A.

Acceleration measurement with one atom interferometer

The atoms are manipulated by a sequence of three Bragg pulses generated in the cavities. Bragg diffraction [13] couples the external atomic states where k is the wave vector of the interrogation light field.

The interferometer sequence is presented in figure 1 both in the space and the time domain. The atoms are first in the state. When they reach the first cavity, the matter wave is split by a first pulse π/2 that put the atoms in an equiprobable superposition of the states . When the atoms reach the appex of their trajectory, they are deflected by a pulse π which reverses the atomic states. When the atomic cloud crosses back the first cavity, a last pulse π/2 closes the interferometer. The transition probability P between the two external states is:

where is the atom phase shift.

Figure 1:

Scheme of the interferometers in the space and in the time domain. The dark blue and the dashed light blue lines represent the two arms of the matter-wave interferometer.

B.

Strain measurement with an array of atom interferometers

The atom phase shift at the output of an atom interferometer at the position X_i in an array of atom interferometer depends on the local horinzontal acceleration of the experiment frame with respect to the atomic cloud reference frame a(X_i) and on the strain variation induced by gravitational waves h. We also need to take into account the main noise sources: the fluctuations of the output mirror position x₂, the laser frequency fluctuations δν and the detection noise ∊(X_i). It is shown in [12] that the effect of the fluctuations of the input mirror position x₁ can be neglected. The expression of is:

where ν₀ is the laser frequency, L is the mean length of the cavity and s_u is the convolution of the time-fluctuation of effect u(t) by the atom interferometer sensitivity function s(t) [14].

Combining the signals of two atom interferometers of the array allows to get rid of the effect of the output mirror position fluctuations:

In this gradiometer configuration, the sensor becomes extremely robust to the cavity vibrations. However, the signal combines the effect of local gravity gradient with the gravitational waves signature. To be able to differentiate those two contributions, we should consider several couples of interferometers in the set with different baselines [12]. Beyond gravitational waves detection, the measurement of local gravity gradients can be very interesting for applications in geophysics as hydrology or underground survey.

A.

Cold atom sources

The cold atom sources are developed at the SYRTE (SYstèmes de Référence Temps Espace) laboratory. It performs the preparation of the atomic cloud and the detection of the state of the atoms after the interferometer. A scheme of the atom source is presented on figure 2. The ⁸⁷RB atoms are loaded in a 2D magneto-optical trap (MOT) which feeds the 3D MOT. The atomic cloud is launched almost vertically. After a phase of moving molasse, the temperature of the cloud is lower than 5 μK. We then select the atoms so that they are in the magnetic state m_F = 0 and they have the good transverse velocity class to fulfill the angle of Bragg requirement when they reach the optical cavities. Initially, the atoms are in the

Figure 2:

Scheme of the cold atom sources used on the MIGA instrument.

state |F = 2 >. The magnetic state is selected by applying a first Raman pulse which will populate mainly the state |f = 1, m_F = 0 >. The atoms remaining in the state |F = 2 > are then blasted. We apply a second Raman pulse to transfer the atoms from the state |F = 1, m_F = 0 > to the state |F = 2, m_F = 0 >. This pulse is long so that it is velocity selective. The atoms remaining in the state |F = 1 > are blasted by a second push beam.

After the interferometer, the atoms fall back trough the detection system. A short Raman pulse is applied for the external state labeling: the atoms in the external state |F = 2, −ħk > are transferred in the state |F = 1, +ħk >. The detection is then done by fluorescence.

B.

Laser and interrogation cavities

To generate the interferometer pulses, laser light at 780 nm resonant with the plan-concave cavities is needed. However, the pulses have to be short to avoid to be too selective in velocity. Therefor, it is not possible to lock the cavities on the laser at 780 nm. A laser beam at 1560 nm is used as an optical link to maintain the alignment of the cavities and a part of this beam is frequency doubled to generate 780 nm pulses. The optical apparatus is presented on figure 3.

Figure 3:

Scheme of the cavities and of the laser system on the MIGA antenna. Adapted from [11].

The master laser at 1560 nm is stabilized at the dν/ν = 10⁻¹⁵ Hz^−1/2 level with a highly stable reference cavity. A small amount of the 1560 nm radiations is used to lock the cavities: the resonance of the cavity is kept using the Pound-Drever-Hall technique [15] and the angular alignment is conserved with the Ward method [16]. The side-bands needed by these two techniques are generated by an Electro-Optic Modulator (EOM) before the light enters the cavities. The other part of the 1560 nm radiations is doubled with a Peridically Pole Lithium Niobate (PPLN) cristal to obtain the 780 nm beam. The impulsions are then generated by Acousto-Optics Modulator (AOM).

