A theoretical framework is developed to study a magnetically levitated nanomagnet in the quantum regime. The system is very rich due to the interaction between its degrees of freedom: position, orientation, and magnetization. In particular, the Einstein--de Haas effect, namely the coupling between the magnetization and the angular momentum of the object, plays a dramatic role. This work sheds new light on one of the few unsolved problem in quantum mechanics, the rigid rotor with a spin. At the same time, it opens up the possibility to model the dynamics of a single magnetic domain nanoparticle in a magnetic trap, an interesting new scenario for future experiments.
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.
We study the reciprocal Barnett and Einstein--de Haas effects in an exactly solvable quantum spin--rotor model that conserves the total angular momentum. For a single spin-
1/2, the model describes rotation-dependent spin polarization, coherent transfer of angular momentum between the spin and the rotor, and the accompanying spin--rotor entanglement. At a recoil-compensation point, all angular-momentum sectors become synchronized, allowing complete spin reversal and a one-quantum shift of an arbitrary rotor wave packet. We then extend the model to two spins coupled to the same rotor, where the shared rotational degree of freedom participates dynamically in the generation of spin--spin entanglement. The singlet forms a dark state, while the triplet sector remains coupled to the mechanical motion. At a special parameter point, the rotor returns to its original dynamical branch and disentangles from the spins, leaving behind a maximally entangled two-spin state locally equivalent to a Bell state.
What is the shortest possible timescale of the Einstein--de Haas effect? Addressing this problem theoretically poses a monumental challenge, for it involves an infinite number of coupled quantum angular momenta. Here, the authors formulate for the first time the problem in a rotationally invariant way, thereby enabling its solution in terms of angulon quasiparticles. Intriguingly, the first calculations reveal already that transfer between electron spin, orbital, and lattice degrees of freedom can occur on the femtosecond time scale.
The rotation of a nanoparticle in a quantum system has many applications, from theory to experiments. This paper will treat nanoparticle rotational dynamics for spin-embedded nanorotors. We will model it as a rigid body that properly treats the rotation in the coframe of the nanorotor in the presence of external fields. Besides rotation, we will further investigate how to create large spatial superpositions in the inhomogeneous external magnetic field, such as in the case of the Stern-Gerlach apparatus. The spin-embedded nanorotors play a crucial role in creating matter-wave interferometers through their spin and external magnetic field interaction Hamiltonian. We aim to provide a holistic interpretation of the dynamics of three Euler angles, their quantum evolution, and the nanorotor's spatial motion in a Stern-Gerlach-type setup, where we will consider one-full-loop interferometry. We will then study how the quantum evolution of all the Euler angles leads to a spin coherence loss upon interference and what manifests the Einstein-de Haas effect in an external magnetic field. In particular, we show that by imparting rotation along the direction of the magnetic field, we can stabilize the nanorotor's libration mode. We will also extend our analysis to a case where the initial state of the libration mode is thermal and discuss the contrast loss due to interference of the nanorotor upon one-loop completion.
The Einstein-de Haas effect is a phenomenon in which angular momentum is transferred from microscopic spins to mechanical rotation of a macroscopic rigid body. We report an observation of the Einstein-de Haas effect in a spinor-dipolar Bose-Einstein condensate, in which the intrinsic magnetic dipole-dipole interaction mediates coherent transfer of angular momentum from atomic spins to collective circulation of a quantum fluid. The depolarized spinor components displayed ring-shaped density distributions that were confirmed as quantized vortices through matter-wave interferometry, revealing a coherent conversion between spin and orbital angular momentum. This observation opens a pathway to exploring ground-state phases with broken chiral symmetry, spin textures, and mass circulation, as well as the Barnett effect in dipolar quantum gases.
Magnetically trapped type-I superconductors are promising candidates for precision experiments at the quantum-to-classical borderline, with applications in quantum sensing of forces and accelerations and fundamental tests of quantum physics. Here, we show how the rotational motion of micron-sized superconductors is strongly affected by (i) the diamagnetic torques due to the gradient of the trapping field and by (ii) the gyromagnetic coupling due to Einstein-de Haas and Barnett effects. We show that this allows the three-dimensional alignment of asperhical superconductors in the trap center, as required for future sensing applications and quantum experiments, and determine the resulting librational trapping frequencies. Finally, we propose an experiment to probe gyromagnetic coupling in levitated superconductors and we discuss how it can be used to control the particle rotation.