Suppressing the Loss of Ultracold Molecules Via the Continuous Quantum Zeno Effect

We investigate theoretically the suppression of two-body losses when the on-site loss rate is larger than all other energy scales in a lattice. This work quantitatively explains the recently observed suppression of chemical reactions between two rotational states of fermionic KRb molecules confined in one-dimensional tubes with a weak lattice along the tubes [Yan et al., Nature (London) 501, 521 (2013)]. New loss rate measurements performed for different lattice parameters but under controlled initial conditions allow us to show that the loss suppression is a consequence of the combined effects of lattice confinement and the continuous quantum Zeno effect. A key finding, relevant for generic strongly reactive systems, is that while a single-band theory can qualitatively describe the data, a quantitative analysis must include multiband effects. Accounting for these effects reduces the inferred molecule filling fraction by a factor of 5. A rate equation can describe much of the data, but to properly reproduce the loss dynamics with a fixed filling fraction for all lattice parameters we develop a mean-field model and benchmark it with numerically exact time-dependent density matrix renormalization group calculations.

Figure 1

(a) A $50:50$ mixture of fermionic KRb molecules in two rotational states, $|0,0⟩$ and $|1,-1⟩$ (indicated by different colors and shapes), is prepared in a deep 3D lattice, which is suddenly made shallow along one dimension ($y$). Along $y$, molecules tunnel with a rate $J/\hslash$ and have a large on-site loss rate ${\mathrm{\Gamma }}_0$ because of chemical reactions. (b) In the Zeno regime, $\hslash {\mathrm{\Gamma }}_0\gg J$, doubly occupied sites are only virtually populated, and the loss occurs at a significantly slower rate ${\mathrm{\Gamma }}_{\text{eff}}\ll {\mathrm{\Gamma }}_0$ for molecules on adjacent sites. For KRb, a multiband analysis of this process is required for all experimental lattice parameters.

Figure 2

(a) Measured number loss of $|\downarrow ⟩$ molecules for an axial (transverse) lattice depth of $V_y=5E_R$ ($V_{\perp }=25E_R$) (circles) and best fit using a rate equation (RE), Eq. (1) (black dashed line). (b) Number loss rate, $\kappa$, as a function of ${\mathrm{\Gamma }}_0$ (fixing $J\approx 570\mathrm{Hz}$ and varying the bare on-site rate via $V_{\perp }$). (c) Number loss rate, $\kappa$, versus $J$ for fixed ${\mathrm{\Gamma }}_0\approx 87\mathrm{kHz}$ (varying $V_y$ and adjusting $V_{\perp }$ accordingly). $V_y$ ($V_{\perp }$) was varied from 5 to $16E_R$ (20 to $40E_R$). Black circles are experimental measurements (error bars represent one standard error). Green short-dashed lines show solutions of the RE Eq. (3) using an effective loss rate ${\mathrm{\Gamma }}_{\text{eff}}$ (single-band approximation). The blue long-dashed line shows the multiband RE using ${\tilde{\mathrm{\Gamma }}}_{\text{eff}}$ in Eq. (3). The multiband and single-band RE results were obtained by fixing the filling fraction to be 6%, and 25% respectively. Panels (b) and (c) directly manifest the continuous quantum Zeno effect: in (b) the measured loss rate $\kappa$ decreases with increasing on-site ${\mathrm{\Gamma }}_0$; in (c) a fit to the experimental data supports $\kappa \propto J^2$, with a ${\chi }^2$ (sum of the squared fitting errors) several times smaller than for a linear fit.

Figure 3

Comparison of experimental loss dynamics for the deepest considered lattice to MF and t-DMRG calculations. (a) Molecule loss vs time for $V_{\perp }=80E_R$ and $V_y=5E_R$ [Identical conventions and conditions as Fig. 2]. The MF matches the experimental data better than the RE (experimental fit). (b) Comparison of t-DMRG simulations (${\chi }_{\mathrm{MPS}}=128$, 2000 trajectories) to MF, for two different cases: (i) an identical trap for the two spin states with trap frequency ${\omega }_{\downarrow }={\omega }_{\uparrow }=2\pi \times 38\mathrm{Hz}$; and (ii) slightly different trap frequencies ${\omega }_{\downarrow }=2\pi \times 38\mathrm{Hz}$, ${\omega }_{\uparrow }=2\pi \times 34.2\mathrm{Hz}$. Shaded areas indicate the standard error of the mean.

Figure 4

(a) Number loss rate, $\kappa$, as a function of ${\mathrm{\Gamma }}_0$ [same data as Fig. 2]. (b) Number loss rate, $\kappa$, vs $J$ for fixed ${\mathrm{\Gamma }}_0$ [same data as Fig. 2]. Black circles are experimental measurements. Blue long-dashed and solid red lines show RE and MF solutions, respectively, using ${\tilde{\mathrm{\Gamma }}}_{\text{eff}}$ (multiband model). The shaded area accounts for $\pm 2\%$ variations around the MF estimate of $f\sim 9\%$ arising from the uncertainty in the initial molecule distribution.