Characterizing heralded single-photon sources with imperfect measurement devices

Any characterization of a single-photon source is not complete without specifying its second-order degree of coherence, i.e., its $g^{(2)}$ function. An accurate measurement of such coherence functions commonly requires high-precision single-photon detectors, in whose absence, only time-averaged measurements are possible. It is not clear, however, how the resulting time-averaged quantities can be used to properly characterize the source. In this paper, we investigate this issue for a heralded source of single photons that relies on continuous-wave parametric down-conversion. By accounting for major shortcomings of the source and the detectors--i.e., the multiple-photon emissions of the source, the time resolution of photodetectors, and our chosen width of coincidence window--our theory enables us to infer the true source properties from imperfect measurements. Our theoretical results are corroborated by an experimental demonstration using a PPKTP crystal pumped by a blue laser, that results in a single-photon generation rate about 1.2 millions per second per milliwatt of pump power. This work takes an important step toward the standardization of such heralded single-photon sources.Comment: 18 pages, 9 figures; corrected Eq. (11) and the description follows Eq. (22

Separation of neutral and charge modes in one dimensional chiral edge channels

Coulomb interactions have a major role in one-dimensional electronic transport. They modify the nature of the elementary excitations from Landau quasiparticles in higher dimensions to collective excitations in one dimension. Here we report the direct observation of the collective neutral and charge modes of the two chiral co-propagating edge channels of opposite spins of the quantum Hall effect at filling factor 2. Generating a charge density wave at frequency f in the outer channel, we measure the current induced by inter-channel Coulomb interaction in the inner channel after a 3-mm propagation length. Varying the driving frequency from 0.7 to 11 GHz, we observe damped oscillations in the induced current that result from the phase shift between the fast charge and slow neutral eigenmodes. We measure the dispersion relation and dissipation of the neutral mode from which we deduce quantitative information on the interaction range and parameters.Comment: 23 pages, 6 figure

Electron quantum optics : partitioning electrons one by one

We have realized a quantum optics like Hanbury Brown and Twiss (HBT) experiment by partitioning, on an electronic beam-splitter, single elementary electronic excitations produced one by one by an on-demand emitter. We show that the measurement of the output currents correlations in the HBT geometry provides a direct counting, at the single charge level, of the elementary excitations (electron/hole pairs) generated by the emitter at each cycle. We observe the antibunching of low energy excitations emitted by the source with thermal excitations of the Fermi sea already present in the input leads of the splitter, which suppresses their contribution to the partition noise. This effect is used to probe the energy distribution of the emitted wave-packets.Comment: 5 pages, 4 figure

Partitioning of on-demand electron pairs

We demonstrate the high fidelity splitting of electron pairs emitted on demand from a dynamic quantum dot by an electronic beam splitter. The fidelity of pair splitting is inferred from the coincidence of arrival in two detector paths probed by a measurement of the partitioning noise. The emission characteristic of the on-demand electron source is tunable from electrons being partitioned equally and independently to electron pairs being split with a fidelity of 90%. For low beam splitter transmittance we further find evidence of pair bunching violating statistical expectations for independent fermions

Single electron quantum tomography in quantum Hall edge channels

We propose a quantum tomography protocol to measure single electron coherence in quantum Hall edge channels and therefore access for the first time the wave function of single electron excitations propagating in ballistic quantum conductors. Its implementation would open the way to quantitative studies of single electron decoherence and would provide a quantitative tool for analyzing single to few electron sources. We show how this protocol could be implemented using ultrahigh sensitivity noise measurement schemes.Comment: Version 3: long version (7 figures): corrections performed and references have been added. Figures reprocessed for better readabilit

Microwave studies of the fractional Josephson effect in HgTe-based Josephson junctions

The rise of topological phases of matter is strongly connected to their potential to host Majorana bound states, a powerful ingredient in the search for a robust, topologically protected, quantum information processing. In order to produce such states, a method of choice is to induce superconductivity in topological insulators. The engineering of the interplay between superconductivity and the electronic properties of a topological insulator is a challenging task and it is consequently very important to understand the physics of simple superconducting devices such as Josephson junctions, in which new topological properties are expected to emerge. In this article, we review recent experiments investigating topological superconductivity in topological insulators, using microwave excitation and detection techniques. More precisely, we have fabricated and studied topological Josephson junctions made of HgTe weak links in contact with two Al or Nb contacts. In such devices, we have observed two signatures of the fractional Josephson effect, which is expected to emerge from topologically-protected gapless Andreev bound states. We first recall the theoretical background on topological Josephson junctions, then move to the experimental observations. Then, we assess the topological origin of the observed features and conclude with an outlook towards more advanced microwave spectroscopy experiments, currently under development.Comment: Lectures given at the San Sebastian Topological Matter School 2017, published in "Topological Matter. Springer Series in Solid-State Sciences, vol 190. Springer

Optical source of individual pairs of colour-conjugated photons

We theoretically demonstrate that Kerr nonlinearity in optical circuits can lead to both resonant four-wave mixing and photon blockade, which can be used for high-yield generation of high-fidelity individual photon pairs with conjugated frequencies. We propose an optical circuit, which, in the optimal pulsed-drive regime, would produce photon pairs at the rate up to 5 × 105  s−1 (0.5 pairs per pulse) with g(2)(0)<10–2g(2)(0)<10−2 for one of the conjugated frequencies. We show that such a scheme can be utilised to generate colour-entangled photons

Coherence measures for heralded single-photon sources

Single-photon sources (SPSs) are mainly characterized by the minimum value of their second-order coherence function, viz. their $g^{(2)}$ function. A precise measurement of $g^{(2)}$ may, however, require high time-resolution devices, in whose absence, only time-averaged measurements are accessible. These time-averaged measures, standing alone, do not carry sufficient information for proper characterization of SPSs. Here, we develop a theory, corroborated by an experiment, that allows us to scrutinize the coherence properties of heralded SPSs that rely on continuous-wave parametric down-conversion. Our proposed measures and analysis enable proper standardization of such SPSs.Comment: 4 pages, 4 figures, corrected Eq. (10