In this thesis three different approaches to control the quantum statistics in nanoscopic devices are investigated. In the first part of the thesis, mechanical oscillations in solid state devices are manipulated by an external laser to show bistabilities, coherent amplification, and enhanced damping. The dynamics is controlled by the frequency of the external laser. This study is performed in a semiclassical approximation, where expectation values of operators are factorized. These effects are used to show the similarities and differences between optomechanical systems and phonon cavities. In the regime of coherent amplification of phonons the theoretical description is extended to a fully quantum mechanical model. This reveals additional resonances due to collective processes that can be addressed via the frequency of the external laser. In the second part, a quantum light source is considered for manipulation of the emission statistics of a second quantum optical system serving as target. A Jaynes-Cummings system is used as a source that may be tuned from nonclassical to thermal emission via the pump strength. The target consists of a cavity with two emitters. The nature of the imprinted statistics is studied by higher order correlation functions. The resulting statistics deviates strongly from thermal, coherent or antibunched statistics. The third part considers coherent self feedback with time-delay, which is motivated by classical Pyragas control. The finite time delay is used as control parameter. The matrix product state evolution in the picture of the quantum stochastic Schrödinger equation is employed as a systematic way of dealing with quantum self-feedback. In this thesis, the approach is extended to include higher order terms in the time evolution operator. This is done systematically so that arbitrary order can be included enabling faster numerical evaluation. This extension of the matrix product state evolution method allows to investigate efficiently the emission statistics of a single mode cavity containing two emitters. It is shown that feedback can enhance antibunching in the light field while also counter-intuitively increasing the number of emitted photons at the same time. Expressing the time evolution operator as a sum of sparse matrices allows to include time dependent Hamiltonians in an efficient manner. Considering the pulsed excitation of a two level emitter, it is demonstrated that emission statistics may be tuned via feedback. This allows to switch between single photon emission and enhanced two photon emission.
In this thesis three different approaches to control the quantum statistics in nanoscopic devices are investigated. In the first part of the thesis, mechanical oscillations in solid state devices are manipulated by an external laser to show bistabilities, coherent amplification, and enhanced damping. The dynamics is controlled by the frequency of the external laser. This study is performed in a semiclassical approximation, where expectation values of operators are factorized. These effects are used to show the similarities and differences between optomechanical systems and phonon cavities. In the regime of coherent amplification of phonons the theoretical description is extended to a fully quantum mechanical model. This reveals additional resonances due to collective processes that can be addressed via the frequency of the external laser. In the second part, a quantum light source is considered for manipulation of the emission statistics of a second quantum optical system serving as target. A Jaynes-Cummings system is used as a source that may be tuned from nonclassical to thermal emission via the pump strength. The target consists of a cavity with two emitters. The nature of the imprinted statistics is studied by higher order correlation functions. The resulting statistics deviates strongly from thermal, coherent or antibunched statistics. The third part considers coherent self feedback with time-delay, which is motivated by classical Pyragas control. The finite time delay is used as control parameter. The matrix product state evolution in the picture of the quantum stochastic Schrödinger equation is employed as a systematic way of dealing with quantum self-feedback. In this thesis, the approach is extended to include higher order terms in the time evolution operator. This is done systematically so that arbitrary order can be included enabling faster numerical evaluation. This extension of the matrix product state evolution method allows to investigate efficiently the emission statistics of a single mode cavity containing two emitters. It is shown that feedback can enhance antibunching in the light field while also counter-intuitively increasing the number of emitted photons at the same time. Expressing the time evolution operator as a sum of sparse matrices allows to include time dependent Hamiltonians in an efficient manner. Considering the pulsed excitation of a two level emitter, it is demonstrated that emission statistics may be tuned via feedback. This allows to switch between single photon emission and enhanced two photon emission.
This thesis discusses the dynamics of quantum-optical systems located in complex, non-markovian photonic environments, using numerical simulations as well as analytical derivations. The main focus lies on time-delayed quantum-coherent feedback effects of the Pyragas type, in analogy to effects well-known in classical physics. Time-delayed feedback is treated as a specific kind of a non-markovian environment. Additionally, the control of qubit entanglement in optical cavities is studied. The thesis consists of three main parts: After an overview of the important concepts of quantum optics, advanced methods for the description and numerical treatment of time-delayed quantum-coherent feedback are presented. The main focus lies on the development of a pseudomode-based approach, which describes time-delayed feedback as the coupling to a complex network of lossy harmonic oscillators. Additionally, further methods for numerical simplification are presented, in particular nonlinear expectation value dynamics for the treatment of arbitrary non-markovian reservoirs, as well as the use of input-output theory for time-delayed feedback. In the second part, applications of time-delayed feedback to control quantum statistics are discussed. First it is demonstrated that time-delayed feedback can be used to create and sustain entanglement between coupled qubits. This approach will then be extended to larger networks of qubits. Afterwards, feedback control is applied to nonlinear quantum-optical systems: It is shown how to use it for the stabilization of Fock states in a cavity containing a Kerr medium, and this analysis is expanded to a cavity containing a two-level system. Furthermore, it is shown how time-delayed feedback can be used to control and enhance the entanglement of photons emitted in a biexciton cascade. In the third and last part, the non-equilibrium dynamics of qubits coupled to a photonic environment consisting of high-Q cavities subject to periodic driving are discussed. First, the connection between bistability and entanglement in a cavity containing two qubits is analyzed. Next a setup of two coupled cavities, containing a qubit each, is examined. The influence of a third cavity in between the two other cavities, simulating a delay line, is analyzed. Furthermore, a protocol is developed on how to overcome dephasing between the two qubits, using a resonant Raman scattering process. It is shown that this protocol can create and sustain high values of entanglement, and is ready to be extended to systems of more than two qubits.
