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

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.

Figure 1

Population inversion versus time plot for $P_{ab}=3(\mathrm{eV}{)}^{-1}$, $\nu =3\mathrm{eV}$, $\mathbf{v}={10}^{-7}\mathrm{eV}$, $E_0=2(\mathrm{eV}{)}^2$.

Figure 2

Population inversion versus time plot for $P_{ab}=1(\mathrm{eV}{)}^{-1}$, $\nu =3\mathrm{eV}$, $\mathbf{v}={10}^{-7}\mathrm{eV}$, $E_0=2(\mathrm{eV}{)}^2$.

Figure 3

Population inversion versus time plot for $P_{ab}=1(\mathrm{eV}{)}^{-1}$, $\nu =3\mathrm{eV}$, $\mathbf{v}={10}^{-8}\mathrm{eV}$, $E_0=3(\mathrm{eV}{)}^2$.

Figure 4

Simultaneous plot of spin PIF (black thick line) and energy PIF (thin line) for the following parameter values: $P_{ab}=0.47(\mathrm{eV}{)}^{-1}$, $b_0=0.10\mathrm{eV}$, $E_0=1.00(\mathrm{eV}{)}^2$, $\nu =1.00\mathrm{eV}$.

Figure 5

Simultaneous plot of spin PIF (black thick line) and energy PIF (thin line) for the following parameter values: $P_{ab}=0.5(\mathrm{eV}{)}^{-1}$, $b_0=0.1\mathrm{eV}$, $E_0=1.0(\mathrm{eV}{)}^2$, $\nu =1.0\mathrm{eV}$.

Figure 6

Simultaneous plot of spin PIF (black thick line) and energy PIF (thin line) for the following parameter values: $P_{ab}=0.2(\mathrm{eV}{)}^{-1}$, $b_0=0.1\mathrm{eV}$, $E_0=1.0(\mathrm{eV}{)}^2$, $\nu =1.0\mathrm{eV}$.