Exploring Dark Energy and Gravity in Space Laboratories Thematic Areas: ☐ Planetary Systems ☐ Star and Planet Formation ☐Formation and Evolution of Compact Objects ☒ Cosmology and Fundamental Physics ☐Stars and Stellar Evolution ☐Resolved Stellar Populations and their Environments ☐Galaxy Evolution ☐Multi-Messenger Astronomy and Astrophysics Principal Author: Name: Nan Yu Institution: Jet Propulsion Laboratory Email: nan.yu@jpl.nasa.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 science 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 nature 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 waves. 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.

1

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 light 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 General Relativity) 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-

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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 speed of light 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 phase transition 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 thin shell effect, facilitating the screening mechanism. Small particles such as single atoms, however, are smaller than the Compton wavelength of the field and experience the full effect of the scalar field. Laboratory experiments are conducted to exploit this enhanced sensitivity by using cold atoms for probing new forces [19] [26] [27] [28] [30]. The results significantly constrain the parameter spaces of the Chameleon and the Symmetron models in a complementary manner to

Figure 1. Recent progresses on constraints of scalar field models. From left: constraints on Chameleon [31], constraints on Symmetron [27], present (LLR) and future constraints on Vainshtein [13], and simulation on scalar field forces on astronomical observations [33].

available cold atom experiment capabilities. Finally, ourfindings are summarized in Sec. VII.

II. DETECTION OF THE CHAMELEONSCALAR FIELD

We follow the method of describing chameleon fields asoutlined in Refs. [4,5]. Chameleon theories include a self-interacting potential VðϕÞ of a scalar field ϕ, and aninteraction potential V intðϕ;ρÞ with matter density ρ. Weconsider, in this paper, the effective potential in the simplestand the lowest order inverse power-law form [4,5]

VeffðϕÞ≡ VðϕÞ þ V intðϕ;ρÞ

¼ Λ4

!1 þ Λn

ϕn

"þ ϕM

ρ; ð1Þ

where Λ sets the strength of the self-interaction, n is apositive integer, and M describes the interaction withnormal matter. The equation of motion, in the static casewhere ρ and ϕ are stationary, is

∇2ϕ ¼ ∂Veff

∂ϕ¼ −n

Λnþ 4

ϕnþ 1þ β

ρMPl

; ð2Þ

where β¼ MPl/M and MPl is the reduced Planck mass.The acceleration on a test particle due to an establishedfield profile ϕ can be obtained from the spatial derivative ofV int [4,5]:

a⃗¼ −β

MPl∇⃗ϕ: ð3Þ

Far away from boundaries, ϕ approaches an equilibriumvalue ϕeq that minimizes Veff

∂Veff

∂ϕ####ϕeq

¼ 0;

ϕeqðρÞ ¼!

βnΛnþ 4

ρMPl

"− 1nþ 1

: ð4Þ

The distance for ϕ to reach ϕeq is short for typical matterdensities, such that the interior of a bulk experiences zeroacceleration from the chameleon field [Eq. (3)]. The bulk,as a whole, experiences negligible chameleon acceleration,which is known as screening [5]. The screening does nothappen to gaseous atoms, due to the microscopic size anddilute density, which makes atoms a much more sensitivetool for chameleon detection. The concept of using atomictest particles for chameleon force detections has beenproposed [5] and experimentally implemented [6 –8], where

acceleration of atoms is precisely measured in a quantuminterferometric way (see Sec. IV).Despite the success of more stringent constraints on the

chameleon theory parameters ðn;Λ;βÞ by atom interfer-ometer measurements [8], major systematic effects need tobe addressed before a complete conclusion for the chame-leon theory can be reached. Being an extra force, chame-leon forces can at best be detected at the precision of known

FIG. 1. Exclusion plots of chameleon parameters. (a) ðβ;ΛÞexclusion plot for n ¼ 1. Region near the upper left corner(yellow) is excluded by the torsion balance experiment [10].Region bounded by the blue curve is excluded by the atominterferometer experiment in Ref. [8]. The blue diamond marksthe parameter set of ðn;Λ;βÞ ¼ ð1; 0.1 meV; 103Þ, and the bluedashed line across it labels parameters that would produce thesame chameleon force. Failure of detecting accelerations calcu-lated in this work based on this parameter set will exclude theshaded region above the dashed line. Λ ¼ Λ0 is of cosmologicalrelevance, and is shown as the horizontal line. (b) ðn;βÞ exclusionplot for Λ ¼ Λ0. Regions excluded by the corresponding experi-ments are labelled. The red diamond marks the embraciveparameter set of ðn;Λ;βÞ ¼ ð10;Λ0; 1Þ, and the red dashedcurve across it labels parameters that would produce the samechameleon force. Failure of detecting accelerations calculated inthis work based on this parameter set will exclude the shadedregion above the dashed curve.

