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arXiv:2206.04088 · Physical Review Research

Catapulting towards massive and large spatial quantum superposition

Run Zhou, Ryan J. Marshman, Sougato Bose, Anupam Mazumdar

Published Dec 2, 2022• 35 citations
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Abstract

A large spatial quantum superposition of size $O(1\text{--}10)\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\text{m}$ for mass $m\ensuremath{\sim}{10}^{\ensuremath{-}17}\text{--}{10}^{\ensuremath{-}14}$ kg is required to probe the foundations of quantum mechanics and test the classical and quantum nature of gravity via entanglement in a laboratory. In this paper, we will show that it is possible to accelerate the two spin states of a macroscopic nanocrystal sourced by the inhomogeneous nonlinear magnetic field in a Stern-Gerlach-type setup. We will assume that the electronic spin can be embedded at the center of the nanocrystal, such as the nitrogen-vacancy (NV) center of diamond. Our analysis will be generic to any dopant or any material. We will show that we can create a desired superposition size within $1\text{--}2$ s by catapulting the trajectories of the two spin states with a modest magnetic field gradient and then recombine the trajectories for a coherent interference. We will show the demanding nature of the precision required in the magnetic field to recover a $99%$ spin coherence confidence level at the moment of interference.

DOI
10.1103/physrevresearch.4.043157

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A large spatial quantum superposition of size O(1–10)\ensuremathμmO(1\text{--}10)\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\text{m}O(1–10)\ensuremathμm for mass m\ensuremath∼10\ensuremath−17–10\ensuremath−14m\ensuremath{\sim}{10}^{\ensuremath{-}17}\text{--}{10}^{\ensuremath{-}14}m\ensuremath∼10\ensuremath−17–10\ensuremath−14 kg is required to probe the foundations of quantum mechanics and test the classical and quantum nature of gravity via entanglement in a laboratory. In this paper, we will show that it is possible to accelerate the two spin states of a macroscopic nanocrystal sourced by the inhomogeneous nonlinear magnetic field in a Stern-Gerlach-type setup. We will assume that the electronic spin can be embedded at the center of the nanocrystal, such as the nitrogen-vacancy (NV) center of diamond. Our analysis will be generic to any dopant or any material. We will show that we can create a desired superposition size within 1–21\text{--}21–2 s by catapulting the trajectories of the two spin states with a modest magnetic field gradient and then recombine the trajectories for a coherent interference. We will show the demanding nature of the precision required in the magnetic field to recover a 9999%99 spin coherence confidence level at the moment of interference.
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 Creating a massive spatial quantum superposition, such as the Schrödinger cat state, where the mass and the superposition size within the range 10−19 − 10−14 kg and Δx ∼ 10 nm − 100 μm, is a challenging task. The methods employed so far rely either on wavepacket expansion or on a quantum ancilla, e.g. single spin dependent forces, which scale inversely with mass. In this paper, we present a novel approach that combines gravitational acceleration and diamagnetic repulsion to generate a large spatial superposition in a relatively short time. After first creating a modest initial spatial superposition of 1 μm, achieved through techniques such as the Stern–Gerlach (SG) apparatus, we will show that we can achieve an ∼102−103 fold improvement to the spatial superposition size (1 μm → 980 μm) between the wave packets in less than 0.02 s by using the Earth’s gravitational acceleration and then the diamagnetic repulsive scattering of the nanocrystal, neither of which depend on the object mass. Finally, the wave packet trajectories can be closed so that spatial interference fringes can be observed. Our findings highlight the potential of combining gravitational acceleration and diamagnetic repulsion to create and manipulate large spatial superpositions, offering new insights into creating macroscopic quantum superpositions.
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)TO(10\text{--}100)\phantom{\rule{0.16em}{0ex}}\mathrm{T}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.
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.
This thesis explores how to create macroscopic matter-wave interferometers (MMWIs) using nanodiamonds with nitrogen-vacancy (NV) centers. MMWIs are important for testing the limits of quantum mechanics and studying the possible quantum nature of gravity. However, building MMWIs with large masses is very challenging because of decoherence and the diamagnetic properties of diamonds. This work presents several experimental schemes to increase the spatial separation of massive quantum objects. The key idea is to use the diamagnetism of diamonds not only as a limitation but also as a tool to help separate wave packets. Methods include catapulting trajectories with nonlinear magnetic fields, using diamagnetic repulsion, combining gravitational acceleration with magnetic fields, and applying inverted harmonic potentials. The results show that it is possible to achieve large spatial superpositions, up to tens of micrometers, in short timescales. While a full-scale MMWI is still difficult to realize, these findings may contribute to future efforts to observe quantum effects in macroscopic systems.