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arXiv:2404.10682 · Physical Review A

Characterization of the multimode nature of single-photon sources based on spontaneous parametric down-conversion

Emil R. Hellebek, Klaus Mølmer, Anders Søndberg Sørensen

Published Aug 27, 2024• 5 citations
arXivHTMLPDF

Abstract

Single-photon sources are necessary components for many prospective quantum technologies. One candidate for a single-photon source is spontaneous parametric down-conversion combined with a heralding photon detection. The heralded light pulse from such a source is typically treated as single mode; this treatment, however, is incomplete. We develop a full multimode description based on the exact Bogoliubov treatment of the down-conversion process. We then provide a perturbative and effective treatment, which illustrates the most important physical mechanisms and permits analytical estimates of the success probability and purity of single-photon states under practical heralding conditions, both without relying on the precise detection time of the heralding photon and when accepting photons only in a narrow window around the time of the detection. This permits us to characterize the emitted light under three different assumptions for the pump pulse. For spontaneous parametric down-conversion with a very short pump pulse, we find the single-mode description to be accurate, while for longer pump pulses and continuous pumping, a multimode description is necessary. Our findings can be used to guide the design of quantum information protocols based on heralded single-photon sources, as their performance may depend on the multimode nature of the sources.

DOI
10.1103/physreva.110.023728

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Single-photon sources are necessary components for many prospective quantum technologies. One candidate for a single-photon source is spontaneous parametric down-conversion combined with a heralding photon detection. The heralded light pulse from such a source is typically treated as single mode; this treatment, however, is incomplete. We develop a full multimode description based on the exact Bogoliubov treatment of the down-conversion process. We then provide a perturbative and effective treatment, which illustrates the most important physical mechanisms and permits analytical estimates of the success probability and purity of single-photon states under practical heralding conditions, both without relying on the precise detection time of the heralding photon and when accepting photons only in a narrow window around the time of the detection. This permits us to characterize the emitted light under three different assumptions for the pump pulse. For spontaneous parametric down-conversion with a very short pump pulse, we find the single-mode description to be accurate, while for longer pump pulses and continuous pumping, a multimode description is necessary. Our findings can be used to guide the design of quantum information protocols based on heralded single-photon sources, as their performance may depend on the multimode nature of the sources.
Heralded single-photon sources are the most commonly used sources for optical quantum technology applications. There is strong demand for accurate prediction of their spectral features and temporal correlations with ever-increasing precision. This is particularly important in connection with the intrinsically stochastic photon-pair generation process in heralded sources. Here we present a complete theoretical description of the temporal correlation of a signal-idler, signal-signal, and signal-signal-idler coincidences of photons generated by continuous-wave pumped cavity-enhanced spontaneous parametric down-conversion. The theory excellently predicts the measurements, which has been experimentally confirmed in our setup utilizing single-photon detectors with high temporal resolution. This enables us to resolve and analyze the multiphoton correlation functions in great detail.
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Various quantum technology applications require high-purity single photons with high generation rate. Although different methods are employed to generate such photons, heralded single photons from spontaneous parametric down-conversion (SPDC) is the most commonly used approach. Photon generation rate from the heralded single-photon sources are limited by the efficiency of the detectors to record coincidence detection of the photon pairs which are lower than the single-photon counts recorded separately on each detector. In this paper we present a revised expression to calculate second-order temporal correlation function, g(2)g^{(2)}g(2) for any fixed time window (bin) and report the experimental characterization of purity of unheralded and heralded single photons from the SPDC process. With an appropriate choice of time bin for a given pump power, without heralding we show that higher rate of single photons with g(2)(0)=0g^{(2)}(0) = 0g(2)(0)=0 can be generated with very high probability.
