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arXiv:quant-ph/9905050 · Physical Review A

Fundamental limit on “interaction-free” measurements

Steven H. Simon, P. M. Platzman

Published Apr 3, 2000• 10 citations
arXivHTMLPDF

Abstract

In ``interaction-free'' measurements, one typically wants to detect the presence of an object without touching it with even a single photon. One often imagines a bomb whose trigger is an extremely sensitive measuring device whose presence we would like to detect without triggering it. We point out that all such measuring devices have a maximum sensitivity set by the uncertainty principle, and thus can only determine whether a measurement is ``interaction-free'' to within a finite minimum resolution. We further discuss exactly what can be achieved with the proposed ``interaction-free'' measurement schemes.

DOI
10.1103/physreva.61.052103

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In interaction-free'' measurements, one typically wants to detect the presence of an object without touching it with even a single photon. One often imagines a bomb whose trigger is an extremely sensitive measuring device whose presence we would like to detect without triggering it. We point out that all such measuring devices have a maximum sensitivity set by the uncertainty principle, and thus can only determine whether a measurement is interaction-free'' to within a finite minimum resolution. We further discuss exactly what can be achieved with the proposed ``interaction-free'' measurement schemes.
It is now well-understood that the complementary wave- and particle-like natures of quanta enable one to make measurements that are “interaction-free” -- one can determine the presence or absence of an object, even a completely absorbing object, without any photons being absorbed. The first proposal of such a scheme was limited to an efficiency of 50% -- at most half of the measurements could be interaction free [1]. By using an application of the Quantum Zeno effect, one can in fact have the fraction of interaction-free measurements arbitrarily close to one [2].
Summary form only given.Using the complementary wave-like and particle-like natures of photons, one can make interaction-free measurements (IFM)-the presence of an object can be determined with no photons being absorbed. By using an application of the quantum Zeno effect (weakly and repeatedly testing for the object's presence so that the otherwise coherent evolution of the interrogating photon is inhibited), we have demonstrated the feasibility of IFMs with an efficiency of >85%, higher than that possible in the original IFM scheme, where, at most, half of the measurements could be interaction free. We also investigate various interaction-free imaging systems, demonstrate imaging with a resolution <5 /spl mu/m, and define the limits to these systems. We also discuss in which sense interaction-free measurements really are not.
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.
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.
It is now well established that the presence of an opaque classical object can be unambiguously determined by an "interaction-free" measurement (IFM), where the object and the probe never directly interact. For quantum objects, we examine "interaction-free" measurement (the object wavefunction is unchanged) and "interaction-free" preparation (the object wavefunction is changed without physical interaction) and find that in general, neither is possible. We propose using high efficiency IFM's as a quantum information bus to connect disjoint quantum systems.