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Home , Atom interferometer, Journal of Cosmology

Exploring Dark and in Space Laboratories

Thematic Areas: ☐ Planetary Systems ☐ Star and Planet Formation ☐Formation and of Compact Objects ☒ and Fundamental ☐Stars and Stellar Evolution ☐Resolved Stellar Populations and their Environments ☐Galaxy Evolution ☐Multi-Messenger and

Principal Author: Name: Nan Yu Institution: Jet Propulsion Laboratory Email: nan.yu@jpl..gov Phone: (818)-354-4093

Co-authors: (names and institutions) Sheng-wey Chiow, Curt J. Cutler, Olivier P. Dore, Eric M. Huff, Ulf E. Israelsson, Jeffrey B. Jewell, Jason D. Rhodes, and Jason R. Williams (Jet Propulsion Laboratory) Justin Khoury and Jeremy Sakstein (University of Pennsylvania) Kazuya Koyama (University of Portsmouth) Clare Burrage (University of Nottingham) Paul Hamilton (University of California, Los Angeles) Holger Mueller (University of California, Berkeley) Phil Bull (Queen Mary University of London)

Abstract: Dark energy is one of the greatest mysteries in today and holds the key to the understanding of cosmology and evolution of our universe, and the potential for discovery of new physics. While astronomical observations are capable of providing ever increased precision in characterizing the dark energy and its history, there is a strong need for understanding the very of dark energy. Precision space laboratory experiments provide opportunities for direct detection of dark energy as well as help addressing other outstanding science questions in the area of gravity including dark matter and gravitational . A confirmed direct detection of dark energy will lead to a fundamental shift in our understanding of gravity, fundamental physics and our universe, stimulating a wide variety of foundational research in cosmology and particle physics.

Science questions addressed The greatest mystery in science today is dark energy. Dark energy constitutes ~69% of the energy and mass of the universe, yet we know do not know what dark energy is. Together with dark matter, more than 95% of the universe’s constituents are only known indirectly. Because of the significance of dark energy to the cosmology and evolution of our universe, and the potential for discovery of new physics, it is no wonder that dark energy is one of the eleven fundamental science questions to be answered in the new century in the 2003 NRC report [1]. It is well emphasized in NASA’s science strategic plans [2] [3]. Indeed, in addition to the existing astrophysics observations, there are new missions being planned and developed, such as WFIRST [4] and Euclid [5]. With larger and better observation telescopes in the near future, the content and evolution of dark energy and dark matter will be better characterized through snapshots of the distribution of baryons over cosmological space-time. However, the nature of the dark energy, i.e., the underlying equation of motion, will not be clearly verified via better data or analysis techniques from astrophysical observations. Particularly, among various feasible dark energy models and their huge parameter space, the ability to constrain or discern different candidate theories is limited, due to uncertainties on the nature of the medium between stellar sources and observatories, and to the fundamental ambiguity of reconstructing dynamics through few points in space-time [6]. What is dark energy? The nature of dark energy itself is obscure and completely unknown today. It could simply be Einstein’s cosmological constant. Yet this poses a conundrum, because straightforward arguments from quantum field theory suggest that the cosmological constant should be more than one hundred orders of magnitude larger than what is observed and attributed to dark energy [7]. The solution to this so-called cosmological constant problem clearly lies outside the known realms of gravity (as described by the ) and the standard model of particle physics. Even well-studied extensions of the standard model, such as supersymmetry, fail to provide answers [8]. New physics yet to be discovered is needed and opportunities to discover its nature await us. The new physics could be unknown fields directly, or modifications of gravity which may also introduce new fields indirectly. New fields should be scalar fields with very light mass, coupling to the particles of the standard model with roughly the same strength as gravity, and interacting with normal matter [9] [10]. This interaction provides us with golden opportunities to search and detect the unknown force experimentally in space through precision measurements of gravity. A discovery of the new field would fundamentally change our understanding of the natural laws of physics. The connection with fundamental physics is clear. The interaction between baryons and the dark energy will cause a violation of Einstein’s equivalence principle (EEP) [11] [12] [13], which states that all objects fall at the same rate in the same gravitational field. EEP is one of the founding pillars of Einstein’s theory of relativity [14], which governs the dynamics on the cosmological scales. A confirmation of dark energy detection or a violation of the equivalence principle will lead to a wide variety of foundational research in cosmology and particle physics. Dark energy as a scalar field Phenomenologically, an energy density in space-time can drive cosmic acceleration if it has an effective negative pressure, and is given a name “dark energy.” The “standard cosmological model,” ΛCDM, consists of a cosmological constant Λ, cold dark matter, and a flat universe [15]. The cosmological constant, which is essentially a measure of the energy density, has to be fine-

