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arXiv:1602.04767 · Optics Express

Double-heralded generation of two-photon-states by spontaneous four-wave-mixing in the presence of noise

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

Published Mar 8, 2016• 12 citations
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Abstract

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.

DOI
10.1364/oe.24.005809

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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.
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.
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 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.
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.
Current sources of heralded single photons based on nonlinear optics operate in a probabilistic manner. In order to build quantum-enhanced devices based around the use of single photons, compact, turn-key and deterministic sources are required. A possible solution is to multiplex a number of sources to increase the single-photon generation probability and in so doing reducing the waiting time to deliver large numbers of photons simultaneously, from independent sources. Previously it has been shown that, in the ideal case, 17 multiplexed sources allow deterministic generation of heralded single photons [Christ and Silberhorn, Phys. Rev. A 85, 023829 (2012)]. Here we extend this analysis to include undesirable effects of detector inefficiency and photon loss on a number of multiplexed sources using a variety of different detectors for heralding. We compare these systems for fixed signal-to-noise ratio to allow a direct comparison of performance for real- world heralded single photon sources.
A technique for conditionally creating single-mode or multimode photon-number states is analyzed using Bayesian theory. We consider the heralded NNN-photon states created from the photons produced by an unseeded optical parametric amplifier when the heralding detector is the time-multiplexed photon-number-resolving detector recently demonstrated by Fitch et al. [Phys. Rev. A 68, 043814 (2003)] and simultaneously by Achilles et al. [Opt. Lett. 28, 2387 (2003)]. We find that even with significant loss in the heralding detector, fields with sub-Poissonian photon-number distributions can be created. We also show that heralded multimode fields created using this technique are more robust against detector loss than are single-mode fields.