C.

Sites infrastructure

The antenna will be implemented 500 m underground at the LSBB laboratory in Rustrel, France, where it will benefit from an ultra low noise facility. A scheme of the planned infrastructures is shown on figure 4.

Figure 4:

Scheme of the infrastructure planned for the MIGA antenna at LSBB. B. The AIs of the initial antenna will be located at (a), (b) and (c). Optical setups for cavity injection will be hosted in room (a). Adapted from [11].

Two perpendicular 350 m long galleries, 3.2 m width, will host the instrument. The antenna will first consist of 3 atom sources equally spaced along one gallery, located in (a), (b) and (c) on figure 4. Future improvements are possible: a second 350 m long gallery can be used for a 2D antenna and both galleries will have empty widenings to keep the possibility of increasing the number of atom interferometers and the spatial resolution of the instrument.

A.

The single source accelerometer

The single source accelerometer (presented on figure 5a) will help to prove the feasibility of fountain interferometer with cavity-enhanced pulses. This experiment is currently under assembly. The pulses are generated in 80 cm long cavities. A plan-concave cavity of this dimension with a concave mirror with a radius of curvature 2 m will have a waist smaller than 500 μm (considering light with a wavelength of 780 nm). At the top of the parabola, because of thermal expansion, the atomic cloud has a diameter about 1 cm. It is therefor not possible to use this kind of cavity in this short setup.

Figure 5:

Scheme of the MIGA preliminary experiment (a) and of the cavities used to generate the atom interferometer (b). f is the focal length of the biconvex lens. The two cavity mirrors are flat.

We developed a stable and compact setup of resonator with two mirrors and an intra-cavity optical system (see figure 5b) [17]. The flat mirrors are placed in the object and image focal planes of the intra-cavity optical system. Entering this resonator with a waist ω₀₁ on the input mirror will result in having a waist ω₀₂ on the output mirror with:

With the wavelength λ=780 nm, the focal length f=40 cm and the input waist ω₀₁=10 μm, the waist ω₀₂ in the second half of the cavity is about 1 cm, which is sufficient to interrogate the atomic cloud.

The method used to keep the laser at 780 nm resonant with the cavity slightly differs from the one used on the final apparatus: unlike the MIGA antenna and its suspended cavities, on this preliminary experiment the 1560 nm optical link laser beam is directly referenced on the resonator, which is rigid. As seen on figure 6a, a fibered RIO diode at 1560 nm seeds the Quantel EYLSA amplifier which provides two outputs: one amplified 100 mW output at 1560 nm and one output at 780 nm where the power can be tuned from 100 mW to 1 W. The 1560 nm output is injected in the cavity and used to lock the RIO laser diode on the resonator and the 780 nm output is used to generated the interferometer cavity enhanced pulses.

Figure 6:

Optical apparatus (a) and method used to generate the 780 nm light beam (b). On (b), the dashed gaussians show the width of the cavity at 1560 nm and at 780 nm, ν_t is the frequency of the side-band used to lock the 1560 nm laser diode on the cavity, δ_m is the modulation frequency. The frequency of the 780 nm laser beam is 2ν_t – 2δ_m.

The optics of the resonator have a double coating to provide high reflectivity for both wavelengths. Because the cavity doesn’t have exactly the same length for the two wavelengths, the frequency of the 780 nm laser beam can’t just be the double of the one of the 1560 nm optical link. To tune the frequency of the 780 nm laser with respect to the optical link frequency, we use the method presented on figure 6b: after the modulation, done by an EOM, instead of injecting the carrier in the cavity as in the classical Pound Drever Hall method, we use a side-band to lock the 1560 nm laser diode. However, it is the frequency of the carrier which is doubled to generate the 780 nm light. Therefor, it is possible to tune the frequency of the 780 nm laser beam so that it is resonant with the cavity by changing the modulation frequency applied on the EOM [18].

B.

The high sensitivity gradiometer

To test the correlations between two atom interferometers interrogated in the same optical cavities, in particular the reduction of the mirror vibration noise, a high sensitivity gradiometer is under development.

A scheme of this experiment is presented on figure 7. Two atom interferometers will be simultaneously interrogated by the resonant field of 5 m long cavities. The mirrors of those plan concave resonators will be suspended and the laser system and the suspension system will be the same than for the final MIGA experiment. This prototype will help us to test all the equipment that will be used on the underground setup and will remain in the LP2N laboratory as a test bench for future upgrades of the MIGA antenna.

Figure 7:

Scheme of the 5 m long baseline gradiometer