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تسجيل مستخدم جديدElectric dipoles on the Bloch sphere
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Amar C. Vutha
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The time evolution of a two-level quantum mechanical system can be geometrically described using the Bloch sphere. By mapping the Bloch sphere evolution onto the dynamics of oscillating electric dipoles, we provide a physically intuitive link between classical electromagnetism and the electric dipole transitions of atomic & molecular physics.
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Internal states of polar molecules can be controlled by microwave-frequency electric dipole transitions. If the applied microwave electric field has a spatial gradient, these transitions also affect the motion of these dipolar particles. This capabil
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Bloch oscillations appear when an electric field is superimposed on a quantum particle that evolves on a lattice with a tight-binding Hamiltonian (TBH), i.e., evolves via what we will call an electric TBH; this phenomenon will be referred to as TBH B
loch oscillations. A similar phenomenon is known to show up in so-called electric discrete-time quantum walks (DQWs); this phenomenon will be referred to as DQW Bloch oscillations. This similarity is particularly salient when the electric field of the DQW is weak. For a wide, i.e., spatially extended initial condition, one numerically observes semi-classical oscillations, i.e., oscillations of a localized particle, both for the electric TBH and the electric DQW. More precisely: The numerical simulations strongly suggest that the semi-classical DQW Bloch oscillations correspond to two counter-propagating semi-classical TBH Bloch oscillations. In this work it is shown that, under certain assumptions, the solution of the electric DQW for a weak electric field and a wide initial condition is well approximated by the superposition of two continuous-time expressions, which are counter-propagating solutions of an electric TBH whose hopping amplitude is the cosine of the arbitrary coin-operator mixing angle. In contrast, if one wishes the continuous-time approximation to hold for spatially localized initial conditions, one needs at least the DQW to be lazy, as suggested by numerical simulations and by the fact that this has been proven in the case of a vanishing electric field.
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