Andriy H. Nevidomskyy

The interaction of an ensemble of two-level atoms and a quantized electromagnetic field, described by the Dicke Hamiltonian, is an extensively studied problem in quantum optics. However, experimental efforts to explore similar physics in condensed matter typically employ bosonic matter modes (e.g., phonons, magnons, and plasmons) that are describable as simple harmonic oscillators, i.e., an infinite ladder of equally spaced energy levels. Here, we examine ultrastrong coupling between a coherent light mode and an ensemble of paramagnetic spins, a finite-multilevel system, in Gd₃Ga₅O₁₂. The electron paramagnetic resonance of Gd³⁺ ions is tuned by a magnetic field into resonance with a Fabry–Pérot cavity mode, resulting in the formation of spin–photon hybrid states, or Zeeman polaritons. We observe that the light–matter coupling strength, measured through the vacuum Rabi splitting, decreases with increasing temperature, which can be explained by the temperature-dependent population difference between the lower and higher-energy states, a trait of a finite-level system. This finding demonstrates that a spin–boson system is more compatible with the Dicke model and has advantages over boson–boson systems for pursuing experimental realizations of phenomena predicted for ultrastrongly coupled light–matter hybrids.

Recent developments have revealed that symmetries need not form a group, but instead can be noninvertible. Here we use analytical arguments and numerical evidence to illuminate how spontaneous symmetry breaking of a noninvertible symmetry is similar yet distinct from ordinary, invertible, symmetry breaking. We consider one-dimensional chains of group-valued qudits, whose local Hilbert space is spanned by elements of a finite group G (reducing to ordinary qubits when G = Z 2 ). We construct Ising-type transverse-field Hamiltonians with Rep ( G ) symmetry whose generators multiply according to the tensor product of irreducible representations (irreps) of the group G . For non-Abelian G , the symmetry is noninvertible. In the symmetry broken phase there is one ground state per irrep on a closed chain. The symmetry breaking can be detected by local order parameters but, unlike the invertible case, different ground states have distinct entanglement patterns. We show that for each irrep of dimension greater than one the corresponding ground state exhibits string order, entanglement spectrum degeneracies, and has gapless edge modes on an open chain—features usually associated with symmetry-protected topological order. Consequently, domain wall excitations behave as one-dimensional non-Abelian anyons with nontrivial internal Hilbert spaces and fusion rules. Our Letter identifies properties of noninvertible symmetry breaking that existing quantum hardware can probe.

The heavy fermion material UTe ₂ is a candidate topological superconductor that exhibits multiple magnetic field–induced superconducting phases. One such phase exists only at fields greater than 40 tesla, a considerable scale given its critical temperature of only 2 K. Here, we extend measurements of this state with fields outside of the bc crystallographic plane and reveal its core structure: The superconducting phase wraps around the b axis in a halo-like fashion and appears to be stabilized by a field component perpendicular to the magnetic easy axis. This angle dependence points to a multicomponent spin-triplet order parameter with a finite angular momentum of the Cooper pairs. The pairing mechanism remains enigmatic, and UTe ₂ ’s specific magnetophilic superconducting tendencies seem incompatible with existing models for field-enhanced superconductivity.