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arXiv:1409.0044 · Physical Review A

Semitransparency in interaction-free measurements

Sebastian Thomas, Christoph Kohstall, Pieter Kruit, Peter Hommelhoff

Published Nov 21, 2014• 61 citations
arXivHTMLPDF

Abstract

We discuss the effect of semitransparency in a quantum-Zeno-like interaction-free measurement setup, a quantum-physics based approach that might significantly reduce sample damage in imaging and microscopy. With an emphasis on applications in electron microscopy, we simulate the behavior of probe particles in an interaction-free measurement setup with semitransparent samples, and we show that the transparency of a sample can be measured in such a setup. However, such a measurement is not possible without losing (i.e., absorbing or scattering) probe particles in general, which causes sample damage. We show how the amount of lost particles can be minimized by adjusting the number of round trips through the setup, and we explicitly calculate the amount of lost particles in measurements which either aim at distinguishing two transparencies or at measuring an unknown transparency precisely. We also discuss the effect of the sample causing phase shifts in interaction-free measurements. Comparing the resulting loss of probe particles with a classical measurement of transparency, we find that interaction-free measurements only provide a benefit in two cases: first, if two semitransparent samples with a high contrast are to be distinguished, interaction-free measurements lose less particles than classical measurements by a factor that increases with the contrast. This implies that interaction-free measurements with zero loss are possible if one of the samples is perfectly transparent. A second case where interaction-free measurements outperform classical measurements is if three conditions are met: the particle source exhibits Poissonian number statistics, the number of lost particles cannot be measured, and the transparency is larger than approximately $\frac{1}{2}$. In all other cases, interaction-free measurements lose as many probe particles as classical measurements or more. Aside from imaging of gray levels, another possible application for interaction-free measurements is the detection of arbitrarily small phase shifts in transparent samples.

DOI
10.1103/physreva.90.053840

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We discuss the effect of semitransparency in a quantum-Zeno-like interaction-free measurement setup, a quantum-physics based approach that might significantly reduce sample damage in imaging and microscopy. With an emphasis on applications in electron microscopy, we simulate the behavior of probe particles in an interaction-free measurement setup with semitransparent samples, and we show that the transparency of a sample can be measured in such a setup. However, such a measurement is not possible without losing (i.e., absorbing or scattering) probe particles in general, which causes sample damage. We show how the amount of lost particles can be minimized by adjusting the number of round trips through the setup, and we explicitly calculate the amount of lost particles in measurements which either aim at distinguishing two transparencies or at measuring an unknown transparency precisely. We also discuss the effect of the sample causing phase shifts in interaction-free measurements. Comparing the resulting loss of probe particles with a classical measurement of transparency, we find that interaction-free measurements only provide a benefit in two cases: first, if two semitransparent samples with a high contrast are to be distinguished, interaction-free measurements lose less particles than classical measurements by a factor that increases with the contrast. This implies that interaction-free measurements with zero loss are possible if one of the samples is perfectly transparent. A second case where interaction-free measurements outperform classical measurements is if three conditions are met: the particle source exhibits Poissonian number statistics, the number of lost particles cannot be measured, and the transparency is larger than approximately 12\frac{1}{2}21​. In all other cases, interaction-free measurements lose as many probe particles as classical measurements or more. Aside from imaging of gray levels, another possible application for interaction-free measurements is the detection of arbitrarily small phase shifts in transparent samples.
Absorption-free (also known as ``interaction-free'') measurement aims to detect the presence of an opaque object using a test particle without that particle being absorbed by the object. Here we consider semitransparent objects that have an amplitude $\ensuremath{\alpha}$ of transmitting a particle while leaving the state of the object unchanged and an amplitude $\ensuremath{\beta}$ of absorbing the particle. The task is to devise a protocol that can decide which of two known transmission amplitudes is present while ensuring that no particle is absorbed by the object. We show that the probabilities of being able to achieve this are limited by an inequality. This inequality implies that absorption-free distinction between complete transparency and any partial transparency is always possible with probabilities approaching 1, but that two partial transparencies can only be distinguished with probabilities less than 1.
Interaction-free measurement (IFM) has been proposed as a means of high-resolution, low-damage imaging of radiation-sensitive samples, such as biomolecules and proteins. The basic setup for IFM is a Mach-Zehnder interferometer, and recent progress in nanofabricated electron-diffraction gratings has made it possible to incorporate a Mach-Zehnder interferometer in a transmission electron microscope (TEM). Therefore, the limits of performance of IFM with such an interferometer and a shot-noise limited electron source (such as that in a TEM) are of interest. In this paper, we compare the error probability and sample damage for ideal IFM and classical imaging schemes, through theoretical analysis and numerical simulation. We consider a sample that is either completely transparent or completely opaque at each pixel. In our analysis, we also evaluate the impact of an additional detector for scattered electrons. Inclusion of the scattering detector results in reduction of error by up to an order of magnitude, for both IFM and classical schemes. We also investigate a sample reillumination scheme based on updating priors after each round of illumination and find that this scheme further reduces error. Implementation of these methods is likely achievable with existing instrumentation and would result in improved resolution in low-dose electron microscopy.
An interaction-free measurement system with a polarization-based Mach-Zehnder interferometer structure is analyzed for semitransparent objects. Here, it is shown that the interaction-free measurement of such objects with 100% detection efficiency is possible in principle if the system loss is negligible. The influence of two system imperfections, the system loss and the low quantum efficiency of the photon detectors, on the interaction-free measurement is also analyzed. Although the two system imperfections limit the maximal detection efficiency that can be achievable, the quantum efficiency of the photon detectors is less important when the system loss becomes small.
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.
Interaction-free measurement is a quantum process where, in the ideal situation, an object can be detected as if no interaction took place with the probing photon. Here we show that the problem of interaction-free measurement can be regarded as a problem of quantum-channel discrimination. In particular, we look for the optimal photonic states that can minimize the detection error and the photon loss in detecting the presence or absence of the object, which is taken to be semitransparent, and the number of the interrogation cycle is assumed to be finite. Furthermore, we also investigated the possibility of minimizing the detection error through the use of entangled photons, which is essentially a setting of quantum illumination. However, our results indicate that entanglement does not exhibit a clear advantage; the same performance can be achieved with unentangled photonic states.