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arXiv:2105.01094 · Physical Review Research

Constructing nano-object quantum superpositions with a Stern-Gerlach interferometer

Ryan J. Marshman, Anupam Mazumdar, R. Folman, Sougato Bose

Published May 2, 2022• 57 citations
arXivHTMLPDF

Abstract

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 $O(10\text{--}100)\phantom{\rule{0.16em}{0ex}}\mathrm{T}$ ${\mathrm{m}}^{\ensuremath{-}1}$ 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.

DOI
10.1103/physrevresearch.4.023087

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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 m\ensuremath−1{\mathrm{m}}^{\ensuremath{-}1}m\ensuremath−1 to construct a large spatial superposition of O(10\ensuremath−4–10\ensuremath−8)mO({10}^{\ensuremath{-}4}\text{--}{10}^{\ensuremath{-}8})\phantom{\rule{0.16em}{0ex}}\mathrm{m}O(10\ensuremath−4–10\ensuremath−8)m for O(10\ensuremath−17–10\ensuremath−14)kgO({10}^{\ensuremath{-}17}\text{--}{10}^{\ensuremath{-}14})\phantom{\rule{0.16em}{0ex}}\mathrm{kg}O(10\ensuremath−17–10\ensuremath−14)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 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 1–21\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.
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.
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.
Quantum mechanics (QM) and General relativity (GR), also known as the theory of gravity, are the two pillars of modern physics. A matter-wave interferometer with a massive particle can test numerous fundamental ideas, including the spatial superposition principle - a foundational concept in QM - in previously unexplored regimes. It also opens the possibility of probing the interface between QM and GR, such as testing the quantization of gravity. Consequently, there exists an intensive effort to realize such an interferometer. While several approaches are being explored, we focus on utilizing nanodiamonds with embedded spins as test particles which, in combination with Stern-Gerlach forces, enable the realization of a closed-loop matter-wave interferometer in space-time. There is a growing community of groups pursuing this path [1]. We are posting this technical note (as part of a series of seven such notes), to highlight our plans and solutions concerning various challenges in this ambitious endeavor, hoping this will support this growing community. Here we discuss the design considerations for a high-precision enhanced-coherence nanodiamond source, review the fabrication processes used to produce nanodiamond pillars measuring 40 x 65 x 80 nm, summarize the characterization work completed to date, and conclude with an outlook on the remaining steps needed to finalize the source fabrication. We would be happy to make available more details upon request.
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.