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arXiv:quant-ph/0309140 · Physical Review A

Improving single-photon sources via linear optics and photodetection

Dominic William Berry, Stefan Scheel, Barry C. Sanders, P. L. Knight

Published Mar 1, 2004• 21 citations
arXivHTMLPDF

Abstract

Triggered single-photon sources produce the vacuum state with nonzero probability, but produce a much smaller multiphoton component. It is therefore reasonable to approximate the output of these photon sources as a mixture of the vacuum and single-photon states with probabilities $1\ensuremath{-}p$ and $p$, respectively. Here we are concerned with increasing the efficiency $p$ by directing multiple copies of the single-photon-vacuum mixture into a linear optical device and applying photodetection on some outputs. We prove that it is impossible, under certain conditions, to increase $p$ via linear optics and conditional preparation based on photodetection. We also establish a class of photodetection events for which $p$ can be improved, although with an added multiphoton component. In addition we prove that it is not possible to obtain perfect single-photon states via this method from imperfect $(p<1)$ inputs.

DOI
10.1103/physreva.69.031806

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Triggered single-photon sources produce the vacuum state with nonzero probability, but produce a much smaller multiphoton component. It is therefore reasonable to approximate the output of these photon sources as a mixture of the vacuum and single-photon states with probabilities 1\ensuremath−p1\ensuremath{-}p1\ensuremath−p and ppp, respectively. Here we are concerned with increasing the efficiency ppp by directing multiple copies of the single-photon-vacuum mixture into a linear optical device and applying photodetection on some outputs. We prove that it is impossible, under certain conditions, to increase ppp via linear optics and conditional preparation based on photodetection. We also establish a class of photodetection events for which ppp can be improved, although with an added multiphoton component. In addition we prove that it is not possible to obtain perfect single-photon states via this method from imperfect (p<1)(p<1)(p<1) inputs.
Triggered single-photon sources produce the vacuum state with non-negligible probability, but produce a much smaller multiphoton component. It is therefore reasonable to approximate the output of these photon sources as a mixture of the vacuum and single-photon states. We show that it is impossible to increase the probability for a single photon using linear optics and photodetection on fewer than four modes. This impossibility is due to the incoherence of the inputs; if the inputs were pure-state superpositions, it would be possible to obtain a perfect single-photon output. In the more general case, a chain of beam splitters can be used to increase the probability for a single photon, but at the expense of adding an additional multiphoton component. This improvement is robust against detector inefficiencies, but is degraded by dark counts or multiphoton components in the input.
Triggered single-photon sources produce the vacuum state with non-negligible probability, but produce a much smaller multiphoton component. It is therefore reasonable to approximate the output of these photon sources as a mixture of the vacuum and single-photon states. We show that it is impossible to increase the probability for a single photon using linear optics and photodetection on fewer than four modes. This impossibility is due to the incoherence of the inputs; if the inputs were pure-state superpositions, it would be possible to obtain a perfect single-photon output. In the more general case, a chain of beam splitters can be used to increase the probability for a single photon, but at the expense of adding an additional multiphoton component. This improvement is robust against detector inefficiencies, but is degraded by distinguishable photons, dark counts or multiphoton components in the input.
Triggered single-photon sources produce the vacuum state with non-negligible probability, but produce a much smaller multiphoton component. We describe a method for increasing the probability of a single photon via a chain of beam splitters. This method has the drawbacks that it introduces a significant multiphoton component, and it can not be used to increase the probability for a single photon above 1/2. Part of the reason for these drawbacks is the incoherence in the photon sources. If the photon sources produced pure states rather than incoherent superpositions, it would be possible to obtain a perfect single photon output. The method for incoherent inputs is robust against detector inefficiencies, but sensitive to dark counts and the multiphoton component in the input.
We answer the question whether linear-optical processing of the states produced by one or multiple imperfect single-photon sources can improve the single-photon fidelity. This processing can include arbitrary interferometers, coherent states, feedforward, and conditioning on results of detections. We show that without introducing multiphoton components, the single-photon fraction in any of the single-mode states resulting from such processing cannot be made to exceed the efficiency of the best available photon source. If multiphoton components are allowed, the single-photon fidelity cannot be increased beyond 1/2. We propose a natural general definition of the quantum-optical state efficiency, and show that it cannot increase under linear-optical processing.
