Loading and spatially resolved characterization of a cold atomic ensemble inside a hollow-core fiber

We present a thorough experimental investigation of the loading process of laser-cooled atoms from a magneto-optical trap into an optical dipole trap located inside a hollow-core photonic bandgap fiber, followed by propagation of the atoms therein. This, e.g., serves to identify limits to the loading efficiency and thus optical depth which is a key parameter for applications in quantum information technology. Although only limited access in 1D is available to probe atoms inside such a fiber, we demonstrate that a detailed spatially resolved characterization of the loading and trapping process along the fiber axis is possible by appropriate modification of probing techniques combined with theoretical analysis. Specifically, we demonstrate the loading of up to $2.1\times {10}^5$ atoms with a transfer efficiency of $2.1\%$ during the course of 50 ms and a peak loading rate of $4.7\times {10}^3$ atoms ${\mathrm{ms}}^{-1}$ resulting in a peak atomic number density on the order of ${10}^{12}{\mathrm{cm}}^{-3}$. Furthermore, we determine the evolution of the spatial density (profile) and ensemble temperature as it approaches its steady-state value of $T=1400\mu \mathrm{K}$, as well as loss rates, axial velocity and acceleration. The spatial resolution along the fiber axis reaches a few millimeters, which is much smaller than the typical fiber length in experiments. We compare our results to other fiber-based as well as free-space optical dipole traps and discuss the potential for further improvements.

Figure 1

(a) Schematic experimental setup. DM, dichroic mirror; aHWP, achromatic half wave plate; PBS, polarizing beam splitter; BS, beam splitter; APD, avalanche photodiode; SPCM, single-photon counting module. (b) Coupling scheme. (c) Scanning electron micrograph of the HCPBGF and false color intensity profile of the FORT.

Figure 2

(a) Level scheme for TROP on the ${\mathrm{D}}_1$ line. (b) Transmission for TROP with $N_a=2.1\left(2\right)\times {10}^5$ atoms ($\square$) and without atoms ($\circ$) inside the HCPBGF. The vertical axis is calibrated to show the actual power inside the HCPBGF.

Figure 3

(a), (c), (d) Time-of-flight measurements to determine the ensemble temperature inside the HCPBGF. The normalized atom number ($\circ$) is plotted vs the time after the FORT has been switched off. The red solid lines show the results of a calculation based on a Gaussian atomic density distribution [see Eq. (1)]. For maximum loading of the fiber (a) we determine the temperature as $T=1.0\left(2\right)\mathrm{mK}$ and a radial ensemble $1/e$ half width of ${\sigma }_a=1.1\mu \mathrm{m}$ for $T_F=3.8\mathrm{mK}$. Due to the finite optical pumping time we included a moving average over a $\sim 1\mu \mathrm{s}$ period in the calculation. For a pulsed loading of 3 ms only, the results are shown for times $t_{\text{if}}=1.5\left(15\right)\mathrm{ms}$ (c) and $t_{\text{if}}=21.5\left(15\right)\mathrm{ms}$ (d), respectively. The temperatures obtained are $T=2.7\left(2\right)\mathrm{mK}$ (c) and $T=1.0\left(4\right)\mathrm{mK}$ (d). In panel (b) we plotted the obtained temperatures ($\circ$) vs the time $t_{\text{if}}$. The temperature from panel (a) is shown for reference ($\square$ and gray-shaded area).

Figure 4

(a) EIT spectra with anticollinear probe and control fields taken at $t_{if}=35\mathrm{ms}$ ($\circ$) and $t_{\text{if}}=65\mathrm{ms}$ ($\square$) after the atoms entered the HCPBGF. The solid lines show the results from a numerical simulation with $d_{\text{opt}}=(2.2;1.3)$ (black; red), ${\mathrm{\Omega }}_c=1.2\left(1\right){\mathrm{\Gamma }}_{D_1}$, $v_a=(0.86;1.16)$ m/s (black; red), ${\gamma }_{21}=(0.16;0.07){\mathrm{\Gamma }}_{D_1}$ (black; red), $T=1\mathrm{mK}$. (b) Measured velocities of the atoms (positive when parallel to the direction of gravity) vs the time $t_{\text{if}}$ they have spent inside the HCPBGF. The estimated uncertainty for determining the velocities is $\pm 0.05$ m/s. For regular loading conditions ($\circ$), we obtain $v_0=0.70\left(6\right)\mathrm{m}$/s and $a_{\text{eff}}=6.8\left(15\right)\mathrm{m}$/${\mathrm{s}}^2$ from a linear least-squares fit. When the depumper is turned on for only $200\mu \mathrm{s}$ just before the measurement, the effective acceleration is larger ($\square$). The black solid (red dashed) line shows the result of the rate equation model (see Appendix pp2) when the depumper is on (off) during loading. Here, we used the measured depumper power, ${\mathrm{\Gamma }}_F^{\left(R\right)}=410{\mathrm{s}}^{-1}$, and $v_0=0.74\mathrm{m}$/s which are both within the experimentally determined uncertainties. If the acceleration were solely determined by gravity, the gray dotted line would show the corresponding dependence. When the notch filter used to suppress resonant scattering by the FORT is removed and the depumper is continuously on during the loading process ($\diamond$), the atoms are effectively accelerated upwards. The blue dashed-dotted line shows the least-squares linear fit yielding $v_0=0.77\left(8\right)$ m/s and $a_{\text{eff}}=-23\left(2\right)\mathrm{m}$/${\mathrm{s}}^2$.

