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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Dynamic realization of quantum measurements in a quantized Stern - Gerlach experiment

C. P. Sun, X. X. Yi, Shou-Xin Zhao, L Zhang, Chunling Wang

Published Feb 1, 1997• 24 citations
Publisher

Abstract

A novel dynamic model for wavefunction collapse in cavity quantum electrodynamics (QED) is proposed associated with the gedanken Stern - Gerlach experiment of the quantized magnetic field. It is used to describe and test the fundamental problems of quantum measurements, such as wavefunction collapse, Schrödinger entanglement states (cats) and quantum decoherence. This model also manifests rich phenomena in atomic optics, such as the splitting of atomic beams, and the generation of even- and odd-coherent states. It is also shown that this model possesses a factorizable structure which has been found in the other dynamic models for wavefunction collapse.

DOI
10.1088/1355-5111/9/1/008

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A novel dynamic model for wavefunction collapse in cavity quantum electrodynamics (QED) is proposed associated with the gedanken Stern - Gerlach experiment of the quantized magnetic field. It is used to describe and test the fundamental problems of quantum measurements, such as wavefunction collapse, Schrödinger entanglement states (cats) and quantum decoherence. This model also manifests rich phenomena in atomic optics, such as the splitting of atomic beams, and the generation of even- and odd-coherent states. It is also shown that this model possesses a factorizable structure which has been found in the other dynamic models for wavefunction collapse.
Abstract The Stern–Gerlach experiment reveals the quantum mechanical nature of spin through the force experienced by a non-relativistic neutral atom in a static magnetic field gradient. A key open question concerns when, along the atom’s trajectory, the spin state collapses into an eigenstate and by what mechanism. We analyze the influence of quantum electrodynamic (QED) vacuum fluctuations on spin dynamics and show that they induce spin self-interactions, leading to decoherence and memory effects. However, the magnitude of these effects is shown to be too small to account for the deterministic collapse of the spin wavefunction.
The Stem-Gerlach (SG) experiments considered as a quantum measurement process measuring the spin states of particles from their spatial distribution. The wave packet collapse or quantum decoherence can he described as a dynamical evolution governed by the interaction between the space degrees of freedom and the spin degrees of freedom. The analytic solution of this exactly solvable model shows that the decaying process of coherence with time in the SG experiment obeys no longer the linear exponential law.
We first consider the Einstein-Podolsky-Rosen (EPR) paradox for the system of two particles with spin 1/2 with entangled spins in first-quantized quantum mechanics (QM). If measurement is governed by wavefunction collapse, then gedanken experiments show that a number of fundamental principles including conservation of angular momentum and the Heisenberg uncertainty principle can be violated. We conclude that the collapse of the spin part of the wavefunction cannot happen and therefore an EPR paradox does not arise for this system. QM unitarity alone is sufficient to rule out "spooky" action at a distance. The absence of spin wavefunction collapse leads to several interesting conclusions about how measurement works in QM: When wavefunction collapse does not happen, (i) a signal from a macroscopic measuring device indicating that a system is in a state S does not necessarily mean that it is or was in S and (ii) the uncertainty in QM at the microscopic level is transmitted to uncertainty in signals for the macroscopic measuring device. We derive two general results on how quantum measurement works and illustrate them in a spin-1/2 measurement. In contrast to first-quantized QM, in quantum field theory we are unable to fully rule out the possibility of wavefunction collapse. However, when we insist on unitarity (thereby excluding the possibility of wavefunction collapse) and additionally take into account in the wavefunction all degrees of freedom involved in the measurement (including those of the equipment, experimentalists, etc.), a consistant acceptable understanding of the Bell-inequality-type experiments involving entangled photon polarizations emerges including the absence of an EPR paradox. The ability of an experimentalist to be aware of his perceptions but unable to be conscious of other components of a generalized Schrodinger Cat plays a role in resolving the Measurement Problem.
It is demonstrated that the collapse of the wavefunction in the quantum measurement process is reflected in the two-particle correlation function for the electron spin, which can in principle be studied by a triple Stern-Gerlach experiment. The change in momentum of a Stern-Gerlach magnet is itself sufficient to allow the determination of the electron spin, subject to the uncertainty principle, if the coherence of the two components of the spin is destroyed by the magnetic field. Similar considerations apply to the two-particle correlation function for the photon polarisation, and two-photon atomic cascades can be used in practice to investigate the measurement process and determine the extension of a photon wavepacket. The irreversibility of quantum mechanical measurements and its relation to the uncertainty principle is briefly considered.
In the context of the measurement problem, we propose to model the interaction between a quantum particle and an "apparatus" through a non-Hermitian Hamiltonian term. We simulate the time evolution of a normalized quantum state split into two spin components (via a Stern-Gerlach experiment) and that undergoes a wave-function collapse driven by a non-Hermitian Hatano-Nelson Hamiltonian. We further analyze how the strength and other parameters of the non-Hermitian perturbation influence the time-to-collapse of the wave function obtained under a Schrödinger-type evolution. We finally discuss a thought experiment where manipulation of the apparatus could challenge standard quantum mechanics predictions.
Abstract In the context of the measurement problem, we propose to model the interaction between a quantum particle and an ‘apparatus’ through a non-Hermitian Hamiltonian term. We simulate the time evolution of a normalized quantum state split into two spin components (via a Stern–Gerlach experiment) and that undergoes a wavefunction collapse driven by a non-Hermitian Hatano-Nelson Hamiltonian. We further analyze how the strength and other parameters of the non-Hermitian perturbation influence the time-to-collapse of the wave function obtained under a Schödinger-type evolution. We finally discuss a thought experiment where manipulation of the apparatus could challenge standard quantum mechanics predictions.