Resonance structure of the cross section in an open quantum system

Franz Kitzka

Abstract A three dimensional wave packet, scattered by a radial symmetric potential of finite range, is studied, especially for the case of resonance scattering. It is found that for the calculation of the differential resonance cross section the three dimensionality of the packet may be neglected in favour of its structure in the direction of propagation. This is correct also for cross sections measured by shortly opened counters, provided that the opening time is greater in its order of magnitude than a time interval characteristic for the spreading of the packet.

Marco Merkli, Haifeng Song

Hichem Eleuch, I. Rotter

Calculations for open quantum systems are performed usually by taking into account their embedding into one common environment, which is mostly the common continuum of scattering wave functions. Realistic quantum systems are coupled however often to more than one continuum. For example, the conductance of an open cavity needs at least two environments, namely the input and the output channel. In the present paper, we study generic features of an open quantum system coupled to two channels. We compare the results with those characteristic of a one-channel system. Of special interest is the parameter range which is influenced by singular (exceptional) points. Here, the states of the system are mixed via the environment and the dynamics is determined, in any case, by nonlinear processes. These processes restore the resonance structure of the cross section in the one-channel case, such that there is no need to consider them in calculations for concrete systems. In the two-channel case, however, they cause new effects. Most interesting is the enhanced conductance of an open cavity in this parameter range. This enhancement follows directly from the properties of the eigenstates of a non-Hermitian Hamilton operator (and is not related to the existence of a superradiant state). The study of the conductance allows, among others, an experimental test of the non-Hermitian quantum physics.

F. Coester

M.V. Kazarnovski, Alexander V. Stepanov

Benjamin B. Dingel

Recently, we reported a general technique that uses a “cross-coupling structure” as a new vehicle to manipulate the resonance features of the coupled resonators. The technique is important for the (i) search for new optical analogues of Quantum Coherence Effects (QCEs) and (ii) generation of fresh and richer optical behaviors of the coupled resonators that could open future applications in optical fiber communication. Here, we review two new configurations based on this technique. The first configuration uses a modified standard double resonator (SDR) which we refer to as Cross-coupled SDR (CC-SDR). It is a new analogue circuit of QCE that generates a new QC phenomenon we call Cross-coupled Resonator Induced Shifted Absorption (CRISA). It is the first-time a cross-coupled structure has been suggested in studying QCE. Its core mechanism is due to its “cross-coupling structure”. Second, we present a modified coupled ring reflector (CRR) configuration where its original directional couplers (DCs) are replaced with cross-coupler(s) to connect the two ring resonators. We refer to it as crisscrossed-assisted CRR (or X-CCR). We review the unique characteristics of these two configurations and discuss their applications as optical devices.