Abstract
An essential ingredient to both the theoretical studies in, and technological applications of, quantum information science is easy availability of entangled states of two or more qubits. Hitherto, these qubits have primarily been photons and/or atoms. Photons are excellent carriers of information—nothing can travel faster than an electromagnetic wave. Also, it is relatively easy to generate states of two or more photonic qubits entangled with respect to either their (linear or circular) polarization, or amplitude and phase.
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Notes
- 1.
In this monograph, these states for atoms, for example, have been specified by (\(L_{0},S_{0},M_{L_{0}},M_{S_{0}}\)) in L-S coupling, or by (\(J_{0},M_{J_{0}}\)) in j-j coupling. It is for this reason that, in the mathematical expressions used herein, the atomic \(densitymatrix\vert 0\rangle \langle 0\vert \) has been averaged over (\(M_{L_{0}},M_{S_{0}}\)), or \(M_{J_{0}}\), as the case may be (See Chap. 3 for a detailed discussion of this point.)
- 2.
See, for example, discussion given on pages 48–49.
- 3.
it is the dependence of the light–matter interaction on the polarization of the former and ∕ or anisotropy of the later. The differences observed due to a change in the helicity (direction of the electric field vector) of a circularly (linearly) polarized light—but, without any change in the nature of the anisotropy of the matter which in the case of a state-selected atom means, for example, that the direction of quantization of J 0 should remain unaltered—have come to be known as circular [196, 340] (linear [341]) “optical” dichroism. The “magnetic” dichroism, on the other hand, arises (see, for example, [342–344]) due to a change in the anisotropy of the matter while polarization of the interacting light remains the same. The magnetic dichroism is called [334] circular or linear depending upon whether the light interacting with the matter has circular or linear polarization.
- 4.
It consists of magnitudes of the transition amplitudes and differences (with signs) of their phases.
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Chandra, N., Ghosh, R. (2013). Conclusions and Prospectives. In: Quantum Entanglement in Electron Optics. Springer Series on Atomic, Optical, and Plasma Physics, vol 67. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24070-6_11
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