Optical repumping and atom number balancing in a two-color MOT

Abstract

We study a novel repumping transition for $^{88}$Sr atoms trapped in a 'blue' magneto-optical trap. We show that, while the repumping efficiency is about three orders of magnitude smaller than for traditional schemes, it is sufficient for recycling all atoms, provided the repumping laser beams are arranged to form a 'green' magneto- optical trap (MOT) helping to cool and confine the atoms and preventing their loss. Our main findings are: (i) that the green MOT configuration is able to trap 10 times more atoms in the blue MOT than using the green transition merely as a repump, and (ii) that the atom numbers in the two-color MOT can be balanced through experimental control parameters. The interest of this scheme lies in its capability of reaching low temperature and its suitability for continuous atomic beam generation.

Figures (7)

• Figure 1: Relevant energy levels of $^{88}\text{Sr}$. Colored arrows mark laser driven transitions, black arrows mark decay channels with their corresponding decay rates given in units of $2\pi\,MHz$Akatsuka21. The most relevant states for this study are labelled with $|1\rangle$ - $|6\rangle$.
• Figure 2: Optical Setup. (a) Schematics of the optical setup and detection units. PBS: polarizing beamsplitter, DM: dichroic mirror, BS: beam sampler, Fl./Abs. camera: Fluorescence/Absorption imaging camera. The elevators create the cooling beams in $z$-direction. All lasers are irradiated continuously, unless stated otherwise. (b) Laser beam configuration for the gRP (left) and gMOT (right) configurations. In figures (a) and (b), gravity is directed along the $z$-direction.
• Figure 3: Fluorescence measurements. Blue fluorescence $\mathcal{F}_\text{blue}$ measured at $461\nm$ with (a) the green lasers in gRP configuration and (b) in gMOT configuration: (left panels) Blue fluorescence normalized to its maximum value in gMOT configuration as a function of the magnetic field gradient and green laser detuning; (right panels) Exemplary linescans (blue circles) for a magnetic field gradient of $B'=114G/cm$ [marked by arrows in the left panels]. The red solid lines show parabolic fits used for extracting the field-gradient-depending detuning at which the fluorescence reaches it's maximal value $\mathcal{F}_\text{blue}^\text{max}(B')$. (c) Maximal blue fluorescences $\mathcal{F}_\text{blue}^\text{@max}$ normalized to its maximum value in gMOT configuration $\mathcal{F}_\text{blue}^\text{max}$ as a function of the magnetic field gradient with the green lasers in gMOT configuration (dots) or in gRP configuration (triangles). The solid lines are polynomial fits to guide the eye. (d) Green fluorescence $\mathcal{F}_\text{green}$ measured at $496\nm$. The black solid line indicates the green laser detuning at which the green MOT potential is deepest as a function of the magnetic field gradient [see Eq. (\ref{['eq:App23']})]. (right) Exemplary linescan (green circles) for a magnetic field gradient of $B'=82G/cm$ [marked by arrows in the left panel]. (e) Field-gradient-depending green laser detunings $\Delta_{34}^{\text{@max}}$ at which the fluorescences are maximal: (blue dots) blue fluorescence with the green laser in gMOT configuration, (blue triangles) blue fluorescence with the green laser in gRP configuration, (green dots) green fluorescence with the green laser in gMOT configuration and additionally the $688nm$ laser, (black) theoretical curve as calculated from Eq. (\ref{['eq:App23']}). The blue solid lines are linear fits to guide the eye. Note, that all spectra have been shifted by $\Delta_{34}/\Gamma_{34}=0.28$ to correct for systematic errors.
• Figure 4: Simulated steady state atom numbers $N_{kk}$ in the states $|2\rangle$, $|4\rangle$, $|5\rangle$, and $|6\rangle$, populations of the two subsystems $N_\text{blue}=\sum_{k=1}^2N_{kk}$, $N_\text{gr:rd}=\sum_{k=3}^6N_{kk}$, and total atom number of the system $N=N_\text{blue}+N_\text{gr:rd}$. (a) Green dots denote atom numbers in the green MOT determined by absorption measurement $N_\text{gr:rd}$ as a function of the saturation of the $688nm$ laser. All solid and dash-dotted lines are simulated with the full Bloch equations [Eq. (\ref{['eq:mod03']})]. The hybrid Bloch-rate equations model yield identical results. (b) Frequency scan of the $688nm$ laser showing the same level populations as in panel (a). The blue/green dots are atom numbers as derived from blue/green fluorescence measurements. (c) Time evolution of the populations in the blue and green subsystems as denoted by their respective colors. Same color and linestyle coding as in panels (a,b). The cyan lines are obtained from the hybrid Bloch-rate equations model starting at $t=0$ in equilibrium of the blue subsystem. The initial atom number assumed in the ground state is set to $N_{11}=10^6$, to generate visible Rabi oscillations in the blue subsystem helping to illustrate separation of time scales for intra-subsystem equilibrium and inter-subsystem pumping. For all plots, the detunings have been set to match the experimental conditions and are (unless varied) $\Delta_{12}=-\Gamma_{12}/2$, $\Delta_{34}=0$, $\Delta_{56}=0$. The remaining parameters have been adjusted to match the experimental data: $s_{12}=1.3$, $s_{34}=2.1$, $s_{56}=25$, $R_\text{load}=10^8\,\text{s}^{-1}$, $\Gamma_\text{blue}=190\,\text{s}^{-1}$, and $\Gamma_\text{gr:rd}=2500\,\text{s}^{-1}$. The saturation parameters agree with measurements of power and beam waist.
• Figure 5: Illustration of the basic idea of the modelling. The atomic level scheme is described as three incoherently coupled two-level systems representing the blue ($|1\rangle-|2\rangle$), the green ($|3\rangle-|4\rangle$) and the red ($|5\rangle-|6\rangle$) transitions Note1. Only the blue subsystem can be adiabatically separated.