1 tuned to yield a stable universe. The quest for an explanation of the cosmological constant, or a broader theoretical framework to describe dark energy, results in various theories that could drive the cosmic acceleration. In quantum field theory approaches, dark energy arises due to vacuum fluctuations, but the resulting energy density is up to 120 orders of magnitude larger than observed. In modified gravity models, GR is modified to encompass the cosmic acceleration without dark energy. The consistency of the and the speed of gravitational waves severely restricts the validity of numerous modified gravity models [16] [17]. In quintessence theories, a new scalar field is introduced to account for the cosmic acceleration. Contrary to the cosmological constant, the quintessence field can vary in space and time [9] [10]. There has been much activity recently both on the theoretical fronts [12] [18] [19] [20] [21] [22] [23] [24] [13] [25] and experimental activities [19] [20] [26] [27] [28] for understanding the dark energy as a new scalar field. It is well known that general relativity has been stringently tested without any sign of violation so far, both with solar system observations and laboratory precision measurements. Therefore, any new interaction and the resulting unknown forces from dark energy must be highly suppressed on solar system scale; otherwise, it would contradict various precision tests of general relativity that have been performed to date. Viable scalar field theories of dark energy achieve this suppression by making the interaction between normal matter and dark energy environment-dependent. The mechanism for doing this is called screening, and works by changing the coupling between matter and dark energy to be dependent on the local mass density or other environmental factors. Three general screening mechanisms have been proposed [23]. Chameleon screening increases the effective mass at high local mass densities, reducing the range of the fifth force [18]; Symmetron models undergo a symmetry-restoring at high densities decoupling the field from matter [22]; and Vainshtein screening such as in Galileon models depends environmentally on the kinetic energy of the field, effectively reducing their matter couplings [29]. In the Chameleon model, the effective mass of the field is large inside and near concentrated baryonic mass distributions, and thus the Compton wavelength of the field and the corresponding force is short ranged. Similarly, in the Symmetron model, the symmetry of the field is restored inside baryonic mass, resulting in a short-ranged force near the surface of the mass. Therefore, only the outer most shell of a large compact body experiences the fifth force. This is known as the SHENG-WEY CHIOW and NAN YUthin shell PHYS. effect, REV. D 97, facilitating044043 (2018) the screening mechanism. Small particles such as single , available cold experiment capabilities. Finally, our accelerationhowever, of atoms is are precisely smaller measured in athan quantum the Compton wavelength of the field and experience the full effect of findings are summarized in Sec. VII. interferometric way (see Sec. IV). Despitethe thescalar success of field. more stringent Laboratory constraints on the experiments are conducted to exploit this enhanced sensitivity by using chameleon theory parameters n; ; β by atom interfer- II. DETECTION OF THE CHAMELEON Λ ometer measurements [8], majorð systematicÞ effects need to SCALAR FIELD cold atoms for probing new forces [19] [26] [27] [28] [30]. The results significantly constrain the be addressed before a complete conclusion for the chame- We follow the method of describing chameleon fields as leonparameter theory can be reached. space Being ans extra of force, the chame- Chameleon and the Symmetron models in a complementary manner to outlined in Refs. [4,5]. Chameleon theories include a self- leon forces can at best be detected at the precision of known NATURE PHYSICS DOI: 10.1038/NPHYS4189 interacting potential V ϕ of a scalar field ϕ, and an LETTERS ð Þ DESMOND, FERREIRA, LAVAUX, and JASCHE PHYS. REV. D 98, 064015 (2018) interaction potential Vint ϕ; ρ with matter density ρ.We ð Þabc10 consider, in this paper, the effective100 potential in the simplest 10 2 and the lowest order inverse power-law form [4,5] Neutron Neutron 8 gravity resonance 10 0 Microspheres This work Veff ϕ V ϕ Vint 10ϕ; ρ Atom interferometry (2015) ð Þ ≡ ð Þþ ð Þ 106 −2 Λn ϕ Torsion 4 This work λ balance

