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Interferometric Quantum-Nondemolition Single-Photon Detectors

Peter Kok, Hwang Lee, Jonathan P. Dowling

Published Mar 1, 2007• 0 citations
OpenAlex

Abstract

Two interferometric quantum-nondemolition (QND) devices have been proposed: (1) a polarization-independent device and (2) a polarization-preserving device. The prolarization-independent device works on an input state of up to two photons, whereas the polarization-preserving device works on a superposition of vacuum and single- photon states. The overall function of the device would be to probabilistically generate a unique detector output only when its input electromagnetic mode was populated by a single photon, in which case its output mode would also be populated by a single photon. Like other QND devices, the proposed devices are potentially useful for a variety of applications, including such areas of NASA interest as quantum computing, quantum communication, detection of gravity waves, as well as pedagogical demonstrations of the quantum nature of light. Many protocols in quantum computation and quantum communication require the possibility of detecting a photon without destroying it. The only prior single- photon-detecting QND device is based on quantum electrodynamics in a resonant cavity and, as such, it depends on the photon frequency. Moreover, the prior device can distinguish only between one photon and no photon. The proposed interferometric QND devices would not depend on frequency and could distinguish between (a) one photon and (b) zero or two photons. The first proposed device is depicted schematically in Figure 1. The input electromagnetic mode would be a superposition of a zero-, a one-, and a two-photon quantum state. The overall function of the device would be to probabilistically generate a unique detector output only when its input electromagnetic mode was populated by a single photon, in which case its output mode also would be populated by a single photon.

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Two interferometric quantum-nondemolition (QND) devices have been proposed: (1) a polarization-independent device and (2) a polarization-preserving device. The prolarization-independent device works on an input state of up to two photons, whereas the polarization-preserving device works on a superposition of vacuum and single- photon states. The overall function of the device would be to probabilistically generate a unique detector output only when its input electromagnetic mode was populated by a single photon, in which case its output mode would also be populated by a single photon. Like other QND devices, the proposed devices are potentially useful for a variety of applications, including such areas of NASA interest as quantum computing, quantum communication, detection of gravity waves, as well as pedagogical demonstrations of the quantum nature of light. Many protocols in quantum computation and quantum communication require the possibility of detecting a photon without destroying it. The only prior single- photon-detecting QND device is based on quantum electrodynamics in a resonant cavity and, as such, it depends on the photon frequency. Moreover, the prior device can distinguish only between one photon and no photon. The proposed interferometric QND devices would not depend on frequency and could distinguish between (a) one photon and (b) zero or two photons. The first proposed device is depicted schematically in Figure 1. The input electromagnetic mode would be a superposition of a zero-, a one-, and a two-photon quantum state. The overall function of the device would be to probabilistically generate a unique detector output only when its input electromagnetic mode was populated by a single photon, in which case its output mode also would be populated by a single photon.
Optical quantum-nondemolition devices can provide essential tools for quantum information processing. Here, we describe several optical interferometers that signal the presence of a single photon in a particular input state without destroying it. We discuss both entanglement-assisted and nonentanglement-assisted interferometers, with ideal and realistic detectors. We found that the existing detectors with 88% quantum efficiency and single-photon resolution can yield output fidelities of up to 89%, depending on the input state. Furthermore, we construct expanded protocols to perform quantum-nondemolition detections of single photons that leave the polarization invariant. For detectors with 88% efficiency, we found polarization-preserving output fidelities of up to 98.5%.
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.
A triggering device sensitive to a single photon is discussed. It is based on a balanced quantum nondemolition (QND) measurement proposed by Chuang and Yamamoto [Phys. Rev. Lett. 76, 4281 (1996)]. The balanced measurement measures the total photon number and obtains no which-path/mode information. Hence, the timing of the photon can be determined without destroying its wave function or entangling the probe field. This could have extensive use in the realization of long-distance quantum communications systems.