Tobias Brandes

Coherent and collective quantum optical effects in mesoscopic systems

A review of coherent and collective quantum optical effects like superradiance and coherent population trapping in mesoscopic systems is presented. Various new physical realizations of these phenomena are discussed, with a focus on their role for electronic transport and quantum dissipation in coupled nano-scale systems like quantum dots. A number of theoretical tools such as Master equations, polaron transformations, correlation functions, or level statistics are used to describe recent work on dissipative charge qubits (double quantum dots), the Dicke effect, phonon cavities, single oscillators, dark states and adiabatic control in quantum transport, and large spin-boson models. The review attempts to establish connections between concepts from Mesoscopics (quantum transport, coherent scattering, quantum chaos), Quantum Optics (such as superradiance, dark states, boson cavities), and (in its last part) Quantum Information Theory.

Quantum chaos triggered by precursors of a quantum phase transition: the dicke model.

We consider the Dicke Hamiltonian, a simple quantum-optical model which exhibits a zero-temperature quantum phase transition. We present numerical results demonstrating that at this transition the system changes from being quasi-integrable to quantum chaotic. By deriving an exact solution in the thermodynamic limit we relate this phenomenon to a localization-delocalization transition in which a macroscopic superposition is generated. We also describe the classical analogs of this behavior.

Chaos and the quantum phase transition in the Dicke model.

We investigate the quantum-chaotic properties of the Dicke Hamiltonian; a quantum-optical model that describes a single-mode bosonic field interacting with an ensemble of N two-level atoms. This model exhibits a zero-temperature quantum phase transition in the N --> infinity limit, which we describe exactly in an effective Hamiltonian approach. We then numerically investigate the system at finite N, and by analyzing the level statistics, we demonstrate that the system undergoes a transition from quasi-integrability to quantum chaotic, and that this transition is caused by the precursors of the quantum phase transition. Our considerations of the wave function indicate that this is connected with a delocalization of the system and the emergence of macroscopic coherence. We also derive a semiclassical Dicke model that exhibits analogues of all the important features of the quantum model, such as the phase transition and the concurrent onset of chaos.

Entanglement and the Phase Transition in Single-Mode Superradiance

We consider the entanglement properties of the quantum phase transition in the single-mode superradiance model, involving the interaction of a boson mode and an ensemble of atoms. For an infinite size system, the atom-field entanglement diverges logarithmically with the correlation length exponent. Using a continuous variable representation, we compare this to the divergence of the entropy in conformal field theories and derive an exact expression for the scaled concurrence and the cusplike nonanalyticity of the momentum squeezing.

Single-Electron-Phonon interaction in a suspended quantum dot phonon cavity

An electron-phonon cavity consisting of a quantum dot embedded in a freestanding GaAs/AlGaAs membrane is characterized using Coulomb blockade measurements at low temperatures. We find a complete suppression of single electron tunneling around zero bias leading to the formation of an energy gap in the transport spectrum. The observed effect is induced by the excitation of a localized phonon mode confined in the cavity. This phonon blockade of transport is lifted at discrete magnetic fields where higher electronic states with nonzero angular momentum are brought into resonance with the phonon energy.

Shot Noise Spectrum of Open Dissipative Quantum Two-Level Systems

We study the current noise spectrum of qubits under transport conditions in a dissipative bosonic environment. We combine (non-)Markovian master equations with correlation functions in Laplace space to derive a noise formula for both weak and strong coupling to the bath. The coherence-induced reduction of noise is diminished by weak dissipation and/or a large level separation (bias). For weak dissipation, we demonstrate that the dephasing and relaxation rates of the two-level systems can be extracted from noise. In the strong dissipation regime, the localization-delocalization transition becomes visible in the low-frequency noise.

Noise Enhancement due to Quantum Coherence in Coupled Quantum Dots

We show that the intriguing observation of noise enhancement in the charge transport through two vertically coupled quantum dots can be explained by the interplay of quantum coherence and strong Coulomb blockade. We demonstrate that this novel mechanism for super-Poissonian charge transfer is very sensitive to decoherence caused by electron-phonon scattering as inferred from the measured temperature dependence.

Nonequilibrium quantum phase transitions in the Dicke model.

We establish a set of nonequilibrium quantum phase transitions in the Dicke model by considering a monochromatic nonadiabatic modulation of the atom-field coupling. For weak driving the system exhibits a set of sidebands which allow the circumvention of the no-go theorem which otherwise forbids the occurrence of superradiant phase transitions. At strong driving we show that the system exhibits a rich multistable structure and exhibits both first- and second-order nonequilibrium quantum phase transitions.

Current switch by coherent trapping of electrons in quantum dots.

We propose a new transport mechanism through tunnel-coupled quantum dots based on the coherent population trapping effect. Coupling to an excited level by the coherent radiation of two microwaves can lead to an extremely narrow current antiresonance. The effect can be used to determine interdot dephasing rates and is a mechanism for a very sensitive, optically controlled current switch.

Two-particle dark state in the transport through a triple quantum dot

We study transport through a triple quantum dot in a triangular geometry with applied bias such that both singly- and doubly-charged states participate. We describe the formation of electronic dark states\char22{}coherent superpositions that block current flow\char22{}in the system, and focus on the formation of a two-electron dark state. We discuss the conditions under which such a state forms and describe the signatures that it leaves in transport properties such as the differential conductance and shot noise.