Carlos Viviescas

Field quantization for open optical cavities

We study the quantum properties of the electromagnetic field in optical cavities coupled to an arbitrary number of escape channels. We consider both inhomogeneous dielectric resonators with a scalar dielectric constant

Semiclassical Propagator of the Wigner Function

\ensuremath{\epsilon}(\mathbf{r})

Field quantization for chaotic resonators with overlapping modes

and cavities defined by mirrors of arbitrary shape. Using the Feshbach projector technique we quantize the field in terms of a set of resonator and bath modes. We rigorously show that the field Hamiltonian reduces to the system-and-bath Hamiltonian of quantum optics. The field dynamics is investigated using the input-output theory of Gardiner and Collet. In the case of strong coupling to the external radiation field we find spectrally overlapping resonator modes. The mode dynamics is coupled due to the damping and noise inflicted by the external field. For wave chaotic resonators the mode dynamics is determined by a non-Hermitean random matrix. Upon including an amplifying medium, our dynamics of open-resonator modes may serve as a starting point for a quantum theory of random lasing.

Photocount Statistics of Chaotic Lasers

Propagation of the Wigner function is studied on two levels of semiclassical propagation: one based on the Van Vleck propagator, the other on phase-space path integration. Leading quantum corrections to the classical Liouville propagator take the form of a time-dependent quantum spot. Its oscillatory structure depends on whether the underlying classical flow is elliptic or hyperbolic. It can be interpreted as the result of interference of a pair of classical trajectories, indicating how quantum coherences are to be propagated semiclassically in phase space. The phase-space path-integral approach allows for a finer resolution of the quantum spot in terms of Airy functions.

Entanglement Dynamics in Open Two-Qubit Systems via Diffusive Quantum Trajectories

Feshbachs projector technique is employed to quantize the electromagnetic field in optical resonators with an arbitrary number of escape channels. We find spectrally overlapping resonator modes coupled due to the damping and noise inflicted by the external radiation field. For wave chaotic resonators the mode dynamics is determined by a non-Hermitean random matrix. Upon including an amplifying medium, our dynamics of open-resonator modes may serve as a starting point for a quantum theory of random lasing.

Quantum theory of multimode fields: applications to optical resonators

We derive the photocount statistics of the radiation emitted from a chaotic laser resonator in the regime of single-mode lasing. Random spatial variations of the resonator eigenfunctions lead to strong mode-to-mode fluctuations of the laser emission. The distribution of the mean photocount over an ensemble of modes changes qualitatively at the lasing transition, and displays up to three peaks above the lasing threshold.

Quantum Chaos, Transport, and Control—in Quantum Optics

We use quantum diffusive trajectories to prove that the time evolution of two-qubit entanglement under spontaneous emission can be fully characterized by optimal continuous monitoring. We analytically determine this optimal unraveling and derive a deterministic evolution equation for the systems concurrence. Furthermore, we propose an experiment to monitor the entanglement dynamics in bipartite two-level systems and to determine the disentanglement time from a single trajectory.

Quantum statistics of overlapping modes in open resonators

A recently developed technique for the system-and-bath quantization of open optical cavities is applied to three resonator geometries: a one-dimensional dielectric, a Fabry–Perot resonator, and a dielectric disc. The system-and-bath Hamiltonian for these geometries is derived starting from Maxwells equations and employed to compute the electromagnetic fields, the resonances, and the cavity gain factors. Exact agreement is found with standard quantization methods based on a modes-of-the-universe description. Our analysis provides a microscopic justification for the system-and-bath quantization even in the regime of spectrally overlapping modes. Combined with random-matrix theory our quantization method can serve as a starting point for a quantum theory of wave-chaotic and disordered optical media.

Average entanglement dynamics in open two-qubit systems with continuous monitoring

Chaos implies unpredictability, fluctuations, and the need for statistical modelling. Quantum optics has developed into one of the most advanced subdisciplines of modern physics in terms of the control of matter on a microscopic scale, and, in particular, of isolated, single quantum objects. Prima facie, both fields therefore appear rather distant in philosophy and outset. However, as we shall discuss in the present review, chaos, and, more specifically, quantum chaos opens up novel perspectives for our understanding of the dynamics of increasingly complex quantum systems, and of ultimate quantum control by tailoring complexity.

Entanglement and Decoherence

We study the quantum dynamics of optical fields in weakly confining resonators with overlapping modes. Employing a recently developed quantization scheme involving a discrete set of resonator modes and continua of external modes we derive Langevin equations and a master equation for the resonator modes. Langevin dynamics and the master equation are proved to be equivalent in the Markovian limit. Our open-resonator dynamics may be used as a starting point for a quantum theory of random lasers.