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arXiv:2609.12124

Evidencing Macroscopic Quantum Coherence using Confined Uniform Magnetic Field

Dipankar Home, Harsh Talwar, Nilaj Saha, Sougato Bose, Arka Banerjee

quant-phSubmitted Sep 10, 2026• Announced Sep 14, 2026• 0 citations
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Abstract

A previously unexplored scheme is devised for creating and certifying coherent quantum superposition of distinctly separated states of a spin-tagged massive object passing through a confined uniform magnetic field. This results in entangling the spatial and spin parts of a two-component Pauli wavefunction such that the entailed coherence can be conveniently certified by spin measurements alone. The implementability of this scheme is analysed using NV-centre nanodiamonds of masses $\sim 10^{10}$ amu based on the current technological capabilities.

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Quantum superposition on nano-mechanical oscillator

Wan, Chuanqi

The probing of the quantum nature of a macroscopic object is an open problem. Approaches in preparing quantum superposition towards a larger scale, which has been progressively accessible in a variety of experimental implementations, may detect new physics or extend the boundary of quantum theory. Development on a nano-mechanical system in the framework of quantum optics and information theory has opened new research directions. It paves ways to manipulate the wavefunction of a massive particle over a large spatial range and probe its quantum behavior to an unprecedented precision. In this thesis, quantum superposition on a mechanical system is studied theoretically in the light of possible implementations under current techniques in order to test superposition principle and the quantum nature of gravity in the mesoscopic region. The work includes two lines of study. In the first line, the motion of the center of mass (c.m.) of the mechanical system is coupled to its internal spin system magnetically, and a Ramsey scheme is developed based on coherent spin control. The wavepacket of the test object, under a spin-dependent force, may then be delocalized to a macroscopic scale. A gravity induced dynamical phase (accrued solely on the spin state, and measured through a Ramsey scheme) is used to reveal the above spatially delocalized superposition of the spin-nano-object composite system that arises during the scheme. A remarkable immunity to the motional noise in the c.m. (initially in a thermal state with moderate cooling) and also a dynamical decoupling nature of the scheme itself is revealed. A careful examination of the perturbation effect due to setup imperfection and environment-induced decoherence is performed, which shows that the Ramsey fringes have a high tolerance on those unwanted faults under realistic experimental conditions. The scheme also facilitates a gravimetry protocol that potentially could be developed for a novel on-chip gravimeter with a precision of $10^{-6}g/\sqrt{\text{Hz}}$. In the second line, an opto-mechanical experiment is proposed to entangle the motion of two mechanical oscillators through their mutual gravitational interaction. The feasibility of such an experiment is critically examined within the framework of cavity optomechanics. It is shown that within the decoherence time of mechanical noise and potentially gravitational induced state collapse, entanglement between mirrors could be obtained when the initial state of the cavity field is prepared in some particular states. Strategies that give enhancement to entanglement generation rate are studied in light of quantum estimation theory. It is shown that for a cavity initially in a coherent state, the resulting entanglement generation rate would be enhanced linearly with the amplitude of the coherent state. Lastly, it shows that in the proposed setup Casimir effect would significantly affect the gravity-induced entanglement. A proper shield can eliminate the detrimental effect of Casimir force, which, however, will constrain the closest distance between the mirrors in its implementation.

