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10 October 2026

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Advances in and Prospects for Matter Wave Interferometry

,
and
1
Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208, USA
2
Center for Fundamental Physics, Northwestern University, Evanston, IL 60208, USA
3
Department of Electrical and Computer Engineering, Northwestern University, Evanston, IL 60208, USA
*
Author to whom correspondence should be addressed.
Atoms2026, 14(10), 82;https://doi.org/10.3390/atoms14100082
This article belongs to the Special Issue Advances in and Prospects for Matter Wave Interferometry
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The field of matter wave interferometry is rapidly advancing on multiple frontiers. Matter wave interference is being realized with increasingly massive objects, creating new avenues to probe foundational questions about quantum mechanics. The interference of sodium nanoparticles with masses in excess of 170,000 Da was recently observed [1]. Additionally, long-baseline atom interferometers are being developed globally [2,3,4,5,6,7,8,9,10], with scientific goals including dark matter searches [11,12,13,14] and gravitational wave detection [8,15,16,17,18,19]. In parallel, researchers are advancing techniques to increase the sensitivity of compact atom interferometers for applications such as inertial navigation [20,21]. Such techniques include trapped atom interferometry [22,23,24,25,26] and point source atom interferometry [27,28,29,30]. Moreover, optimal control strategies have been implemented to improve the robustness of atom interferometers against noise and experimental limitations [31,32,33,34,35,36,37,38,39,40]. The papers in this Special Issue [41,42,43,44,45,46] cover all of these important frontiers.
In general, the sensitivity of an atom interferometer improves as the duration of the interferometer is increased. Atom interferometers in free space are therefore fundamentally limited by the available time before the atoms fall to the bottom of the vacuum chamber. This limitation can be circumvented by confining the atom interferometer in a trap, allowing interferometer durations limited only by the timescales over which coherence can be preserved. Recent years have seen impressive advances in trapped atom interferometry. For instance, interferometers using atoms trapped in an optical lattice have achieved coherence times of up to 70 s [23] and been used to measure gravity from a small source mass [22]. By loading atoms into an excited band of the lattice and tuning the lattice to a ‘magic depth,’ it has been demonstrated that dephasing from laser intensity fluctuations can be dramatically reduced [24]. Other related developments include the realization of large-area trapped Sagnac atom interferometers for rotation sensing [25,26] and of programmable optical lattice interferometers for inertial and gravitational sensing [40].
Xin et al. [41] investigate the coherence properties of atom interferometers that combine momentum kicks from Raman laser pulses with restoring forces from optical dipole potentials. They first implement a Ramsey interferometer with the atoms trapped in a three-dimensional optical lattice under three different conditions: (1) a thermal ensemble of atoms loaded into the lattice, (2) atoms cooled to the ground state of each lattice site, and (3) atoms in a momentum squeezed state that have reduced momentum uncertainty at the cost of increased position uncertainty, consistent with the Heisenberg uncertainty principle. For short Ramsey times, the squeezed-state interferometer exhibits the highest fringe visibility due to its smaller momentum spread. For all three cases, the authors identify inhomogeneities in the trap frequency across different lattice sites as a significant source of decoherence. They note that the coherence of the ground-state interferometer decays most slowly, since the ground state remains most localized within the lattice site and therefore is less impacted by the anharmonicity that becomes increasingly substantial away from the center of the site. Xin et al. also implement a two-dimensional atom interferometer in a single-beam optical trap. A double-diffraction Raman beam splitter acts along the axial direction of the trap, while an initial displacement in the radial direction leads to radial motion during the sequence. They determine that the coherence time is limited by radial trap anharmonicities. This paper highlights the critical importance of trap harmonicity for further extending coherence times. The authors point to time-averaged optical potentials or optical potentials shaped via spatial light modulators as future routes to reduce anharmonicity.
Currently, many platforms make use of GPS or equivalent systems developed by other nations for navigation. However, signals from such systems can be jammed and may be inaccessible in some terrains. These are also not useful for underwater or deep space navigation. To overcome these challenges, there is a strong interest in developing inertial navigation systems based on Inertial Measurement Units (IMUs) that combine multiple gyrosopes and accelerometers, with accuracy matching or exceeding those of GPS-like systems. There is a wide range of technologies that have been used to develop IMUs to date. However, none of them are accurate enough for demanding navigation applications. It should be noted that in addition to inertial navigation, extremely sensitive accelerometers and gyroscopes can be used for precision tests of fundamental physics, including general relativity. For example, very accurate accelerometers can be used for testing possible violation of the equivalence principle predicted by theories of quantum gravity, such as string theory. An ultra-sensitive gyroscope can be used for testing one of the most important predictions of general relativity, namely the gravitational frame dragging effect, manifested as the Lense–Thirring effect. As such, there is continuing interest in improving the sensitivity of accelerometers and gyroscopes.
