Adiabatic quantum Zeno dynamics of bosonic atom pairs with large inelastic losses

We report on experiments exploring the non-Hermitian dynamics of pairs of two-level atoms tightly confined in an optical lattice and driven by a near-resonant laser. Although spontaneous emission is negligible for the long-lived excited state, two-body dissipation arises from strong inelastic collisions between two atoms in the excited state. We demonstrate quasi-adiabatic control of the internal state of the pairs in the quantum Zeno regime where inelastic losses dominate. Preparing each atom pair in the longest-lived eigenstate of the non-Hermitian Hamiltonian describing the dissipative dynamics, we measure a lifetime enhanced by more than two orders of magnitude in comparison to the bare two-body lifetime. The measured enhancement factor is in quantitative agreement with the expected lifetime of the prepared “non-Hermitian dressed state.”

Figure 1

(a) Sketch of the energy levels of a pair of bosonic atoms with internal states $g,e$. The parameters $p=(U_{ee}-U_{gg})/2$ and $q=U_{eg}-(U_{gg}+U_{ee})/2$ characterize the shifts of the transition frequencies due to state-dependent interactions $U_{\alpha \beta }$ ($\alpha ,\beta =\{g,e\}$), $\delta$ is the laser detuning from the atomic resonance, and ${\mathrm{\Gamma }}_{ee}$ is a two-body loss rate for two atoms in the excited state $e$. (b), (c) Real and imaginary parts of the eigenvalues of the effective Hamiltonian in the regime of weak dissipation with $\mathrm{\Omega }/{\mathrm{\Gamma }}_{ee}=1$. (d), (e): Same in the quantum Zeno regime $\mathrm{\Omega }/{\mathrm{\Gamma }}_{ee}=0.1$. The thin dotted lines in (b), (d) indicate the uncoupled energy levels $gg,eg,ee$. The vertical dashed lines in (b)–(e) mark the position of the one-photon resonances. The dash-dotted lines in (e) indicate the decay rates calculated from the effective Hamiltonian in the $\{gg,eg\}$ subspace [Eq. (11)]. We used the experimental values from Table  1.

Figure 2

Lifetime measurement for a final detuning ${\delta }_f/\left(2\pi \right)=650\mathrm{Hz}$ and nominal Rabi frequency $\mathrm{\Omega }/\left(2\pi \right)=150\mathrm{Hz}$. The figure shows the total atom number (irrespective of the internal state) versus hold time. The decay is attributed to two-body losses in doubly occupied sites initially occupying the center of the trap. The presence of an outer shell of singly occupied sites explains the nonzero asymptote. The inset shows a sketch of the temporal profile of the ramp.

Figure 3

Measurement of decay rates of the non-Hermitian dressed eigenstates. Solid: Numerically calculated decay rates. Dashed: Lifetime expected when treating the non-Hermitian part as a perturbation.

Figure 4

(a) Total atom number and $g$ population following the ${\lambda }_2$ dressed state (descending frequency ramps at constant speed $\dot{\delta }$). Note that the frequency axis is reversed, so that the ramp time increases from left to right. The insets show a sketch of the “trajectories” in the $\mathrm{\Omega }-\delta$ plane. (b) Total populations $N_2$ and $N_1$ of the central core and of the outer shell, respectively. The first can be interpreted as a measure of the survival probability of doubly occupied sites. We observe an excellent agreement with the expected population of the $|{\lambda }_2\rangle$ dressed eigenstate (solid lines), which provides evidence for quasi-adiabatic following. The population $N_1$ of singly occupied sites remains approximately constant. For such sites, the frequency ramp amounts to an adiabatic passage from $g$ to $e$ for large final detunings.