Atomic “Bomb Testing”: The Elitzur–Vaidman Experiment Violates the Leggett–Garg Inequality

Carsten Robens,Wolfgang Alt,Clive Emary,Dieter Meschede,Andrea Alberti

doi:10.1007/978-3-319-64346-5_10

Abstract

Elitzur and Vaidman have proposed a measurement scheme that, based on the quantum superposition principle, allows one to detect the presence of an object—in a dramatic scenario, a bomb—without interacting with it. It was pointed out by Ghirardi that this interaction-free measurement scheme can be put in direct relation with falsification tests of the macro-realistic worldview. Here we have implemented the “bomb test” with a single atom trapped in a spin-dependent optical lattice to show explicitly a violation of the Leggett–Garg inequality—a quantitative criterion fulfilled by macro-realistic physical theories. To perform interaction-free measurements, we have implemented a novel measurement method that correlates spin and position of the atom. This method, which quantum mechanically entangles spin and position, finds general application for spin measurements, thereby avoiding the shortcomings inherent in the widely used push-out technique. Allowing decoherence to dominate the evolution of our system causes a transition from quantum to classical behavior in fulfillment of the Leggett–Garg inequality.

Highlights

IntroductionMeasuring physical properties of an object whether macroscopic or microscopic is in most cases associated with an interaction
Quantum mechanics formalizes the loss of interference in terms of the quantum measurement process, showing that measurements are generally invasive as they entail a modification of the subsequent quantum evolution
On the left-hand side, we present the procedure with no “bomb” present, which comprises Q(t1) and Q(t3) measurements, but not Q(t2): the spin preparation is followed by a π/2 pulse, a variable waiting time, a second π/2 pulse with adjustable microwave phase φ, and a non-destructive spin measurement mapping the spin state onto different positions as described in Sec

Summary

Introduction

Measuring physical properties of an object whether macroscopic or microscopic is in most cases associated with an interaction. Scattering photons off an object allows one to detect its presence in a given region of space This produces a small perturbation of its state by direct momentum transfer. It is well known from numerous discussions on the physics of the quantum measurement process [1, 2]) that a measurement in general modifies the quantum evolution unless the object is already in an eigenstate of the measurement apparatus [3]. This is even the case when the measurement yields a negative outcome, that is, when we did not find the particle on a certain trajectory that had originally a non-vanishing probability amplitude to be occupied. While the quantum measurement process is still intensely debated in the literature [4], we adopt here the pragmatic view that a measurement applied to a superposition state causes a sudden reduction of the wave function to a smaller Hilbert space

Objectives

Results

Conclusion