Λ 1 ρ; 1 4 1 1.5 − − cham n Neutrons 10 −4 (meV)

ϕ(meV) M 10 10 log ¼ þ 1þ ð Þ   µ Λ Torsion balance 2 −6 where Λ sets the strength of the self-interaction,Atom interferometryn is a 10 (2015) Atom positive integer, and M describes0.1 the interaction with 100 −8 interferometry normal matter. The equation of motion, in theThis static work case Torsion balance (2015) where ρ and ϕ are stationary, is 10−2 −10 10−10 10−5 1 2 4 6 8 10 −6 −4 −2024 Veff n 2ϕ ∂ M[MPl] log[Ms/GeV] ∇ ¼ ϕ ∂ Figuren 3 |4 Constraints on screened scalar fields. a,Figure Chameleon field:1. Recent the shaded progresses areas in the M–⇤ planeon areconstraints ruled out at the 95%of scalar confidence field level. M models/M . From left: constraints on Chameleon [31], constraints on Λ þ ρ Pl n β ; 2 gives− then 1 coupling strength to normal matter in relation to gravity; ⇤ ⇤0 2.4meV (indicated by the black line) could drive cosmic acceleration today. A ¼ ϕ þ þ MPl ð Þ Symmetron= [27]⇡ , present (LLR) and future constraints on Vainshtein [13], and simulation on scalar field forces on comparison is made to previous experiments: neutron interferometry28/neutron gravity resonance29, microsphere force sensing30, and torsion balance1,27. b, Chameleon limits in the n– plane with ⇤ astronomical⇤ , showing the narrowing observations gap in which basic [33] chameleon. theories could remain viable. n is the power where β MPl/M and MPl is the reduced Planckcham mass. = 0 ¼ law index describing the shape of the chameleon potential; M /M is the strength of the matter coupling. c, Symmetron fields: constraints by atom The acceleration on a test particle due to an established cham ⌘ Pl interferometry complement those from torsion pendulum experiments10,11 (shown with µ 0.1meV) for the range of µ considered. For µ<10 1.5 meV, the field profile ϕ can be obtained from the spatial derivative of = field vanishes entirely inside the vacuum (see Methods), leaving this parameter space unconstrained. The same e￿ect produces the sharp cuto￿ in our Vint [4,5]: limits at low MS. β a⃗ − ⃗ ϕ: 3 only¼ aM onePl ∇ order of magnitudeð rangeÞ left for the coupling strength 7. Arkani-Hamed, N. et al. The string landscape, black holes and gravity as the 2 M. Furthermore, for all ⇤>5.1meV, this gap is fully closed, ruling weakest force. J. High Energy Phys. 2007, 060 (2007). Far away from boundaries,out allϕ suchapproaches models. an Our equilibrium symmetron limits are complementary to 8. Burrage, C., Copeland, E. J. & Hinds, E. A. Probing dark energy with atom 1,10,11 interferometry. J. Cosmol. Astropart. Phys. 2015, 042 (2015). value ϕeq that minimizestorsionVeff pendula as well. We improve previous constraints on µ 9. Hamilton, P. et al. Atom-interferometry constraints on dark energy. Science by two orders of magnitude throughout the entire range of MS and 349, 849–851 (2015). FIG. 1. Exclusion plots of chameleon parameters. (a) β; Λ FIG. 2. Correlations of predicted (upper) and observed (lower) signal with Newtonian potential Φ (left) and magnitude of fifth force Veff probed by our experiment. Our constraint is strongest in the regime 10. Burrage, C., Kuribayashi-Coleman,ð Þ A., Stevenson, J. & Thrussell, B. ∂ 0; exclusion plot for n 1. Region near the upper left corner acceleration a5 (right). The prediction is calculated as in Fig. 1, again for the case λC 5 Mpc, ΔG=GN 1, and Φ and a5 are the ϕ where the atom is screened, where for µ 0.1meV we rule out¼ <1. Constraining symmetron fields with atom interferometry. J. Cosmol. Astropart. modal averages over the 1000 Monte Carlo model realizations. In the top row, the red¼ points are for the full¼ chameleon-h i or symmetron-h i ϕeq ¼ (yellow) is excluded by the torsion balance experiment [10]. ∂ = Phys. 2016, 041 (2016). screened model, the blue points are the same as the red except without the r values of screened galaxies set to 0, and the green points Tests of gravity in1 the ultraweak-fieldRegion regime bounded with a miniature, by the blue in- curve is excluded by the atom − à β ρ n 1 11. Brax, P. & Davis, A.