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arXiv:2312.05170

Large Spin Stern-Gerlach Interferometry for Gravitational Entanglement

Lorenzo Braccini, Martine Schut, Alessio Serafini, Anupam Mazumdar, Sougato Bose

Published Dec 8, 2023• 0 citations
arXivHTMLPDF

Abstract

Recently, there has been a proposal to test the quantum nature of gravity in the laboratory by witnessing the growth of entanglement between two masses in spatial quantum superpositions. The required superpositions can be created via Stern-Gerlach interferometers, which couple an embedded spin qubit quantum state to the spatial dynamics of each mass. The masses would entangle only if gravity is quantum in nature. Here, we generalise the experiment to an arbitrary spin $j$ or equivalently to an ensemble of uniformly coupled spins. We first exemplify how to create a generalized Stern-Gerlach interferometer, which splits the mass into $2j+1$ trajectories. This shows that a controlled protocol can be formulated to encode the amplitudes of any spin state to a spatial superposition. Secondly, two masses in spatial superpositions of the above form are left to interact via gravity, and the entanglement is computed. Different families of initial spin states are varied to find the optimal spin state that maximizes the entanglement. We conclude that larger spins can offer a modest advantage in enhancing gravity-induced entanglement.

DOI
10.48550/arxiv.2312.05170

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Recently, there has been a proposal to test the quantum nature of gravity in the laboratory by witnessing the growth of entanglement between two masses in spatial quantum superpositions. The required superpositions can be created via Stern-Gerlach interferometers, which couple an embedded spin qubit quantum state to the spatial dynamics of each mass. The masses would entangle only if gravity is quantum in nature. Here, we generalise the experiment to an arbitrary spin jjj or equivalently to an ensemble of uniformly coupled spins. We first exemplify how to create a generalized Stern-Gerlach interferometer, which splits the mass into 2j+12j+12j+1 trajectories. This shows that a controlled protocol can be formulated to encode the amplitudes of any spin state to a spatial superposition. Secondly, two masses in spatial superpositions of the above form are left to interact via gravity, and the entanglement is computed. Different families of initial spin states are varied to find the optimal spin state that maximizes the entanglement. We conclude that larger spins can offer a modest advantage in enhancing gravity-induced entanglement.
Abstract We investigate the generation rate of the quantum entanglement in a system composed of multiple massive particles with large spin, where the mass of a single particle can be split into multiple trajectories by a generalized Stern–Gerlach interferometer. Taking the coherent spin states as the initial state and considering the gravitational interaction due to Newtonian potential, we compute the generation rate of the entanglement for different configurations of the setup. Explicitly, the optimal polar angles of the spin are found numerically for systems with three and four particles, respectively. We conclude that the amount of the entanglement increases with the number of particles as well as the spin, and the configuration of the prism with a particle at the center generates the best rate of the entanglement.
Abstract Witnessing the quantum nature of gravity through the entanglement of two masses has recently been proposed. Both non-Gaussian and Gaussian protocols have been shown to be useful for this purpose. In non-Gaussian protocols the complete 1 / r gravitational interaction can in principle be utilized for entanglement generation, as long as quantum superpositions of a spatial splitting Δ x comparable to the distance d between two masses can be generated. In practice, however, all non-Gaussian protocols proposed to date rely on embedded qubits—typically spins—to read out the entanglement: spin correlations are used to witness the entanglement developed between the masses during interferometry. Here we show that if superpositions of distinct spatially localized states of each mass can be created, then a spinless version of the non-Gaussian protocol is possible: simple position correlation measurements alone can yield a spatial qubit witness of the entanglement between the masses. We find that the principal new requirement for the viability of this protocol is a position squeezing of the wavefunction by approximately seven orders of magnitude, applied at a specific stage of the experiment.
The quantum gravity-induced entanglement of masses (QGEM) protocol for testing quantum gravity using entanglement witnessing utilizes the creation of spatial quantum superpositions of two neutral, massive matter-wave interferometers kept adjacent to each other, separated by a distance d . The mass and the spatial superposition should be such that the two quantum systems can entangle solely via the quantum nature of gravity. Despite being charge-neutral, many electromagnetic backgrounds can also entangle the systems such as the dipole-dipole and Casimir-Polder interactions. To minimize electromagnetic-induced interactions between the masses, it is pertinent to isolate the two superpositions by a conducting plate. However, the conducting plate will also exert forces on the masses and hence the trajectories of the two superpositions would be affected. To minimize this effect, we propose to trap the two interferometers such that the trapping potential dominates over the attraction between the conducting plate and the matter-wave interferometers. The superpositions can still be created via the Stern-Gerlach effect in the direction parallel to the plate, where the trapping potential is negligible. The combination of trapping and shielding provides a better parameter space for the parallel configuration of the experiment, where the requirement on the size of the spatial superposition, to witness the entanglement between the two masses purely due to their quantum nature of gravity, decreases by at least two orders of magnitude as compared to the original protocol paper. Published by the American Physical Society 2024
A key open problem in physics is the correct way to combine gravity (described by general relativity) with everything else (described by quantum mechanics). This problem suggests that general relativity and possibly also quantum mechanics need fundamental corrections. Most physicists expect that gravity should be quantum in character, but gravity is fundamentally different to the other forces because it alone is described by spacetime geometry. Experiments are needed to test whether gravity, and hence space-time, is quantum or classical. We propose an experiment to test the quantum nature of gravity by checking whether gravity can entangle two micron-sized crystals. A pathway to this is to create macroscopic quantum superpositions of each crystal first using embedded spins and Stern-Gerlach forces. These crystals could be nanodiamonds containing nitrogen-vacancy (NV) centres. The spins can subsequently be measured to witness the gravitationally generated entanglement. This is based on extensive theoretical feasibility studies and experimental progress in quantum technology. The eventual experiment will require a medium-sized consortium with excellent suppression of decoherence including vibrations and gravitational noise. In this white paper, we review the progress and plans towards realizing this. While implementing these plans, we will further explore the most macroscopic superpositions that are possible, which will test theories that predict a limit to this.
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 analytically solve the entangling quantum dynamics of two interacting Stern-Gerlach Interferometers~(SGI). Each SGI exploits an operator-valued force applied by a qubit to create and recombine a non-Gaussian state of matter. The entangling phase between the two qubits generated by the leading-order gravitational interaction of the massive degrees of freedom is found to be mass-independent, both for unitary and open dynamics, irrespective of the temperature and squeezing of the initial states. Further, we show that the solution of the four interferometric paths reveals that the mere presence of the interaction does not allow for a perfect recombination of the centre of mass. This second-order effect, alongside higher-order interaction terms, can be used to bound the mass from above and below, thus restricting the experiment's regime to mesoscopic masses. By solving the open dynamics which includes diffusion and dephasing with initial squeezed thermal states, the bounds are tightened by the inclusion of realistic experimental noise. We discuss diamagnetic levitated masses with embedded NV-centres as a specific physical implementation.