Light-Assisted Collisions in Tweezer-Trapped Lanthanides

Abstract

We present a quantitative investigation of one- and two-body light-mediated processes that occur to few erbium atoms in an optical tweezer, when exposed to near-resonant light. In order to study the intertwined effects of recoil heating, cooling and light-assisted collisions, we develop a first-principles Monte Carlo algorithm that solves the coupled dynamics of both the internal and external degrees of freedom of the atoms. After validating our theoretical model against experimental data, we use the predictive power of our code to guide our experiment and, in particular, we explore the performance of different transitions of erbium for light-assisted collisions in terms of their efficiency and fidelity for single-atom preparation.

Figures (12)

• Figure 1: In-trap population dynamics of few erbium atoms under horizontal yellow-light irradiation. (a) Single-atom scattering via absorption and emission, leading to recoil heating. (b) Two-atom LAC, coupled to dressed states with attractive (red) or repulsive (blue) resonant DDI. (c) Evolution of trap-occupation probability for $0$ (diamonds), $1$ (squares), $2$ (circles), and $>2$ atoms (triangles). Each point is an average of 200 runs, and error bars reflect uncertainties according to binomial classification with one standard deviation confidence intervals. Solid lines show MC simulations initialized from experimental populations. Left inset: zoom into the initial 50 ms of time evolution of in-tweezer population. Right inset: atom trajectory $\mathbf{r}_1 = (x, y, z)$ in a single exemplary run (colors: $x$–blue, $y$–green, $z$–yellow). (d) Number-resolved ultrafast imaging after a $7\,$ms LAC pulse. The histogram shows about 3000 repetitions. For (c-d), the yellow light has $\Delta_{\rm h} = -1.2\,\Gamma_{\rm L}$, $s_{0,\rm h} = 0.64$, with tilt angle $\theta_{\rm h} \approx 11\degree$ to the $x$–$y$ plane. Gravity points along $-z$.
• Figure 2: Effect of axial cooling on the single-atom survival. (a) Calculated two-dimensional intensity map $s_{0,q} = (s_{0,\rm h}, s_{0,\rm v})$ of the single-atom survival probability. In the color scale, we choose white as the color identifying $80\%$ survival probability. Colored markers indicate the parameters used in (b): circles for $s_{0,q}= (0.64, 0.35)$ and triangles for $s_{0,q} = (0.64, 0)$. The gray line corresponds to $R_{\rm scatt} = 75\times10^3\,\text{s}^{-1}$. (b) Single-atom survival vs. $\Delta_{\rm v}$, with (circles, solid line) and without (band, dashed line) vertical cooling. Markers and bands show experimental data, whereas lines represent theoretical data. (c) Single-atom histograms obtained with the narrow-line yellow imaging for $s_{0,\rm v} = 0$ (left) and $s_{0,\rm v} = 0.5$ (right), with $40\,$ms of exposure time and $\Delta_{\rm h,v} = -1.0\,\Gamma_{\rm L}$, taken with 5600 repetitions. Error bars in (b) reflect one-sigma standard errors including propagated errors from LAC efficiency and survival. Number of MC runs and initial conditions as in Fig. \ref{['fig:fig1']}. In panels (a-b), $\Delta_{\rm h} = -1.2\,\Gamma_{\rm L}$; in (a,c), $\Delta_{\rm v} = -1.2\,\Gamma_{\rm L}$, and the illumination time is 30 ms. More experimental details can be found in supmat.
• Figure 3: Light-assisted collisions as a function of detuning. (a) Two-body LAC rate (blue) extracted from time trace of the occupation probability as a function of the illumination time (b-c) by fitting the curves with a rate equation and an exponential decay (see supmat for more details). For comparison, the one-body loss rate due to recoil heating is also shown (yellow). In (b) and (c), the detunings of the yellow light are $\Delta_{\rm L} \approx -0.5\,\Gamma_{\rm L}$ and $\Delta_{\rm L} \approx -1.3\,\Gamma_{\rm L}$, respectively. For all the plots, $s_{0,q} = (0.64, 0.39)$.
• Figure 4: Single-atom preparation efficiency. Left side: panels (a-d) depict the average atom number versus light detuning, for the blue ($\lambda_{\rm L} = 401\,$nm, $\Gamma_{\rm L}/(2\pi) = \mathrm{28}\,$MHz), the yellow, the orange ($\lambda_{\rm L} = 631\,$nm, $\Gamma_{\rm L}/(2\pi)=28\,$kHz) and the red ($\lambda_{\rm L} = 841\,$nm, $\Gamma_{\rm L}/(2\pi) = \mathrm{8}\,$kHz) transitions, respectively, with $s_{0, q} = (1.00,0)$ (solid, light color) and $s_{0,q} = (1.00, 0.55)$ (solid, dark color), during an irradiation time $t_{\rm irr}$ (see main text). In (b), we consider $20\,\times t_{\rm irr}$ in order to highlight the effect of axial cooling. The dotted line marks $\Delta_{\rm h} = 0$, and the dashed lines correspond to simulations without DDI. Right side: evolution of one-atom trap-occupation probability for the detuning corresponding to the minimum of the LAC feature, with $s_{0,\rm v} = 0$ and $\Delta_{\rm L}/\Gamma_{\rm L} = 0, -0.5, -1.4$, and $-2.8$ for the blue, yellow, orange, and red transitions, and the corresponding $t_{\rm irr} = 2.4\,\upmu$s, $0.76\,$ms, $5.9\,$ms, and $36\,$ms. We multiply the x-axis of the right panel of (a) by $0.1$.
• Figure S1: Histograms of ultrafast blue imaging at the single- and few-atom regime over $5000$ repetitions, with a tweezer power of 1.6mW ($U_0/k_{\rm B} \sim$ 150µK). In the Panels (a) and (b) ((c) and (d)) the duration of the LAC pulse is 7ms (30ms). Panels (a) and (c) ((b) and (d)) depict the distribution of collected photons keeping the tweezer light ON (OFF) during the imaging.