Tests of fundamental physics provide a relatively straightforward first step on the road from laboratory proof-of-principle experiments to applications, as the instrument stays in a well-controlled laboratory environment, is operated by scientists and the main focus is on increasing precision. We review several developments, starting with the use of atom interferometry as a tool to determine fundamental constants.

Fundamental constants

Atomic masses and fine-structure constant α

When an atom absorbs a photon, it also absorbs the photon’s momentum, resulting in a change of its kinetic energy by an amount equal to the recoil energy. Extending the laser-pulse sequence in an atom interferometer to four π/2 pulses creates two closed interferometers (Fig. 3a). The difference between the phase shifts of the two interferometers17 is proportional to the recoil energy acquired during the beamsplitter π/2 pulses.

Fig. 3: Modified interferometer schemes. Differential measurements between the phase shifts in two simultaneously operated interferometers lead to common-mode suppression of many noise sources, such as vibration and laser noise. a | A four-pulse scheme creates two closed interferometers whose differential phase shift is directly related to the kinetic energy associated with the photon recoil. b | A gravity gradiometer scheme involves two atom interferometers at two different heights within the gravitational potential interrogated by the same laser beam. c | Additional laser pulses (blue arrows) increase the spacetime area of the atom interferometer, thus enhancing the sensitivity. This technique can be applied to single interferometers for inertial sensing and gravimetry and to pairs of interferometers for gradiometry measurements, such as the one shown in panel b. Full size image

Combining this interferometer scheme with a precise determination of the wavelength of the light used for the laser pulses allows to obtain a precise value of h/m X , where h denotes Planck’s constant and m X is the mass of the atomic species17. In the new SI units18, where the value of h is fixed, this approach provides a direct measurement of the inertial mass at microscopic scales. A link to macroscopic scales can then be established through the silicon spheres of the Avogadro Project19, whose total number of atoms can be very accurately determined.

In addition, an accurate quantification of h/m X also provides an accurate way of determining the fine-structure constant13,17,20, α, by linking the two quantities with the Rydberg constant, R ∞ , which can be determined with great accuracy through spectroscopy. In fact, the most accurate results for the fine-structure constant to date, corresponding to α = 1/137.035999046(27) with a relative uncertainty of 2 × 10−10, have been obtained based on this approach13 and surpass those obtained from the measurement of the anomalous magnetic moment of the electron21. Comparing the two results can be regarded as a high-precision test of quantum electrodynamics13,22.

Newton’s gravitational constant, G

Of all fundamental constants of nature, the gravitational constant G is by several orders of magnitude14 the least accurately determined one. By performing a differential measurement with a pair of atom interferometers in a gradiometer configuration (Fig. 3b), the local gravitational field generated by a well-characterized source mass can be precisely determined, and G accurately inferred23. Results approaching the accuracies of state-of-the-art measurements with macroscopic test masses, mainly torsion-balance experiments24,25,26, have already been obtained and found G = 6.67191(99) × 10−11 m3 kg−1 s−2, with a relative uncertainty of 150 ppm14. Significant future improvements with an atom interferometer are anticipated27.

Testing the equivalence principle

The equivalence principle28,29 states that local physical phenomena in a freely falling frame are equivalent to those in the absence of gravitational fields, provided that tidal effects can be neglected. The differential acceleration between two test masses in free fall, expressing a violation of the universality of free fall (UFF), which is a central aspect of the equivalence principle, is typically quantified by the dimensionless Eötvös parameter. This quantity corresponds to the difference in the ratios of the gravitational and inertial masses of the two objects, divided by their average. Although classical tests have reached uncertainties in the Eötvös ratio below 10−14, no deviation from the equivalence principle has been reported so far30,31,32,33.

Atom interferometers34,35,36,37,38 offer a complementary and very clean approach for probing the equivalence principle, as the test samples are intrinsically isotopically pure and are in a well-specified spin state. This feature can be exploited to search for spin-dependent UFF violations by comparing the results for different spin polarizations. More importantly, atom interferometers provide access to atomic elements, which are technically impractical to use as macroscopic test masses. In this way, it is possible to significantly expand the parameter space, for example, with respect to atomic elements or isotopes with different neutron versus proton numbers39.

Atom interferometry also opens up new possibilities for testing quantum aspects of the equivalence principle using atoms in superpositions of internal states40 or with pairs of entangled atoms of different species41. A variation using a macroscopically delocalized coherent superposition of atomic clocks42,43 has also been proposed for tests of the universality of the gravitational redshift.

Dark-matter and dark-energy searches

Astrophysical and cosmological observations have established44 that dark energy and dark matter are the dominant contributions to the average energy density of the Universe. Ordinary matter made of standard, model particles makes up only 5% of its content. However, the precise nature of dark matter and dark energy remains elusive, despite considerable efforts in observational astrophysics and experimental high-energy physics over several decades. Precision measurements based on atom interferometry and atomic clocks can make contributions in the quest to understand the nature of dark matter and dark energy.

