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Physical Review A

Efficient interaction-free measurements in a high-finesse interferometer

Tedros Tsegaye, E. Goobar, Anders Karlsson, Gunnar G. Bjork, M. Y. Loh, K. H. Lim

Published May 1, 1998• 56 citations
Publisher

Abstract

Interaction-free measurements were realized using a high-finesse Fabry-P\'erot cavity as a measurement apparatus. A figure of merit based on the maximum likelihood estimation, which takes into account real experimental conditions, is used to analyze the efficiency of this measurement scheme. The probability of detecting the presence of an object within the cavity without any photons actually ``hitting'' the object was approximately 85%. The probability of asserting the absence of the object was approximately 75%. Assuming that the a priori probability of the object being present was 1/2, the likelihood of knowing whether the object was present or not was 80%. The obtained results and the limitations of our setup are discussed.

DOI
10.1103/physreva.57.3987

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Interaction-free measurements were realized using a high-finesse Fabry-P'erot cavity as a measurement apparatus. A figure of merit based on the maximum likelihood estimation, which takes into account real experimental conditions, is used to analyze the efficiency of this measurement scheme. The probability of detecting the presence of an object within the cavity without any photons actually ``hitting'' the object was approximately 85%. The probability of asserting the absence of the object was approximately 75%. Assuming that the a priori probability of the object being present was 1/2, the likelihood of knowing whether the object was present or not was 80%. The obtained results and the limitations of our setup are discussed.
Summary form only given.The purpose of an interaction-free measurement is to detect the presence of an object without letting any energy quanta be absorbed by the object. In this work we present interaction-free measurement results using a Fabry-Perot interferometer as a measurement apparatus. If the cavity of the interferometer is empty, an incoming photon will be transmitted through the interferometer. If an absorbent is placed between the mirrors, the photon will be reflected by the first mirror. By detecting which way the photon takes, we will gain information about the presence of the absorbent without losses/interaction. For a perfect measurement, the figure of merit will be equal to the mirror reflectivity R. Thus, in theory, one can approach the perfect interaction-free measurement simply by increasing R.
Recently, it has been pointed out that it is possible to make a quantum-mechanical interaction-free measurement (IFM), in which the existence of an object in a given region of space may be determined seemingly without interacting with it.1,2 In the embodiment first proposed by Elitzur and Vaidman,3 a standard Michelson interferometer is aligned so that incident single photons (obtained in our experiment by using parametric downconversion; see Fig. 1) must exit by the same port in which they entered, in the absence of any object within the interferometer. The presence of an object (e.g., the mirror leading to detector DB) in one of the arms completely changes the possible outcomes because the constructive interference is interrupted. Now it is possible that the photon will exit from the other exit port, to detector DIfm. By detecting the photon in this case, one can claim with certainty that an object was within the interferometer, even though the photon could not have interacted with it. If the beam splitter has a very low reflectivity, then the fraction of IFMs approaches 1/2.
The so-called 'interaction-free' measurement is a very interesting quantum effect that allows discovering the presence of an opaque object in a given spatial domain, with the probability that the object absorbs a photon being, in principle, as low as desired. This probability is bounded from below only by a value of the order of 1/ωτ, where ω is the frequency of light and τ is the measurement time. This corresponds to the average absorbed energy of the order of /τ. The 'interaction-free' technique can also be used to measure the coordinate of an object but only under the condition that the object is prepared in a special 'discretized' quantum state. Such is, for instance, the state of a ponderomotive meter of electromagnetic energy, which, in principle, enables the interaction-free' measurement of the energy contained in an electromagnetic cavity. Estimations show that with modern experimental equipment and with the help of 'interaction-free' measurement, single atoms can be registered inside optical cavities.
"Interaction-free measurements" (IFM) originate from the latest quantum interferometric technologies. The latest research of quantum optics demonstrates, by using the complementary wavelike and particlelike natures of photons, it is possible to make interaction-free measurements by which the presence of an object can be determined with no photons being absorbed. The paper introduces the concept of "Interaction-free Measurement" (IFM), the original Elitzur-Vaidman scheme, the "High Efficiency Interaction-free Measurement", the application of quantum Zeno effect and the improved scheme proposed by Kwiat et al. The EV scheme is implemented in a Mach-Zehnder interferometer. Theoretically this paper also draws a conclusion in IFM feasibility by analyzing the wave functions of photon at various locations in the interferometer.