Levitated systems have great potential in quantum sensing and exploring fundamental physics at the macroscopic scale. Of particular interest are recent works suggesting that a levitated ferromagnet can beat the standard quantum limit of magnetometry, a benchmark for quantum sensors. In this work, we show how a microscopic theory capturing atomic-scale spin-lattice interactions can be used to fully explain the emergence of collective precession dynamics of a levitated ferromagnet and the origin of its enhanced magnetometric sensitivity beyond that of independent spins. Our theory further takes us to two innovative experimental designs of immediate interest: measurement of the celebrated Berry phase with a precessing ferromagnetic needle and the use of its nutation motion to sense a low-frequency oscillating magnetic field. With a microscopic theory established for levitated ferromagnetic needles, future studies of macroscopic quantum effects and the associated quantum-classical transition also become possible.
Levitated systems have great potential in quantum sensing and exploring quantum effects at the macroscopic scale. Of particular interest are recent works suggesting that a levitated ferromagnet can beat the standard quantum limit of magnetometry. This work offers a theoretical model to analyze and understand critical features of the precessing dynamics of a levitated ferromagnetic needle, indeed much like a macrospin, in the presence of a weak magnetic field. The dynamics from the atomic scale reveals how the standard quantum limit is surpassed, thus verifying sensing advantages when compared with a collection of independent spins. Our theory further takes us to two additional experimental designs of immediate interest: measurement of the celebrated Berry phase with a precessing ferromagnetic needle and the use of its nutation motion to sense a low-frequency oscillating magnetic field. With a microscopic theory established for levitated ferromagnetic needles, future studies of macroscopic quantum effects and the associated quantum-classical transition also become possible.
The Greenberger-Horne-Zeilinger (GHZ) state is a key resource for quantum information processing and quantum metrology. The atomic GHZ state can be generated by one-axis twisting (OAT) interaction H_{OAT}=χJ_{z}^{2} with χ the interaction strength, but it requires a long evolution time χt=π/2 and is thus seriously influenced by decoherence and losses. Here we propose a three-body collective-spin XYZ model which creates a GHZ-like state in a very short timescale χt∼lnN/N for N particles. We show that this model can be effectively produced by applying Floquet driving to an original OAT Hamiltonian. Compared with the ideal GHZ state, the GHZ-like state generated using our model can maintain similar metrological properties reaching the Heisenberg-limited scaling, and it shows better robustness to decoherence and particle losses. This Letter opens the avenue for generating GHZ-like states with a large particle number, which holds great potential for the study of macroscopic quantum effects and for applications in quantum metrology and quantum information.
We propose a system for passive magnetic levitation and three-dimensional harmonic trapping of soft ferromagnets. Our protocol utilizes the magnetic-field gradient for vertical trapping, and the finite-size effect of the Meissner effect for horizontal trapping. We provide numerical and analytical estimations of possible mechanical dissipations to show that our system allows high mechanical Q factors above Q>108 , and quantum control of the levitated object is within reach of current technologies. The utilization of the soft ferromagnet's internal collective spin excitation may allow quantum mechanical phenomena with particles as large as the submillimeter scale.
We develop a quantum model for the rotational dynamics of a freely floating levitated ferromagnetic gyroscope (LFG), emphasizing the interplay between intrinsic spin
S, mechanical angular momentum
L, and magnetic torque. The conserved total angular momentum projection along the
z-directed magnetic field
B,
Jz=Sz+Lz, is quantized, leading in the small-libration-amplitude limit to discrete precessional states
∣m⟩ (eigenstates of
Jz with eigenvalues
Jz=mℏ) and librational harmonic oscillator states
∣n⟩ (
n=0,1,2,…). The discreteness of the energies and dynamical variables is governed by the quantum precession scale
ΩQ=ℏ/I, where
I is the moment of inertia of the LFG. We find that the phenomenon of LFG precession persists into high-field regimes where the magnitude of the rotational angular momentum associated with precession exceeds the total intrinsic spin. We analyze the complementary quantum limits of localized semiclassical LFG orientation wave packets and exact
Jz-eigenstates
∣m⟩, clarifying the relation between classical precession signals and the underlying quantized spin-rotor dynamics. We further show that radio-frequency fields can drive
Δm=±1 and
Δn=±1 transitions, enabling ladder spectroscopy, tilt-angle control, and sideband-like coupling between precession and libration. The coupled dynamics also exhibit branch-point magnetic resonances where precession and librational motion become strongly coupled. These results establish a framework for using LFGs not only as ultrasensitive torque and magnetic-field sensors, but also as controllable mesoscopic quantum systems. The techniques developed here may be applied to searches for exotic, beyond-the-standard model spin-dependent interactions, ultralight dark matter, and spin-gravity couplings.
The superposition principle is one of the bizarre predictions of quantum mechanics. Nevertheless, it has been experimentally verified using electrons, photons, atoms, and molecules. However, a similar experimental demonstration using a nano or micro particle is still missing and various proposals have been put forward in the literature for creating such a state. In the existing proposals, the attainable spatial separations between the delocalized states are less than the size of the particles that have been used to create such states. In this article, using a
50 nm levitated ferromagnetic particle and existing technologies, we show that a spatial separation of
1 mm between the superposed states is readily achievable. This may lead to the possibility of testing quantum gravity, collapse models and gravity induced state reduction.