Cold-atom sources for the Matter-wave laser Interferometric Gravitation Antenna (MIGA)

The Matter-wave laser Interferometric Gravitation Antenna (MIGA) is an underground instrument using cold-atom interferometry to perform precision measurements of gravity gradients and strains. Following its installation at the low noise underground laboratory LSBB in the South-East of France, it will serve as a prototype for gravitational wave detectors with a horizontal baseline of 150 meters. Three spatially separated cold-atom interferometers will be driven by two common counter-propagating lasers to perform a measurement of the gravity gradient along this baseline. This article presents the cold-atom sources of MIGA, focusing on the design choices, the realization of the systems, the performances and the integration within the MIGA instrument.


Overview of the future MIGA instrument
The future system relies on horizontal Bragg interferometers 20,21 where three light pulses are used to split, deflect and recombine the atomic waves. The cold atoms enter the interferometer from the bottom and interact with two horizontal pairs of counterpropagating Bragg lasers 22 separated by a distance of 30.6 cm in the vertical axis. The splitting and recombination ( π/2 ) pulses are done with the bottom beam while the deflection ( π ) pulse is performed with the top beam. The separation between the 2 beams corresponds to an interferometer with a pulse separation time T = 250 ms. The Bragg transitions at each position are based on the interaction of the atom with two counter-propagating laser beams of the same frequency, which couple the momentum states |� p − � k� and |� p + � k� , where p is the momentum of the atom and � k = 2π û is the wave vector of the lasers ( ≃ 780 nm, û unit vector of the laser propagation). With a vertical launch velocity v 0 = 4.45 m/s, the time spent from the launch to the apogee ( π Bragg pulse) is t ap = 454 ms.
The experimental sequence starts with a cold atom production phase during which the Rubidium 87 atoms are collected in a magneto-optical trap (MOT), laser cooled using polarization gradient cooling and vertically launched. On their way up before the interferometer, the atoms are prepared in the desired quantum state (internal state and velocity). On the way down, the probability for an atom to be in a given output momentum state is detected using a momentum-to-internal state labelling technique based on a Raman transition 23 , followed by a fluorescence detection.

