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Large Splitting Massive Schrödinger Kittens

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

Published May 5, 2021• 1 citation
OpenAlex

Abstract

Probing quantum mechanics, quantum aspects of general relativity along with the sensing and the 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 ${\cal O}(10-100)$ Tm$^{-1}$ to construct a large spatial superposition of ${\cal O}(10^{-4}-10^{-8})$ m for masses ${\cal O}(10^{-16}-10^{-14})$ kg over a time period of up to $0.1-10$ seconds.

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

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Placing a large mass in a large spatial superposition, such as a Schr\"odinger cat state, is a significant and important challenge. In particular, the large spatial superposition $[O(10--100)\phantom{\rule{4pt}{0ex}}\textmu{}\mathrm{m}]$ of mesoscopic masses $[m\ensuremath{\sim}O({10}^{\ensuremath{-}14}--{10}^{\ensuremath{-}15})\phantom{\rule{0.16em}{0ex}}\mathrm{kg}]$ makes it possible to test the quantum nature of gravity via entanglement in the laboratory. To date, the proposed methods of achieving this spatial delocalization are to use wave-packet expansions or quantum ancilla- (for example, spin-) dependent forces, all of whose efficacy reduces with mass. Thus increasing the spatial splitting independently of the mass is an important open challenge. In this paper we present a method of achieving a mass-independent enhancement of superposition via diamagnetic repulsion from current-carrying wires. We analyze an example system which uses the Stern-Gerlach effect to creating a small initial splitting and then apply our diamagnetic repulsion method to enhance the superposition size $O(400--600)\phantom{\rule{4pt}{0ex}}\textmu{}\mathrm{m}$ from an initial modest split of the wave function. We provide an analytical and numerical analysis of our scheme.

arXiv:2210.05689•Physical Review A•Mar 16, 2023•26 citations
Probing quantum mechanics, quantum aspects of general relativity along with the sensing and the 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){\cal O}(10-100)O(10−100) Tm−1^{-1}−1 to construct a large spatial superposition of O(10−4−10−8){\cal O}(10^{-4}-10^{-8})O(10−4−10−8) m for masses O(10−16−10−14){\cal O}(10^{-16}-10^{-14})O(10−16−10−14) kg over a time period of up to 0.1−100.1-100.1−10 seconds.
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 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.
Macroscopic quantum superpositions of massive objects are very interesting as they have several potential applications, ranging from the exploration of the interaction of gravity with quantum mechanics to quantum sensing. In this article, we propose two related schemes to prepare a spatial superposition of massive quantum oscillator systems with a high Q factor via a superposition of magnetic forces. In the first method, we propose a large spatial superposition of a levitated spherical magnet generated via magnetic forces applied by adjacent flux qubits. We find that in this method the spatial superposition extent Δ z is independent of the size of the particle. In the second method, we propose a large spatial superposition of a magnetically levitated flux qubit, generated via our driving the levitated qubit inductively. In both schemes, we show that ultralarge superpositions Δ z / δ z ZPM ∼ 10 4 – 10 6 are possible, where δ z ZPM is the zero-point motional extent.
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.
It has been a long-standing goal to bring massive objects into a superposition of different locations in real space, not only to confirm quantum theory in new regimes, but also to explore the interface with gravity. The main challenge is usually thought to arise from forces or scattering due to environmental fields and particles that decohere the large object's wave function into a statistical mixture. We unveil a decoherence channel which cannot be eliminated by improved isolation from the environment. It originates from sound waves within the object, which are excited as part of any splitting process and carry partial information. This puts stringent constraints on future spatial superpositions of large objects. Published by the American Physical Society 2024
Placing a large mass in a large spatial superposition, such as a Schr\"odinger cat state, is a significant and important challenge. In particular, the large spatial superposition $[O(10--100)\phantom{\rule{4pt}{0ex}}\textmu{}\mathrm{m}]$ of mesoscopic masses $[m\ensuremath{\sim}O({10}^{\ensuremath{-}14}--{10}^{\ensuremath{-}15})\phantom{\rule{0.16em}{0ex}}\mathrm{kg}]$ makes it possible to test the quantum nature of gravity via entanglement in the laboratory. To date, the proposed methods of achieving this spatial delocalization are to use wave-packet expansions or quantum ancilla- (for example, spin-) dependent forces, all of whose efficacy reduces with mass. Thus increasing the spatial splitting independently of the mass is an important open challenge. In this paper we present a method of achieving a mass-independent enhancement of superposition via diamagnetic repulsion from current-carrying wires. We analyze an example system which uses the Stern-Gerlach effect to creating a small initial splitting and then apply our diamagnetic repulsion method to enhance the superposition size $O(400--600)\phantom{\rule{4pt}{0ex}}\textmu{}\mathrm{m}$ from an initial modest split of the wave function. We provide an analytical and numerical analysis of our scheme.