Measuring position and momentum together

Arkady Bolotin

As per Einstein's design, particles are introduced into the double-slit experiment through a small hole in a plate which can either move up and down (and its momentum can be measured) or be stopped (and its position can be measured). Suppose one measures the position of the plate and this act verifies the statement that the interference pattern is observed in the experiment. However, if it is possible to think about the outcome that one would have obtained if one had measured plate's momentum instead of its position, then it is possible to consider, together with the aforesaid statement, another statement that each particle passes through either slit of the double-slit screen. Hence, the proposition affirming the wave-like behavior and the proposition affirming the particle-like behavior might be true together, which would imply that Bohr's complementarity principle is incorrect. The analysis of Einstein's design and ways to refute it based on an approach that uses exclusively assignments of the truth values to experimental propositions is presented in this paper.

Paul Busch, PEKKA J. LAHTI, Juha-Pekka Pellonpää +1 more

Chao Meng, Warwick P. Bowen

Abstract We explore the generation of nonclassical mechanical states by combining continuous measurement and feedback control. We find that feedback-induced spring softening can greatly enhance position squeezing, allowing squeezing despite measurement rates slower than the mechanical frequency. Conversely, even from a pure position measurement, we find that spring hardening can enable momentum squeezing, in a new regime we term the fast feedback regime. We interpret these effects as arising from correlations between the feedback drive and the measurement imprecision noise, which in turn effectively modify the measurement rates for position and momentum. Together, this significantly lowers the barrier to measurement-based preparation of nonclassical mechanical states at room temperature.

Chao Meng, Warwick P. Bowen

We explore the generation of nonclassical mechanical states by combining continuous position measurement and feedback control. We find that feedback-induced spring softening can greatly enhance position squeezing. Conversely, even with a pure position measurement, we find that spring hardening can enable momentum squeezing. Beyond enhanced squeezing, we show that feedback also mitigates degradation introduced by background mechanical modes. Together, this significantly lowers the barrier to measurement-based preparation of nonclassical mechanical states at room temperature.

D. M. Appleby