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arXiv:1206.3847 · Science

Emergence of a Measurement Basis in Atom-Photon Scattering

Yinnon Glickman, Shlomi Kotler, Nitzan Akerman, Roee Ozeri

Published Mar 7, 2013• 9 citations
arXivHTMLPDF

Abstract

After measurement, a wave-function is postulated to collapse on a predetermined set of states--the measurement basis. Using quantum process tomography, we show how a measurement basis emerges in the evolution of the electronic spin of a single trapped atomic ion after spontaneous photon scattering and detection. This basis is determined by the excitation laser polarization and the direction along which the photon was detected. Quantum tomography of the combined spin-photon state reveals that although photon scattering entangles all superpositions of the measurement-basis states with the scattered photon polarization, the measurement-basis states themselves remain classically correlated with it. Our findings shed light on the process of quantum measurement in atom-photon interactions.

DOI
10.1126/science.1229650

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After measurement, a wave-function is postulated to collapse on a predetermined set of states--the measurement basis. Using quantum process tomography, we show how a measurement basis emerges in the evolution of the electronic spin of a single trapped atomic ion after spontaneous photon scattering and detection. This basis is determined by the excitation laser polarization and the direction along which the photon was detected. Quantum tomography of the combined spin-photon state reveals that although photon scattering entangles all superpositions of the measurement-basis states with the scattered photon polarization, the measurement-basis states themselves remain classically correlated with it. Our findings shed light on the process of quantum measurement in atom-photon interactions.
Spontaneous photon scattering by an atomic qubit is a notable example of environment-induced error and is a fundamental limit to the fidelity of quantum operations. In the scattering process, the qubit loses its distinctive and coherent character owing to its entanglement with the photon. Using a single trapped ion, we show that by utilizing the information carried by the photon, we are able to coherently reverse this process and correct for the scattering error. We further used quantum process tomography to characterize the photon-scattering error and its correction scheme and demonstrate a correction fidelity greater than 85% whenever a photon was measured.
Quantum entanglement is central to both the foundations of quantum mechanics and the development of new technologies in information processing, communication, and sensing. Entanglement has been realised in a variety of physical systems, spanning atoms, ions, photons, collective excitations, and hybrid combinations of particles. Remarkably, however, photons and free electrons -- the quanta of light and their most elementary sources -- have never been observed in an entangled state. Here, we demonstrate quantum entanglement between free electrons and photons. We show that entanglement is produced when an electron, prepared in a superposition of two beams, passes a nanostructure and generates transition radiation in a polarisation state tied to the electron path. By implementing quantum state tomography, we reconstruct the full density matrix of the electron-photon pair, and show that the Peres-Horodecki separability criterion is violated by more than 7 standard deviations. Based on this foundational element of emerging free-electron quantum optics, we anticipate manifold developments in enhanced electron imaging and spectroscopy beyond the standard quantum limit. More broadly, the ability to generate and measure entanglement opens electron microscopy to previously inaccessible quantum observables and correlations in solids and nanostructures.
We present a set of exact system solutions to a model we developed to study wave function collapse in the quantum spin measurement process. Specifically, we calculated the wave function evolution for a simple harmonic oscillator of spin \frac{1}{2}, with its magnetic moment in interaction with a magnetic field, coupled to an environment that is a bath of harmonic oscillators. The system's time evolution is described by the direct product of two independent Hilbert spaces: one that is defined by an effective Hamiltonian, which represents a damped simple harmonic oscillator with its potential well divided into two, based on the spin and the other that represents the effect of the bath, i.e., the Brownian motion. The initial states of this set of wave functions form an orthonormal basis, defined as the eigenstates of the system. If the system is initially in one of these states, the final result is predetermined, i.e., the measurement is deterministic. If the bath is initially in the ground state,and the wave function is initially a wave packet at the origin, it collapses into one of the two potential wells depending on the initial spin. If the initial spin is a vector in the Bloch sphere not parallel to the magnetic field, the final distribution among the two potential wells is given by the Born rule applied to the initial spin state with the well-known ground state width. Hence, the result is also predetermined. We discuss its implications to the Bell theorem[1]. We end with a summary of the implications for the understanding of the statistical interpretation of quantum mechanics.
Aiming at the controversies between traditional interpretations of polarization optics and mainstream theoretical explanations of the quantum entanglement CHSH experiment, this paper proposes a new physical hypothesis: the light transmission and blocking effects of polarizers are essentially the direction-matching screening effect between the intrinsic spin direction of photons and the atomic arrangement structure of the polarizer grating. Photon spin direction and the atomic barrier exhibit a 90° directional interaction switching: weak interaction and transmission when parallel, strong interaction and blocking when deflected 90° perpendicular, and recovery of transmission when rotated another 90°. The CHSH experiment, currently used to prove the existence of quantum entanglement, does not verify superluminal quantum correlation, quantum state superposition, collapse, or other theories. Its experimental phenomena entirely stem from the intrinsic opposite spin-matching property of photon pairs at the moment of generation. Like electron-positron pairs, photons naturally carry opposite spin states when excited in pairs. Polarization detection is only the screening and observation of the pre-existing spin states of photons, rather than a measurement that alters the quantum state of photons. Based on this, all polarization experiments and CHSH observations can be reasonably explained by a classical microscopic spin mechanism, avoiding the logical paradox of action-at-a-distance in quantum entanglement theory.