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arXiv:0906.1502 · Journal of Physics A Mathematical and Theoretical

Using the no-signaling condition for constraining the nonidealness of a Stern–Gerlach set-up

Dipankar Home, A. K. Pan

Published Jan 22, 2009• 2 citations
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Abstract

On the basis of a variant of the EPR-Bohm example, we show that the no-signaling condition can be employed as a useful tool for deriving a constraint on a suitably defined measure of the 'nonidealness' of a Stern–Gerlach (SG) set-up. In this demonstration, a key ingredient is provided by the characteristics of the exact solution of the time-dependent Schrödinger equation as applied to a most general SG set-up.

DOI
10.1088/1751-8113/42/8/085301

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On the basis of a variant of the EPR-Bohm example, we show that the no-signaling condition can be employed as a useful tool for deriving a constraint on a suitably defined measure of the 'nonidealness' of a Stern–Gerlach (SG) set-up. In this demonstration, a key ingredient is provided by the characteristics of the exact solution of the time-dependent Schrödinger equation as applied to a most general SG set-up.
We critically examine the quantum-mechanical modelling of a measurement process using the Stern–Gerlach (SG) setup in the most general context, probing in particular for nonideal situations, the subtleties involved in the connection between the notion of 'distinguishability' of apparatus states defined in terms of the inner product and the spatial separation among the wave packets emerging from the SG setup. The quantitative studies highlighting some of the unexplored features of this relationship are presented in terms of an appropriately defined measure for the spatial separation between the emerging wave packets. It is also indicated how the effects arising from such departures from the idealness can be empirically tested for different values of the relevant parameters.
Explaining the behavior of macroscopic objects from the point of view of the quantum paradigm has challenged the scientific community for the past century. A mechanism of gravitational self-interaction, governed by the so-called Schr\"odinger-Newton equation, is among the proposals that aim to shed some light on it. Despite all efforts, this mechanism has been proven difficult to probe. Here, we consider a Stern-Gerlach-like experiment to try it out. The Schr\"odinger-Newton equation can be analytically solved under certain proper conditions, and a change-of-phase effect induced by the gravitational self-interacting potential can be calculated.
Abstract The Stern–Gerlach (SG) effect provided the first direct experimental evidence of the quantization of electron spin. Although some analog SG effects have been proposed in optical systems, finding a perfect optical analog for the SG effect remains a challenge. Here, a novel optical SG effect is demonstrated in periodically poled electro‐optical crystals. Induced by an applied electric field, the principal axes of crystal rock periodically along the propagation direction of light. When the quasi‐phase‐matching condition is satisfied, the electro‐optical coupling process within the periodically poled crystal can be accurately described by the Schrödinger–Pauli equation for spin‐1/2 particles. The output photons can be deflected toward opposite directions according to their intrinsic spin angular momentum (circular polarizations), since the transversely varying duty cycle of crystal arises an effective magnetic‐field gradient. Moreover, the output photons can be separated according to two arbitrary orthogonal polarization states, allowing us to construct high‐speed electro‐optically tunable polarization beam splitters for arbitrary orthogonal polarization states. Therefore, the optical SG effect provides not only a perfect optical analog for the quantum SG effect but also a useful optical element for optics and quantum physics.
Abstract Stern‐Gerlach (SG) effect, initially found for unveiling the existence of quantized electron spins, is now a general concept describing a state‐dependent separation. It is widely explored in optics to achieve a function of optical splitting, but the current schemes always require a polarization‐ or wavelength‐dependent process, thus showing limitations for broader applications. Here, spatial modes of an optical field are employed as another degree of freedom to demonstrate an SG effect. Two modes of a pair of coupled waveguides are found to be in analog to the electron spins. They are able to undergo a splitting upon a spatially‐dependent waveguide coupling, which plays the role of a non‐uniform magnetic field. In an experiment, such a splitting is realized in two coupled non‐parallel slab waveguides, and its strength is adjusted at ease by varying the parameters of this proposed structure. This SG‐related optical splitting may find applications in the field of optical sensing and signal processing.