SHENG-WEY CHIOW and NAN YU PHYS. REV. D 97, 044043 (2018)

044043-2

NATURE PHYSICS DOI: 10.1038/NPHYS4189 LETTERS

10−10

M[MPl]10−5 1

0.1

1

10

100a b c

Torsionbalance

This work

Atom interferometry(2015)

Neutrons

Microspheres

10−2

102

100

104

106

�ch

am

108

1010

Torsion balance

n

Neutron interferometry Neutrongravity resonance

Atom interferometry (2015)

This work

−10

−8

−6

−4

−2

0

2

−6 −4 −2 0 2 4

log[Ms/GeV]

Torsionbalance

Atominterferometry

(2015)

This work

µ (

meV

)10

−1

10−1

.5

2 4 6 8 10

log (m

eV)

Λ

λ

Figure 3 | Constraints on screened scalar fields. a, Chameleon field: the shaded areas in the M–⇤ plane are ruled out at the 95% confidence level. MPl/Mgives the coupling strength to normal matter in relation to gravity; ⇤=⇤0 ⇡2.4 meV (indicated by the black line) could drive cosmic acceleration today. Acomparison is made to previous experiments: neutron interferometry28/neutron gravity resonance29, microsphere force sensing30, and torsion balance1,27.b, Chameleon limits in the n–�cham plane with ⇤=⇤0, showing the narrowing gap in which basic chameleon theories could remain viable. n is the powerlaw index describing the shape of the chameleon potential; �cham ⌘MPl/M is the strength of the matter coupling. c, Symmetron fields: constraints by atominterferometry complement those from torsion pendulum experiments10,11 (shown with µ=0.1 meV) for the range of µ considered. For µ< 10�1.5 meV, thefield vanishes entirely inside the vacuum (see Methods), leaving this parameter space unconstrained. The same e�ect produces the sharp cuto� in ourlimits at low MS.

only a one order of magnitude range left for the coupling strengthM . Furthermore, for all ⇤>5.1meV, this gap is fully closed, rulingout all such models. Our symmetron limits are complementary totorsion pendula1,10,11 as well. We improve previous constraints on �by two orders ofmagnitude throughout the entire range ofMS andµprobed by our experiment. Our constraint is strongest in the regimewhere the atom is screened,where forµ=0.1meVwe rule out�<1.

Tests of gravity in the ultraweak-field regimewith aminiature, in-vacuum sourcemass probe screened field theories with the potentialto explain the accelerated expansion of our universe. In the future,technologies such as lattice interferometry13 in our optical cavity andlarge momentum transfer Bragg beam splitters will allow us to holdquantum probe particles in proximity to a miniature source mass,evading geometric constraints from the source mass’ small size,and boosting sensitivity. With modest improvements, chameleonfields at the cosmological energy density will be either discovered orcompletely ruled out. This also will enable study of novel quantumphenomena such as the gravitational Aharonov–Bohm e�ect12, andprovide even better resolution of atom–source mass interactions.

MethodsMethods, including statements of data availability and anyassociated accession codes and references, are available in theonline version of this paper.

Received 24 January 2017; accepted 25 May 2017;published online 3 July 2017

References1. Kapner, D. J. et al . Tests of the gravitational inverse-square law below the

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8. Burrage, C., Copeland, E. J. & Hinds, E. A. Probing dark energy with atominterferometry. J. Cosmol. Astropart. Phys. 2015, 042 (2015).

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19. Perlmutter, S. et al . Measurements of � and 3 from 42 high- redshiftsupernovae. Astrophys. J. 517, 565–586 (1999).

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© 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.

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This again implies that the greater part of theobserved signal must be of non-fifth-force origin.

These estimations of the fifth force effect are relativelycoarse. A precise quantitative determination of the prefer-ence of the data for ΔG > 0—and of the constraints on ΔGand λC that it implies—requires the full likelihood formal-ism of Sec. IV. It is to this that we now turn.

