Quantum dynamics of large spins in static and rotating magnetic fields: Entanglement resonances and kinks

TL;DR

This work addresses the quantum dynamics of a large spin in a static plus rotating magnetic field by mapping the problem onto a non-interacting gas of spin-1/2 particles, enabling exact analytical solutions for arbitrary spin size and initial states. The authors derive a time-independent rotating-frame Hamiltonian and obtain explicit expressions for state populations, dipole moments, and adiabatic behavior; they further extend the analysis to two spins interacting via dipole-dipole couplings, revealing entanglement resonances and kinks tied to the rotating-frame energy spectrum. Key results include resonance-driven periodic oscillations between the lowest and highest stretched states, the ability to coherently transfer population to a maximally stretched state from a ground-like initial state, and rich entanglement structures in the two-spin system that depend on Zeeman and dipolar strengths. The findings have implications for quantum control in large-spin platforms (e.g., dysprosium) and dipolar quantum gases, highlighting regimes where exact dynamics are tractable and where entanglement can be tuned via rotating fields and dipolar interactions.

Abstract

We examine the quantum dynamics of a large spin in the presence of static and rotating magnetic fields. By mapping the system onto a gas of non-interacting spin-1/2 particles, we derive exact analytical results for the dynamics with different initial states. The dynamics exhibit periodic oscillations between two maximally stretched states, irrespective of how large the spin is. Further, we observe periodic transitions between sublevels with magnetic quantum numbers of opposite signs. Additionally, the dynamics features the periodic transfer of the spin to the maximally stretched state starting from a superposition state. The evolution of the dipole moment is also explored in each case, and as expected, it is precessing about the instantaneous, resultant magnetic field. Furthermore, we extend our analysis to a pair of spins, taking into account the dipole-dipole interactions between them. We analyze how the ground state entanglement between the spins depends on the external fields. The quantum dynamics of the two spins reveal entanglement resonances and kinks, which can be identified from the energy spectrum when weak transverse field strengths are considered. Finally, we discuss the regime in which the dipolar interactions are relatively weak.

Figures (11)

• Figure 1: (a) $(S_{\text{min}})^{1/2J}$ as a function of $\Omega/\omega_z$ and $B_\perp/B_z$. (b) shows maximum population attained in $|m_j = +J\rangle$ as a function of $\Omega/\omega_z$ for an initial state, $|\psi_0\rangle = |m_j = -J\rangle$ and $B_{\perp}/B_z=0.1$. As $J$ increases it gets narrow and tails decay rapidly.
• Figure 2: (a) $(S_{min})^{1/2J}$, (b) $(P_{2J,max})^{1/2J}$ and (c) $(P_{GS,min})^{1/2J}$ as a function of $\Omega/\omega_z$ and $B_\perp /B_z$. The dashed line in (b) shows the criteria $\Omega/\omega_z=B/B_z$, where $B=\sqrt{B_\perp^2+B_z^2}$ and that in (c) corresponds to $\Omega/\omega_z=(B/B_z)^2$ where the overlap vanishes and the population is periodically transferred to the highest stretched state along the instantaneous magnetic field.
• Figure 3: Variation of $S(t)^{1/2J}$ with time for $B_\perp/B_z=1$ for different rotation frequencies.
• Figure 4: Ground state properties of a spin pair. (a)-(c) show $\langle J_x \rangle/2J$ of the ground state of the Hamiltonian in equation (\ref{['h2s']}) at $t=0$ as function of field strengths for different $J$. (d)-(f) show the corresponding entanglement entropy of one spin.
• Figure 5: The maximum entanglement entropy of the ground state for fixed $J$ and $\beta_z$, and $\beta_\perp$ is being varied.