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arXiv:quant-ph/0602225 · Physical Review A

Production of heralded pure single photons from imperfect sources using cross-phase-modulation

Thomas Konrad, Michael Nock, Artur Scherer, Jürgen Audretsch

Published Sep 25, 2006• 7 citations
arXivHTMLPDF

Abstract

Realistic single-photon sources do not generate single photons with certainty. Instead they produce statistical mixtures of photons in Fock states $\ensuremath{\mid}1⟩$ and vacuum (noise). We describe how to eliminate the noise in the output of the sources by means of another noisy source or a coherent state and cross-phase-modulation (XPM). We present a scheme that announces the production of pure single photons and thus eliminates the vacuum contribution. This is done by verifying a XPM-related phase shift with a Mach-Zehnder interferometer.

DOI
10.1103/physreva.74.032331

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Realistic single-photon sources do not generate single photons with certainty. Instead they produce statistical mixtures of photons in Fock states \ensuremath∣1⟩\ensuremath{\mid}1⟩\ensuremath∣1⟩ and vacuum (noise). We describe how to eliminate the noise in the output of the sources by means of another noisy source or a coherent state and cross-phase-modulation (XPM). We present a scheme that announces the production of pure single photons and thus eliminates the vacuum contribution. This is done by verifying a XPM-related phase shift with a Mach-Zehnder interferometer.
Single-photons sources are crucial devices in the development of practical quantum communication and quantum computation. However, such sources are still a technological challenge. One option is to use weak coherent states to mimic single-photon pulses or to produce a pair of photons with parametric down conversion and to detect one of them to herald the presence of the other. In this direction, the present work shows how to produce better approximations of single-photon pulses by using a nonlinear phase modulator in a Mach-Zehnder interferometer. The proposed scheme is explained and applications are discussed.
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.
We study the operation of linear optics schemes for entanglement distribution based on nonlocal photon subtraction when input states, produced by imperfect single-photon sources, exhibit both vacuum and multiphoton contributions. Two models for realistic photon statistics with radically different properties of the multiphoton ``tail'' are considered. The first model assumes occasional emission of double photons and linear attenuation, while the second one is motivated by heralded sources utilizing spontaneous parametric down-conversion. We find conditions for the photon statistics that guarantee generation of entanglement in the relevant qubit subspaces and compare it with classicality criteria. We also quantify the amount of entanglement that can be produced with imperfect single-photon sources, optimized over setup parameters, using as a measure entanglement of formation. Finally, we discuss verification of the generated entanglement by testing Bell's inequalities. The analysis is carried out for two schemes. The first one is the well-established one-photon scheme, which produces a photon in a delocalized superposition state between two nodes, each of them fed with one single photon at the input. As the second scheme, we introduce and analyze a linear optics analog of the robust scheme based on interfering two Stokes photons emitted by atomic ensembles, which does not require phase stability between the nodes.
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 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.
Quantum information processing provides remarkable advantages over its classical counterpart. Quantum optical systems have been proved to be sufficient for realizing general quantum tasks, which, however, often rely on single-photon sources. In practice, imperfect single-photon sources, such as a weak-coherent-state source, are used instead, which will inevitably limit the power in demonstrating quantum effects. For instance, with imperfect photon sources, the key rate of the Bennett-Brassard 1984 (BB84) quantum key distribution protocol will be very low, which fortunately can be resolved by utilizing the decoy-state method. As a generalization, we investigate an efficient way to simulate single photons with imperfect ones to an arbitrary desired accuracy when the number of photonic inputs is small. Based on this simulator, we can thus replace the tasks that involve only a few single-photon inputs with the ones that make use of only imperfect photon sources. In addition, our method also provides a quantum simulator to quantum computation based on quantum optics. In the main context, we take a phase-randomized coherent state as an example for analysis. A general photon source applies similarly and may provide some further advantages for certain tasks.