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arXiv:0707.4660 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Influence of Lorentz-violating terms on a two-level system

Manoel M. Ferreira, Adalto R. Gomes, Rafael Christ de Castro Lopes

Published Nov 29, 2007• 5 citations

Abstract

The influence of Lorentz- and $CPT$-violating terms of the extended standard model on a semiclassical two-level system is analyzed. It is shown that the Lorentz-violating background (when coupled with the fermion sector in a vector way) is able to induce modifications on the Rabi oscillation pattern, promoting sensitive modulations on the usual oscillations. As for the term involving the coefficient coupled in an axial vector way, it brings about oscillations both on energy states and on the spin states (implied by the background). It is also seen that such backgrounds are able to yield state oscillations even in the absence of the electromagnetic field. The foreseen effects are used to establish upper bounds on the Lorentz-violating coefficients.

DOI: 10.1103/physrevd.76.105031

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The influence of Lorentz- and

CPT

-violating terms of the extended standard model on a semiclassical two-level system is analyzed. It is shown that the Lorentz-violating background (when coupled with the fermion sector in a vector way) is able to induce modifications on the Rabi oscillation pattern, promoting sensitive modulations on the usual oscillations. As for the term involving the coefficient coupled in an axial vector way, it brings about oscillations both on energy states and on the spin states (implied by the background). It is also seen that such backgrounds are able to yield state oscillations even in the absence of the electromagnetic field. The foreseen effects are used to establish upper bounds on the Lorentz-violating coefficients.

In this work, we consider the effects of the Lorentz-violating (LV) term $ v_μ\barψγ^μψ$ belonging to the fermion sector of the extended standard model on the dynamics of a quantum two-level system. We examine how its non-relativistic counterpart,

{(\mathbf{p}-e \mathbf{A})\cdot }\mathbf{v}/{m_{e},}

affects the Rabi oscillations of a two-level atom coupled with a quantum cavity electromagnetic field. Taking an initial coherent field state in a resonant cavity, it was found that the LV background increases the Rabi frequency and the time interval between collapses and revivals of the population inversion function. It was found that initial field states with low mean number of photons are better probes in order to establish more stringent upper bounds on the background magnitude. In particular, for an initial vacuum state in the cavity the upper limit

\text{v}_{x}<10^{-10}eV

was attained.

The extension of Standard Model of the Fundamental Particles which consider the Lorentz Symmetry Violation governed by a background tensor field presented by Colladay and Kostelecky consider the hypothesis of having a privileged direction in the space-time. Here we investigated a extension of the Schrödinger Equation inspired on that model taking into account a background scalar field. We analyze the behavior of this modified Schrödinger equation on a particle trapped in a well and quantum harmonic oscillator.

From the effects of the Lorentz symmetry violation in the CPT-even gauge sector of the Standard Model Extension determined by a tensor background [Formula: see text], we establish a possible scenario where an analogue of the He–McKellar–Wilkens effect can stem from. Besides, we build quantum holonomies associated with the analogue of the He–McKellar–Wilkens effect and discuss a possible analogy with the geometric quantum computation. Finally, we investigate the dependence of the energy levels on the He–McKellar–Wilkens geometric phase induced by Lorentz symmetry breaking effects when the particle is confined to a hard-wall confining potential.

Abstract We investigate the quantum dynamics of a spin-(1/2) neutral particle under the effects of Lorentz symmetry violation, characterized by a fixed time-like background vector and azimuthal electric fields added to the potential of a pure quartic oscillator. These effects, induced by the background vector that defines a preferred spacetime direction, modify the dynamics of the spin-(1/2) neutral particle and give rise to a doubly anharmonic oscillator-like potential. The main challenge is to find analytical solutions to the Schrödinger equation, considering that this nonlinear potential models realistic quantum physics scenarios. Finally, we obtain bound-state solutions in the nonrelativistic limit for the Schrödinger-Pauli equation of a spin-(1/2) neutral particle. An interesting quantum effect is observed: the constant associated with the pure quartic oscillator term is quantized, meaning it depends on the system's quantum numbers.

We analyze the nonrelativistic quantum dynamics of a single neutral spin half particle, with non-zero magnetic and electric dipole moments, moving in an external electromagnetic field in presence of Lorentz symmetry violation background. Also, we study the geometric phase for this model taking into account the parameter that breaks the Lorentz symmetry. We investigate the He-McKellar-Wilkens effect in this context and we verify that Lorentz violation parameter contribute to increase the electric dipole moment of the particle.