Preparation of non-classical photon states in laser-driven quantum-dot-cavity systems under the influence of acoustic phonons

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In this project we shall explore theoretically possibilities to prepare non-classical photon states, such as, e.g., Schrödinger-cat states, Fock states or polarization entangled two-pair states, in quantum-dot-cavity systems. Such states can not only be used to test the basics of quantum mechanics but also serve as central building blocks for possible applications in photonics, quantum-information-processing and quantum-cryptography.We shall investigate in how far the photon state in a quantum-dot-cavity system can be manipulated by different laser excitations. Of particular interest are the new physical effects evoked by the interaction with lattice oscillations (phonons) which cannot be avoided in semiconductor based quantum dot systems. Phonons may be an obstacle for the preparation; but it is also possible that phonon-assisted processes may enable new preparation protocols.We shall also study how far the generation of photon-pairs, which arise from the decay of a biexciton (i.e. a state with two electron-hole pairs) in the resonator, can be influenced by external laser fields and what role phonons play in this case. Also the so far unexplored possibility to switch between different types of entanglement will be investigated.Two-time correlation functions shall be evaluated avoiding the usually invoked quantum regression theorem which is not valid for systems with a non-Markovian environment (here provided by the phonons). Two-time correlation functions are directly connected to measurable quantities and contain important information about the non-classical properties of photons. New physical insights in particular into the significance of non-Markovian effects are expected to be found by simulating key quantities of photonic systems such as the indistinguishability, the coherence, the degree of entanglement as well as by recording the photon statistics of N-photon bundles.All calculations within this project will be performed using numerically complete path-integral methods without any approximation to the usually used models. For the quantum-dissipative multi-level systems studied here, such a complete treatment has become available only recently due to a methodological progress reached by the group of the applicant. First studies reveal that even advanced well established approximate methods lead to large deviations from the numerically complete results in praxis-relevant parameter ranges. The errors are particularly large for photonic properties, which are the focus oft the present project. Thus, the numerically complete treatment is decisive for reaching conclusive results.