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arXiv:quant-ph/0510016 · Journal of Physics A Mathematical and Theoretical

Understanding entangled spins in QED

Haijun Wang, W. T. Geng

Published Sep 4, 2007• 7 citations

Abstract

We have studied the stability of two entangled spins dressed by electrons by calculating the scattering phase shifts. The interaction between electrons is interpreted by fully relativistic QED and the screening effect is described phenomenologically in the Debye exponential form e −α r . Our results show that if the (Einstein–Podolsky–Rosen-) EPR-type states are kept stable under the interaction of QED, the spatial wavefunction will be constrained to be parity dependent. The spin-singlet state s = 0 and the polarized state along the z -axis give rise to two different kinds of phase shifts . Interestingly, the interaction between electrons in the spin-singlet pair is found to be attractive. Using this attraction we propose a mechanism to produce entangled pairs of massive spin-1/2 particles.

DOI: 10.1088/1751-8113/40/38/012

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We have studied the stability of two entangled spins dressed by electrons by calculating the scattering phase shifts. The interaction between electrons is interpreted by fully relativistic QED and the screening effect is described phenomenologically in the Debye exponential form e −α r . Our results show that if the (Einstein–Podolsky–Rosen-) EPR-type states are kept stable under the interaction of QED, the spatial wavefunction will be constrained to be parity dependent. The spin-singlet state s = 0 and the polarized state along the z -axis give rise to two different kinds of phase shifts . Interestingly, the interaction between electrons in the spin-singlet pair is found to be attractive. Using this attraction we propose a mechanism to produce entangled pairs of massive spin-1/2 particles.

Pairs of atoms have been prepared in an entangled state of the Einstein-Podolsky-Rosen (EPR) type. They were produced by the exchange of a single photon between the atoms in a high

Q

cavity. The atoms, entangled in a superposition involving two different circular Rydberg states, were separated by a distance of the order of 1 cm. At variance with most previous EPR experiments, this one involves massive particles. It can be generalized to three or more atoms and opens the way to new tests of nonlocality in mesoscopic quantum systems.

The correlation and fluctuation of both entangled electrons and spin-polarized pairs affected by two rotating magnetic fields in a setup proposed by J. Carlos Egues etc. (Phys. Rev. Lett. {\bf 89}(2002) 176401) are studied theoretically by using scattering approach. Differing from polarized pair, the entangled electron pairs are shown to behave like a composite particle with the total spins and its

z

components. The singlet and triplet states exhibit different bunching and antibunching features, which can be easily adjusted by the magnetic fields. The correlations and variances can show up distinguish output signals for the four incident states. Our results are expected to be tested by using coincident technique.

Entanglement is the superposition of two or more particles in multiple states. An example is given for the double-well potential; another involves particles with spin 1/2. Measurement of spin is carried out by a Stern–Gerlach apparatus, using the deflection of a spin by a magnet. Entangled spin-1/2 states, namely triplet states having total spin 1, and the singlet state, with spin 0, are also examined; the latter state appears in same form when expressed in spin up/down along any Cartesian coordinate. The determination of one of the spins in an entangled singlet state immediately determines the other, resulting in a “spooky action at a distance.” Einstein, Podolsky, and Rosen (EPR) claimed to show, on the basis of local realism, that quantum mechanics must be incomplete because of this feature. Their logic suggests that one might explain the instantaneous results by invoking “hidden variables” not contained in a quantum treatment.

Entangled EPR spin pairs can be treated using the statistical ensemble interpretation of quantum mechanics. As such the singlet state results from an ensemble of spin pairs each with its own specific axis of quantization. This axis acts like a quantum mechanical hidden variable. If the spins lose coherence they disentangle into a mixed state that contains classical correlations. In this paper an infinitesimal phase decoherence is introduced to the singlet state in order to reveal more clearly some of the correlations. It is shown that a singlet state has no classical correlations.

Entangled EPR spin pairs can be treated using the statistical ensemble interpretation of quantum mechanics. As such the singlet state results from an ensemble of spin pairs each with an arbitrary axis of quantization. This axis acts as a quantum mechanical hidden variable. If the spins lose coherence they disentangle into a mixed state. Whether or not the EPR spin pairs retain entanglement or disentangle, however, the statistical ensemble interpretation resolves the EPR paradox and gives a mechanism for quantum "teleportation" without the need for instantaneous action-at-a-distance.