A trapped-ion quantum tunneling rotor (QTR) is in a quantum superposition of two different Wigner crystal orientations. In a QTR system, quantum tunneling drives the coherent transition between the two different Wigner crystal orientations. We theoretically study the quantum dynamics of a QTR, particularly when the spin state of one of the ions is flipped. We show that the quantum dynamics of an
N-ion QTR can be described by continuous-time cyclic quantum walks. We also investigate the quantum dynamics of the QTR in a magnetic field. Flipping the spin state breaks the rotational symmetry of the QTR, making the quantum-tunneling-induced rotation distinguishable. This symmetry breaking creates coupling between the spin state of the ions and the rotational motion of the QTR, resulting in different quantum tunneling dynamics.
All elements of a quantum algorithm for calculations of rotationally inelastic molecule + atom scattering within the framework of a mixed quantum/classical theory are outlined. In this approach, the rotational motion of the molecule is described quantum mechanically using the time-dependent Schrödinger equation, while the scattering process of two collision partners is treated classically. The matrix of potential coupling is precomputed on a classical processor, whereas the quantum hardware is used to propagate the system of coupled equations for the rotational state-to-state transitions. All quantum circuits needed for practical implementation of the algorithm are presented. First, the quantum codes written in Qiskit are rigorously tested by running calculations for a N 2 + O collision on a classical emulator of quantum hardware using a realistic potential energy surface of this system and comparing these results against the results obtained by the MQCT code. Next, these codes are run on the actual quantum hardware, such as the publicly available IBM Brisbane, Kyiv, and Sherbrooke . A very good agreement with benchmark data was obtained. To the best of our knowledge, this is the first proof-of-principle calculation of inelastic scattering implemented successfully on a quantum computer using a case study within mixed quantum/classical framework.
We study the quantum dynamics of the rotational degree of freedom of a nano-magnet trapped in a superconducting trap. The nano-magnet is modeled as a magnetic dipole with magnetization pinned to the easy axis of the particle. The magnetic trap then leads to a potential barrier that hinders free rotation of the particle, but through which it can tunnel. We identified rest-gas scattering as the most important decoherence mechanism at low temperatures. A shape of the particle sufficiently close to perfect rotational symmetry about the rotational axis can protect the rotational tunneling against this decoherence mechanism, and we identify experimentally feasible parameter regimes where rotational tunneling should be observable.
Angular momentum is a difficult knowledge point for undergraduates to understand in quantum mechanics. In this paper, a number of numerical experiments are designed to help students build visual images of angular momentum. The design concept is to break the boundaries between elementary and advanced quantum mechanics, basic theory and cutting-edge research, guide students to calculate and draw by themselves, discuss with each other, and build their own physical pictures. Through this efficient way of learning by doing, students can get an intuitive sense of abstract concepts from some simple calculations. The discussion starts from rotation operation, gradually increases the difficulty to squeezing operation, and introduces the basic concepts of spin squeezed state and Husimi Q representation. This design skillfully links classroom teaching with frontier research, bringing deeper thinking and inspiration to undergraduates.
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.
This thesis explores the dynamics of a heteronuclear diatomic molecular ion, possessing a permanent electric dipole moment, µ, which is trapped in a linear Paul trap and can interact with an off-resonance laser field. To build our model we use the rigid-rotor approximation, where the dynamics of the molecular ion are limited to its translational and rotational motions of the center-of-mass. These dynamics are investigated by carrying out suitable numerical calculations. To introduce our numerical methods, we divide our research topic into two different subjects. First, we ignore the rotational dynamics of the ion by assuming µ = 0. By this assumption, the system resembles an atomic ion, which mainly exhibits translational motion for its center of the mass when exposed to an external trapping field. To study this translational behavior, we implement full-quantum numerical simulations, in which a wave function is attributed to the ion. Finally, we study the quantum dynamics of the mentioned wave packet and we compare our results with those obtained classically. In the latter case, we keep the permanent dipole moment of the ion and we study the probable effects of the interaction between the dipole moment and the trapping electric field, on both the translational and the rotational dynamics of the trapped molecular ion. In order to study these dynamics, we implement both classical and semi-classical numerical simulations. In the classical method, the rotational and the translational motions of the center of mass of the ion are obtained via classical equations of motion. On the other hand, in the semi-classical method, while the translational motion of the center-of-mass is still obtained classically, the rotation is treated full-quantum mechanically by considering the rotational wave function of the ion. In the semi-classical approach, we mainly study the probable couplings between the rotational states of the molecular ion, due to the interaction of the permanent dipole moment with the trapping electric field. In the end, we also present a semi-classical model, where the trapped molecular ion interacts with an off-resonance laser field.