Photons have proven to be excellent carriers of quantum information, and play essential roles in numerous quantum information processing (QIP) applications. In particular, heralded single- photon sources via spontaneous parametric-down conversion (SPDC) have been a key technology for demonstrating small-scale QIP, yet their low generation efficiency is a critical limitation for further scaling up optical QIP technology. In order to efficiently overcome the probabilistic nature of SPDC, here we demonstrate time multiplexing for up to 30 time slots of a periodically pumped heralded single-photon source, using a switchable low-loss optical storage cavity. We observe a maximum single-photon probability of 38.6% in periodic output time windows, corresponding to 6 times enhancement over a non-multiplexed source, but with no increase in the contribution of unwanted multi-photon events. Combining this time-multiplexing technique with a heralded source producing pure single-photon states should enable larger scale optical QIP systems than ever realized.
This thesis presents experimental progress towards highly efficient generation of cavity- enhanced, narrow-band multiphotons using spontaneous parametric downconversion. It also suggests theoretical proposals for new applications of multiphoton sources in quantum information technology. Photons prepared in Fock states, with a well-defined number of particles, are the essence of the quantum nature of light, and their unique nonclassical properties help us to develop quantum information technology. The generation of Fock states has been most commonly achieved by using spontaneous parametric down-conversion (SPDC) through the χ(2) nonlinearity in bulk crystals. During the SPDC process the nonlinear crystal emits photon-number correlated modes, and a photon-number- resolving measurement in one mode heralds the preparation of the other mode in a Fock state. The fidelity and the success rate of Fock state generation is limited by the multimode nature of SPDC emission. In this thesis, I will investigate the use of cavity-enhanced SPDC modes for higher fidelity photon pair generation, in which the well defined mode of the cavity is enhanced and results in the narrow-band source of the heralded single-photons with up to 80% heralding efficiency. The heralding efficiency is defined as the ratio between number of coincidences and single events on the heralding mode. The photon-number-resolving ability of high-quantum-efficiency transition edge sensors is used for the heralding and detection. We further discuss the feasibility of Fock state generation with higher photon numbers upon improving the data acquisition and analysis techniques. We also demonstrate and implement an interferometry scheme that exploit the phase of the photon and is capable of reading boundless bits of digital information using a single photon. This thesis also introduces new theoretical proposals for using Fock states to obtain quantum advantages for various quantum information applications, here to increase the efficiency in reading out information stored in a classical digital memory and to discriminate optical phases with lower error rates than is feasible with classical protocols.
Over the past decade, much effort has been made in identifying and characterizing systems that can form a building block of quantum networks, among which semiconductor quantum dots (QD) and spontaneous parametric down-conversion (SPDC) source are two of the most promising candidates. The work presented in this thesis will be centered on investigating and engineering the mentioned systems for generating customizable single photons. A type-II SPDC source can generate a highly flexible pair of entangled photons that can be used to interface disparate quantum systems. In this thesis, we have successfully implemented a cavity-SPDC source that emits polarization correlated photons at 942 nm with a lifetime of 950-1050ps that mode matches closely with InAs/GaAs QD photons. The source emits 80 photon pairs per second per mW pump power within the 150MHz bandwidth. Though the detection of idler photons, the source is capable of emitting heralded photons with g2≤0.5 for up to 40 mW pump power. For a low pump power of ~5 mW, the heralded g2 is 0.06, indicating that the system is an excellent heralded single photon source. By directly exciting a single QD with cavity-SPDC photons, we have demonstrated a heralded-absorption of SPDC photons by QD, resulting in the coupling of the two systems. Due to the large pump bandwidth, the emitted source is highly multimode in nature, requiring us to post-filter the downconverted field, resulting in a lower photon pair emission rate. We propose placing an intra-cavity etalon to suppress the multi-mode emissions and increase the photon count rate. Understanding and experimentally implementing two-photon interference (HOM) measurements will be crucial for building a scalable quantum network. A detailed theoretical description of HOM measurements is given and is experimentally demonstrated using photons emitted by QD. Through HOM measurements we demonstrated that the QD sample in the study is capable of emitting indistinguishable photons, with the visibility exceeding 95%. As an alternative approach to modifying the spectral mode of single photons, we performed phase modulation of photons emitted by a QD to generate additional sidebands that are separated by several GHz. By performing HOM measurements, we have shown that the central component and the sidebands are in the superposition states and the spectrally modified photons have a well-preserved indistinguishability. Such spectrally engineered photons can be used for phase-encoded cryptography applications. These experimental results should lay the foundations towards building a scalable hybrid quantum network.