On the realization of interaction-free measurements

A pMsiblc realistic implemenwion of a method for inkmtion-free measurements. due to Elitzur and Vaidman. is proposed and discussed. It is argwd that the effed can be obse~ed in an optical laboratory. The interaction-free measurements of Elitzur and Vaidman [l] is a proposal to consider a well known device and ask a question which is, in a sense, opposite to what is usually asked. The suggested procedure achieved a surprising result which is a complete contradiction to classical intuition. Assume that an experimentalist claims he has built a super-detector with an efficiency of 100% for all kinds of particles (including photons). He says that it is now on a table in a dark room and it is ready to count particles coming from all directions. You, however, suspect that there is nothing on the table. Is it possible to find out which one of these possibilities is hue without the detector (if it is really there) counting any particle? Classically, the only way to verify the existence of the detector requires sending it some test particles. However, then the detector invariably clicks. The task of locating the detector without the occurrence of any click seems to be impossible. Remarkably, quantum mechanics allows this, with, however, one reservation: we do not always succeed in finding it without the click. Our method is based on the Mach-Zehnder interferometer used in classical optics. In principle, it can work with any type of particle. The particle reaches the first beamsplitter which has transmission coefficient $. The transmitted and reflected pmts of the particle's wave are then reflected by the mirrors and finally reunite at another similar bwnsplitter (figure I@)). ' h o detectors collect the particles after they pass through the second beamsplitter. We can mange the positions of the beamsplitters and the mirrors such that because of destructive interference, no particles are detected by one of the detectors, say Dz, and all are detected by DI .We position the interferometer in such a way that one of the mutes of the particle passes through the place where the super-detector might be (figure l(b)). We send a single particle through the system. There are three possible outcomes of this measurement (i) the super-detector clicks, (ii) detector DI clicks, (iii) detector Dz clicks. The probability for the first case is $. In the second case (for which the probability is a), the measurement does not succeed either. The particle wuld have reached DI in both cases: when the super-detector is, and when it is not there. Finally, in the third case, when the detector Dz clicks (the probability for which is $), we haw achieved our goal: we know that the super-detector is inside the interferometer and it did not click. Let us estimate now the probability for a successful experiment Even the ideal experiment does not always succeed. We have seen that the probability for success hen is 0954-8998194/030119+08$19.50 @ 1994 IOP Publishing Ltd 119 120 Letter to the Editor Figure 1. (e) If there is no object inside the interferometer. D2 never clicks. (b) When D2 chcb aftn sending just one panicle we know that the super-detector is inside the interferometer although it did not count any particle. only f . But we also have the probability $ not to trigger the super-detector without finding it. Trying again and again, until success or the click, leads to the probability f of locating the untriggered super-detector. We have shown [l] that by modifying the transmission coefficients of the beam splitters in the interferometer we can obtain (almost) a probability 4 for success. This is, however, a gedanken experiment. A super-detector with 100% efficiency, a Mach-Zehnder interferometer with complete destructive interference in one detector, a single particle source-these are not devices that can be found in a standard laboratory. Let us now discuss a few points which are relevant for a realization of the idea in a real laboratory. We do not need a super-detector sensitive to all kinds of particles. It can be replaced by a photon detector of a certain energy range, while we restrict ourselves to use only such photons. We do not need a source of single photons. We assume that the click is loud enough for us to hear, so all we need is a weak source of photons and fast switch that stops the beam when detector D2 clicks. (The single-photon source [Z] is necessary if we want to locate an object and be sure that it was not disturbed in any way whatsoever, even if the object does not click.) Letter to the Editor