Table of contents

Light is composed of photons, but only recently has it become relatively common, albeit still challenging, to manipulate single or few photons. This special issue presents state-of-the-art theory and experiment concerning the production of few-photon states of light, processing the states, and performing highly sensitive low-noise detection at the single-photon level.

In many cases, the connection between photon manipulation and quantum information science is apparent. Few-photon sources have applications for quantum cryptography and optical quantum computing. Photon processing can involve producing entangled states of light as resources for quantum information processing, performing optical gates for example by interferometry, and realizing quantum memory to store information and synchronize gate operations. Ultimately the photons are carriers of information, and this information is acquired by detectors, which have to be reliable, highly sensitive, fast and operate with low noise. Many of these photon generation, processing and detection issues are exemplified in the papers presented here.

This special issue thus serves as a compendium of recent results in the area of few-photon optics, covering the development of new sources, the characterization and improvement of detection schemes, and the analysis and proposal of processing protocols. We trust that this issue will serve as a valuable resource for the community for years to come.

In this paper, we report the controlled coupling of fluorescence from a single NV-centre in a single nanodiamond to the high-Q modes of a preselected microsphere. Microspheres from an ensemble with a finite size distribution can be characterized precisely via white light Mie-scattering. The mode spectrum of individual spheres can be determined with high precision. A sphere with an appropriate spectrum can be selected, and a nanodiamond containing a single NV-centre can be coupled to it. The spectral position of the calculated lowest order whispering gallery modes are found to be in very good agreement with the experimentally observed resonances of the coupled fluorescence from the single NV-centre.

We present the development and operation of a tunable, frequency-stabilized, narrow-bandwidth source of entangled photon pairs, which can be tuned to the two D–P transitions in Ca⁺ ions at 850 and 854 nm. The source is based on spontaneous parametric down-conversion in periodically poled KTiOPO₄ (PPKTP) followed by tunable optical filters. Its output bandwidth of 22 MHz coincides with the absorption bandwidth of the calcium ions. Its spectral power density is 1.0 generated pairs (s MHz mW)⁻¹. Here, we report details of the setup which was first described in Haase et al (2009 Opt. Lett.34 55).

Individual colloidal core-shell nanocrystals represent very promising single photon emitters. Recently, progress concerning the synthesis of their shell enabled strong reduction of their fluorescence intermittency, which was their main drawback. We show that the synthesis of thick shells also enables us to modify the Auger effect efficiency which is a crucial parameter to control the quantum optical properties of an individual nanocrystal fluorescence. We demonstrate that these improvements open the possibility of generating quantum cascades of photons.

Many recent experiments employ several parametric down-conversion (PDC) sources to get multiphoton interference. Such interference has applications in quantum information. We study here how effects due to photon statistics, misalignment and partial distinguishability of the PDC pairs originating from different sources may lower the interference contrast in multiphoton experiments.

We have recently realized experimental schemes to implement the action of single-photon creation and annihilation operators onto completely classical and fully incoherent thermal light states (Parigi et al 2007 Science317 1890). By applying alternated sequences of the creation and annihilation operators we observed that the resulting states depend on the order in which the two quantum operators are applied, thus obtaining the most direct experimental test of non-commutativity. Here we provide an extensive and detailed discussion of the main experimental issues related to the realization of these schemes.

We examine two set-ups that reveal different operational implications of path–phase complementarity for single photons in a Mach–Zehnder interferometer (MZI). In both set-ups, the which-way (WW) information is recorded in the polarization state of the photon serving as a 'flying which-way detector'. In the 'predictive' variant, using a fixed initial state, one obtains duality relation between the probability to correctly predict the outcome of either a which-way (WW) or which-phase (WP) measurement (equivalent to the conventional path-distinguishability–visibility). In this set-up, only one or the other (WW or WP) prediction has operational meaning in a single experiment. In the second, 'retrodictive' protocol, the initial state is secretly selected for each photon by one party, Alice, among a set of initial states which may differ in the amplitudes and phases of the photon in each arm of the MZI. The goal of the other party, Bob, is to retrodict the initial state by measurements on the photon. Here, a similar duality relation between WP and WW probabilities governs their simultaneous guesses in each experimental run.

