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PRL 105, 010405 (2010) PHYSICAL REVIEW LETTERS 2 JULY 2010

"Measuring Small Longitudinal Phase Shifts:Weak Measurements or Standard Interferometry?
Nicolas Brunner1 and Christoph Simon2
A cornerstone of quantum mechanics is that a measurement generally perturbs the system. Indeed, during the process of a (standard) quantum measurement, the state of the system is projected onto one of the eigenstates of the measured observable. However, in 1988, in the context of foundational research on the arrow of time in quantum theory, Aharonov, Albert, and Vaidman [1] discovered that quantum mechanics offers a much larger variety of
measurements. As a matter of fact, the only restriction quantum mechanics imposes on measurements is a tradeoff between information gain and disturbance. Therefore, strong (or standard) quantum measurements are only part of the game. There are also ‘‘weak’’ measurements [2], which disturb the system only very little, but which give only limited information about its quantum state. Weak measurements lead to striking results when postselection comes into play. In particular, the ‘‘weak value’’ found by a weak measurement on a preselected and postselected system can be arbitrarily large, where the most
famous example is the measurement of a spin particle leading to a value of 100 [1]. Because of such unorthodox predictions, weak measurements were initially controversial [3] and were largely considered as a strange and purely theoretical concept. However, they turn out to be a useful ingredient for exploring the foundations of quantum mechanics. In particular, they bring an interesting new perspective to famous quantum paradoxes, as illustrated by recent experiments [4] on Hardy’s paradox [5,6]. Furthermore, they also perfectly describe superluminal light propagation in dispersive materials [7,8], polarization effects in optical networks [9], and cavity QED experiments [10]. Weak measurements have been demonstrated in numerous experiments [4,7,8,11] and were recently shown to be relevant in solid-state physics as well [12]. Already in 1990 Aharonov and Vaidman [13] pointed out the potential offered by weak measurements for performing very sensitive measurements. More precisely, when weak measurements are judiciously combined with preselection and postselection, they lead to an amplification phenomenon, much like a small image is magnified by a microscope. This effect is of great interest from an experimental perspective, since it gives access to an experimental sensitivity beyond the detector’s resolution, therefore enabling the observation of very small physical effects"

"Hardy's paradox is a thought experiment in quantum mechanics devised by Lucien Hardy[1][2] in which a particle and its antiparticle may interact without annihilating each other. The paradox arises in that this may only occur if the interaction is not observed and so it seemed that one might never be able to confirm this.[3] Experiments[4][5] using the technique of weak measurement[3] have studied an interaction of polarized photons and these have demonstrated that the phenomenon does occur. However, the consequence of these experiments maintain only that past events can be inferred about after their occurrence as a probabilistic wave collapse. These weak measurements are considered by some[who?] to be an observation themselves, and therefore part of the causation of wave collapse, making the objective results only a probabilistic function rather than a fixed reality." Wikipedia