Observing the transition from quantum to classical energy correlations with photon pairs

We experimentally demonstrate a method to control the relative amount of quantum and classical energy correlations between two photons from a pair emitted by spontaneous parametric downconversion. Decoherence in the energy basis is achieved by applying random spectral phases on the photons. As a consequence a diverging temporal second order correlation function is observed and is explained by a mixture between an energy entangled pure state and a fully classically correlated mixte state.Comment: 4 pages, 3 figure

Experimental violation of a d-dimensional Bell inequality using energy-time entangled photons

We experimentally study the violation of the CGLMP inequality for entangled 2-qubit and 2-qutrit states with different degrees of entanglement using numerically optimized measurement settings. The qudits are encoded and manipulated in the frequency spectrum of broadband energy-time entangled photons by taking into account a spatial light modulator. The latter allows to discretize the spectrum into bins. By controlling each frequency bin individually, the generation of maximally and non-maximally entangled qutrits is verified through quantum state tomography.Comment: 7 pages, 3 figure

Computing the Entropy of a Large Matrix

Given a large real symmetric, positive semidefinite m-by-m matrix, the goal of this paper is to show how a numerical approximation of the entropy, given by the sum of the entropies of the individual eigenvalues, can be computed in an efficient way. An application from quantum-optics illustrates the new algorithm

Shaping frequency entangled qudits

Quantum entanglement between qudits - the d-dimensional version of qubits - is relevant for advanced quantum information processing and provides deeper insights in the nature of quantum correlations. Encoding qudits in the frequency modes of photon pairs produced by continuous parametric down-conversion enables access to high-dimensional states. By shaping the energy spectrum of entangled photons, we demonstrate the creation, characterization and manipulation of entangled qudits with dimension up to 4. Their respective density matrices are reconstructed by quantum state tomography. For qubits and qutrits we additionally measured the dependency of a d-dimensional Bell parameter for various degrees of entanglement. Our experiment demonstrates the ability to investigate the physics of high-dimensional frequency entangled qu$d$it states which are of great importance for quantum information science.Comment: 17 pages, 3 figure

Versatile shaper-assisted discretization of energy-time entangled photons

We demonstrate the capability to discretize the frequency spectrum of broadband energy-time entangled photons by means of a spatial light modulator to encode qudits in various bases. Exemplarily, we implement three different discretization schemes, namely frequency bins, time bins and Schmidt modes. Entangled qudits up to dimension $d=4$ are then revealed by two-photon interference experiments with visibilities violating a $d$-dimensional Bell inequality.Comment: 22 pages, 11 figure

Self-calibrating Optical Low-Coherence Reflectometry with Energy-Time Entangled Photons for Absolute Distance Measurements

Optical low-coherence reflectometry is capable of unambiguously measuring positions of stacked, partially reflective layers in a sample object. It relies on the low coherence of the light source and the absolute distances are obtained from the position reading of a mechanical motor stage. We show how to exploit the simultaneous high and low coherence properties of energy-time entangled photon pairs to directly calibrates the position scale of an OLCR scan with a reference laser wavelength. In experiment, a precision of 1.6\,nm and good linearity is demonstrated.Comment: 5 pages, 6 figure

Super-Resolution Quantum Imaging at the Heisenberg Limit

Quantum imaging exploits the spatial correlations between photons to image object features with a higher resolution than a corresponding classical light source could achieve. Using a quantum correlated $N$-photon state, the method of optical centroid measurement (OCM) was shown to exhibit a resolution enhancement by improving the classical Rayleigh limit by a factor of $1/N$. In this work, the theory of OCM is formulated within the framework of an imaging formalism and is implemented in an exemplary experiment by means of a conventional entangled photon pair source. The expected resolution enhancement of a factor of two is demonstrated. The here presented experiment allows for single-shot operation without scanning or iteration to reproduce the object in the image plane. Thereby, photon detection is performed with a newly developed integrated time-resolving detector array. Multi-photon interference effects responsible for the observed resolution enhancement are discussed and possible alternative implementation possibilities for higher photon number are proposed

Tuning curve of type-0 spontaneous parametric down-conversion

We study the tuning curve of entangled photons generated by type-0 spontaneous parametric down-conversion in a periodically poled KTP crystal. We demonstrate the X-shaped spatiotemporal structure of the spectrum by means of measurements and numerical simulations. Experiments for different pump waists, crystal temperatures, and crystal lengths are in good agreement with numerical simulations.Comment: 7 pages, 6 figure