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arXiv:1608.07626 · New Journal of Physics

Dynamical modeling of pulsed two-photon interference

Kevin A. Fischer, Kai Müller, Konstantinos G. Lagoudakis, Jelena Vuckovic A

Published Nov 29, 2016• 66 citations
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Abstract

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.

DOI
10.1088/1367-2630/18/11/113053

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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.
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Summary form only given. On-demand single-photon sources that produce a single photon as a response to a deterministic input are widely regarded as critical light sources for quantum key distribution, quantum repeaters, and quantum information science generally [1]. The wavepackets from such a source must have low probability to contain more than one photon, exist in a pure state so they may interfere with one another, and have a spatio-temporal profile that is appropriate for their application [2]. A very popular source for generating high quality single-photon wavepackets is the quantum two-level system, an artificial atom with one ground and one excited state, often implemented using solid-state quantum dots embedded within microcavities [3]. The two-level system is excited with a short resonant pulse of width τFWHM that prepares the system in its excited state, called a π-pulse, where it subsequently decays and emits a single photon with almost unity probability. Because the typical pulse lengths are orders of magnitude shorter than the lifetime of the system, it is often not appreciated that there is finite chance for an ideal two-level system to emit more than one photon at a time.
We introduce the basic concepts and characteristic properties of single-photon emitters based on resonator effects in optical cavities, and provide a review of the most prominent implementations. First we discuss the elementary principles of cavity quantum electrodynamics, which determine how single quantum systems couple to the quantised field modes of optical resonators, and then show how to exploit these principles in order to generate single photons on demand. Furthermore, we elucidate how to study the properties of the photons, namely their singleness and their spectral characteristics. In particular, it is explained how to use a Hanbury-Brown and Twiss interferometer to determine whether the photons arrive one-by-one, and how to probe their mutual indistinguishability with two-photon interference experiments of the Hong–Ou–Mandel type. Finally, we present a classification scheme applicable to most cavity-based photon emitters realised to date. This scheme allows us to assess the pros and cons of the most significant approaches – in particular with regard to photonic quantum computing and quantum communication, which are among the most promising applications to date.
We propose and demonstrate a method for an independent verification of a degree of single photon purity and coherence applicable for all single-photon emitters used in pulsed mode. Using two-time second-order correlation measurements, we reconstruct the dynamics of the nonclassical photon wavepacket. This reveals the temporal evolution of the photon field during the excitation-relaxation cycle of an emitter. The technique allows for the simultaneous measurement of multiphoton content and decoherence. Here we applied this technique to characterize a nonclassical state produced from a single InAs quantum dot (QD). We experimentally observe variations in the degree of multiphoton content and coherence of the wavepacket. A rate equation is introduced to explain multiphoton variations of our source and is found to describe the observed two-dimensional second-order correlation function accurately.
Multiphoton interference is an important phenomenon in modern quantum mechanics and experimental quantum optics, and it is fundamental for the development of quantum information science and technologies. Over the last three decades, several theoretical and experimental studies have been performed to understand the essential principles underlying such interference and to explore potential applications. Recently, the two-photon interference (TPI) of phase-randomized weak coherent states has played a key role in the realization of long-distance quantum communication based on the use of classical light sources. In this context, we investigated TPI experiments with weak coherent pulses at the single-photon level and quantitatively analyzed the results in terms of the single- and coincidence-counting rates and one- and two-photon interference-fringe shapes. We experimentally examined the Hong-Ou-Mandel-type TPI of phase-randomized weak coherent pulses to compare the TPI effect with that of correlated photons. Further experiments were also performed with two temporally- and spatially separated weak coherent pulses. Although the observed interference results, including the results of visibility and fringe shape, can be suitably explained by classical intensity correlation, the physics underlying the TPI effect needs to be interpreted as the interference between the two-photon states at the single-photon level within the utilized interferometer. The results of this study can provide a more comprehensive understanding of the TPI of coherent light at the single-photon level.
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.