The space cold atom interferometer for testing the equivalence principle in the China Space Station

The precision of the weak equivalence principle (WEP) test using atom interferometers (AIs) is expected to be extremely high in microgravity environment. The microgravity scientific laboratory cabinet (MSLC) in the China Space Station (CSS) can provide a higher-level microgravity than the CSS itself, which provides a good experimental environment for scientific experiments that require high microgravity. We designed and realized a payload of a dual-species cold rubidium atom interferometer. The payload is highly integrated and has a size of 460 mm × 330 mm × 260 mm. It will be installed in the MSLC to carry out high-precision WEP test experiment. In this article, we introduce the constraints and guidelines of the payload design, the compositions and functions of the scientific payload, the expected test precision in space, and some results of the ground test experiments.

designed and realized a payload of a dual-species cold rubidium atom interferometer. 23 The payload is highly integrated and has a size of 460 mm × 330 mm × 260 mm. It will 24 be installed in the MSLC to carry out high-precision WEP test experiment. In this article, 25 we introduce the constraints and guidelines of the payload design, the compositions and

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GR describes gravity as a spacetime geometry, but gravity cannot be quantized by 35 quantum mechanics (QM). Many new theories (loop quantum gravity, noncommutative geometry, and the fifth force) [1][2][3] have been proposed to solve the incompatibility 37 between GR and QM. These theories generally require violation of the WEP. Therefore, 38 high-precision tests of the WEP are important for identifying these new theories and 39 searching for new physics. 40 The WEP test is usually carried out by measuring the accelerations of two different Atom interferometers provide a new method for testing the WEP using 49 microscopic atoms. By measuring the differential acceleration of the two atomic clouds 50 using dual-species AI, a high-precision WEP test can be realized. The first results of the 51 WEP test based on AI came from S. Fray et al. in 2004, they measured the gravitational 52 accelerations of 85 Rb and 87 Rb atoms and obtained a test precision of 10 −7 . [9] 53 Subsequently, various AI-based WEP test experiments were carried out. [10][11][12][13][14][15][16][17] The test 54 mass covers rubidium, potassium, strontium, etc. The highest test precision was 55 obtained by P. Asenbaum et al. in 2020, they carried out an AI-based WEP experiment 56 using ultracold atoms of the Rb isotope, and obtained a test precision of 10 −12 . [18] 57 Testing the WEP using AI does not only improve the test precision but also extend the 58 test category. This is because microscopic atoms can be prepared in different quantum 59 states, such as spin or superposition states. [19][20][21] The WEP test using these atomic states 60 is a direct quantum test of the theory of gravity. 61 The microgravity environment has many advantages that the WEP test 62 experiments of both macroscopic and microscopic test masses can benefit from. For 63 macroscopic objects, the French Space Agency has carried out a satellite project called 64 MICROSCOPE. [22] By measuring the differential accelerations of two concentric 65 cylinders of platinum and titanium alloy, a WEP test precision of 10 −15 had been 66 achieved, [22] and it is the highest test precision of the WEP up to now. For microscopic 67 atoms, owing to zero gravity, atom interferometer in space can achieve a long 68 interference time, thus significantly improving the measurement precision. Many AI-69 based WEP test projects in space have been proposed, including QUANTUS, [23] 70 MAIUS, [24,25] ICE, [26,27] STE-QUEST, [28] etc. The QUANTUS is a drop-tower project 71 which is pre-research for satellite project. It has achieved 87 Rb MOT, [29] 87 Rb BEC [30] 72 and Mach-Zehnder interferometer. [31] The MAIUS is a sounding-rocket project. It has successfully prepared BEC [24] and verified the coherence of BEC in microgravity. [25] 74 ICE is a parabolic flight project, it has obtained the Ramsey fringes and realized a WEP 75 test with precision of 10 −4 using 87 Rb and 39 K atoms. [27] The STE-QUEST project is a 76 satellite project proposed by the European Space Agency (ESA). Its scientific objective 77 is to test the WEP using 87 Rb and 41 K atoms and achieve a test precision at the level of 78 10 −17 . [28] In addition to testing the WEP, AI in space can be also used to detect the 79 gravitational wave and dark energy, projects like Q-WEP, [32] QTEST, [ The remainder of this paper is organized as follows. In Section 2, we introduce the 95 constraints and guidelines of AI payload design. In Section 3, we introduce the detailed 96 design of the scientific payload, including its composition and functions. In Section 4, 97 we introduce the scientific experimental process in space. In Section 5, we analyze the 98 expected test precision of the WEP test. In Section 6, we present the experimental 99 results of the ground test. The scientific payload is installed in a magnetic suspension bench (MSB) which 102 is inside the MSLC. The first problem we have to solve is finding a proper scheme that 103 can achieve a relatively high test-precision and fit the design constraints. The most important advantage of microgravity for AI is that it can significantly 106 increase the interference time. However, a long interference time implies a low 107 expansion rate of the atomic cloud, which equivalently implies a low effective atomic 108 ensemble temperature. For rubidium, if one wants the atomic cloud to expand to 1 cm 109 (full width at half maximum) within 2.5 s, then the equivalent temperature is calculated 110 to be 29 nK.

