We analyze the fundamental coherence limit of a nano-object with an embedded spin in a Stern-Gerlach interferometer. This limit stems from the which-path information provided by the object's rotational degrees of freedom due to the evolution of their quantum uncertainty. We show that such interferometry is straightforward in a weak magnetic field and short duration. Large wave packet separation is made possible with proper fine-tuning over long durations. This opens the door to fundamental tests of quantum theory and quantum gravity. The results and conclusions are extendable to any type of interferometry with complex objects.
We analyze the fundamental coherence limit of a nano-object with an embedded spin in a Stern-Gerlach interferometer. This limit stems from the which-path information provided by the object's rotational degrees of freedom due to the evolution of their quantum uncertainty. We show that such interferometry is straightforward in a weak magnetic field and short duration. Large wave packet separation is made possible with proper fine-tuning over long durations. This opens the door to fundamental tests of quantum theory and quantum gravity. The results and conclusions are extendable to any type of interferometry with complex objects.
Realizing a spatial superposition with massive objects is one of the most fundamental challenges, as it will test quantum theory in new regimes, probe quantum-gravity, and enable to test exotic theories like gravitationally induced collapse. A natural extension of the successful implementation of an atomic Stern-Gerlach interferometer (SGI), is a SGI with a nano-diamond (ND) in which a single spin is embedded in the form of a nitrogen-vacancy center (NV). As the ND rotation, and with it the rotation of the NV spin direction, may inhibit such a realization, both in terms of Newtonian trajectories and quantum phases, we analyze here the role of rotations in the SGI. We take into account fundamental limits, such as those imposed by the quantum angular uncertainty relation and thermal fluctuations. We provide a detailed recipe for which a superposition of massive objects is enabled. This may open the door not only to fundamental tests, but also to new forms of quantum technology.
We discuss the coherent splitting and recombining of a nanoparticle in a mesoscopic “closed-loop” Stern–Gerlach interferometer in which the observable is the spin of a single impurity embedded in the particle. This spin, when interacting with a pulsed magnetic gradient, generates the force on the particle. We calculate the internal decoherence, which arises as the displaced impurity excites internal degrees of freedom (phonons) that may provide WelcherWeg information and preclude interference. We estimate the constraints this decoherence channel puts on future interference experiments with massive objects. We find that for a wide range of masses, forces, and temperatures, phonons do not inhibit Stern–Gerlach interferometry with micro-scale objects. However, phonons do constitute a fundamental limit on the splitting of larger macroscopic objects if the applied force induces phonons.
Stern-Gerlach and/or matter-wave interferometry has garnered significant interest amongst members of the scientific community over the past few decades. Early theoretical results by Schwinger et al. demonstrate the fantastic precision capabilities required to realize a full-loop Stern-Gerlach interferometer, i.e., a Stern-Gerlach setup that houses the capability of recombining the split wave-packets in both, position and momentum space over a certain characteristic interferometric time. Over the years, several proposals have been put forward that seek to use Stern-Gerlach and/or matter-wave interferometry as a tool for a myriad of applications of general interest, some of which include tests for fundamental physics (viz., quantum wave-function collapse, stringent tests for the Einstein equivalence principle at the quantum scale, breaking the Standard Quantum Limit (SQL) barrier, and so forth), precision sensing, quantum metrology, gravitational wave detection and inertial navigation. In addition, a large volume of work in the existing literature has been dedicated to the possibility of using matter-wave interferometry for tests of quantum gravity. Inspired by the developments in this timely research field, this Perspective attempts to provide a general overview of the theory involved, the challenges that are yet to be addressed and a brief outlook on what lays ahead.
The Stern-Gerlach effect, found a century ago, has become a paradigm of quantum mechanics. Unexpectedly, until recently, there has been little evidence that the original scheme with freely propagating atoms exposed to gradients from macroscopic magnets is a fully coherent quantum process. Several theoretical studies have explained why a Stern-Gerlach interferometer is a formidable challenge. Here, we provide a detailed account of the realization of a full-loop Stern-Gerlach interferometer for single atoms and use the acquired understanding to show how this setup may be used to realize an interferometer for macroscopic objects doped with a single spin. Such a realization would open the door to a new era of fundamental probes, including the realization of previously inaccessible tests at the interface of quantum mechanics and gravity.
The Stern-Gerlach effect, found a century ago, has become a paradigm of quantum mechanics. Unexpectedly, until recently, there has been little evidence that the original scheme with freely propagating atoms exposed to gradients from macroscopic magnets is a fully coherent quantum process. Several theoretical studies have explained why a Stern-Gerlach interferometer is a formidable challenge. Here, we provide a detailed account of the realization of a full-loop Stern-Gerlach interferometer for single atoms and use the acquired understanding to show how this setup may be used to realize an interferometer for macroscopic objects doped with a single spin. Such a realization would open the door to a new era of fundamental probes, including the realization of previously inaccessible tests at the interface of quantum mechanics and gravity.
Probing quantum mechanics and quantum aspects of general relativity, along with the sensing and constraining of classical gravity, can all be enabled by unprecedented spatial sizes of superpositions of massive objects. In this paper, we show that there is a feasible setup sourced by realizable magnetic field gradients O(10–100)T ${\mathrm{m}}^{\ensuremath{-}1}$ to construct a large spatial superposition of $O({10}^{\ensuremath{-}4}\text{--}{10}^{\ensuremath{-}8})\phantom{\rule{0.16em}{0ex}}\mathrm{m}$ for $O({10}^{\ensuremath{-}17}\text{--}{10}^{\ensuremath{-}14})\phantom{\rule{0.16em}{0ex}}\mathrm{kg}$ masses within a time of up to 0.1--10 seconds. The scale of superpositions is unrestricted as long as quantum coherence can be maintained for a required amount of time.