-C. Atomic interferometry test of dark energy. Phys. Rev. D show the case where screening is entirely switched off. The black dashed line shows the threshold Φc , above which galaxies are vacuum source massþ probe screened fieldinterferometer theories with experiment the potential in Ref. [8]. The blue diamond marks j j ϕeq ρ n 4 : 4 94, 104069 (2016). screened. The median sizes of the error bars in the four directions—minimal 68% bounds for the prediction, 1σ for the observations—are ð Þ¼to explainnΛ þ theMPl accelerated expansionð Þ ofthe our parameter universe. set In of then; future,; β 1; 0.1 meV; 103 , and the blue   Λ 12. Hohensee, M. A., Estey, B., Hamilton, P., Zeilinger, A. & Müller, H. Force-free shown by the red crosses in the top left corners (the uncertainties in r are the same size as the red point). While the predictions show a dashed13 line across itð labelsÞ¼ð parameters that wouldÞ produce the h Ãi technologies such as lattice interferometry in our optical cavity and gravitational : proposed gravitational Aharonov–Bohm experiment. clear cutoff in r for Φ > Φc and a positive correlation with a5 [Eq. (4)], this is not apparent in the observations. The distance for ϕ to reach ϕ is short for typical matter same chameleon force. Failure of detecting accelerations calcu- à j j j j large momentumeq transfer Bragg beam splitters will allow us to hold Phys. Rev. Lett. 108, 230404 (2012). densities, such that thequantum interior of probe a bulk particles experiences in proximity zero lated to a miniaturein this work source based onmass, this parameter13. Charrière, set will R., Cadoret, exclude M., the Zahzam, N., Bidel, Y. & Bresson, A. Local gravity This again implies that the greater part of the method of Sec. IV E for setting the measurement uncer- acceleration from the chameleon field [Eq. (3)]. The bulk, shaded region above the dashed line. ΛmeasurementΛ0 is of cosmological with the combination of atom interferometry and Bloch evading geometric constraints from the source mass’ small size, ¼ observed signal must be of non-fifth-force origin. tainties θ . This ought to manifest in an agreement between as a whole, experiences negligible chameleon acceleration, relevance, and is shown as the horizontaloscillations. line. (b) n;Phys.β exclusion Rev. A 85, 13639 (2012). i and boosting sensitivity. With modest improvements, chameleon ð Þ These estimations of the fifth force effect are relatively the results of that model and those of the others in that plot for Λ Λ0. Regions excluded by14. theKovachy, corresponding T. et al. Quantum experi- superposition at the half-metre scale. Nature 528, which is known as screeningfields at[5] the. The cosmological screening energy does not density will be either¼ discovered or coarse. A precise quantitative determination of the prefer- section where θ is parametrized and fitted for. Here ments are labelled. The red diamond530–533 marks (2015). the embracive happen to gaseous atoms, due to the microscopic size and ence of the data for G>0—and of the constraints on G we show this explicitly for the screened model with completely ruled out. This also will enableparameter study set of novel of n; quantumΛ; β 10; Λ15.0; 1Hu,, Z.-K.and theet al. red Demonstration dashed of an ultrahigh-sensitivity atom-interferometry Δ Δ dilute density, which makes atoms a much more sensitive ð 12Þ¼ð Þ and λ that it implies—requires the full likelihood formal- λ 1.8 Mpc.13 Figure 4 shows the posteriors of phenomena such as the gravitational Aharonov–Bohmcurve across it labels eect parameters, and that wouldabsolute produce gravimeter. thePhys. same Rev. A 88, 43610 (2013). C C ism of Sec. IV. It is to this that we now turn. ¼ ¯ ¯ tool for chameleon detection. The concept of using atomic chameleon force. Failure of detecting accelerations calculated in ΔG=GN; θ in the case where θ θ arcsec is a free provide even better resolution of atom–source mass interactions. 