Measurements of the fine-structure constant α require methods from across subfields and are thus powerful tests of the consistency of theory and experiment in physics. Using the recoil frequency of cesium-133 atoms in a matter-wave interferometer, we recorded the most accurate measurement of the fine-structure constant to date: α = 1/137.035999046(27) at 2.0 × 10 accuracy. Using multiphoton interactions (Bragg diffraction and Bloch oscillations), we demonstrate the largest phase (12 million radians) of any Ramsey-Bordé interferometer and control systematic effects at a level of 0.12 part per billion. Comparison with Penning trap measurements of the electron gyromagnetic anomaly - 2 via the Standard Model of particle physics is now limited by the uncertainty in - 2; a 2.5σ tension rejects dark photons as the reason for the unexplained part of the muon's magnetic moment at a 99% confidence level. Implications for dark-sector candidates and electron substructure may be a sign of physics beyond the Standard Model that warrants further investigation.

If dark energy -which drives the accelerated expansion of the universeconsists of a light scalar field, it might be detectable as a "fifth force" between normalmatter objects, in potential conflict with precision tests of gravity. Chameleon fields and other theories with screening mechanisms, however, can evade these tests by suppressing the forces in regions of high density, such as the laboratory. Using a cesium matter-wave interferometer near a spherical mass in an ultra-high vacuum chamber, we reduce the screening mechanism by probing the field with individual atoms rather than bulk matter. Thus, we constrain a wide class of dark energy theories, including a range of chameleon and other theories that reproduce the observed cosmic acceleration.Cosmological observations have now firmly established that the universe is expanding at an accelerating pace, which can be explained by dark energy permeating all of space and accounting for ∼ 70% of the energy density of the universe (1). What constitutes dark energy, and why it has its particular density, remain as some of the most pressing open questions in physics. What is clear is that dark energy presents us with a new energy scale, of order meV. It is natural to speculate that new (usually scalar) fields might be associated with that scale that make up all or part of the dark energy density (2,3). String theory with compactified extra dimensions, for instance, features a plethora of scalar fields, which typically couple directly to matter fields unless protected by a shift symmetry as for axions (4,5). If the fields are light, this coupling would be observable as a "fifth force", in potential conflict with precision tests of gravity (6). 2Theories with so-called screening mechanisms, on the other hand, have features that suppress their effects in regions of high density, so that they may couple to matter but nonetheless evade experimental constraints (7). One prominent example is the chameleon field, whose mass depends on the ambient matter density (8,9). It is light and mediates a long-range force in sparse environments, such as the cosmos, but becomes massive and thus short-ranged in a high-density environment, such as the laboratory (see Fig. S1). This makes it difficult to detect by fifth-force experiments.Burrage, Copeland and Hinds (10) have recently proposed to use atom interferometers (11,12) to search for chameleons. An ultrahigh-vacuum chamber containing atomic test particles simulates the low-density conditions of empty space, liberating the chameleon field to become long-ranged and, thus, measurable. Here, we use a cavity-based atom interferometer (13,14) measuring the force between cesium-133 atoms and an aluminum sphere to search for a range of screened dark energy theories that can reproduce the current dark energy density (Fig. 1A, B).The chameleon dark energy field ϕ in equilibrium is determined by minimizing a potential density V(ϕ)+V int , which is the sum of a self-interaction term V(ϕ) and a term V int describing the interaction wit...

One of the central predictions of metric theories of gravity, such as general relativity, is that a clock in a gravitational potential U will run more slowly by a factor of 1 + U/c(2), where c is the velocity of light, as compared to a similar clock outside the potential. This effect, known as gravitational redshift, is important to the operation of the global positioning system, timekeeping and future experiments with ultra-precise, space-based clocks (such as searches for variations in fundamental constants). The gravitational redshift has been measured using clocks on a tower, an aircraft and a rocket, currently reaching an accuracy of 7 x 10(-5). Here we show that laboratory experiments based on quantum interference of atoms enable a much more precise measurement, yielding an accuracy of 7 x 10(-9). Our result supports the view that gravity is a manifestation of space-time curvature, an underlying principle of general relativity that has come under scrutiny in connection with the search for a theory of quantum gravity. Improving the redshift measurement is particularly important because this test has been the least accurate among the experiments that are required to support curved space-time theories.

