum. All states act cooperatively.Comment: 28 pages, 22 Postscript figure

An Algorithmic Test for Diagonalizability of Finite-Dimensional PT-Invariant Systems

A non-Hermitean operator does not necessarily have a complete set of eigenstates, contrary to a Hermitean one. An algorithm is presented which allows one to decide whether the eigenstates of a given PT-invariant operator on a finite-dimensional space are complete or not. In other words, the algorithm checks whether a given PT-symmetric matrix is diagonalizable. The procedure neither requires to calculate any single eigenvalue nor any numerical approximation.Comment: 13 pages, 1 figur

Coupling of whispering-gallery modes in size-mismatched microdisk photonic molecules

Mechanisms of whispering-gallery (WG) modes coupling in microdisk photonic molecules (PMs) with slight and significant size mismatch are numerically investigated. The results reveal two different scenarios of modes interaction depending on the degree of this mismatch and offer new insight into how PM parameters can be tuned to control and modify WG-modes wavelengths and Q-factors. From a practical point of view, these findings offer a way to fabricate PM microlaser structures that exhibit low thresholds and directional emission, and at the same time are more tolerant to fabrication errors than previously explored coupled-cavity structures composed of identical microresonators.Comment: 3 pages with 5 figures (to appear in Opt. Lett. 2007

Low-optical-loss, low-resistance Ag/Ge based ohmic contacts to n-type InP for membrane based waveguide devices

We present the development of Ag/Ge based ohmic contacts to n-type InP with both low contact resistances and relatively low optical losses. A specific contact resistance as low as 1.5×10-6 O cm2 is achieved by optimizing the Ge layer thickness and annealing conditions. The use of Ge instead of metal as the first deposited layer results in a low optical absorption loss in the telecommunication wavelength range. Compared to Au based contacts, the Ag based metallization also shows considerably reduced spiking effects after annealing. Contacts with different lengths are deposited on top of InP membrane waveguides to characterize the optical loss before and after annealing. A factor of 5 reduction of the propagation loss compared to the conventional Au/Ge/Ni contact is demonstrated. This allows for much more optimized designs for membrane photonic devices

Observation of a Chiral State in a Microwave Cavity

A microwave experiment has been realized to measure the phase difference of the oscillating electric field at two points inside the cavity. The technique has been applied to a dissipative resonator which exhibits a singularity -- called exceptional point -- in its eigenvalue and eigenvector spectrum. At the singularity, two modes coalesce with a phase difference of $\pi/2 .$ We conclude that the state excited at the singularity has a definitiv chirality.Comment: RevTex 4, 5 figure