B. Constraints on ΔG and λC

1. Effect of noise model

From Sec. VA it is clear that for any reasonable value ofΔG=GN modified gravity accounts for at most a smallfraction of the total gas-star offset, justifying the fiducial

method of Sec. IV E for setting the measurement uncer-tainties θi. This ought to manifest in an agreement betweenthe results of that model and those of the others in thatsection where θ is parametrized and fitted for. Herewe show this explicitly for the screened model withλC ¼ 1.8 Mpc.13 Figure 4 shows the posteriors offΔG=GN; θ̄g in the case where θ ¼ θ̄ arcsec is a freeparameter, and fΔG=GN; A; Bg and fΔG=GN;C;D; E; Fgfor the models of Eqs. (28) and (29) respectively. These areto be compared with Fig. 5, which shows the ΔG=GN

FIG. 2. Correlations of predicted (upper) and observed (lower) signal with Newtonian potential Φ (left) and magnitude of fifth forceacceleration a5 (right). The prediction is calculated as in Fig. 1, again for the case λC ¼ 5 Mpc, ΔG=GN ¼ 1, and hΦi and ha5i are themodal averages over the 1000 Monte Carlo model realizations. In the top row, the red points are for the full chameleon- or symmetron-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 pointsshow the case where screening is entirely switched off. The black dashed line shows the threshold jΦcj, above which galaxies arescreened. The median sizes of the error bars in the four directions—minimal 68% bounds for the prediction, 1σ for the observations—areshown by the red crosses in the top left corners (the uncertainties in hr"i are the same size as the red point). While the predictions show aclear cutoff in r" for jΦj > jΦcj and a positive correlation with a5 [Eq. (4)], this is not apparent in the observations.

13We focus on this value of λC because it maximizes the overalllikelihood, as will be shown in Sec. V B 3.

DESMOND, FERREIRA, LAVAUX, and JASCHE PHYS. REV. D 98, 064015 (2018)

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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 wave 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 laser-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

4

Cold Atom Laboratory (CAL) is currently operating on the International Space Station as a multi-user facility, and serves as a pathfinder for future atomic sensors in space [40]. Moreover, the atom interferometer demonstration on a sounding rocket shows the robustness of atomic sensors [41] [42].

The inherent high sensitivity and stability of atomic sensors have been proposed, investigated and exploited for direct detection of dark energy, direct detection of dark matter, gravitational wave detections, and tests of EEP, among many other physics measurements. For instance, Chameleon and Symmetron dark energy models are tested and constrained using cold Cs and Rb atoms at University of California at Berkeley and Imperial College, UK, respectively [26] [28]. Dark matter measurement concepts are proposed using cold atoms in space [43] [44] [45]. Cold-atom based EEP tests are conducted [46] [47] [48] [49] and proposed [50] [51]. Note that, while the MICROSCOPE mission placed a bound on EEP at the 10-14 level using bulk masses [52], atomic 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 gravitational wave detection schemes are proposed using ultracold atoms on the ground and in space [45] [53] [54] [55] [56] [57]. Figure 2 illustrates the state of the art on atomic sensing in space.

Science measurement opportunities Led by the discovery of dark energy and dark matter, growing observational evidence points to the need for new physics aimed at answering important questions related to the most fundamental laws of Nature [58]. Efforts to discover new fundamental symmetries, investigations of the limits of established symmetries, tests of the general theory of relativity, detection of gravitational waves, and attempts to understand the nature of dark matter were among the topics at the focus of scientific 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 quantum mechanics 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

Figure 2. From Left: hardware of CAL on the ISS [40], BEC generation on CAL [40], and BEC interferometer in microgravity [59].

DRAFT

Figure 2. Onset of Bose-Einstein condensate in low-Earth orbit aboard the International Space

Station. From left to right, the final frequency of a forced evaporation ramp using an RF knife in

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. At the conclusion of the evaporation ramp,

the magnetic trap potential is decompressed and extinguished before imaging the atoms 22 ms

later. The BEC critical temperature is measured to occur at 130 nK ( 500 nk in the original trap).