We present a test of the local Lorentz invariance of post-Newtonian gravity by monitoring Earth's gravity with a Mach-Zehnder atom interferometer that features a resolution of up to 8 x 10{-9}g/sqrt[Hz], the highest reported thus far. Expressed within the standard model extension (SME) or Nordtvedt's anisotropic universe model, the analysis limits four coefficients describing anisotropic gravity at the ppb level and three others, for the first time, at the 10 ppm level. Using the SME we explicitly demonstrate how the experiment actually compares the isotropy of gravity and electromagnetism.

We present up to 24-photon Bragg diffraction as a beam splitter in light-pulse atom interferometers to achieve the largest splitting in momentum space so far. Relative to the 2-photon processes used in the most sensitive present interferometers, these large momentum transfer beam splitters increase the phase shift 12-fold for Mach-Zehnder (MZ) and 144-fold for Ramsey-Bordé (RB) geometries. We achieve a high visibility of the interference fringes (up to 52% for MZ or 36% for RB) and long pulse separation times that are possible only in atomic fountain setups. As the atom's internal state is not changed, important systematic effects can cancel.

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We present an analytic theory of the diffraction of (matter) waves by a lattice in the "quasi-Bragg" regime, by which we mean the transition region between the long-interaction Bragg and "channelling" regimes and the short-interaction Raman-Nath regime. The Schrödinger equation is solved by adiabatic expansion, using the conventional adiabatic approximation as a starting point, and re-inserting the result into the Schrödinger equation to yield a second order correction. Closed expressions for arbitrary pulse shapes and diffraction orders are obtained and the losses of the population to output states otherwise forbidden by the Bragg condition are derived. We consider the phase shift due to couplings of the desired output to these states that depends on the interaction strength and duration and show how these can be kept negligible by a choice of smooth (e.g., Gaussian) envelope functions even in situations that substantially violate the adiabaticity condition. We also give an efficient method for calculating the effective Rabi frequency (which is related to the eigenvalues of Mathieu functions) in the quasi-Bragg regime.

We investigate leading order deviations from general relativity that violate the Einstein equivalence principle in the gravitational standard model extension. We show that redshift experiments based on matter waves and clock comparisons are equivalent to one another. Consideration of torsion balance tests, along with matter wave, microwave, optical, and Mössbauer clock tests, yields comprehensive limits on spin-independent Einstein equivalence principle-violating standard model extension terms at the 10 −6 level.Gravity makes time flow differently in different places. This effect, known as the gravitational redshift, is the original test of the Einstein equivalence principle (EEP) [1] that underlies all of general relativity; its experimental verification [2-6] is fundamental to our confidence in the theory. Atom interferometer (AI) tests of the gravitational redshift [4,6] have a precision 10 000 times better than tests based on traditional clocks [3], but their status as redshift tests has been controversial [7]. Here, we show that the phase accumulated between two atomic wave packets in any interferometer equals the phase between any two clocks running at the atom's Compton frequency following the same paths, proving that atoms are clocks. For a quantitative comparison between different redshift tests, we use the standard model extension (SME) [8][9][10][11], which provides the most general way to describe potential low energy Lorentz symmetry-violating (thus EEP-violating) signatures of new physics at high energy scales. We show that all EEP tests are sensitive to the same five terms in the minimal gravitational SME [9][10][11] and, for the first time, comprehensively rule out EEP violation in redshift tests greater than a few parts per million for neutral matter.If two clocks are located at different points in spacetime, they can appear to tick at different frequencies, despite having the same proper frequency ω 0 in their local Lorentz frames. For clocks moving with nonrelativistic velocities v 1 and v 2 in a weak gravitational potentialThe first term is the gravitational redshift, originally measured [2] by Pound and Rebka in 1960, while the second term is the time dilation due to the clocks' relative motion. The redshift term can be isolated from the time dilation if the clocks' trajectories are known.The state of each clock can be described by a timevarying phase. If two clocks 1 and 2 are synchronized to have identical phase ϕ 0 = 0 at time t = 0, then theirMach-Zehnder clock or atom interferometer. Two otherwise freely falling clocks (or halves of an atomic wavepacket) receive momentum impulses that change their velocity by ±vr. The dashed lines indicate trajectories without gravity.specializing to a homogenous gravitational field so that φ 1 −φ 2 = g· r 12 , with r 12 being the clocks' distance vector and g the local acceleration of free fall. If the clocks are freely falling, then their motion is an extremum of their respective actions [12]Thus δϕ f is proportional to the difference S 1 − S 2 in the...