Spontaneous emission from a two-level atom tunneling in a double-well potential

We study a two-level atom in a double-well potential coupled to a continuum of electromagnetic modes (black-body radiation in three dimensions at zero absolute temperature). Internal and external degrees of freedom of the atom couple due to recoil during emission of a photon. We provide a full analysis of the problem in the long wavelengths limit up to the border of the Lamb-Dicke regime, including a study of the internal dynamics of the atom (spontaneous emission), the tunneling motion, and the electric field of the emitted photon. The tunneling process itself may or may not decohere depending on the wavelength corresponding to the internal transition compared to the distance between the two wells of the external potential, as well as on the spontaneous emission rate compared to the tunneling frequency. Interference fringes appear in the emitted light from a tunneling atom, or an atom in a stationary coherent superposition of its center-of-mass motion, if the wavelength is comparable to the well separation, but only if the external state of the atom is post selected.

Figure 1

Two-level atom in a double-well potential interacting with a continuum of electromagnetic waves. Right panel: coordinate system used, with the atom tunneling in the $z$ direction, and the atomic dipole in the $x\text{−}z$ plane.

Figure 2

(Color online) Amplitude of the tunneling motion for $t⪢{\Gamma }^{-1}$ for $\eta =\pi /2$ as a function of $\beta$ and $\text{ln}\gamma$.

Figure 3

(Color online) Tunneling motion $⟨z\left(t\right)⟩$ in units of $b/2$ as a function of $\tau \equiv \Delta t$ and $\text{ln}\gamma$ for $\beta =3$, $\eta =0$ with the initial value $⟨z\left(0\right)⟩=b/2$.

Figure 4

(Color online) Polar plot of the angular dependence of $G_{\pm }^{\left(1\right)}\left(\mathbf{r},\mathbf{r};t,t\right)$ (red dashed and blue dotted curves) and $G^{\left(1\right)}\left(\mathbf{r},\mathbf{r};t,t\right)=G_{+}^{\left(1\right)}\left(\mathbf{r},\mathbf{r};t,t\right)+G_{-}^{\left(1\right)}\left(\mathbf{r},\mathbf{r};t,t\right)$ (green solid curve) for $\beta =3$, $\eta =0$, and an initially delocalized state $c_{\mathbf{0}+e}\left(0\right)=1$.