16. Fang, B. et al. Metrology with atom interferometry: inertial sensors from f g ¼ test particles for chameleon force detections has been parameter, and ΔG=GN; A; B and ΔG=GN; C; D; E; F this work based on this parameter setlaboratory will exclude to field the applications. shaded J. Phys. Conf. Ser. 723, 12049 (2016). f g f g B. Constraints on G and λC for the models of Eqs. (28) and (29) respectively. These are proposed [5] and experimentallyMethods implemented [6 –8], where region above the dashed curve. 17. Schmöle, J. et al. A micromechanical proof-of-principle experiment for Δ to be compared with Fig. 5, which shows the ΔG=GN measuring the gravitational force of milligram masses. Class. Quantum Gravity 1. Effect of noise model Methods, including statements of data availability and any 33, 125031 (2016). associated accession codes and references, are available in the 18. Collaboration, P. Planck 2015 results. XIII. Cosmological parameters. From Sec. VA it is clear that for any reasonable value of G=G modified gravity accounts for at most a small 13 online version of this paper. 044043-2 Astron. Astrophys. 594, A13 (2016). Δ N We focus on this value of λC because it maximizes the overall 19. Perlmutter, S. et al. Measurements of  and 3 from 42 high- redshift fraction of the total gas-star offset, justifying the fiducial likelihood, as will be shown in Sec. VB3. Received 24 January 2017; accepted 25 May 2017; supernovae. Astrophys. J. 517, 565–586 (1999). published online 3 July 2017 20. Joyce, A., Jain, B., Khoury, J. & Trodden, M. Beyond the cosmological standard model. Phys. Rep. 568, 1–98 (2015). 064015-14 21. Will, C. M. The confrontation between general relativity and experiment. References Living Rev. Relat. 17, 4 (2014). 1. Kapner, D. J. et al. Tests of the gravitational inverse-square law below the 22. Elder, B. et al. Chameleon dark energy and atom interferometry. Phys. Rev. D dark-energy length scale. Phys. Rev. Lett. 98, 21101 (2007). 94, 44051 (2016). 2. Colella, R., Overhauser, A. W. & Werner, S. A. Observation of gravitationally 23. Brax, P., van de Bruck, C., Davis, A.-C., Khoury, J. & Weltman, A. Detecting induced quantum interference. Phys. Rev. Lett. 34, 1472–1474 (1975). dark energy in orbit: the cosmological chameleon. Phys. Rev. D 70, 3. Peters, A., Chung, K. & Chu, S. Measurement of gravitational acceleration by 123518 (2004). dropping atoms. Nature 400, 849–852 (1999). 24. Khoury, J. & Weltman, A. Chameleon fields: awaiting surprises for tests of 4. Hornberger, K., Gerlich, S., Haslinger, P., Nimmrichter, S. & Arndt, M. gravity in space. Phys. Rev. Lett. 93, 171104 (2004). Colloquium: quantum interference of clusters and . Rev. Mod. Phys. 25. Olive, K. A. & Pospelov, M. Environmental dependence of masses and coupling 84, 157–173 (2012). constants. Phys. Rev. D 77, 43524 (2008). 5. Rosi, G., Sorrentino, F., Cacciapuoti, L., Prevedelli, M. & Tino, G. M. Precision 26. Hinterbichler, K., Khoury, J., Levy, A. & Matas, A. Symmetron cosmology. measurement of the Newtonian using cold atoms. Nature Phys. Rev. D 84, 103521 (2011). 510, 518–521 (2014). 27. Upadhye, A. Dark energy fifth forces in torsion pendulum experiments. 6. Fixler, J. B., Foster, G. T., McGuirk, J. M. & Kasevich, M. A. Atom Phys. Rev. D 86, 102003 (2012). interferometer measurement of the newtonian constant of gravity. Science 315, 28. Li, K. et al. Neutron limit on the strongly-coupled chameleon field. Phys. Rev. D 74–77 (2007). 93, 62001 (2016).