The right-most image shows an atom cloud with 49k total atoms, 26% condensed in a BEC at a

temperature of 17 nK measured from the distribution of the surrounding thermal cloud.

trap, carrying their energy away and leaving the remaining sample colder. Evaporation

stagnates as the temperature drops relative to the trap barrier height (trap depth), so that

it is necessary to lower the trap depth in order to force evaporation to continue. Experiments

that confine atoms in a harmonic magnetic trap, such as CAL, typically do this with an

RF knife – radio frequency photons tuned to change an atom’s internal magnetic state at a

6

magnitude. By applying delta-kick cooling (DKC) [28–30]we have been able to reduce the expansion and to enhancethe signal at longer interferometry times. We study thecoherent evolution of the BEC for increasing temporaland spatial separation of the wave packets inside the inter-ferometer by monitoring the single-shot contrast and shapeof the fringes [31].

Our experiments are performed with an asymmetricMach-Zehnder interferometer (AMZI) [20,32] shown inFig. 1. Here we display the temporal evolution of theatomic density distribution of the BEC interferometer foran experiment on ground [Fig. 1(a)] and the correspondingexperimental sequence for forming the interferometer[Fig. 1(b)]. A macroscopic wave packet is coherently split,redirected, and brought to a partial overlap by successiveBragg scattering at moving light crystals [26,33,34]. Theyare generated by pulses of two counter-propagating laserbeams separated by the two-photon recoil energy of15 kHz and detuned from the F ¼ 2 ! F ¼ 3 transitionof the D 2 line of

87Rb by 800 MHz to reduce spontaneousscattering. There exists a close analogy to the Young double-slit experiment [Fig. 1(c)], where one pair of overlappingBECs plays the role of a pair of coherent light waves ema-nating from two slits separated by a distance d. Similar to theresulting interference pattern in the far field of the double slit,

the fringe spacing in our expanding cloud, being the distancebetween two local maxima of the density, increases with thetotal expansion time Tex of the BEC and is inversely propor-tional to the displacement d of the two clouds.Figure 2 illustrates our experiments in microgravity

performed at the drop tower. We show the complete tem-poral sequence [Fig. 2(a)], which differs from the previousexperiments with the apparatus [15] in three importantfeatures: (i) We employ DKC to reduce the expansionduring the free fall by briefly (2 ms) switching on thetrap with frequencies of (10, 22, 27) Hz generated by theatom chip 30 ms after the release. (ii) In order to eliminatedetrimental effects of residual magnetic fields we transferthe BEC into the nonmagnetic state jF ¼ 2; m F ¼ 0i bycoupling the Zeeman levels with a chirped radio-frequencypulse (adiabatic rapid passage) [35]. (iii) At the time T0

after the release of the BEC, we implement the sequence ofthe AMZI outlined in Fig. 1 and detect the interferencepattern at Tex after the release using absorption imagingwith a single laser pulse as illustrated in Fig. 2(b). In Fig. 2(c)we show typical images of the interfering BECs and thecorresponding column density profiles for two differentvalues of Tex .Figure 3 summarizes the central results of our Letter

on probing the coherent evolution of a BEC with an

(a) (b) (c)

FIG. 1 (color). Temporal AMZI for a BEC based on Bragg scattering at a light grating: experimental images on ground (a),schematic sequence (b), and analogy to the Young double-slit experiment (c). The evolution of the BEC and the AMZI is visualized bya series of absorption images (a) of the atomic densities separated by 1 ms. The incomplete transfer is a consequence of the largermean-field energy of the BEC necessary for the ground experiment. The interferometer starts at the time T0 after the release of theBEC, when a !=2 pulse (b) made out of two counter-propagating light beams of frequency ! and !þ " creates a coherentsuperposition of two wave packets that drift apart with the two-photon recoil velocity vrec ¼ 11:8 mm=s. After T they are redirected bya ! pulse and partially recombined after T # "T by a second !=2 pulse. A nonzero value of "T leads to a spatial interferencepattern, which we record after # ¼ 53 ms in free fall. Similar to the far-field pattern observed in the Young double-slit experiment(c), the fringe spacing l scales linearly with the time of expansion Tex ¼ T0 þ 2T # "T þ # and is inversely proportional tothe separation d ¼ vrec"T of the wave packets. The scaling factor is the ratio of Planck’s constant h and the mass m Rb of theRubidium atoms.

PRL 110, 093602 (2013) P HY S I CA L R EV I EW LE T T E R Sweek ending

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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.

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