Figure 5

(a) EIT spectra with collinear probe and control fields taken at $t_{\text{if}}=15\left(1\right)\mathrm{ms}$ ($\circ$) after the atoms entered the HCPBGF. The solid line shows the result of a numerical simulation with $d_{\text{opt}}=2.0\left(1\right)$, ${\mathrm{\Omega }}_c=1.4\left(1\right){\mathrm{\Gamma }}_{D_1}$, $T=1\mathrm{mK}$, $v_0=1.0$ m/s, ${\gamma }_{21}=0.07\left(2\right){\mathrm{\Gamma }}_{D_1}$. (b) Averaged dephasing rates ${\gamma }_{21}$ vs $t_{\text{if}}$ as extracted from multiple measurements such as in panel (a). The error bars represent an estimated uncertainty of $0.02{\mathrm{\Gamma }}_{D_1}$.

Figure 6

Measured number of atoms $N_a^{\left(\text{MOT}\right)}$ above the HCPBGF vs time $t^{\prime }$ after start of the transfer from the MOT to the HCPBGF. The atom number above the HCPBGF is measured by fluorescence imaging. The error bars correspond to the standard deviation of 20 successive measurements. The MOT repumper is switched off near $t^{\prime }=0\mathrm{ms}$. The atom cloud reaches the HCPBGF tip around $t^{\prime }=15\mathrm{ms}$. The MOT quadrupole field is switched off at $t^{\prime }=45\mathrm{ms}$. The insets show false color images of the atom cloud above the HCPBGF tip (yellow structure at lower end) at two different timings.

Figure 7

(a) Measured $N_a$ vs relative FORT power $P_F/P_F^{\text{max}}$ with ($\circ$) and without ($\square$) sub-Doppler cooling above the HCPBGF. The solid lines are linear fits to the corresponding experimental data for $P_F/P_F^{\text{max}}\le 0.7$. (b) Number of atoms $N_a$ loaded into the HCPBGF vs the power $P_{\text{DFR}}$ of the DFR (of a single beam) for different depumper powers. The error bars in the vertical direction correspond to an estimated $8\%$ uncertainty. The depumper peak Rabi frequency inside the HCPBGF was around $1.4{\mathrm{\Gamma }}_{D_2}$ ($\circ$), $2.9{\mathrm{\Gamma }}_{D_2}$ ($\square$), and $7.6{\mathrm{\Gamma }}_{D_2}$ ($\diamond$), respectively.

Figure 8

Measured $N_a$ inside the HCPBGF ($\circ$) vs time $t^{\prime }$ after the start of the transfer from the MOT. The MOT quadrupole field strength is schematically shown by the gray dotted line. The error bars correspond to a $10\%$ measurement uncertainty of $N_a$. Numerical results of the evolution based on Eqs. (3) and (4) for $a_{\text{eff}}=g=+9.81\mathrm{m}$/${\mathrm{s}}^2$, ${\mathrm{\Gamma }}_L={\beta }_L=0$ are shown by the gray dashed-dotted line and for $a_{\text{eff}}=+6.8\mathrm{m}$/${\mathrm{s}}^2$, $v_0=0.8$ m/s, ${\mathrm{\Gamma }}_L=40\left(5\right){\mathrm{s}}^{-1}$ and ${\beta }_L=1\left(1\right)\times {10}^{-11}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ by the blue solid line. The loading rate $R\left(t\right)$ is taken from the data shown in the inset with an amplitude scaling factor of $S_f=2$ to account for losses during the initial $5\mathrm{ms}$ inside the fiber. The red dashed line shows the results when an acceleration of $a_{\text{eff}}=-23\mathrm{m}$/${\mathrm{s}}^2$ inside the HCPBGF is assumed (see text). Inset: $N_a$ vs $t^{\prime }$ for a loading time of 1 ms. The error bars correspond to an uncertainty in the measurement of 1300 atoms. The red solid line shows the idealized evolution of $N_a$ used for the simulations.