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© 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved. bulk mass experiments and astronomical observations. Future microgravity experiment concepts could take advantage of better environmental controls and longer proximity time of atoms to a source mass available in microgravity, and it is anticipated that orders of magnitude improvement in sensitivity will confirm or rule out the models [31]. It is intriguing that recent observational studies suggest potential evidence of the thin-shell effect. The reported displacement of the centroids of hydrogen (H I) and stellar masses of galaxies, if confirmed, would be the first evidence of screening and possibly existence of a new scalar field [32] [33]. Figure 1 summarizes recent progresses on dark energy scalar field models. The Vainshtein model, on the other hand, is difficult to constrain in research laboratory experiments due to their predicted weak long range force strength. An astrophysical constraint was reported [34], while recent multi-messenger gravitational detections suggest potential invalidation of Vainshtein models [16] [17] [35] [36]. Despite the weakness of the Vainshtein force, which is about 1010 smaller than gravitational force, a direct measurement of the Vainshtein field due to the Sun is shown possible in the solar system with modern precision measurement techniques in space [37]. Such measurements will be the first direct constraint placed on Vainshtein models and shed light on the models from an orthogonal perspective and complementarily to multi-messenger astronomy. Enabling precision measurement advances Since ancient times, astronomical observations have provided new insight on where we are and how Nature works. It remains one of the most powerful ways to explore and understand the universe. At the same time, to understand new fields and new interactions, high energy (accelerator) physics plays a crucial role to understand fundamental interactions and how the world is put together. However, the particle colliders can’t probe gravity, while the next generation laboratory experiments can. Through ever increasing precision measurements that test interactions and dynamics predicted by the established laws of physics, laboratory precision measurements have the ability to seek small violations and probe physics at the Planck scale. In the last few decades, there has been an explosion of new technologies that provide exquisite tools for precision measurements. Highly accurate optical clocks for time and frequency measurements and atom interferometers for weak force measurements are two major breakthroughs out of these developments. A continued program of testing fundamental physics would make unprecedented progress by moving to space laboratories, whether it is large gravity variation, large spatial extents, or speed and orientation. It turns out that clock and atom interferometer technology can benefit from operation on a space platform [38] [39]. In particular, atom interferometers use -cooled atomic particles as free fall test masses. It exploits the quantum nature of atomic particles as matter waves and forms matter-wave interferometers for sensitive inertial force measurements. The measurement sensitivity increases quadratically with the interaction time. With the possibility of many seconds of interaction times in space, very sensitive inertial force measurements can be made. Thus, conducting space laboratory precision measurements provides a unique ability to explore unknown physics, complementary to both the observational science in astronomy and accelerator science in high energy physics, and generates science data and knowledge that are not available from either observational or high energy physics measurements. The atomic sensor technology has been demonstrated in research laboratories worldwide, commercialized for terrestrial applications, and matured for space deployment. In particular, the