•Oct 1, 2017•7 citations
A previously unexplored scheme is devised for creating and certifying coherent quantum superposition of distinctly separated states of a spin-tagged massive object passing through a confined uniform magnetic field. This results in entangling the spatial and spin parts of a two-component Pauli wavefunction such that the entailed coherence can be conveniently certified by spin measurements alone. The implementability of this scheme is analysed using NV-centre nanodiamonds of masses ∼1010\sim 10^{10}∼1010 amu based on the current technological capabilities.
We propose an interferometric scheme based on an untrapped nano-object subjected to gravity. The motion of the center of mass (c.m.) of the free object is coupled to its internal spin system magnetically, and a free flight scheme is developed based on coherent spin control. The wave packet of the test object, under a spin-dependent force, may then be delocalized to a macroscopic scale. A gravity induced dynamical phase (accrued solely on the spin state, and measured through a Ramsey scheme) is used to reveal the above spatially delocalized superposition of the spin-nano-object composite system that arises during our scheme. We find a remarkable immunity to the motional noise in the c.m. (initially in a thermal state with moderate cooling), and also a dynamical decoupling nature of the scheme itself. Together they secure a high visibility of the resulting Ramsey fringes. The mass independence of our scheme makes it viable for a nano-object selected from an ensemble with a high mass variability. Given these advantages, a quantum superposition with a 100 nm spatial separation for a massive object of 10^{9} amu is achievable experimentally, providing a route to test postulated modifications of quantum theory such as continuous spontaneous localization.
An open challenge in physics is to expand the frontiers of the validity of quantum mechanics by evidencing nonclassicality of the centre of mass state of a macroscopic object. Yet another equally important task is to evidence the essential nonclassicality of the interactions which act between macroscopic objects. Here we introduce a new tool to meet these challenges: massive spatial qubits. In particular, we show that if two distinct localized states of a mass are used as the ∣0⟩|0\rangle∣0⟩ and ∣1⟩|1\rangle∣1⟩ states of a qubit, then we can measure this encoded spatial qubit with a high fidelity in the σx,σyσ_x, σ_yσx​,σy​ and σzσ_zσz​ bases simply by measuring its position after different durations of free evolution. We show how this technique can be used to reveal an irreducible nonclassicality through a Bell-inequality violation arising from the entanglement of the centre of mass of a nano-crystal with its spin in a Stern-Gerlach setup. Secondly, we show how our methodology, in conjuction with the Casimir interaction, offers a powerful method to create and certify non-Gaussian entanglement between two neutral nano-objects. Fundamentally, the generation of such an entanglement provides an empirical means for demonstrating an inherent quantumness of the Casimir interaction.
An open challenge in physics is to expand the frontiers of the validity of quantum mechanics by evidencing nonclassicality of the center of mass state of a macroscopic object. Yet another equally important task is to evidence the essential nonclassicality of the interactions which act between macroscopic objects. Here we introduce a new tool to meet these challenges: massive spatial qubits. In particular, we show that if two distinct localized states of a mass are used as the $|0\ensuremath{\rangle}$ and $|1\ensuremath{\rangle}$ states of a qubit, then we can measure this encoded spatial qubit with a high fidelity in the ${\ensuremath{\sigma}}_{x},{\ensuremath{\sigma}}_{y}$, and ${\ensuremath{\sigma}}_{z}$ bases simply by measuring its position after different duration of free evolution. This technique can be used reveal the irreducible nonclassicality of the spin and center of mass entangled state of a nanocrystal implying macrocontextuality. Further, in the context of Casimir interaction, this offers a powerful method to create and certify non-Gaussian entanglement between two neutral nano-objects. The entanglement such produced provides an empirical demonstration of the Casimir interaction being inherently quantum.
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.
We propose a current-carrying-chip scheme for generating spatial quantum superpositions using a levitating nanodiamond with a built-in nitrogen-vacancy (NV) centre defect. Our setup is quite versatile and we aim to create the superposition for a mass range of 10−19 kg<m<10−15 kg10^{-19}~{\rm kg}< m< 10^{-15}~{\rm kg}10−19 kg<m<10−15 kg and a superposition size O(10)μm<Δx<O(1)nm{\cal O}(10) {\rm μm} < Δx < {\cal O}(1){\rm nm}O(10)μm<Δx<O(1)nm, respectively, in t≤0.1t\leq 0.1t≤0.1s, depending on the position we launch from the center of the diamagnetic trap. We provide an in-depth analysis of two parallel chips that can create levitation and spatial superposition along the xxx-axis, while producing a very tight trap in the yyy direction, and the direction of gravity, i.e., the zzz direction. Numerical simulations demonstrate that our setup can create a one-dimensional spatial superposition state along the x-axis. Throughout this process, the particle is stably levitated in the z-direction, and its motion is effectively confined in the y-direction for a Gaussian initial condition. This setup presents a viable platform for a diamagnetically levitated nanoparticle for a table-top experiment exploring the possibility of creating a macroscopic Schrödinger Cat state to test the quantum gravity induced entanglement of masses (QGEM) protocol.
The probing of the quantum nature of a macroscopic object is an open problem. Approaches in preparing quantum superposition towards a larger scale, which has been progressively accessible in a variety of experimental implementations, may detect new physics or extend the boundary of quantum theory. Development on a nano-mechanical system in the framework of quantum optics and information theory has opened new research directions. It paves ways to manipulate the wavefunction of a massive particle over a large spatial range and probe its quantum behavior to an unprecedented precision. In this thesis, quantum superposition on a mechanical system is studied theoretically in the light of possible implementations under current techniques in order to test superposition principle and the quantum nature of gravity in the mesoscopic region. The work includes two lines of study. In the first line, the motion of the center of mass (c.m.) of the mechanical system is coupled to its internal spin system magnetically, and a Ramsey scheme is developed based on coherent spin control. The wavepacket of the test object, under a spin-dependent force, may then be delocalized to a macroscopic scale. A gravity induced dynamical phase (accrued solely on the spin state, and measured through a Ramsey scheme) is used to reveal the above spatially delocalized superposition of the spin-nano-object composite system that arises during the scheme. A remarkable immunity to the motional noise in the c.m. (initially in a thermal state with moderate cooling) and also a dynamical decoupling nature of the scheme itself is revealed. A careful examination of the perturbation effect due to setup imperfection and environment-induced decoherence is performed, which shows that the Ramsey fringes have a high tolerance on those unwanted faults under realistic experimental conditions. The scheme also facilitates a gravimetry protocol that potentially could be developed for a novel on-chip gravimeter with a precision of 10−6g/Hz10^{-6}g/\sqrt{\text{Hz}}10−6g/Hz​. In the second line, an opto-mechanical experiment is proposed to entangle the motion of two mechanical oscillators through their mutual gravitational interaction. The feasibility of such an experiment is critically examined within the framework of cavity optomechanics. It is shown that within the decoherence time of mechanical noise and potentially gravitational induced state collapse, entanglement between mirrors could be obtained when the initial state of the cavity field is prepared in some particular states. Strategies that give enhancement to entanglement generation rate are studied in light of quantum estimation theory. It is shown that for a cavity initially in a coherent state, the resulting entanglement generation rate would be enhanced linearly with the amplitude of the coherent state. Lastly, it shows that in the proposed setup Casimir effect would significantly affect the gravity-induced entanglement. A proper shield can eliminate the detrimental effect of Casimir force, which, however, will constrain the closest distance between the mirrors in its implementation.