Spatial Pauli blocking of spontaneous emission in optical lattices

Spontaneous emission by an excited fermionic atom can be suppressed due to the Pauli exclusion principle if the relevant final states after the decay are already occupied by identical atoms in the ground state. Here we discuss a setup where a single atom is prepared in the first excited state on a single site of an optical lattice under conditions of very tight trapping. We investigate these phenomena in the context of two experimental realizations: (1) with alkali-metal atoms, where the decay rate of the excited state is large, and (2) with alkaline-earth-metal-like atoms, where the decay rate from metastable states can be tuned in experiments. This phenomenon has potential applications towards reservoir engineering and dissipative many-body state preparation in an optical lattice.

Figure 1

(Color online) (a) ${\Gamma }_{\mathrm{eff}}\ll \nu$: The two atoms prepared in the internal excited state $|e\rangle$ and the internal ground state $|g\rangle$ feel the same external harmonic oscillator potential. In the Lamb-Dicke limit ($\eta \ll 1$), the dominant decay channel for a single particle $|e\rangle |0\rangle \to |g\rangle |0\rangle$ with a rate ${\Gamma }_0$ is now blocked by the ground-state atom due to the Pauli exclusion principle. The excited atom decays under change of its motional state with a rate ${\Gamma }_{\mathrm{eff}}$ that is reduced of order ${\eta }^2$. (b) ${\Gamma }_{\mathrm{eff}}\gg \nu$: In this scenario, the notion of motional eigenstates is meaningless for atoms in $|e\rangle$. Yet again, both atoms can be prepared in the same initial motional state represented by the wave packet $|0\rangle$ (solid line). Dispersion of the motional wave packet for the excited atom (dashed line) is slow compared to the effective decay dynamics. As before, the dominant decay channel is blocked and the effective decay rate is reduced of order ${\eta }^2$.

Figure 2

(Color online) Relevant level structure (not to scale) and experimental sequence for alkaline-earth-metal-like atoms (${}^{171}\mathrm{Yb}$ in this example). (I) Two atoms per lattice site are prepared in $|g\uparrow \rangle$ and $|g\downarrow \rangle$, respectively; (II) one atom is excited from $|g\downarrow \rangle$ to the metastable state $|e\uparrow \rangle$ under a flip of its nuclear spin; (III) spontaneous emission from $|e\uparrow \rangle$ is induced by admixing the fast decaying state $|i\uparrow \rangle$. Nuclear-spin flips during the induced decay are suppressed by applying a large external magnetic field, which decouples nuclear and electronic spin in the ${}^1{P}_1$ manifold. Consequently the induced decay from $|e\uparrow \rangle$ to $|g\uparrow \rangle$ is Pauli blocked.

Figure 3

(Color online) Relevant level structure (not to scale) and experimental sequence for alkali-metal atoms (${}^{40}\mathrm{K}$ in this example). (I) Two atoms per lattice site are prepared in $|g\rangle$ and $|i\rangle$, respectively; (II) first, one atom is excited from $|g\rangle$ to the excited state $|e\rangle$; (III) then the other atom is transferred from $|i\rangle$ to $|g\rangle$. This pulse sequence is fast on the time scale given by ${\Gamma }^{-1}$. Choosing states with maximal $m_F$ values ensures that $|g\rangle$ and $|e\rangle$ form a closed two-level system. The decay of the excited atom back to $|g\rangle$ is Pauli blocked.

Figure 4

Zeeman diagram of the ${}^1{P}_1$ manifold. The eigenstates approach product states of electronic and nuclear spin for a large magnetic field. The states suitable for dressing the metastable excited state $|e\uparrow \rangle$ without flipping the nuclear spin during the decay are $|m_F^{+}\rangle$ with $m_F=3/2,1/2,-1/2$. In the inset, the probability for decaying without nuclear-spin flip is plotted as a function of the external magnetic field.

Figure 5

(Color online) (a) Energy diagram of the initial state: two fermions with blocking atom in a superposition of the motional states $|0\rangle$ and $|1\rangle$. (b) Spatial intensity distribution $I_t\left(x\right)$ of the emitted photon wave packet at time $t$ for the limiting cases where the blocking atom is in $|0\rangle$ or $|1\rangle$, respectively. In both cases, the outgoing wave packet propagates with the speed of light and falls off exponentially with a width $c/\left[(1-\alpha {\eta }^2)\Gamma \right]$ for the initial state $|g1;e0\rangle$ [$c/\left(\alpha {\eta }^2\Gamma \right)$ for the initial state $|g0;e0\rangle$]. (c) The blocking atom is prepared in a superposition of motional states; we choose ${\mu }_0=1-{\eta }^2/2$ and ${\mu }_1=i\sqrt{1-{\mu }_0^2}$. As this is the motional state which the excited atom would reach by sending out a photon along the negative $\widehat{\mathbf{x}}$ axis, emission in this direction is suppressed at the beginning of the atomic decay ($t=0$). Hence the photon intensity is zero at $x=-ct$ and has a maximum at $x=+ct$. During the decay of the excited atom, the blocking atom oscillates in the trap with a frequency $\nu$, which imprints the spatial period $2\pi c/\nu$ onto the photon wave packet.