3 week ending PRL 110, 093602 (2013) PHYSICAL REVIEW LETTERS 1 MARCH 2013

magnitude. By applying delta-kick cooling (DKC) [28–30] the fringe spacing in our expanding cloud, being the distance we have been able to reduce the expansion and to enhance between two local maxima of the density, increases with the the signal at longer interferometry times. We study the total expansion time Tex of the BEC and is inversely propor- coherent evolution of the BEC for increasing temporal tional to the displacement d of the two clouds. and spatial separation of the wave packets inside the inter- Figure 2 illustrates our experiments in microgravity ferometer by monitoring the single-shot contrast and shape performed at the drop tower. We show the complete tem- of the fringes [31]. poral sequence [Fig. 2(a)], which differs from the previous Our experiments are performed with an asymmetric experiments with the apparatus [15] in three important Mach-Zehnder interferometer (AMZI) [20,32] shown in features: (i) We employ DKC to reduce the expansion Cold Atom Laboratory (CAL) is currently operating on the International SpaceFig. 1 .Station Here we as display a multi the temporal- evolution of the during the free fall by briefly (2 ms) switching on the user facility, and serves as a pathfinder for future atomic sensors in space [40]atomic. Moreover, density distribution the atom of the BEC interferometer for trap with frequencies of (10, 22, 27) Hz generated by the an experiment on ground [Fig. 1(a)] and the corresponding atom chip 30 ms after the release. (ii) In order to eliminate interferometer demonstration on a sounding rocket shows the robustness ofexperimental atomic sequencesensors for [41] forming the interferometer detrimental effects of residual magnetic fields we transfer [42]. [Fig. 1(b)]. A macroscopic wave packet is coherently split, the BEC into the nonmagnetic state F 2;m F 0 by redirected, and brought to a partial overlap by successive coupling the Zeeman levels with a chirpedj ¼ radio-frequency¼ i The inherent high sensitivity and stability of atomic sensors have been proposed,Bragg scattering investigated at moving lightand crystals [26,33,34]. They pulse (adiabatic rapid passage) [35]. (iii) At the time T0 are generated by pulses of two counter-propagating laser after the release of the BEC, we implement the sequence of exploited for direct detection of dark energy, direct detection of dark matter,beams gravitational separated by the wave two-photon recoil energy of the AMZI outlined in Fig. 1 and detect the interference 15 kHz and detuned from the F 2 F 3 transition pattern at Tex after the release using absorption imaging detections, and tests of EEP, among many other physics measurements. For instance, Chameleon87 ¼ ! ¼ of the D 2 line of Rb by 800 MHz to reduce spontaneous with a single laser pulse as illustrated in Fig. 2(b). In Fig. 2(c) and Symmetron dark energy models are tested and constrained using coldscattering. Cs and There Rb exists atoms a close analogy at to the Young double- we show typical images of the interfering BECs and the University of California at Berkeley and Imperial College, UK, respectivelyslit [26] experiment [28]. [Fig.Dark1(c) matter], where one pair of overlapping corresponding column density profiles for two different BECs plays the role of a pair of coherent light waves ema- values of Tex . measurement concepts are proposed using cold atoms in space [43] [44] [45]nating. from Cold two- slitsatom separated based by a distance d. Similar to the Figure 3 summarizes the central results of our Letter EEP tests are conducted [46] [47] [48] [49] and proposed [50] [51]. resulting Note interference that, while pattern in the the far field of the double slit, on probing the coherent evolution of a BEC with an -14 MICROSCOPE mission placed a bound on EEP at the 10 level using bulk masses [52](a), atomic (b) (c) tests at or beyond the current limit will provide a quantum mechanical constraint that is fundamentally distinct from the classical counterpart. Last but not least, several detection schemes are proposed using ultracold atoms on the ground and in space [45] [53] [54] [55] [56] [57].

Figure 2 illustrates the DRAFT Figure 2. From Left: hardware of FigureCAL 2. Onseton ofthe Bose-Einstein ISS condensate[40], inBEC low-Earth generation orbit aboard the International on SpaceCAL [40], and state of the art on atomic BEC interferometer in microgravityStation. [59]. From left to right, the final frequency of a forced evaporation ramp using an RF knife in sensing in space. a magnetic atom chip trap is lowered, increasing the phase space density (PSD) and forming BEC marked by a signature spike in the central density. AtFIG. the conclusion 1 (color). of the evaporation Temporal ramp, AMZI for a BEC based on Bragg scattering at a light grating: experimental images on ground (a), the magnetic trap potential is decompressed and extinguishedschematic before imaging sequence the atoms 22 (b), ms and analogy to the Young double-slit experiment (c). The evolution of the BEC and the AMZI is visualized by later. The BEC critical temperature is measured to occura at series 130 nK ( 500 of nk absorption in the original trap). images (a) of the atomic densities separated by 1 ms. The incomplete transfer is a consequence of the larger The right-most image shows an atom cloud with 49k totalmean-field atoms, 26% condensed energy in a BEC of at the a BEC necessary for the ground experiment. The interferometer starts at the time T0 after the release of the Science measurement opportunities temperature of 17 nK measured from the distribution ofBEC, the surrounding when thermal a cloud.=2 pulse (b) made out of two counter-propagating light beams of frequency ! and !  creates a coherent þ superposition of two wave packets that drift apart with the two-photon recoil velocity vrec 11:8 mm=s. After T they are redirected by Led by the discovery of dark energy and dark matter, growingtrap, carrying their observational energy away and leaving the remaininga evidence pulse sample colder. and partiallyEvaporation points recombined to the after T T by a second =2 pulse. A nonzero¼ value of T leads to a spatial interference stagnates as the temperature drops relative to the trappattern, barrier height which (trap depth), we sorecord that after  53 ms inÀ free fall. Similar to the far-field pattern observed in the Young double-slit experiment need for new physics aimed at answering important questionsit is necessary torelated lower the trap depth to in order the to force most evaporation tofundamental continue. Experiments laws (c), the fringe spacing l scales¼ linearly with the time of expansion T T 2T T  and is inversely proportional to that confine atoms in a harmonic magnetic trap, such as CAL, typically do this with an ex ¼ 0 þ À þ of Nature [58]. Efforts to discover new fundamental symmetries,RF knife – radio frequency photons investigations tuned to changethe an atom’s separation internal magneticofd the statev atrec a limitsT of the of wave packets. The scaling factor is the ratio of Planck’s constant h and the mass m Rb of the Rubidium atoms.¼ established symmetries, tests of the general theory of relativity, detection6 of gravitational waves, and attempts to understand the nature of dark matter were among the topics at the focus of scientific 093602-2 research at the end of the last century. With the advances in precision metrology and gravity measurements, today, physics is standing at the threshold of major discoveries. The fundamental physical laws of Nature are currently described by the Standard Model and Einstein’s general theory of relativity. However, there are important reasons to question the validity of this description. Despite the beauty and simplicity of general relativity and the success of the Standard Model, our present understanding of the fundamental laws of physics has several shortcomings. In particular, if gravity is to be quantized, general relativity will have to be modified; however, the search for a realistic theory of quantum gravity remains a challenge. This continued inability to merge gravity with together with the challenges posed by the discovery of dark energy indicates that the pure tensor gravity of general relativity needs modification or augmentation. It is believed that new physics is needed to resolve this issue. Theoretical models of the kinds of new physics that can solve the problems above typically involve new physical interactions, some of which could manifest themselves as a violation of the