We numerically show that time-delayed coherent feedback controls the statistical output characteristics of driven quantum emitters. Quantum feedback allows us to enhance or suppress a wide range of classical and nonclassical features of the emitted quantum light. As an exemplary quantum system, we use a pumped cavity containing two emitters. By applying phase-selective feedback, we demonstrate that photon antibunching and bunching can be increased for a given set of parameters in orders of magnitude due to intrinsically and externally controllable quantum interferences. Our modeling is based on a fully non-Markovian quantum simulation of a structured photon continuum. We show that an approximative method in the Schr\"odinger picture allows a very good estimate for quantum feedback induced features for low pump rates.
In this proceeding we show how to formulate the quantum stochastic Schrodinger equation (QSSE) of the Jaynes-Cummings-model, where the cavity mode is subject to coherent feedback as control mechanism. We start from the Jaynes-Cummings Hamiltonian and the Hamiltonian for feedback on the cavity mode and derive the QSSE and show how to represent the system state as a matrix product state in order to derive a numerically tractable model for the case of the Jaynes-Cummings model subject to feedback. We compare the dynamics for stabilization of the Rabi oscillation with the solution of the Schrodinger equation in the single excitation regime. Furthermore, we compare this with the behavior for the case with two excitations in the system.
Quantum interference and coherence lead to many interesting phenomenon and applications in quantum optics. In this dissertation, we study the quantum coherent properties in the following systems and aspects. We first investigate the optical bistability in a combined cavity-cold atoms system. In such a system the atom-photon interaction provides an optical lattice to the atoms and affects the mechanical motion of the atoms while atoms induce a position dependent phase shift on the cavity field. This highly nonlinearity induces optical bistability of intra-cavity photon number with respect to the pumping light added along the cavity axis. We show that the presence of this bistability can be controlled by a second pumping field added perpendicular to the cavity axis. It is also found that the critical input intensity of switching from one branch of bistability to the other depends on the the way of the field being added. This behavior is similar to the anomalous switching of the dispersive optical bistability of atomic media in the cavity. We also study the effect of counter-rotating terms in the control of spontaneous emission. We make use of a unitary transformation method and investigate the effect of dynamic energy shifts on the spontaneous emission modification via quantum interference in a four-level atomic system. We show that the counter-rotating terms, which are normally neglected in the usual investigation of atomic systems, do produce a significant influence on the evolution of the atomic amplitudes and the emission spectrum. This effect of counter-rotating terms can be observed in the time scale of the decay rate even when the dipole moments of the two upper levels are orthogonal to each other. The effect of counter-rotating terms on the spontaneous emission in a 3-D anisotropic photonic crystal is also discussed. It is shown that the behavior of the emission is similar to the case making rotating wave approximation, i.e., the localized and propagating fields are also separated by two characteristic atomic transition frequencies. However, the two characteristic frequencies are shifted due to the full Lamb shift which is obtained with counter-rotating terms being included in the Hamiltonian. We also utilize the unitary transformation method to show how the Lamb shift in a multi-level atom can be controlled by a driving field. Finally, we propose a subwavelength atom localization scheme for an atom located in a standing-wave field. The strategy is based on the observation that the photon statistics of resonance fluorescence depends on the position-dependent Rabi frequency.
The proposal for single-photon generation utilizing quantum interference of two coupled cavity modes with weak Kerr nonlinearity under resonant coherent driving has been successfully put forward in previous work [T. C. H. Liew and V. Savona, Phys. Rev. Lett. 104, 183601 (2010)]. Here we suggest an alternative scheme to explore the statistical properties of the photons and their control in a parametrically amplified photonic molecule that is composed of a pair of coupled cavities, both containing the degenerate optical parametric amplifier (DOPA), by means of extending the model of Liew and Savona. Due to the destructive quantum interference effect between different paths for two-photon excitation, the photons in both cavity modes can exhibit a strong antibunching effect when one of the two cavities is coherently driven by an external laser field. In order to intuitively understand the strong photon antibunching phenomenon occurring in our DOPA photonic molecule, the approximate analytical solutions of the system are provided via the Schr\"odinger equation and further are compared with the full numerical solutions via the master equation. The in-depth results reveal that the two solutions are in good agreement. For the two cavity modes, we achieve the optimal antibunching conditions in terms of the nonlinear gain and the strength ratio between the two pump laser fields based on analytical calculations, gaining deep insight into the rich physics of photon statistics. We also show that the statistical properties of the photons can be well controlled by regulating the relative phase between the two pump laser fields and the tunneling rate between the two cavity modes. Furthermore, we address the second-order cross-correlation function between the two cavity modes and find that a strong intermodal antibunching can be efficiently generated. Our approach via the DOPA photonic molecule architecture can be useful to generate tunable single-photon sources or controlled photonic quantum gates.
Semiconductor nanostructures such as quantum dots (QDs) have offered unique opportunities to investigate quantum optical effects in solid-state systems. These include quantum interference, Rabi oscillations, as well as photon antibunching, and were previously observable only in isolated atoms or ions. In addition, QDs can be integrated into optical microcavities, making them attractive for applications in quantum information processing and high efficiency quantum light sources. Despite much progress towards these goals, one area that was little explored is coherent control of such solid-state quantum emitters in cavities. The main technical hurdle lies in overcoming the laser background scattering. By using a sample structure in which QDs are embedded in a planar Fabry-Perot cavity and by using an orthogonal excitation geometry, we have achieved a nearly complete elimination of laser background scattering. This in turn allows us to show resonantly controlled light emission of quantum dots in the cavity including (a) Rabi flopping using pulse control, (b) direct observation of Mollow triplets in the frequency domain, and (c) simultaneously measured first-order and second order photon-photon correlations.