High-flux source system for matter-wave interferometry exploiting tunable interactions

Atom interferometers allow determining inertial effects to high accuracy. Quantum-projection noise as well as systematic effects impose demands on large atomic flux as well as ultralow expansion rates. Here we report on a high-flux source of ultracold atoms with free expansion rates near the Heisenberg limit directly upon release from the trap. Our results are achieved in a time-averaged optical dipole trap and enabled through dynamic tuning of the atomic scattering length across two orders of magnitude interaction strength via magnetic Feshbach resonances. We demonstrate Bose-Einstein condensates with more than $6\times {10}^4$ particles after evaporative cooling for 170 ms and their subsequent release with a minimal expansion energy of 4.5 nK in one direction. Based on our results we estimate the performance of an atom interferometer and compare our source system to a high performance chip trap, as readily available for ultraprecise measurements in microgravity environments.

Figure 1

Schematic representation of the crossed ODT setup. A single-frequency laser source (Coherent Mephisto MOPA) is split into two independent beams, allowing for up to $16\mathrm{W}$ per path. Beam waists were determined with a beamcam (DataRay TaperCamD-LCM), while the crossing angle of the beams within the chamber was measured with vertical imaging. Time-averaged potentials are implemented with AODs (AA Opto-Electronic DTSXY-400-1064), allowing us to independently modulate each beam's center position in the horizontal and vertical directions with a maximum modulation amplitude of $1.5\mathrm{m}\mathrm{m}$ (resp. $1.8\mathrm{m}\mathrm{m}$ for the secondary beam). In this paper, only the horizontal axes of the AODs are modulated using a software defined radio (Ettus USRP X310) to provide the waveform, while the vertical axes are driven with a constant frequency. For intensity stabilization, less than $0.1\%$ of the optical power is detected by an amplified photodetector (Femto OE-200) and used to control the diffraction efficiency of the AOD via a homebuild PID controller together with a voltage controlled attenuate (MiniCircuits ZX73-2500-$\mathrm{S}+$).

Figure 2

Ramps optimized for evaporative cooling on different time scales with constant evaporative flux, together with the resulting phase space densities. Along each of the four ramps, markers indicate start and end points of the six sections, which are individually optimized. Trap depths (a) and frequency curves (b) are obtained from a simulation of the confining potential. Here, the error bands are estimated as the $2\sigma$-uncertainty interval via error propagation, taking measurements of the beam waist, intensity, and geometry within the chamber into account. For modeling the scattering length (c) we follow Ref. [44], together with the properties of the individual resonances as reported in Ref. [49]. Our experimentally determined magnetic field uncertainty is used to assign the error bands. The inset shows the overall behavior of the scattering length in between the resonances at 32.6 and $162.8G$ for atoms in $|F=1,m_{\text{F}}=-1\rangle$. Magnetic field values used in this paper are highlighted by the shaded area. To determine the PSD (d), we perform atom number measurements at each marker position, averaging over 100 experimental cycles. Temperatures are obtained from fitting the expansion velocity to time-of-flight measurements of the ensemble size with data taken between 1 and $30\mathrm{m}\mathrm{s}$ of free fall with 1-ms spacing and at least four measurements at each point in time.

Figure 3

Final particle numbers in the condensate, against total evaporation time. Our previously achieved results with constant scattering length in a 1960-nm trap are depicted with black pentagons, while our current results with variable scattering length in the 1064-nm trap are highlighted, following the color and shape coding of Fig. 2. The error bars are given by the standard deviation of 100 measurements of the particle number for each point. For comparison, the performance of other fast BEC sources is depicted with gray upside-down triangles.

Figure 4

Expansion energy of the BEC at different scattering lengths in horizontal (a) and vertical (b) direction. For each data point we perform a TOF series, determining the ensemble size between 10 and $26\mathrm{m}\mathrm{s}$ of free fall with 1-ms spacing and at least four measurements per point. Contrary to the measurements performed in Sec. 2b we do not measure below $10\mathrm{m}\mathrm{s}$ to avoid the resolution limitation of our detection system. The insets show the TOF series for the data taken at $308{\mathrm{a}}_0$, which are used together with the measurements at $203{\mathrm{a}}_0$ to determine the trap frequencies, by fitting a scaling approach, shown as solid lines, with the error band corresponding to the stated trap frequency error. The error bars of the energy measurements originate as one-sigma deviation from the fit error of the expansion velocity and from the magnetic field uncertainty for the scattering length. Error bands of the simulations are obtained via a Monte Carlo method within the trap frequency interval.

Figure 5

Calculated instability of a Mach-Zehnder atom interferometer at the standard quantum limit using different source configurations with our evaporation sequence. We show the expected instability for different pulse separation times for an immediate release from the trap (solid lines) and compare them to an interferometer after performing an additional matter-wave collimation to $50\mathrm{p}\mathrm{K}$ (dashed lines). The shaded areas show the respective performance of a chip-based source system with values taken from Ref. [36] for the case of an immediate release from the trap and from Ref. [35] for the DKC case.