Description of the cold atom head
The cold atom production. A two-dimensional magneto-optical trap (2D MOT) fed by a rubidium alloy dispenser is realized in a vacuum chamber connected to the atom preparation chamber by a differential vacuum tube (see Figs. 1b and 2), allowing to reach a loading rate of 6 × 10 8 atoms/s in a three-dimensional MOT (3D MOT).
The atoms from the 3D MOT are then simultaneously cooled down and vertically accelerated to a velocity of v 0 = 4.45 m/s in a moving molasses. Two acousto-optic modulators respectively driving three top and three bottom MOT beams allow to apply a detuning δ between each pair of counterpropagating beams. The three pairs of beams are mutually perpendicular and form a angle of arccos( 1  www.nature.com/scientificreports/ The laser system. The laser system used for the cold-atom sources is described in 24 . We give a short description here for consistency. The different lasers used to cool and manipulate the atoms are delivered from an all-fibered laser module. The laser architecture is based on frequency doubled telecom lasers. A Master laser is locked using a Rubidium 85 saturated absorption spectroscopy signal and references 3 slave lasers which are respectively used for the 2D MOT cooling laser, the 3D MOT cooling and Raman 2 laser, and the 3D MOT repumper and Raman 1 laser. The 3 slave lasers are all phase locked to the Master laser via an adjustable frequency offset. The repumping light for the 2D MOT is generated by a fiber electro-optic phase modulator at 1560 nm fed with the appropriate microwave frequency. After amplification of the 1560 nm light emitted by laser diodes in Erbium doped fiber amplifiers and second harmonic generation in PPLN waveguide cristals, the 780 nm light is sent to optical splitters and guided to the experiment chamber using several optical fibers. The laser module nominally delivers 300 mW total power for the 2D MOT, 150 mW total power for the 3D MOT, 350 mW in the Raman 1 beam and up to 700 mW in the Raman 2 beam. The relative power and polarization fluctuations at the fiber outputs have been measured to be below one percent rms on a timescale of 100 hours. The phase lock signals are controlled by radio and microwave frequency sources all referenced to a stable 100 MHz quartz oscillator. The full laser system is hosted in a 1.7 × 0.5 × 0.5 m 3 transportable rack. The control of the laser system and of the experiment is provided by home-made electronics 25 . The magnetic shield and bias field. The three AI parts of the instrument will be enclosed in mu-metal in order to maintain the stray magnetic field to a low level (see Fig. 3). The interferometer regions will be enclosed in a 2404 × 598 × 720 mm magnetic shield in order to suppress the measurement bias due to the second order Zeeman effect. The atoms preparation region is also shielded in order to keep a low magnetic field during the moving molasses sequence. After turning off the MOT magnetic field, residual magnetic field at the position of the 3D MOT of ≈ 7 mG was measured in-situ by microwave spectrocopy of the atomic hyperfine transition. During the molasses sequence, we further adjust the magnetic field using three pairs of Helmholtz coils in order to optimize the temperature of the cloud. During the state preparation phase and the detection phase, a homogeneous horizontal bias magnetic field of ≈ 200 mG is produced by 4 vertical copper rods disposed around the atom head in order to define a quantization axis. www.nature.com/scientificreports/ Preparation of the atoms before the interferometer. In order to inject the atoms with the right velocity in the Bragg interferometer, the quantum state (momentum and spin state) of the atoms is prepared on their way up, before the interrogation region. A first counter-propagating velocity-selective Raman pulse (beam 'Raman 1' in Fig. 4) is used to select the atoms from a mix of the Zeeman sub-levels of |F = 2� to the m F = 0 Zeeman sub-level of the |F = 1� hyperfine state, with a relatively narrow velocity class in the direction of the Raman lasers (e.g. corresponding to a temperature of ≈ 100 nK). The atoms which are not transferred to |F = 1� by the Raman transition are then pushed by a laser tuned on resonance with the cycling transition ('push 1' in Fig. 4). A similar Raman/push procedure is then applied a second time to clean the remaining unwanted F = 1 atoms produced by spontaneous emission during the first Raman selection pulse. For this purpose, we use a second Raman light pulse ('Raman 2' , 1/e 2 beam waist of w = 30 mm) to transfer the atoms back to the F = 2 state. The remaining atoms in the F = 1 state are pushed with an orthogonal beam tuned on the F = 1 → F ′ = 0 transition ('push 2').
The angle of the Raman beams with respect to the horizontal plane is set to few degrees in order to introduce a Doppler effect and thus lift the degeneracy between the |p� → |p + 2 k� and |p� → |p − 2 k� transitions. The atoms must enter the interrogation region with a well defined velocity in order to fulfill the resonance condition in the Bragg interferometer where the laser beams are horizontal (wavevector � k = k� e x ). For a 2n k transition coupling the momentum states |� p 0 � → |� p 0 + 2n � k� , the input momentum must fulfill p 0x = −n k . The vertical velocity at the first Bragg pulse is gT ≃ 2.5 m.s −1 , resulting in an angle θ = n k/MgT ≃ n × 3.2 mrad of the atom trajectory with respect to gravity. A rough control of this angle can be obtained by adjusting the directions of the www.nature.com/scientificreports/ 3D MOT Raman beams. Then, a more controlled step consists in selecting the right horizontal velocity class with the two step Raman selection by using different two-photon detunings for the 'Raman 1' and 'Raman 2' beams.
Detection of the atomic state. After their interrogation by the Bragg beams in the interferometer, the two different momentum states | ± n k� of the atoms are labeled to two different internal states with the Raman 2 laser beam (see Fig. 4). More precisely, the velocity selective feature of the Raman transition is used to transfer the |F = 2, −n k� atoms to the F = 1 internal state, while the |F = 2, n k� atoms remain in the F = 2 internal state. The internal state of the atoms can then be resolved by state selective fluorescence detection. The falling atomic cloud crosses a series of horizontal light sheets. Detection of the population in F = 2 (that corresponds to the |F = 2, n k� output state of the interferometer) is first realized by measuring the fluorescence induced by a first light sheet beam tuned on resonance with the F = 2 → F ′ = 3 transition. The retro-reflected light sheet is partially blocked at the reflection mirror so that the F = 2 atoms are pushed away in the process. The F = 1 atoms are then re-pumped to the F = 2 state using a thinner intermediate light sheet tuned to the F = 1 → F ′ = 2 transition. Those atoms are then detected in a third light sheet similar to the first one, measuring the population initially in F = 1 (that corresponds to the |F = 2, −n k� output state of the interferometer).
The preparation and detection systems CAD drawings are shown in Fig. 5. The fluorescence light emitted by the atoms in the two light sheets is collected by a lens with a 2% collection efficiency and imaged on a two-quadrant photodiode. Figure 6 shows a typical time of flight fluorescence signal. The atomic population in a hyperfine state is retrieved by integrating the signal in the corresponding photodiode. The transition probability is deduced from the signals from the two light sheets (see section 2.6) after correction of systematic cross-talks between the two optical systems. The signal to noise ratio of the detection system is limited by electronic noise on the photodiode due to its dark current. The contribution from the electronic   Fig. 7a shows Rabi oscillations on the Raman 1 transition for different Raman light intensities. We observe a maximum transition probability of 10% for a Rabi frequency of � R ≈ 2π × 100 kHz. This is mostly limited by atoms from the molasses are distributed among all the different spin projection states and only a fraction of the atoms being initially in F = 2 , m F = 0 . Moreover, transverse inhomogeneities of the light intensity lead to the damping of the oscillations and limit the contrast.
Raman velocimetry allows to estimate the temperature of the cloud. We performed Raman spectroscopy for different Rabi frequencies, adjusting the pulse duration to half a Rabi period. Figure 7b shows the FWHM extracted from a Gaussian distribution adjustment as a function of the Rabi frequency. For large Rabi frequency the width of the peak is Fourier limited, whereas it reaches a constant value of ≈ 90 kHz when the Rabi frequency is below 50 kHz. This value is limited by the Doppler effect induced by the atomic velocity spread, which corresponds to an atomic temperature of ≈ 2 µK.
The main function of the Raman 1 beam is to allow for a narrow horizontal velocity selection in order to couple the atoms to the Bragg interferometer with the right velocity. Figure 8a shows Raman spectroscopy performed with the top Raman beam (Raman 2), for different horizontal velocity distributions selected using Raman 1. For each peak we performed a Raman 1 transition with a different frequency, and a light intensity and pulse duration corresponding to a Fourier limited Gaussian FWHM of ≈ 23 kHz in order to select a velocity spread corresponding to an effective temperature of 150 nK along this direction. The spectroscopy was performed with a longer Raman 2 pulse in order to resolve the Doppler induced frequency width related to this temperature. Gaussian adjustments of the spectra are in good agreement with an effective temperature of 150 nK. The Fig. 8b shows the same experiment, but for a single mean velocity selected and various effective temperatures. These results demonstrate that we have a good control on the momentum distribution that will enter the interferometer. Figure 9 shows Rabi oscillations for the upper Raman transition, after velocity selection with the bottom Raman beam. That transition is the last step of the state preparation sequence, that allows to enter the Bragg interferometer in the state F = 2 , m F = 0 with a narrow velocity spread along the interferometer axis, and the right velocity for the first Bragg transition. In the process of selecting internal state and velocity, 98% of the atoms are removed and we obtain an effective flux of 1.2 × 10 7 atoms/s in the interferometer. Quantum projection noise www.nature.com/scientificreports/ associated with that flux would allow to reach the expected 10 −12 s −2 gravity gradient sensitivity 19 , with a 500 ms total interferometer duration, a contrast of about 50% , and n = 4 order Bragg transitions.
Output state measurement. The measurement of the output state of the interferometer relies on the combination of external state labelling by a Raman transitions on the way down, and state selective fluorescence detection (see Fig. 4). We evaluated the contrast of the Raman 2 transition on the way up and on the way down by  www.nature.com/scientificreports/ recording Rabi oscillations visible on Fig. 9. The selection pulse on the way up occurs at T = 80 ms after launch, on the way down it occurs at t = 853 ms. At the latter time we estimate the atom cloud diameter (FWHM of the atomic distribution) to be 3.3 cm. We obtain a transfer efficiency of 55% , limited by light intensity inhomogeneity across the laser beam due to the limited size of the gaussian profile of the beam (3.5 cm FWHM). The use of a top-hat laser profile is expected to increase this contrast to more than 70% 26 . This transfer efficiency affects directly the sensitivity of the instrument. Besides, any intensity fluctuations of the Raman 2 laser will affect the stability of the state measurement. We measured a Raman 2 laser intensity shot to shot standard deviation of σ I /I ≃ 0.01 which translate in a transfer probability fluctuation of σ P /P ≃ 0.0005 which is not currently limiting. In the future, the power stability of the Raman 2 beam will be actively stabilized in order to reach the ultimate expected performances of the instrument. Finally, we investigated the detection noise by measuring the standard deviation of the measured transition probability, as a function of the number of atoms (N) detected, for a sample in a state of equal repartition between the two hyperfine levels (see Fig. 10). This corresponds to the 1/2 transition probability state often used as the output state of an interferometer. For low atom numbers, the noise follows a 1/N behaviour due to the electronic noise of the detection photodiodes. For high atom numbers, the noise saturates at a floor independent of the atom number, limited by fluctuations in the balance of the detection efficiency between the two hyperfine states. This noise floor level can be decreased by improving the power stability of the detection lasers.

