Realization of a measurement of a ‘‘weak value’’

Abstract

%e present the first realization of a measurement of a "weak value, " a concept recently introduced by Aharonov, Albert, and Vaidman (AAV). Our experiment uses a birefringent crystal to separate the two linear-polarization components of a laser beam by a distance small compared to the laser-beam waist. This "weak measurement" is followed by a strong measurement which translates the centroid of the beam by a distance far larger than the birefringence-induced separation. In addition, we present data corresponding to orthogonal initial and final states, for which the weak value is not defined. This interference eAect may have application in the amplification and detection of weak eff'ects.

Advantages of nonclassical pointer states in postselected weak measurements

“…After first optical implementation of weak value [4], it has been applied in different fields to observe very tiny effects, such as beam deflection [5][6][7][8][9][10], frequency shifts [11], phase shifts [12], angular shifts [13,14], velocity shifts [15], and even temperature shift [16]. Weak value has a nature of being a complex number, which lead the weak measurements to provide an ideal method to examine some fundamentals of quantum physics.…”

Quantum averages of weak values

“…The usefulness of this description has been demonstrated, both theoretically and experimentally, in a number of applications in which novel aspects of quantum processes have been uncovered when analyzed in terms of * Electronic address: abotero@uniandes.edu.co weak values. These include photon polarization interference [7,8,9,10,11], barrier tunnelling times [12,13,14], photon arrival times [15,16], anomalous pulse propagation [17,18,19], correlations in cavity QED experiments [20], complementarity in "which-way" experiments [21,22], non-classical aspects of light [23,24], communication protocols [25] and retrodiction "paradoxes" of quantum entanglement [26,27,28].…”

Comment on “Linear optics implementation of weak values in Hardy’s paradox”

“…Measurement of a single-particle weak value is straightforward when the pointer variable is another degree of freedom in the quantum system. Examples include a Stern-Gerlach device for measuring spin by coupling to the transverse momentum of the particle, or the optical analogy with polarization [12]. Difficulties begin when one means to measure joint properties of multiple particles.…”