Tuning the sharpness of quantum measurements using position entangled atomic states

As rigorously proven by Paul Busch in 2007, quantum systems are necessarily disturbed by measurement [arXiv:0706.3526].  The amount of disturbance, interpreted here as state change, is related to the information gained, hence a measurement scheme that induces no state change yields no new information. Standard projective measurements, such as the measurement of an excited state energy (with respect to the ground
state) by coupling a quantum system to a photon and then detecting the photon absorption, are maximally disruptive since they project the initial state of the system into an eigenstate of the measured observable.  By contrast, so-called weak measurements provide an observer with little information and, in turn, disrupt the quantum state very little.  Also, known as "unsharp", "fuzzy" or "gentle", such measurements have been considered in the context of measuring the quantum trajectory of a system using weak continuous measurements [Rev. Mod. Phys. 82, 1155 (2010)]. 
One scheme for implementing unsharp measurements is to first entangle a target quantum system with an ancillary quantum system and then carry out a measurement on the ancilla.  By adjusting the degree of entanglement, the sharpness of the measurement on the target system can be controlled. 
In this talk, we explore how tunable position-entangled quantum states of atoms can be used to realize tunable quantum measurements.  Entangled states of atomic pairs are created by Feshbach resonance coupling and measurements of the ancilla are conducted either by ancilla selective scattering of single photons or by hard collisional localization of the ancilla by the scattering of room-temperature atoms in the background vapor of the apparatus.