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The usual way for obtaining such a low temperature is to use the evaporative 112 cooling method. However, both the magnetic trap and optical trap of the evaporative 113 cooling scheme require a large amount of power consumption, which is far beyond the 114 rated power consumption of the payload design. Therefore, we propose a three-   The experimental scheme of the velocity selection method and the corresponding 131 coordinate frame are shown in Fig. 1. The cold atomic clouds after 3D cooling are 132 localized in the center of the vacuum chamber, the Raman laser is reflected by a 133 polarization beam splitter (PBS) and acts on the cold atomic clouds in the z-direction. 134 After the Raman interference process, the fluorescence of the atomic clouds is excited 135 by the 3D cooling laser beams, which propagate along the x-axis and in the y-z plane.  First, we consider the velocity selection scheme in the one-dimensional (1D) case.

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Assuming that the temperature after the PGC process is Te, the average atomic cloud  In the following of the article, we denote i = 1, 2 for the 85  Raman laser was much easier to produce for our phase-modulation based optical system. The phase shear method is an effective way to extract the interference fringe. [40] 184 It has advantages of obtaining interference fringes in a single measurement, eliminating 185 noise from atom number fluctuations and detection laser, and greatly suppressing the   (2) is altered  Rabi frequencies eff,i of the Rb isotope can be expressed as 237 4,j,a,2 5, j,b,2 5, j,a,2 6, j,b,2 eff,2 j 4, j,a,2 5, j,a,2    The principle of the optical system is shown in Fig. 5 the driven frequency of FEOM4 is ranging from 5.0 to 6.9 GHz.

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The outputs of FEOM2 and FEOM4 are combined and injected into a tapered   where  = 1 − 2 is the differential phase and k = 2(keff,1 − keff,2) is the differential 425 wave vector.

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For the first term in Eq. (7), the parameters keff,1, T can be set by the experiment, precision. The second term has a suppression ratio term k 2keff,1, which was 510 −7 in 432 our experiment, and a relative acceleration term a2 g. If one wants the value of this term 433 to be less than 10 −11 , it results in an upper limit for the residual acceleration a2 of 434 210 −5 g, and this can be guaranteed by the MSB. Therefore, the measured precision of 435  is primarily limited by the differential phase .

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Many factors influence the value of , and we list the most important terms as 437 below, and we set T=1 for the following calculation.
where Ncounts,i is the total number of photoelectrons recorded by the camera, m is the  The rotation of the payload and gravity gradient of the Earth and CSS induces a 468 phase shift to the interference fringe. The rotation-induced phase shift is given by Eq.

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(3), and the gravity gradient-induced phase is where Tzz is the (z, z) component of the gravity gradient tensor, and zi and vz,i are the  common. This is because that we use the velocity selection method, so the selected 519 atomic clouds have a same expansion rate, and the difference of effective Raman 520 vectors of the Rb atoms is small, this will induce similar phase shifts for the two AIs, 521 as illustrated in the paper. [42] For a mirror with a diameter of 22 mm, and has a peak 522 aberration of  5, the differential phase is calculated to be about 2.3 rad.

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The estimated uncertainties of the WEP test experiment for 100 shots are listed in 524    imaged. To realize the phase shear of an atomic cloud, the angle of the deflector was 568 linearly scanned during the interference to induce a phase shift. 569 We used principal component analysis (PCA) process to obtain the interference 570 fringe from the atomic interference images. We used 38 images for the process and took 571 the 4th order of the processed images. The curve in Fig. 7  the Raman laser to be in resonance again. The obtained curve is shown as red solid line.

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The contrast of the obtained interference fringe is very low. This is mainly caused 581 by the following reasons. First, during the interference process, the laser intensities of 582 the three Raman pulses were different because the atoms fell in the x-direction, and the 583 Raman laser was propagated in the z-direction. Second, after the interference process, 584 we detected atoms in the state F=3>. However, during the interference process, most 585 atoms were populated in the F=2> magnetic sublevels. The single-photon transition 586 effect of the Raman laser pumped a proportion of these atoms to the F=3> state, and 587 this contributed to the background of the interference fringe. Third, the interference 588 time was too short to set a stable angular sequence for the deflector. We could only scan 589 the angle at a certain rate, therefore, we could hardly optimize the three angles of the 590 deflector for the three Raman pulses, as described in Section 2.3, which induced a 591 decoherence effect caused by the initial size of the atomic cloud. However, all of these 592 factors can be relieved for the experiment in space.  The data that support the findings of this study are available from the 631 corresponding author upon reasonable request.