Numerical Optical Centroid Measurements

Optical imaging methods are typically restricted to a resolution of order of the probing light wavelength $\lambda_p$ by the Rayleigh diffraction limit. This limit can be circumvented by making use of multiphoton detection of correlated $N$-photon states, having an effective wavelength $\lambda_p/N$. But the required $N$-photon detection usually renders these schemes impractical. To overcome this limitation, recently, so-called optical centroid measurements (OCM) have been proposed which replace the multi-photon detectors by an array of single-photon detectors. Complementary to the existing approximate analytical results, we explore the approach using numerical experiments by sampling and analyzing detection events from the initial state wave function. This allows us to quantitatively study the approach also beyond the constraints set by the approximate analytical treatment, to compare different detection strategies, and to analyze other classes of input states.Comment: 15 pages, 18 figure

Creation, applications and detection of entanglement in quantum optical systems

In this work, three applications aimed at studying or exploiting various aspects of entanglement are considered. In the first project, the entanglement between two atoms inside a multimode resonator is investigated in the presence of retardation. Retardation is associated with the finite time required by a photon to propagate between atoms and cavity boundaries. It is found that retardation affects the atomic populations as well as the entanglement dynamics to a large degree. The second project is a study of entangled states of light to obtain an enhanced resolution. We have simulated optical centroid measurements for spatial resolution enhancement with various types of non-classical input states. By numerically simulating the measurement scheme, we optimize the detection parameters for an experimental implementation and also study the multiphoton absorption required for quantum lithography. The third project uses the scattered light from a resonantly driven correlated system to obtain information about the system. Techniques have been proposed using which in certain detection directions, n-atom correlations can be directly accessed in an experiment via light scattering with a significant count rate. Moreover, such detection of correlations is not limited to a particular spatial geometry but can be utilized for generalized geometries, too

Effect of retardation on the dynamics of entanglement between atoms

The role of retardation in the entanglement dynamics of two distant atoms interacting with a multi-mode field of a ring cavity is discussed. The retardation is associated with a finite time required for light to travel between the atoms located at a finite distance and between the atoms and the cavity boundaries. We explore features in the concurrence indicative of retardation and show how these features evolve depending on the initial state of the system, distance between the atoms and the number of modes to which the atoms are coupled. In particular, we consider the short-time and the long time dynamics for both the multi- and sub-wavelength distances between the atoms. It is found that the retardation effects can qualitatively modify the entanglement dynamics of the atoms not only at multi- but also at sub-wavelength distances. We follow the temporal evolution of the concurrence and find that at short times of the evolution the retardation induces periodic sudden changes of entanglement. To analyze where the entanglement lies in the space spanned by the state vectors of the system, we introduce the collective Dicke states of the atomic system that explicitly account for the sudden changes as a periodic excitation of the atomic system to the maximally entangled symmetric state. At long times, the retardation gives rise to periodic beats in the concurrence that resemble the phenomenon of collapses and revivals in the Jaynes-Cummings model. In addition, we identify parameter values and initial conditions at which the atoms remain separable or are entangled without retardation during the entire evolution time, but exhibit the phenomena of sudden birth and sudden death of entanglement when the retardation is included.Comment: 16 pages, 14 figure