Avoided level crossings in open quantum systems

Abstract

At high level density, two states avoid usually crossing at the critical value $a_{\mathrm{cr}}$ of the parameter $a$ by which the system is controlled. The wavefunctions of the two states are mixed in a finite parameter range around $a_{\mathrm{cr}}$. This holds true for discrete states as well as for narrow resonance states which are coupled via the environment of scattering wavefunctions. We study the influence of avoided level crossings onto four overlapping complex eigenvalues of a symmetric non-Hermitian operator. The mixing of the two wavefunctions around $a_{\mathrm{cr}}$ is simulated, in each case, by assuming a Gaussian distribution around $a_{\mathrm{cr}}$. At high level density, the Gaussian distributions related to avoided crossings of different levels may overlap. Here, new effects arise, especially from the imaginary part of the coupling term via the environment. The results show, moreover, the influence of symmetries onto the multi-level avoided crossing phenomenon.

Contribution to the Special Issue "Quantum Physics with Non-Hermitian Operators: Theory and Experiment", Fortschritte der Physik - Progress of Physics 2012

References in corpus (8)

• Review: Semiconductor Quantum Light Sources
• Polaritonic Bistability in Semiconductor Microcavities
• Signatures of three coalescing eigenfunctions
• Dynamics of quantum systems
• Phase transitions in open quantum systems
• Ultrafast stimulated Raman parallel adiabatic passage by shaped pulses
• Influence of branch points in the complex plane on the transmission through double quantum dots
• Dynamical stabilization and time in open quantum systems

Cited by in corpus (7)

• Open quantum systems and Dicke superradiance
• Passive $\mathcal{P}\mathcal{T}$-symmetry breaking transitions without exceptional points in dissipative photonic systems
• Observation of slowly decaying eigenmodes without exceptional points in Floquet, dissipative, synthetic circuits
• Width bifurcation and dynamical phase transitions in open quantum systems
• Linear Quantum Entropy and Non-Hermitian Hamiltonians
• Dynamical stabilization and time in open quantum systems
• Generation and protection of Maximally Entangled State between many modes in an optical network with dissipation