Rapid generation and number-resolved detection of spinor rubidium Bose-Einstein condensates

High data acquisition rates and low-noise detection of ultracold neutral atoms present important challenges for the state tomography and interferometric application of entangled quantum states in Bose-Einstein condensates. In this paper, we present a high-flux source of ${}^{87}\mathrm{Rb}$ Bose-Einstein condensates combined with a number-resolving detection. We create Bose-Einstein condensates of $2\times {10}^5$ atoms with no discernible thermal fraction within 3.3 s using a hybrid evaporation approach in a magnetic and optical trap. For the high-fidelity tomography of many-body quantum states in the spin degree of freedom [M. Hetzel, et al., arXiv:2207.01270], it is desirable to select a single mode for a number-resolving detection. We demonstrate the low-noise selection of subsamples of up to 16 atoms and their subsequent detection with a counting noise below 0.2 atoms. The presented techniques offer an exciting path towards the creation and analysis of mesoscopic quantum states with improved fidelities and towards their exploitation for fundamental and metrological applications.

Figure 1

Overview of the production time for different BEC sources with a given final atom number. Orange squares are atom-chip-based experiments, teal circles correspond to magnetically trapped ensembles, blue triangles show all-optical evaporation, and yellow diamonds represent hybrid magnetic and optical methods. Sources featuring other atomic species than rubidium are marked in gray. The red star marks the result of this work corresponding to an atomic flux of $6\times {10}^4 \mathrm{atoms}/\mathrm{s}$. Solid lines illustrate the atomic flux of the best-performing experiments per category.

Figure 2

(a) Computer-aided design of the ultrahigh-vacuum system with the two-chamber setup and the coil system. The system contains two glass cells for the $2{\mathrm{D}}^{+}$ MOT and for the 3D MOT and BEC generation, which are connected via two differential pumping stages at a ${45}^{\circ }$ angle. The connection tube and the science cell are individually pumped by two pump arrangements. The coil system surrounding the science cell is assembled by a pair of vertical 3D-MOT coils, a pair of horizontal quadrupole coils, and a pair of orthogonally aligned Helmholtz coils. The science cell and the coil arrangement are optimized for a high-NA optical access along the $x$ direction. (b) Cross section of the two-chamber setup and the coil system. Atoms are released from dispensers, building up the pressure inside the $2{\mathrm{D}}^{+}$ MOT. A pusher beam guides the $2{\mathrm{D}}^{+}$-MOT beam through the two differential pumping stages into the science chamber, where they are captured and cooled.

Figure 3

Schematic of the experimental sequence. The upper and lower panels illustrate the light and magnetic fields, respectively. The field strengths and the time axis are not to scale. The BEC is created within 3.3 s in a hybrid evaporation approach in a magnetic and optical trap. Subsequently, the desired spin component is chosen and analyzed in the number-resolving mMOT setup.

Figure 4

Histogram of the fluorescence signal for up to 16 atoms. The signal (blue bars) shows a clear quantization for integer atom numbers. The individual peaks are fitted with Gaussian distributions (black curve), whose widths are shown in the inset. The linear fit (solid red line in the inset) is compatible with a previously determined single-particle resolution limit of 400 atoms.

Figure 5

Characterization of the detection offset. (a) The frequent use of the $2{\mathrm{D}}^{+}$ MOT temporarily increases the background gas and therefore the mMOT loading rate from initially 0.1 $\mathrm{atoms}/\mathrm{s}$ (cyan rectangles) to 3.4 $\mathrm{atoms}/\mathrm{s}$ (blue circles) after 7.5 h of operation. (b) The detection offset linearly depends on the number of atoms before removal. The red curve shows a linear fit with an initial offset that is caused by a nonperfect optical removal of atoms. The red star marks the detection offset in Ref. [28]. (c) The extinction ratio of the optical removal improves with an increasing subsequent waiting time before detection.