Pyragas control allows to stabilize unstable states in applied nonlinear science. We propose to apply a quantum version of the Pyragas protocol to control individual photon-probabilities in an otherwise only globally accessible photon-probability distribution of a quantum light emitter. The versatility of quantum Pyragas control is demonstrated for the case of a two-level emitter in a pulsed laser-driven half cavity. We show that one-and two-photon events respond in a qualitatively different way to the half-cavity induced feedback signal. One-photon events are either enhanced or suppressed, depending on the choice of parameters. In contrast, two-photon events undergo exclusively an enhancement up to 50% for the chosen pulse areas. We hereby propose an implementation of quantum Pyragas control via a time-delayed feedback setup.

We investigate theoretically the many-emitter phonon laser based on optically driven semiconductor quantum dots within an acoustic nanocavity. We map the phonon laser Hamiltonian to a Tavis-Cummings type interaction with an unexpected additional many-emitter energy shift. This many-emitter interaction with the cavity mode results in a variety of resonances dependent on the number of participating emitters. We show that the many-emitter phonon laser also includes the single emitter resonance besides these collective phenomena. However, we obtain a high quantum yield addressing these collective resonances. We clearly demonstrate the best setup for maximal enhancement and show that the output can be increased even more via lasing at the two phonon resonance.The optical laser is indispensable for fundamental physics and many applications and is well understood by now 1,2 . Adapting the concept of coherent amplification by stimulated emission to sound waves, the phonon laser is a promising candidate for a new type of non demolishing measurement 3 . In the past few years there have been different theoretical and experimental proposals for phonon lasing such as trapped ions 4,5 , compound microcavities 6 , NV-centers 7 , electromagnetic resonators 8 and semiconductor devices 9-14 . For most applications, especially for the latter, the embedding of the active medium within an acoustic cavity forms the basis for stimulated phonon emission. The design and technological control of such cavities have been progressing in the past years [15][16][17][18][19][20] . In a semiconductor device, two superlattices confine one single phonon mode within a spacer in between [15][16][17] . A careful design allows long phonon lifetimes due to a high quality factor up to Q = 10 5 of the acoustic nanocavity [18][19][20] . Based on such a phonon cavity, we investigate theoretically phonon lasing in a semiconductor nanodevice with quantum dots 21 as active medium and external coherent optical excitation 22 for coherent phonon generation via the induced raman process 12,13 . We want to extend the single emitter case 12 to many emitters 23,24 and focus on collective effects of the phonon lasing regime.In analogy to the Tavis-cummings model 25,26 we focus on identical emitters coupled via the cavity phonon field. First discovered by Dicke 27 , superradiance is one example for collective effects with applications to optical lasers 28-30 and has been investigated recently for phonons in general 31,32 . The coherent pump of identical emitters supports the buildup of collective quantum coherences 31,33,34 . We clarify that collective phenomena also appear in the phonon lasing regime and show an enhancement of the coherent cavity phonon field addressing collective processes. Even if there are similarities to the optical laser, the phonon laser differs fundamentally in the interaction as the electron-phonon coupling is diagonal. This results in a Tavis-Cummings type interaction with an additional new type of interaction between the emitters via the c...

We investigate the Heisenberg XXZ-chain with long-range interactions in the Z-dimension. By applying two magnetic boundary reservoirs we drive the system out of equilibrium and induce a nonzero steady state current. The long-range coupled chain shows nearly ballistic transport and linear response for all potential differences of the external reservoirs. In contrast, the common isotropic nearest-neighbor coupling shows negative differential conductivity and a transition from diffusive to subdiffusive transport for a far from equilibrium driving. Adding disorder, the change in the transport for nearest neighbor coupling is therefore highly dependent on the driving. We find for the disordered long-range coupled XXZ-chain, any change in the transport behavior is independent of the potential difference and the coupling strengths of the external reservoirs.

We investigate a semiconductor quantum dot as a microscopic analog of a basic optomechanical setup. We show, that optomechanical features can be reproduced by the solid-state platform, arising from parallels of the underlying interaction processes, which in the optomechanical case is the radiation pressure coupling and in the semiconductor case the electron-phonon coupling. In optomechanics, phonons are typically induced via confined photons, acting on a movable mirror, while in the semiconductor system the phonons are emitted by the laser-driven electronic system. There are analogous effects present for both systems, featuring bistabilities, optically induced phonon lasing and enhanced phonon loss. Nonetheless, the different statistical nature of the optical cavity and the electronic system also leads to qualitative differences.

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