Many different formalisms exist for computing the phase of a matter-wave interferometer. However, it can be challenging to develop physical intuition about what a particular interferometer is actually measuring or about whether a given classical measurement provides equivalent information. Here, we investigate the physical content of the interferometer phase through a series of thought experiments. In low-order potentials, a matter-wave interferometer with a single internal state provides the same information as a sum of position measurements of a classical test object. In high-order potentials, the interferometer phase becomes decoupled from the motion of the interferometer arms, and the phase contains information that cannot be obtained by any set of position measurements on the interferometer trajectory. This phase shift in a high-order potential fundamentally distinguishes matter-wave interferometers from classical measuring devices.
Many different formalisms exist for computing the phase of a matter-wave interferometer. However, it can be challenging to develop physical intuition about what a particular interferometer is actually measuring or about whether a given classical measurement provides equivalent information. Here, we investigate the physical content of the interferometer phase through a series of thought experiments. In low-order potentials, a matter-wave interferometer with a single internal state provides the same information as a sum of position measurements of a classical test object. In high-order potentials, the interferometer phase becomes decoupled from the motion of the interferometer arms, and the phase contains information that cannot be obtained by any set of position measurements on the interferometer trajectory. This phase shift in a high-order potential fundamentally distinguishes matter-wave interferometers from classical measuring devices.
We introduce a new theoretical framework based on Feynman diagrams to compute phase shifts in matter wave interferometry. The method allows for analytic computation of higher order quantum corrections, beyond the traditional semi-classical approximation. These additional terms depend on the finite size of the initial matter wavefunction and/or have higher order dependence on ℏ. We apply the method to compute the response of matter wave interferometers to power law potentials and potentials with an arbitrary spatial dependence. The analytic expressions are validated by comparing to numerical simulations, and estimates are provided for the scale of the quantum corrections to the phase shift response to the gravitational field of the earth, anharmonic trapping potentials, and gravitational fields from local proof masses. We also find that for certain experimentally feasible parameters, these corrections are large enough to be measured and could lead to systematic errors if they are not mitigated. We find that to first order in a spatially dependent potential, quantum corrections vanish when the initial matter wavepacket has spherical symmetry and the potential satisfies Laplace's equation. We anticipate these quantum corrections will be especially important for trapped matter wave interferometers and for free-space matter wave interferometers in the presence of proof masses. These interferometers are becoming increasingly sensitive tools for mobile inertial sensing, gravity surveying, tests of gravity and its interplay with quantum mechanics, and searches for dark energy.
The wave-particle duality is a key concept of quantum physics and extending quantum superpositions to bodies of increasing mass and complexity has become a key goal to numerous research groups. Such experiments are motivated by the desire to probe and better understand the quantum-classical interface in advanced tests of spontaneous or gravity-induced wave function collapse and in the search for non-linear modifications of quantum theory. High mass interferometry has been proposed to serve in the search for light dark matter via weak recoil decoherence as well as in tests of the weak equivalence principle by comparing a large variety of quantum systems with very distinct internal composition, excitation, mass, shape or angular momentum. Here we discuss the experimental state of the art in high-mass matter-wave interferometry, as well as new perspectives from cluster and nanoparticle physics to push quantum superpositions by 3 to 4 orders of magnitude in mass or up to 6 orders of magnitude in 'macroscopicity'. We discuss different near-field interferometer configurations that shall become useful in near-future demonstrations of quantum phenomena with objects as diverse as proteins, metal clusters and dielectric nanoparticles.
We discuss new de Broglie coherence experiments in a near-field molecule interferometer with a variety of large organic molecules. While de Broglie coherence is to first order only associated with the center-of-mass motion of the diffracted particle, we here investigate the question as to which extent the internal molecular property is relevant for, compatible with or detrimental for maintaining coherence in the translational degree of freedom. External perturbations, such as inhomogeneous external electric fields, may influence the delocalized molecules inside the matter wave interferometer and they allow us to access the molecular polarizabilities, permanent or even fluctuating electric dipole moments. We extract information about the molecular states from the interference phase shifts as well as from the observed dephasing in a Kapitza-Dirac Talbot-Lau-Stark-deflectometer. We discuss the relevance of our experiments with regard to both molecule metrology and the foundations of quantum mechanics, i.e. the preservation of coherence for highly complex particles in external fields.
Matter-wave interferometers, either with electrons, atoms or molecules, owe their sensitivity to the accuracy of phase-shift measurements. One may, however, raise the question whether the shift undergone by interference fringes, when external forces are applied, actually differs from the shift of classical trajectories. For the case of a magnetic perturbation, we provide experimental evidence and a vector demonstration that interference patterns only undergo a global shift. The experiment is performed with the photodetachment microscope, with a uniform magnetic field superimposed over the whole volume accessible to the interfering electron. Identity of the fringe and trajectory shifts is established for any two-wave interferometer using charged particles, submitted to a magnetic field.
The interference of waves, be they photons, atoms, or electrons, and the measured phase shift induced as the waves take a different route around the arms of an interferometer are widely used in applications ranging from global positioning systems and gravity wave detectors down to the more mundane characterization of optical materials. The sensitivity of the interferometer in measuring the phase shift is affected by noise contributions to the signal. To combat this noise, piezoelectric actuators are typically used to adjust the system to an optimum measuring point for maximum sensitivity. This approach has drawbacks, however, for certain applications where the determination of arbitrary phase shifts is important. Pezzé et al. introduce a method and protocol of photon counting at the output paths to determine the phase. They show that the classical, or thermal, noise can be eliminated without bias (i.e., no tinkering with the phase shift is necessary). At this quantum limit, only quantum uncertainty affects the precision of the phase measurement. — ISO
Very Long Baseline Atom Interferometry (VLBAI) corresponds to ground-based atomic matter-wave interferometry on large scales in space and time, letting the atomic wave functions interfere after free evolution times of several seconds or wave packet separation at the scale of meters. As inertial sensors, e.g., accelerometers, these devices take advantage of the quadratic scaling of the leading order phase shift with the free evolution time to enhance their sensitivity, giving rise to compelling experiments. With shot noise-limited instabilities better than 10−9 m/s2 at 1 s at the horizon, VLBAI may compete with state-of-the-art superconducting gravimeters, while providing absolute instead of relative measurements. When operated with several atomic states, isotopes, or species simultaneously, tests of the universality of free fall at a level of parts in 1013 and beyond are in reach. Finally, the large spatial extent of the interferometer allows one to probe the limits of coherence at macroscopic scales as well as the interplay of quantum mechanics and gravity. We report on the status of the VLBAI facility, its key features, and future prospects in fundamental science.