Extensive manipulation of transition rates and substantial population inversion of rotating atoms inside a cavity

Abstract

We investigate the transition rates of a centripetally accelerated atom inside a high-quality cavity and show that they can be extensively tuned by adjusting the cavity resonance and the rotation frequency. Crucially, while inertial atoms cannot be excited in vacuum, rotation induces spontaneous excitation via the circular Unruh effect, with the cavity serving only as an amplifier. Using experimentally feasible parameters, we demonstrate that, in one scenario, the excitation rate can reach $\sim 10^7~\mathrm{s}^{-1}$ while emission remains negligible, enabling substantial population inversion. In another scenario, both excitation and emission can simultaneously attain $\sim 10^7~\mathrm{s}^{-1}$, corresponding to millions of transitions per second for a single atom. These findings highlight a powerful method for manipulating atomic transition rates for quantum applications and open a promising route toward experimental verification of the circular Unruh effect with state-of-the-art quantum technologies.

Figures (3)

• Figure 1: Emission rate $\Gamma_{\downarrow}$ and excitation rate $\Gamma_{\uparrow}$ as functions of the cavity's normal mode frequency $\omega_{c}$. The superscripts "in", "cav" and "free" correspond to inertial atoms in the cavity, centripetally accelerated atoms in the cavity, and centripetally accelerated atoms in free space, respectively. The insets in panels (a) and (b) show transition rates near the resonance conditions $\omega_c \approx \Omega$ and $\omega_c \approx 2\Omega - \omega_0$, respectively. The calculations assume isotropic atomic polarization and use experimentally feasible parameters from Ref. Lochan20: $d = 10^{-29} \, \text{Cm}$, $V=10^{-14} \, \text{m}^3$, $Q = 10^7$, $R = 50 \, \text{nm}$, $\Omega=5\, \text{GHz}$, with (a) $\omega_{0} = 10 \, \text{MHz}$ and (b) $\omega_{0} = 6.25 \, \text{GHz}$. Note that in panel (a), the emission and excitation rates in free space do not overlap, satisfying $\Gamma_{\downarrow}^{\rm free}>\Gamma_{\uparrow}^{\rm free}$.
• Figure 2: Transition rates and the ratio of excitation to emission rates of a centripetally accelerated atom in a cavity as functions of the rotational angular velocity. Calculations assume isotropic atomic polarization and experimentally feasible parameters from Ref. Lochan20: $d = 10^{-29} \, \mathrm{Cm}$, $V = 10^{-14} \, \mathrm{m}^3$, $Q = 10^7$, $R = 50 \, \mathrm{nm}$, $\omega_0 = 10 \, \mathrm{MHz}$, and $\omega_c=5\, \mathrm{GHz}$. Note that here we consider only the regime where the rotational angular velocity exceeds the atomic transition frequency.
• Figure 3: Comparison between (a) the emission rate $\Gamma_\downarrow$ and (b) the excitation rate $\Gamma_\uparrow$ for rotating atoms and inertial ones inside a cavity immersed in a thermal bath. The superscripts "in, thermal" and "cir, thermal" denote inertial atoms and centripetally accelerated atoms inside the cavity, respectively. Insets in panels (a) and (b) show the transition rates in the vicinity of the resonance condition $\omega_c \approx \Omega$. Calculations assume isotropic atomic polarization and experimentally feasible parameters: $d = 10^{-29} \, \mathrm{Cm}$, $V = 10^{-14} \, \mathrm{m}^3$, $Q = 10^7$, $R = 50 \, \mathrm{nm}$, $\Omega = 5 \, \mathrm{GHz}$, $\omega_0 = 10 \, \mathrm{MHz}$, and $T = 300\, \mathrm{K}$.