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arXiv:2306.13646 · Scientific Reports

Perfect single-photon sources

Sana Khalid, Fabrice P. Laussy

Published Feb 1, 2024• 13 citations
arXivHTMLPDF

Abstract

We introduce the gapped coherent state in the form of a single-photon source (SPS) that consists of uncorrelated photons as a background, except that we demand that no two photons can be closer in time than a time gap [Formula: see text]. While no obvious quantum mechanism is yet identified to produce exactly such a photon stream, a numerical simulation is easily achieved by first generating an uncorrelated (Poissonian) signal and then for each photon in the list, either adding such a time gap or removing all photons that are closer in time from each other than [Formula: see text]. We study the statistical properties of such a hypothetical signal, which exhibits counter-intuitive features. This provides a neat and natural connection between continuous-wave (stationary) and pulsed single-photon sources, with also a bearing on what it means for such sources to be perfect in terms of single-photon emission.

DOI
10.1038/s41598-023-47585-9

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We introduce the gapped coherent state in the form of a single-photon source (SPS) that consists of uncorrelated photons as a background, except that we demand that no two photons can be closer in time than a time gap [Formula: see text]. While no obvious quantum mechanism is yet identified to produce exactly such a photon stream, a numerical simulation is easily achieved by first generating an uncorrelated (Poissonian) signal and then for each photon in the list, either adding such a time gap or removing all photons that are closer in time from each other than [Formula: see text]. We study the statistical properties of such a hypothetical signal, which exhibits counter-intuitive features. This provides a neat and natural connection between continuous-wave (stationary) and pulsed single-photon sources, with also a bearing on what it means for such sources to be perfect in terms of single-photon emission.
Single-photon sources are at the heart of quantum-optical networks, with their uniquely quantum emission and phenomenon of two-photon interference allowing for the generation and transfer of nonclassical states. Although a few analytical methods have been briefly investigated for describing pulsed single-photon sources, these methods apply only to either perfectly ideal or at least extremely idealized sources. Here, we present the first complete picture of pulsed single-photon sources by elaborating how to numerically and fully characterize non-ideal single-photon sources operating in a pulsed regime. In order to achieve this result, we make the connection between quantum Monte-Carlo simulations, experimental characterizations, and an extended form of the quantum regression theorem. We elaborate on how an ideal pulsed single-photon source is connected to its photocount distribution and its measured degree of second- and first-order optical coherence. By doing so, we provide a description of the relationship between instantaneous source correlations and the typical experimental interferometers (Hanbury-Brown and Twiss, Hong–Ou–Mandel, and Mach–Zehnder) used to characterize such sources. Then, we use these techniques to explore several prototypical quantum systems and their non-ideal behaviors. As an example numerical result, we show that for the most popular single-photon source—a resonantly excited two-level system—its error probability is directly related to its excitation pulse length. We believe that the intuition gained from these representative systems and characters can be used to interpret future results with more complicated source Hamiltonians and behaviors. Finally, we have thoroughly documented our simulation methods with contributions to the Quantum Optics Toolbox in Python in order to make our work easily accessible to other scientists and engineers.
Summary form only given. One efficient approach for generating single photons is based on using a two-level atom, which inherently cannot emit more than one photon at the time. As early as the 1980s, this quantum feature was identified as the gateway to creating single photon sources (SPS's), where a regular excitation sequence would produce a stream of photons with photon number fluctuations below the shot noise. Such an ideal intensity squeezed SPS would be desirable for a range of applications, including quantum imaging, sensing, enhanced precision measurements and information processing.
This chapter reviews the characteristic figure of merits of the deterministic single-photon source (SPS) based on a quantum emitter in a semiconductor solid-state system. SPS is a solid-state device capable of emitting single photons on demand. The most fundamental characteristic of the SPS is that it should emit only one photon at a time. This ability is tested in the so-called Hanbury, Brown, and Twiss experiment. A second characteristic for the SPS is that the emitted photons should be quantum mechanically indistinguishable, meaning that the emitted photons should have the same wavelength, phase variation across the pulse, polarization, optical mode profile, etc. The third important characteristic of the SPS is its efficiency or brightness. The ideal SPS should be deterministic and provide single photons on demand. It should act as a "single-photon gun" such that every trigger releases exactly one photon into the collection optics. A major workhorse for generating single photons has been the spontaneous parametric down-conversion process.
A standard laser produces a coherent state of light with a Poissonian photon number distribution. Generation of single photons on demand is a key requirement for quantum key distribution and quantum information processing systems based on photonic qubits. One of the generation schemes for single photons is to use a single semiconductor quantum dot embedded in a monolithic microcavity. An optical pump pulse or electrical pump pulse generates more than one electron–hole pairs in a quantum dot. Those electron–hole pairs recombine to generate photons one by one via spontaneous emission. The last photon emitted from a quantum dot has a unique wavelength, differing from the other photons, because the multiparticle interaction inside a quantum dot modulates an emission wavelength. One can selectively extract this last photon by a narrow band optical filter, so that single photons are extracted from the system no matter how many electron–hole pairs are injected into the quantum dot initially.
A single-photon source is a key advancement for quantum computing, quantum sensing, metrology, and quantum communication. These applications use single photons and have demanding standards for the effectiveness of single-photon generation. All available single photon source (SPS) is probabilistic and the search for deterministic SPS is challenging and relatively new. In this work, we explore a quantitative approach that can be applied to various sources with well-defined mathematical distribution functions in photon emission. If we have a photon number distribution, then we can easily compute the possibility of emission of a single photon from the source. Here, we observe the single photon possibility in a quantum state named as New Generalised Binomial State. Furthermore, this criterion has been applied to a single photon added New Generalised Binomial state and a single photon subtracted New Generalised Binomial State too. This technique helps us to characterize the quality of a single photon source. We explore the variation of SPS probability with different parameters and it is found that probability varies with the total number of photons in a system, the q parameter should be negative and the addition of a Photon is more suitable than subtraction for single photon source criterion.
Some very interesting pure non-Gaussian states in quantum optics have already been produced experimentally (with one pulsed laser): the single-photon-added coherent states, among others. Important interference phenomena by superposing beams from two independent masers or lasers have been investigated earlier experimentally and theoretically. By pursuing on both subjects altogether, we propose a possible new experiment to generate single-photon-added coherent states, by employing two independent laser sources, both in continuous regime and having approximately equal frequencies and coherence times tc: we expect that such generations could occur during times of the order of tc/3 (possibly, a bit shorter). This expectation follows from a fully quantized multimode analysis of the temporal mode structure, which extends previous studies of parametric down conversion and balanced homodyne detection