Among the most sensitive gyroscopes are optical ones based on the Sagnac effect. This is a special relativistic effect, which produces a time delay between two paths of a Mach–Zehnder Interferometer (MZI) that is proportional to its area and the component of the rate of rotation normal to the plane of the MZI. This delay, which is purely geometric, is independent of the phase velocity of the waves propagating along the two arms of the MZI. Therefore, for any type of wave, the phase shift resulting from this delay is given simply by the product of the delay and the frequency of the wave. For an atom interferometer, the relevant frequency is the Compton frequency, which is given by the resting energy of the atom divided by Planck’s constant. Since the Compton frequency is much larger than optical frequencies, the phase shift produced in a typical atomic MZI, employing Rb atoms, for example, is more than eleven orders of magnitude bigger than that for a typical optical MZI, employing a Helium–Neon laser, for example. However, the actual sensitivity of a gyroscope also depends on other factors, namely the area enclosed by the MZI and the signal-to-noise ratio, which in turn depends on the number of particles interrogated within the measurement time. These factors are typically much larger for an optical MZI than an atomic MZI, to the extent that the net sensitivity to rotation for these two different technologies remains comparable at present. Therefore, further improvement in an atomic MZI is needed to realize the full potential of the extremely large Compton frequency. These include efforts to increase the area enclosed, using the process of large momentum transfer, as well as generation of entangled states of atoms via processes such as spin squeezing.
An atomic MZI can also measure acceleration. However, in a conventional atomic MZI, the phase shift observed is due to both rotation and acceleration. Several approaches exist that make it possible to separately measure the effects of acceleration and rotation. Two of the papers in this Special Issue, namely references [42,43], deal with such approaches. Specifically, reference [42] theoretically investigates a simplified approach for realizing a complete IMU employing the technique of point-source interferometry, employing atoms released from a magneto-optic trap. Reference [43] investigates experimentally technical challenges in realizing a gyroscope and accelerometer employing two counter-propagating MZIs, based on slow atomic beams.
Reference [42] investigates the use of large momentum transfer (LMT), realized via Raman transitions, to increase the sensitivity of the IMU. Calculations indicating the fundamental limits on the sensitivity and bandwidth that could be achieved in future experiments are shown. Reference [43] presents an experimental study in the context of a scheme where two counter-propagating slow atomic beams are to be used for realizing an accelerometer and a gyroscope. This study focused on characterizing the properties of one such beam, resulting from a 2D MOT, using co-propagating Raman excitations. They demonstrate that the beam can be operated in a continuous mode as well as pulsed mode. The longitudinal mean velocity and spread thereof were measured using a pulsed version of the atomic source, while the transverse velocity spread was determined by imaging of the fluorescence from the atomic beam. It is shown that, despite the residual longitudinal velocity spread and the fairly high transverse velocity spread, a robust interference signal in the form of Ramsey fringes is observable for co-propagating Raman transitions.
Matter wave interference in general has been demonstrated to be a powerful tool for precision measurement, and its sensitivity can be harnessed for testing the fundamental nature of quantum mechanics. To this end, this Issue covers two ends of the mass spectrum for the interfering particle, ranging from a single neutron [45] to dielectric nanospheres with masses of up to 10 8 atomic mass units [44].
In the former, Danner et al. [45] provide a review of a series of quantum optics experiments involving interferometry with single neutrons, where “double-slit” neutron diffraction is achieved with precisely fabricated crystalline silicon beamsplitters. The authors describe tests that rely on the principles of weak measurement to examine the “quantum Cheshire Cat” effect in some variants, where the neutron’s presence in the paths of the interferometer can appear to differ from the presence of its spin (i.e., it appears as if the neutron follows one path while its spin follows another, in analogy to a cat being separate from its grin in Lewis Carroll’s 1865 book, Alice’s Adventures in Wonderland). Also described in the review is the direct test of a commutation relation. All results of the experiments described confirm the predictions of quantum theory, however counter-intuitive they may be.
At the opposite end of the mass spectrum, Wardak et al. [44] describe protocols to achieve Talbot–Lau diffraction of silica nanospheres of sizes ranging from 10 6 to 10 8 atomic mass units. The de Broglie wavelength of such massive objects is challengingly small for far-field diffraction double-slit experiments, so such massive objects instead can achieve matter wave interference through near-field effects such as the Talbot effect. The Talbot–Lau interferometer, based on this effect and the use of an additional grating to create wave packet coherence, has been used to achieve matter wave interference for sodium nanoparticles [1] of size of order 10 5 atomic mass units. Wardak et al. describe a novel “throw-and-catch” design, where cooled and trapped nanoparticles are launched vertically upward into a retro-reflected optical grating, and then measured on their return path downwards. Such experiments could pave the way for testing wave-particle duality, one of the hallmark features of quantum theory, at unprecedented superposition mass scales.
In practice, the sensitivity of atom interferometers is often limited by experimental imperfections and compromises. For example, atom interferometers on moving platforms will experience degraded pulse efficiencies due to factors such as vibrations that detune laser pulses from resonance via Doppler shifts and translate the laser beams so that they are no longer ideally aligned with the atoms. Even in the absence of vibrations, the intrinsic velocity spread of the atom cloud causes a corresponding spread in detunings, and the finite size of the cloud leads to a spread of laser intensities experienced by different parts of the cloud. Optimal control techniques provide a powerful toolbox for designing atom interferometers with increased robustness against such experimental challenges. Accordingly, interest in applying this toolbox to atom interferometry continues to grow, with applications ranging from inertial navigation to long-baseline atom interferometers [31,32,33,34,35,36,37,38,39,40].
Goerz et al. [46] employ optimal control theory to design beam splitter and mirror pulse waveforms that are especially robust against variations in the laser detuning and intensity. They simulate a full interferometer in which these pulses are combined with rapid adiabatic passage interactions that increase the momentum splitting up to 20 photon recoils. The simulations demonstrate that the incorporation of the optimized pulses, in place of basic Rabi π / 2 and π pulses, leads to a dramatic increase in fringe contrast.
In summary, this Special Issue brings together research that advances the forefront of matter wave interferometry across different areas: from large-baseline to compact sensors, from atoms to nanoparticles, and from fundamental to applied.

Conflicts of Interest

The authors declare no conflicts of interest.

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