4 Equivalence Principle, variation of fundamental constants, modification of the inverse square law of gravity at various distances, Lorentz-symmetry breaking, or large-scale gravitational phenomena. The new interactions in turn introduce corrections to the current model of spacetime around massive bodies. Each of these manifestations offers an opportunity for experiment and could lead to a major discovery. Space is one of the most likely places where these manifestations may be investigated. While providing access to greater variation of gravitational potentials, greater velocities, and full orientation coverage, space also extends the well-understood and controlled laboratory environments. These experiments have already been so successful on Earth and that the increased precision in space makes their discovery potential limitless. In light of the advancement of dark energy theories, the encouraging indication of the screening effect due to dark energy scalar fields in astrophysics observations, and the maturation and potential of atomic sensor technologies, there is a strong motivation and justification for space laboratory science measurements in the coming decades that probe the dark energy field, the possible dark matter ultra-light field, and test fundamental physics laws. Complementary to what can be learned from future observational telescopes, dedicated space laboratories will enable stringent tests of dark energy models and possible direct detection of dark energy. One possible mission concept is the Gravity Observation and Detection of Dark energy Explorer in Solar System (GODDESS) that comes out of a recent NIAC study [37]. The primary science objective is to detect the dark energy force sourced by the Sun as predicted by the Galileon model. The predicted galileon force is 10-10 smaller than the solar gravitational force at 1 AU distance away from the Sun. In the conceptual measurement scheme, a tetrahedral constellation of four spacecraft orbiting around the Sun measures the force gradients along the trajectory. Cold atoms onboard each spacecraft are used as test masses and quantum sensors, and laser ranging interferometers between the spacecraft measure relative displacements to yield force gradient. Gradient measurements are then combined to yield the force gradient tensor. The gravitational force, which follows the inverse-square law, has no divergence and contributes zero to the trace of the gradient tensor, and thus summing over the diagonal elements of the gradient tensor reveals the galileon influence. The trace measurement scheme completely mitigates the effects of the much stronger gravity backgrounds and allows the spacecraft to fly freely without the need for precise orbit control. A preliminary analysis shows that 3 years of continuous data collection in a 1 AU orbit around the Sun will detect the galileon force with a signal to noise of 3, based on the cosmologically observed Hubble’s constant that governs the galileon model. Such a mission will not only constrain the galileon scalar field model, but also Chameleon and Symmetron fields. Moreover, the tetrahedra constellation of precise differential gravity gradient measurements in GODDESS offers the opportunity to achieve other significant science objectives. The measurements from GODDESS would also provide rich and diverse scientific data for testing gravity field theories in general beyond Newtonian gravity, hunting for ultra-light fields of dark matter, as well as detecting gravitational waves in the mid band frequency spectrum between those of LIGO and LISA, as described in the NIAC report.

5 References

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