Conclusion
We presented a characterization of the cold-atom sources developed for the MIGA interferometer. They allow the production of 10 7 atoms per second selected in the desired velocity class for the Bragg interferometer, with a tunable effective temperature in the 100 nK range along the interferometer axis, which fulfills the requirements for the future gravitation antenna. The interferometer's output state can be measured by a detection system comprising velocity selective Raman spectroscopy coupled to hyperfine state sensitive fluorescence detection. We reach a signal to noise ratio of 1000 with atoms in the desired state for interferometry, and a shot-to-shot standard deviation on the transition probability of 5 × 10 −4 . The performances of the detection system will be improved by power stabilization of the fluorescence laser and the Raman 2 laser.
To date, five atom source units have been produced, three of which will be part of the 150 m long gradiometer in Rustrel and two others will be part of a 1.5 m long gradiometer in LP2N in Bordeaux. More atom sources can be produced for potential extensions of the MIGA instrument (second horizontal axis, or extension of the baseline with more atom interferometers). Further characterisation and optimisation will be carried out during integration of the subsystem to the instrument. A possible design evolution may include the use of top-hat beam shapers to increase the contrast of Raman transitions 26 , adaptation of the detection system to large momentum transfer in the interferometer, or the use of interleaved interferometry 27 .

Data availability
The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.
Received: 20 September 2022; Accepted: 1 November 2022 Figure 10. Standard deviation of the measured transition probability, as a function of the number of atoms detected. The green line corresponds to 1/N the noise limit associated to the electronic noise from the photodiodes shown in Fig. 6. The red dashed line corresponds to the quantum projection noise proportionnal to 1/ √ N .