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Register a new userComplementarity and uncertainty relations for matter wave interferometry
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We establish a rigorous quantitative connection between (i) the interferometric duality relation for which-way information and fringe visibility and (ii) Heisenbergs uncertainty relation for position and modular momentum. We apply our theory to atom interferometry, wherein spontaneously emitted photons provide which way information, and unambiguously resolve the challenge posed by the metamaterial `perfect lens to complementarity and to the Heisenberg-Bohr interpretation of the Heisenberg microscope thought experiment.
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Uncertainty relations and complementarity relations are core issues in quantum mechanics and quantum information theory. By use of the generalized Wigner-Yanase-Dyson (GWYD) skew information, we derive several uncertainty and complementarity relations with respect to mutually unbiased measurements (MUMs), and general symmetric informationally complete positive operator valued measurements (SIC-POVMs), respectively. Our results include some existing ones as particular cases. We also exemplify our results by providing a detailed example.
Matter-wave interferometry provides a remarkably sensitive tool for probing minute forces and, potentially, the foundations of quantum physics by making use of interference between spatially separated matter waves. Furthering this development requires ever-increasing stability of the interferometer, typically achieved by improving its physical isolation from the environment. Here we introduce as an alternative strategy the concept of dynamical decoupling applied to spatial degrees of freedom of massive objects. We show that the superposed matter waves can be driven along paths in space that render their superposition resilient to many important sources of noise. As a concrete implementation, we present the case of matter-wave interferometers in a magnetic field gradient based on either levitated or free-falling nanodiamonds hosting a color center. We present an in-depth analysis of potential sources of decoherence in such a setup and of the ability of our protocol to suppress them. These effects include gravitational forces, interactions of the net magnetic and dipole moments of the diamond with magnetic and electric fields, surface dangling bonds, rotational degrees of freedom, Casimir-Polder forces, and diamagnetic forces. Contrary to previous analyses, diamagnetic forces are not negligible in this type of interferometers and, if not acted upon lead to small separation distances that scale with the inverse of the magnetic field gradient. We show that our motional dynamical decoupling strategy renders the system immune to such limitations while continuing to protect its coherence from environmental influences, achieving a linear-in-time growth of the separation distance independent of the magnetic field gradient. Hence, motional dynamical decoupling may become an essential tool in driving the sensitivity of matter-wave interferometry to the next level.
Starting from an elementary model and refining it to take into account more realistic effects, we discuss the limitations and advantages of matter-wave interferometry in different configurations. We focus on the possibility to apply this approach to scenarios involving antimatter, such as positrons and positronium atoms. In particular, we investigate the Talbot-Lau interferometer with material gratings and discuss in details the results in view of the possible experimental verification.
We analyze Einsteins recoiling slit experiment and point out that the inevitable entanglement between the particle and the recoiling-slit was not part of Bohrs reply. We show that if this entanglement is taken into account, one can provided a simpler answer to Einstein. We also derive the Englert-Greenberger-Yasin duality relation from this entanglement. In addition, we show that the Englert-Greenberger-Yasin duality relation can also be thought of as a consequence of the sum uncertainty relation for certain observables of the recoiling slit. Thus, the uncertainty relations and entanglement are both an integral part of the which-way detection process.
Matter-wave interferometry with solids is highly susceptible to minute fluctuations of environmental fields, including gravitational effects from distant sources. Hence, experiments require a degree of shielding that is extraordinarily challenging to achieve in realistic terrestrial or even space-based set-ups. Here, we design protocols that exploit the spatial correlations that are inherent in perturbations due to distant sources to reduce significantly their impact on the visibility of interference patterns. We show that interference patterns that are robust to such type of noise can be encoded in the joint probability distribution of two or more interferometers, provided that these are initialized in suitable states. We develop a general framework that makes use of N+1 interferometers that may differ in their masses to correct for environmental potential fields up to order N in their multipole expansion. Remarkably, our approach works for fields that fluctuate stochastically in any time scale and does not require the presence of quantum correlations among the different interferometers. Finally, we also show that the same ideas can be extended to the protection of entanglement between pairs of interferometers.
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