Holger Friedrich Hofmann

Quantum phase gate for photonic qubits using only beam splitters and postselection

We show that a beam splitter of reflectivity one-third can be used to realize a quantum phase gate operation if only the outputs conserving the number of photons on each side are postselected.

Violation of local uncertainty relations as a signature of entanglement

Entangled states represent correlations between two separate systems that are too precise to be represented by products of local quantum states. We show that this limit of precision for the local quantum states of a pair of N-level systems can be defined by an appropriate class of uncertainty relations. The violation of such local uncertainty relations may be used as an experimental test of entanglement generation.

Nonlinear interaction of two photons with a one-dimensional atom: Spatiotemporal quantum coherence in the emitted field

The nonlinear photon-photon interaction mediated by a single two-level atom is studied theoretically based on a one-dimensional model of the field-atom interaction. This model allows us to determine the effects of an atomic nonlinearity on the spatiotemporal coherence of a two-photon state. Specifically, the complete two-photon output wave function can be obtained for any two-photon input wave function. It is shown that the quantum interference between the components of the output state associated with different interaction processes causes bunching and antibunching in the two-photon statistics. This theory may be useful for various applications in photon manipulation, e.g., quantum information processing using photonic qubits, quantum nondemolition measurements, and the generation of entangled photons.

Generation of highly nonclassical n-photon polarization states by superbunching at a photon bottleneck

It is shown that coherent superpositions of two oppositely polarized n-photon states can be created by postselecting the transmission of n independently generated photons into a single-mode transmission line. It is thus possible to generate highly nonclassical n-photon polarization states using only the bunching effects associated with the bosonic nature of photons. The effects of mode-matching errors are discussed and the possibility of creating n-photon entanglement by redistributing the photons into n separate modes is considered.

Quantum Filter for Nonlocal Polarization Properties of Photonic Qubits

We present an optical filter that transmits photon pairs only if they share the same horizontal or vertical polarization, without decreasing the quantum coherence between these two possibilities. Various applications for entanglement manipulations and multiphoton qubits are discussed.

Entanglement and four-wave mixing effects in the dissipation-free nonlinear interaction of two photons at a single atom

We investigate the nonlinear interaction between two photons in a single-input pulse at an atomic two-level nonlinearity. A one-dimensional model for the propagation of light to and from the atom is used to describe the precise spatiotemporal coherence of the two-photon state. It is shown that the interaction generates spatiotemporal entanglement in the output state similar to the entanglement observed in parametric down-conversion. A method of generating photon pairs from coherent pump light using this quantum-mechanical four-wave mixing process is proposed.

Continuous-variable teleportation of single-photon states

The properties of continuous-variable teleportation of single-photon states are investigated. The output state is different from the input state due to the nonmaximal entanglement in the Einstein-Podolsky-Rosen beams. Thephoton statistics of the teleportation output are determined and the correlation between the field information β obtained in the teleportation process and the change in photon number is discussed. The results of the output photon statistics are applied to the transmission of a qubit encoded in the polarization of a single photon.

Quantum-state tomography for spin- l systems

We show that the density matrix of a spin-

Efficiencies for the single-mode operation of a quantum optical nonlinear shift gate

l

Gain tuning and fidelity in continuous-variable quantum teleportation

system can be described entirely in terms of the measurement statistics of projective spin measurements along a minimum of