A class of theories attempting to explain dark energy, known as chameleon models45, involve a light scalar field that can mediate a long-range interaction and give rise to a ‘fifth force’. However, through its interaction with matter, the chameleon field acquires a much larger effective mass in regions where the matter density is not too low. This fact leads to a screening of the interaction, which can, in this way, evade tests of the equivalence principle with macroscopic masses. However, microscopic test masses, such as atoms in a vacuum chamber, should hardly be affected by the screening mechanism, as opposed to the source mass. Hence, atoms could be much more sensitive to forces mediated by chameleon fields45. Atom interferometric measurements have already been able to exclude large regions of the parameter space for such models46,47.

Extensive searches48 for massive dark-matter candidates known as WIMPs (weakly interacting massive particles) have not yet provided a widely accepted direct observation, spurring a growing experimental interest in exploring a wider range of dark-matter hypotheses. In this respect, the possibility that dark matter could be attributed to coherent oscillations within sub-galactic regions of ultralight scalar or pseudoscalar fields has recently been gaining increasing attention49. These oscillations could lead to small periodic variations in space and time of the parameters of the standard model, which could be detected in highly sensitive gravimetry measurements as a small modulation in the time of the acceleration experienced by freely falling atoms50. They could also produce small oscillations of the transition energies between electronic states that could be identified by comparing different atomic clocks at the same location51 or pairs of identical atom interferometers separated by long distances but interrogated by common laser beams50. Experimentally, the search for dark matter and dark energy with atom interferometry is in the early stages and provides a fascinating direction for future development.

Gravitational-wave detection

Atom interferometry offers a complementary approach52,53 to the established laser interferometry for the detection of gravitational waves. Two atom interferometers coherently manipulated by the same light field can be interpreted as a differential phase metre tracking the distance traversed by the light field. Based on this principle, space-borne detectors54,55 have been proposed which target a similar performance as the laser interferometer used in the Laser Interferometer Space Antenna (LISA) project55,56.

Atom interferometers have been proposed to cover the gap in the frequency band of 0.1–10 Hz between LISA and ground-based laser interferometers such as Virgo and the Advanced Laser Interferometer Gravitational Wave Observatory (AdvLIGO)57. Concepts for setups on Earth with a vertical52 or horizontal57 baseline have been discussed, with developments towards the latter geometry under way in the Matter-wave laser Interferometric Gravitation Antenna (MIGA) consortium59.

The European Laboratory for Gravitation and Atom-Interferometric Research (ELGAR) facility proposes to design the first long-baseline infrastructure using quantum physics to study spacetime and gravitation. With a correlated array of atom interferometers, it is possible to discriminate between gravitational-wave signals at low frequencies in the range of 0.1–10 Hz and Newtonian gravitational noise from the environment58, which allows a frequency band not covered by other gravitational-wave detectors to be adressed.

In addition to the detection of gravitational waves, this facility is expected to contribute to other studies; for example, to the monitoring of Earth’s gravitational field over time and its rotation rate in three dimensions.

Increasing the measurement precision

Although atom interferometers are the state of the art in determining the fine-structure constant, many of the other fundamental physics applications still require significant improvements to surpass the sensitivity achieved by other methods. In addition to scaling the sensitivity with longer interferometer times in large, atomic fountains60,61,62,63,64 or in space65,66, there are numerous ideas which allow many orders of magnitude improvement. For example, one approach is to increase the number of laser pulses at each interaction point (Fig. 3c), leading to large-momentum beamsplitters67,68, where a large number, N, of photon momenta are transferred, leading to an N-fold increase in sensitivity. Whereas beamsplitters with hundreds of photon recoils have been demonstrated, real sensitivity improvements have only been observed69,70 for photon exchanges of N ≈ 30, because technical challenges (such as wavefront curvature70,71,72,73,74 and non-zero excitation probabilities) still limit the achievable interferometer contrast. Further advances are promised by atom-number squeezing74 and quantum non-demolition measurements75, which increase the signal-to-noise ratio in the interferometer readout.

Research groups worldwide are working on combining the above schemes to achieve up to billion-fold boosts in sensitivity, aiming at UFF tests below the 10−15 level, determinations of the gravitational constant at the 1-ppm level27,76 and gravitational-wave strain sensitivities of 10−21 Hz−1/2. These experimental efforts are accompanied by developments in the accurate modelling of atom interferometry, allowing the identification of all the relevant noise sources and systematic effects, and the design of suitable mitigation strategies. Detailed studies of the phase-shift contributions in light-pulse atom interferometers already exist, including the effects of accelerations77, rotations, gravity gradients78,79,80,81,82,83 and even branch-dependent forces81. Many of these studies take advantage of a useful decomposition of the wave-packet evolution in terms of central trajectories and centred wave packets78,80,81,84.

A deeper theoretical understanding of atom interferometry, combined with a precise control of the relevant parameters, allows an accurate engineering of the environment85,86. This understanding can also be exploited to develop new techniques87 to circumvent major limitations imposed, for example, by uncertainties in the initial position and velocity of the atomic cloud in the presence of gravity gradients. Indeed, the technique76,87 for compensating the effects of gravity gradients enables significant breakthroughs in measurements of the gravitational constant27,76, G, and tests of the equivalence principle60 with atom interferometry.

Most theoretical approaches to date are non-relativistic, except for phase-shift calculations of freely falling atoms relying on a semi-classical ansatz88,89,90, but a fully relativistic description of atom interferometry in curved spacetime43 has recently been developed. This technique is particularly valuable for investigating interferometry schemes sensitive to relativistic effects.