Single photons are the smallest excitation states of the elctromagnetic field. They can be experimentally created but there is no apparatus that performs this task with 100% efficiency. Many techniques and theorems of optical quantum information theory use single photons. In order to utilize them for information processing, it is reasonable to know if they had been successfully produced. In other words: One needs heralded single photons. How to achieve this, is the main result of this diploma thesis. The task has been to improve the efficiency of already existing single photon sources. An apparatus had to be found which postprocesses the output of such sources in order to either herald the photons or at least to improve the efficiency. This apparatus is explicitly allowed to use other optical sources, for example coherent states (laser). The situation has been formally represented by the assumption that single photon sources produce a mixture of vacuum and the single photon state. It is known that experimental set-ups also create higher photon contributions. These contributions are considered to be small in corresponding publications. For some cases they even seem to vanish at all. One can distinguish two regimes concerning the techniques which have been used in this work: linear and nonlinear optics. Linear optical tools, for example the beam splitter, do not absorb photons in the ideal case, but it is not easy to implement useful transformations by their means. Absorption and weak coupling are drawbacks which arise mainly in nonlinear optical media. This work shows that the interactions two-photon absorption and cross phase modulation can be used in schemes, which enable the heralding of single photons. Already there are some linear optical quantum gates which manipulate optical states by means of single photons. Photons do not interact with each other directly, in contrast to electrons for example. Therefore quantum gates which act on more than one mode are interesting. The effective interaction of these gates is not quitecomparable to unitary dynamics. Moreover, these gates do not function in each case. Measurements required in auxiliary modes yield different results for each single case and in order to obtain the desired effect the cases have to be selected according to the measurement results. It has been investigated, how such gates perform if they have statistical mixtures as a resource instead of perfect single-photon states. Yet, no improvement of the single-photon contribution has been accomplished by means of these apparatuses. Hereby it has not been disproved that it is possible to achieve this goal using other apparatuses and techniques of linear optics. Yet, it has been shown that an enhancement is possible but then a non-vanishing two-photon contribution is appended. One of the most basic quantum gates is the conditional sign flip. The optical 8 interaction cross phase modulation acts in quite the same way considering only single photons. This effect enables the heralding of single photons in the ideal case. Within this work it has been shown that a Mach-Zehnder interferometer, a cross phase modulating medium and a photo-detector can be employed for this purpose. One could use any source of light as input to the interferometer but a strong coherent state (laser) may be preferred for the purpose of enhancing the interaction. The absorption of two-photon states is another non-linear effect. Astonishingly this effect serves to generate a heralded single-photon state given two imperfect single-photon sources. First the photon adding tool is employed which consists of a beam splitter and a photo-detector. By means of that and the statistical mixtures of two single-photon sources one creates a mixture which contains vacuum, the single-photon state and additionally the two-photon Fock state. This mixture propagates through a Mach-Zehnder interferometer. The interferometer is adjusted such that it is transparent for incoming light. In addition to the interferometer alone a two-photon absorbing medium is placed in one of its arms. For this reason there is a chance that the two-photon contribution entering the interferometer is absorbed within this medium. We cannot exclude this unfortunate case. A detector is placed in one of the two output modes. The interferometer is adjusted such that the single photon state does not leave in the mode in which the detector is placed, but always in the other mode. The detector can only click if the two-photon state propagates through the interferometer and if it is not destroyed in the absorbing medium. If the detector then receives one photon it is obvious that another one must leave in the other mode. The whole phenomenon is very similar to the concept of null measurement. Although not a main result, it has been shown here that the so-called Hong-Ou-Mandel effect can be generalized. It has been proven that the beam splitter transforms Fock states with equal Fock number into superpositions of Fock numbers which are even in each mode. Another effect on special odd Fock states is conjectured.