Two-dimensional open quantum system in dissipative bosonic heat bath, external magnetic field, and two time-dependent electric fields

Non-Markovian dynamics of a charged particle in a two-dimensional harmonic oscillator linearly coupled to a neutral bosonic heat bath is investigated in an external uniform magnetic field and two perpendicular time-dependent electric fields. The analytical expressions for the time-dependent and asymptotic angular momentum are derived for the Markovian and non-Markovian dynamics. The dependence of the angular momentum on the frequency of the electric field, cyclotron frequency, collective frequency, and anisotropy of the heat bath is studied. The angular momentum (or magnetization) of a charged particle can be ruled by varying the frequency of the electric field.

Figure 1

In the Markovian (red dashed lines) and non-Markovian (black solid lines) cases, the calculated $z$ components $L_{z1}\left(t\right)$ and $L_{z2}\left(t\right)$ of angular momentum as functions of time $t$ at the indicated friction coefficients. Here $T_0=0.1\mathrm{meV}, \hslash {\omega }_c=1\mathrm{meV}, \hslash {\omega }_0=1\mathrm{meV}, \hslash {\omega }_e=\hslash {\omega }_e^{\max }=0.62\mathrm{meV}$, and $\hslash \gamma =12\mathrm{meV}$.

Figure 2

The calculated asymptotic $z$ component $L_{z1}\left(\infty \right)/\hslash$ of angular momentum as a function of $\hslash {\omega }_c$. Here $T_0=0.1\mathrm{meV}$ and $\hslash \gamma =12\mathrm{meV}$ for non-Markovian dynamics. In the Markovian and non-Markovian cases, Eq. (16) and Eq. (B2) are used, respectively.

Figure 3

The calculated asymptotic $z$ component $L_{z2}\left(\infty \right)/\hslash$ of angular momentum as a function of $\hslash {\omega }_e$ for non-Markovian dynamics at (a) $\hslash {\omega }_c=1\mathrm{meV}$ and (b) $\hslash {\omega }_c=0$ for $\hslash {\omega }_0=1\mathrm{meV}$. The calculated $L_{z2}^a\left(\infty \right)/\hslash$ at (c) $\hslash {\omega }_c=0$ and $L_{z2}^b\left(\infty \right)/\hslash$ at (d) $\hslash {\omega }_c=1\mathrm{meV}$ for $\hslash {\omega }_x=1.5\hslash {\omega }_y=1.5\mathrm{meV}$. Here $\hslash {\lambda }_y=0.1\mathrm{meV}, \hslash \gamma =12\mathrm{meV}, E_{x0}=E_{y0}={10}^5$ V/m, and $\mu =0.067m_0$. The solid, dashed, and dash-dotted lines correspond to the cases with ${\lambda }_x/{\lambda }_y=1.1$, 1.5, and 2, respectively.

Figure 4

The calculated asymptotic $z$ component $L_{z2}\left(\infty \right)/\hslash$ of angular momentum as a function of $\hslash {\omega }_e$ at different ratios of collective frequencies. Here $\hslash {\lambda }_x=1.5\hslash {\lambda }_y=0.15\mathrm{meV}, \hslash {\omega }_c=1\mathrm{meV}, \hslash {\omega }_y=1\mathrm{meV}$, and $\hslash \gamma =12\mathrm{meV}$.

Figure 5

The calculated asymptotic $z$ component $L_{z2}\left(\infty \right)/\hslash$ of angular momentum as a function of $\hslash {\omega }_e$ for a free particle ($\hslash {\omega }_0=0$) at (a) $\hslash {\omega }_c=0$ and (b) $\hslash {\omega }_c=1\mathrm{meV}$ in the non-Markovian case.

Figure 6

The calculated asymptotic $z$ component $L_{z2}\left(\infty \right)/\hslash$ of angular momentum as a function of $\hslash {\omega }_c$ for the Markovian and non-Markovian dynamics. Here $\hslash {\omega }_0=1\mathrm{meV}$ and $\hslash \gamma =12\mathrm{meV}$.

Figure 7

The calculated asymptotic $z$ component $L_{z2}\left(\infty \right)/\hslash$ of angular momentum as a function of $\hslash {\omega }_c$ for a free particle ($\hslash {\omega }_0=0$).

Figure 8

The calculated asymptotic $z$ component $L_{z2}\left(\infty \right)/\hslash$ of angular momentum as a function of $\hslash {\omega }_0$. Here $\hslash {\lambda }_y=0.1\mathrm{meV}$, and the solid, dashed, dotted, and dash-dotted lines correspond to the cases with ${\lambda }_x/{\lambda }_y=1$, 1.1, 1.5, and 2, respectively.