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# Control of single quantum excitations in cavities

Julia Kabuß:

Quantum emitters, such as semiconductor quantum dots or other nanostuctures, coupled to photonic or acoustic cavities exhibit non-linear and non-Markovian interactions. For such devices, it is highly desirable to control single and few excitations, such as single photons or coherent phonon wave packets. In the quantum limit, studied here, not only mean values of observables, such as the average phonon number obey a non-linear dynamics. Their statistics is of most importance, since fluctuations can be as large as the mean value. Our goal is to establish methods to control the quantum statistics of cavity photons and phonons in the limit where fluctuations dominate the dynamics. We focus on two examples:

First, we discuss single photon control in a quantum dot-cavity system, coupled to an external mirror to provide delayed feedback. Here, we study a regime, where classical factorization and Markovian feedback schemes break down. We discuss, that the external mirror, providing a structured external mode continuum enforces self-feedback temporal delay effects leading to modied singlephoton Rabi-oscillations [1]. In contrast, in the limit of many photons, we apply classical factorization about mean values of observables for the description of time-delayed self-feedback of a quantum dot microcavity laser. Such lasers can work in a regime between the classical regime (Lang-Kobayashi model [2]) and quantum limit and are ideal candidates to study the transition between both regimes. The laser characteristics is studied on the level of light eld intensities and light eld statistics, where significant differences between a quantized and a classical approach arise.

Second, we discuss a novel scheme of a quantum dot-phonon laser, based on the coupling of an optically pumped quantum dot to an acoustic cavity mode [3]. Making use of external pumping at the anti-Stokes resonance, single phonons, chaotic phonons and coherent phonon laser action can be obtained as a function of the external control eld. We compare a fully quantum approach with a reduced classical model valid for the coherent phonon laser regime. Subsystem approach in the semiclassical regime, predicts coherent phonon laser action on the basis of the statistical properties of the phonon cavity eld as well as the threshold behavior of the system.

[1] A. Carmele, J. Kabuß, F. Schulze, S. Reitzenstein, and A. Knorr "Single Photon Delayed Feedback: A Way to Stabilize Intrinsic Quantum Cavity Electrodynamics", Phys. Rev. Lett. 110, 013601 (2013).

[2] C. Otto, K. Lüdge and E. Schöll: "Modeling Quantum Dot Lasers with Optical Feedback: Sensitivity of Bifurcation Scenarios" phys. stat. sol. (b) 247, 829-845 (2010).

[3] J. Kabuß, A. Carmele, T. Brandes, and A. Knorr, "Optically Driven Quantum Dots as Source of Coherent Cavity Phonons: A Proposal for a Phonon Laser Scheme", Phys. Rev. Lett. 109, 054301 (2012).