Engineering a thermal squeezed reservoir by energy-level modulation

We show that a thermal reservoir can effectively act as a squeezed reservoir on atoms that are subject to energy-level modulation. For sufficiently fast and strong modulation, for which the rotating-wave approximation is broken, the resulting squeezing persists at long times. These effects are analyzed by a master equation that is valid beyond the rotating-wave approximation. As an example we consider a two-level atom in a cavity with Lorentzian linewidth, subject to sinusoidal energy modulation. A possible realization of these effects is discussed for Rydberg atoms.

Figure 1

Temperature-dependent response of the cavity reservoir, ${\gamma }_T\left(\omega \right)$ (blue solid line) and ${\Delta }_T\left(\omega \right)$ (red dashed line) [Eq. (25)]. Here ${\gamma }_c$ is the atomic decay rate to the cavity reservoir in the absence of modulation, and ${\omega }_a=10\kappa$ is taken.

Figure 2

Effective reservoir squeezing $\gamma \left|M\right|$ as a function of modulation parameters $z$ and $m$ [Eqs. (27) and (29)]. Taking ${\omega }_a=10\kappa$ and $n_a={10}^3$ in Eqs. (25) and (30), the difference between $N$ and $M$ is plotted in (a), (b), and (c) and apparently cannot go lower than the “classical squeezing” bound $\left|M\right|\le N$, as argued in Sec. 2. (a) $m=2$, (b) $m=1$, (c) $z=1$. (d) The ratio $\left|M\right|/(N+0.5)$, which determines the difference between the two atomic-dipole quadrature dephasing rates, is plotted for $m=2$.

Figure 3

Atom fluorescence spectrum [Eq. (33)] for modulation parameters $z=3,m=2$, and with ${\omega }_a=10\kappa$, $n_a={10}^3$. (a) The spectrum under the influence of modulation (blue solid line) is compared to that in the absence of modulation (red dashed line, multiplied here by factor 5). The modulated case has a much narrower spectrum. (b) The spectrum in the modulated case (blue solid line) compared with a Lorentzian of width $\gamma (N+0.5)$ (red dashed line). It is apparent that the shape of the spectrum in the modulated case is not that of a single Lorentzian, as indeed can be seen in Eq. (33).

Figure 4

Resonance fluorescence spectrum under the influence of modulation and effective squeezing, as a function of the relative driving field phase $\varphi$, for $\varphi =\pi$ (blue solid line), $\varphi =\pi /2$ (red dashed line), and $\varphi =0$ (black dotted line). The modulation parameters are (a) $z=1,m=2$ and (b) $z=3,m=2$. As in Figs. 2 and 3, ${\omega }_a=10\kappa$ and $n_a={10}^3$ are taken.