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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Noise characterization in double-heralded generation of two-photon-states by spontaneous four-wave-mixing

Roger Allan Paul Smith, Dileep V. Reddy, Dashiell L. P. Vitullo, Michael G. Raymer

Published Sep 13, 2016• 0 citations
Publisher

Abstract

In quantum optics experiments, heralding, a form of conditional state preparation, is a useful tool for creating photon-number states from nonlinear optical sources for quantum-information science experiments. Heralding occurs when one photon from a correlated pair is detected to herald the presence of the other photon, labeled the signal photon. However, as heralding is extended to two or more photon pairs, the presence of noise photons in the herald channel quickly degrades the photon statistics of the signal photons. We create two-photon number states from a non-degenerate, third-order nonlinear optical fiber source with double heralding and present a method for verifying these photon-number states. The consequences of noisy heralding on the statistics of states created via third-order nonlinear processes are analyzed. We present a method for estimating the effects of noise photons on the signal photon statistics. Additionally, we prove the equivalence between noise in the herald channel and a loss in the signal channel. We utilize this equivalence to infer the photon statistics of the photon-number states in the signal channel that would be present in the absence of noise in the herald channel. By measuring the statistics of the signal channels with noise in the herald channel and comparing to the inferred, noise-free distribution, we can estimate the potential benefits of additional noise-reducing procedures on the experiment.

DOI
10.1117/12.2236534

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In quantum optics experiments, heralding, a form of conditional state preparation, is a useful tool for creating photon-number states from nonlinear optical sources for quantum-information science experiments. Heralding occurs when one photon from a correlated pair is detected to herald the presence of the other photon, labeled the signal photon. However, as heralding is extended to two or more photon pairs, the presence of noise photons in the herald channel quickly degrades the photon statistics of the signal photons. We create two-photon number states from a non-degenerate, third-order nonlinear optical fiber source with double heralding and present a method for verifying these photon-number states. The consequences of noisy heralding on the statistics of states created via third-order nonlinear processes are analyzed. We present a method for estimating the effects of noise photons on the signal photon statistics. Additionally, we prove the equivalence between noise in the herald channel and a loss in the signal channel. We utilize this equivalence to infer the photon statistics of the photon-number states in the signal channel that would be present in the absence of noise in the herald channel. By measuring the statistics of the signal channels with noise in the herald channel and comparing to the inferred, noise-free distribution, we can estimate the potential benefits of additional noise-reducing procedures on the experiment.
We present an experimental method for creating and verifying photon-number states created by non-degenerate, third-order nonlinear-optical photon-pair sources. By using spatially multiplexed, thresholding single-photon detectors and inverting a conditional probability matrix, we determine the photon-number probabilities created through heralded spontaneous four-wave-mixing. The deleterious effects of noise photons on reliable heralding are investigated and shown to degrade the conditional preparation of two-photon number states more than they degrade conditional single-photon states. We derive the equivalence between the presence of unwanted noise in the herald channel and loss in the signal channel of heralded experiments. A procedure for characterizing the noise-photon contributions, and a means of estimating the herald noise-free photon-number distribution is demonstrated.
The creation of optical states of light that are quantum mechanical in nature in optical fibers is discussed and demonstrated experimentally. Specifically, two- photon states created by spontaneous four-wave-mixing in commercially available single-mode, birefringent fibers are studied. When creating photon states of light, it is important to verify the created states are of the proper photon number distribution and free of noise. We detail a method for combining thresholding, non-number resolving detectors to characterize the photon number distribution created via SFWM and a procedure to quantify the noise sources present in the process. Frequency translation in optical fibers with two-photon states is discussed and experimental considerations are presented.
We investigate theoretically the spontaneous four-wave mixing (FWM) process that occurs in optical waveguides, as a source of quantum correlated photon-pairs. We consider that the waveguide used to implement the spontaneous FWM process presents a high value of nonlinear parameter, γ = 93.4 W-1m-1, and a non-negligible value of loss coefficient, α = 133.3 dB/m. Moreover, the theoretical model also consider the Raman scattering that inevitably accompanies the FWM process, and generates time-uncorrelated (noise) photon pairs. We use the coincident-to-accidental ratio (CAR) as a figure of merit of the photon pair source, and we were able to observe a CAR of the order of 65 in a high loss regime. After, we use the time-correlated photon pairs generated by the spontaneous FWM process to implement a heralded single photon source at waveguide output. In this scenario, the detection of one photon of the pair heralds the presence of the other photon. The quality of the source was studied by the evaluation of the second order coherence function for one photon of the pair conditioned by the detection of its twin photon. We observe that the presence of a high loss coefficient tends to improve the quality of the photon source, when compared with the lossless regime, even considering the Raman noise photons. We obtain a value for the conditional second order coherence function of the order of 0.11 in absence of loss, and a value of 0.03 for a loss coefficient of 133.3 dB/m.
Single photon sources are fundamental elements for quantum information science, mainly for quantum key distribution (QKD) applications. Nevertheless, on-demand single photon sources are difficult to obtain, and their implementation in a practical application, such as QKD, demands further developments. A different approach to a single photon source is based on the generation of quantum correlated photon-pairs. In that case, the detection of one photon of the pair heralds the presence of the second photon. In this work, we present a heralded single photon source based on the spontaneous four-wave mixing (FWM) process in optical fibers. We characterize theoretically the heralded photon source by means of the conditional second-order coherence function, gc(2) , with gc(2) = 0 for a perfect single photon source. We observe the nonclassical nature of the source, with gc(2) ≪ 1 far below the classical limit. Our results also show that the Raman scattering in general degrades the quality of the source, due to the generation of uncorrelated photons. However, our findings show that in some frequency regimes we are able to observe a gc(2) ≈ 10−3. Moreover, our analysis shows that the propagation of the photons in a standard single mode fiber (SSMF) does not change significantly the value of gc(2), for distances of L < 25/α, with α the loss coefficient of the SSMF. This results can help to guide the development of single photon sources for quantum information applications.
Single photons exhibit nonclassical, counterintuitive behavior that can be exploited in the developing field of quantum technology. They are needed for various applications such as quantum key distribution, optical quantum information processing, quantum computing, intensity measurement standards, and others yet to be discovered in this developing field. This drives the current intensive research into the realization of true deterministic sources of single photons on demand. Lacking such a source, many researchers default to the well-established workhorse: spontaneous parametric down-conversion that generates entangled signal-idler pairs. Since this source is thermal statistical in nature, it is common to use a detected idler photon to herald the production of a signal photon. The need exists to determine the quality of the single photons generated in the heralded signal beam. Quite often, the literature reports a heralded second-order coherence function of the signal photons conditioned on the idler photons using readily available single-photon detectors. In this work we examine the applicability of this technique to single-photon characterization and the consequences of the fact that the most commonly used single-photon detectors are not photon-number resolving. Our results show that this method using non-photon-resolving detectors can only be used to characterize the signal-idler correlations rather than the nature of the signal-photon state alone.
We experimentally study the generation of photon pairs via spontaneous four-wave mixing with two distinct laser pulses. We find that the dual-pump technique enables new capabilities: 1) a new characterization methodology to measure noise contributions, source brightness and photon-collection efficiencies directly from raw photon-count measurements; 2) an enhanced ability to generate heralded single photons in a pure quantum state; and 3) the ability to derive upper and lower bounds on heralded-photon quantum state purity from measurements of photon-number statistics even in the presence of noise. Such features are highly valuable in photon-pair sources for quantum applications.