We propose a scheme for building a heralded two-qutrit entangled state from polarized photons. An optical circuit is presented to build the maximally entangled two-qutrit state from two heralded Bell pairs and ideal threshold detectors. Several schemes are discussed for constructing the two Bell pairs. We also show how one can produce an unbalanced two-qutrit state that could be of general purpose use in some protocols. In terms of the applications of the maximally entangled qutrit state, we mainly focus on how to use the state to demonstrate a violation of the Collins–Gisin–Linden–Massar–Popescu inequality under the restriction of measurements which can be performed using linear optical elements and photon counting. Other possible applications of the state, such as for higher dimensional quantum cryptography, teleportation and generation of heralded two-qudit states, are also briefly discussed.

We demonstrate entanglement swapping of polarization entangled photons using an interferometric Bell-state measurement operating at the theoretical limit of 50% efficiency capable of identifying two of the four Bell states. Our experiment represents the highest quality of entanglement swapping so far, with the correlations of the final entangled states showing an overlap fidelity with the ideal Bell states of F = 0.892, and a violation Bell's inequality for both swapped entangled states. In order to achieve this high-quality operation we have optimized various experimental error sources of our setup including the quality of optical elements, as well as the constraints due to the coherence and the group-velocity mismatch of the pump and down-conversion photons. Our results are relevant for experiments that involve interferences of independent photons and pulsed multi-photon states, such as in quantum computing, quantum metrology and quantum communication with quantum repeaters.

In the one-way model of quantum computing, quantum algorithms are implemented using only measurements on an entangled initial state. Much of the hard work is done upfront when creating this universal resource, known as a cluster state, on which the measurements are made. Here we detail a new proposal for a scalable method of creating cluster states using only a single multimode optical parametric oscillator (OPO). The method generates a continuous-variable cluster state that is universal for quantum computation and encoded in the quadratures of the optical frequency comb of the OPO. This work expands on the presentation in Menicucci, Flammia and Pfister (2008 Phys. Rev. Lett.101, 130501).

Interaction of a control and a signal field with an ensemble of three-level atoms allows direct mapping of the quantum state of the signal field into long-lived coherences of an atomic ground state. For a vapour of caesium atoms, using electromagnetically induced transparency (EIT) and Zeeman coherences, we compare the case where a tunable single sideband is stored independently of the other one to the case where the two symmetrical sidebands are stored using the same transparency window. We study the conditions in which simultaneous storage of two non-commuting variables carried by light and subsequent read-out is possible. We show that excess noise associated with spontaneous emission and spin relaxation is small, and we evaluate the quantum performance of our memory by measuring the signal transfer coefficient T and the conditional variance V and using the T–V criterion introduced by Hétet et al (2008 Phys. Rev. A77), Roch et al (1997 Phys. Rev. Lett.78) and Ralph and Lam (1998 Phys. Rev. Lett.81) as a state-independent benchmark.

We experimentally characterize the performance of the electron multiplying charge-coupled device (EMCCD) camera for the detection of single photons. The tests are done with the photon pairs generated from parametric downconversion (PDC). The gain, time response and noise performance of the EMCCD are characterized. In addition, we attempt to use the camera to measure the spatial correlations of PDC. The results reveal the capabilities and limits of the EMCCD as a single-photon-detector array for the applications of quantum optics, astronomy and microscopy.

The fidelity of postselecting devices based on direct photon number detection can be significantly improved by insertion of a phase-insensitive optical amplifier in front of the detector. The scheme is simple, and the cost to the probability of obtaining the appropriate detector outcome is low.

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 towards the standardization of such heralded single-photon sources.

Continuous-variable quantum key distribution protocols have been implemented recently, based on Gaussian modulation of the quadratures of coherent states. A present limitation of such systems is the finite efficiency of the detectors, that can in principle be compensated for by the use of classical optical preamplifiers. Here we study this possibility in detail, by deriving the modified secret key generation rates when an optical parametric amplifier is placed at the output of the quantum channel. After presenting a general set of security proofs, we show that the use of preamplifiers does compensate all the imperfections of the detectors when the amplifier is optimal in terms of gain and noise. Imperfect amplifiers can also enhance the system performance, under conditions which are generally satisfied in practice.