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. Realizing ultrastrong light-matter coupling in condensed matter systems has largely relied on bosonic matter modes. Here, the authors report ultrastrong coupling between a cavity photon mode and paramagnetic spins in gadolinium gallium garnet, consistent with the spin-boson physics described by the Dicke model.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. Realizing ultrastrong light-matter coupling in condensed matter systems has largely relied on bosonic matter modes. Here, the authors report ultrastrong coupling between a cavity photon mode and paramagnetic spins in gadolinium gallium garnet, consistent with the spin-boson physics described by the Dicke model.

Nature CommunicationsAug 5, 20260 citations

Light modulation by a magnetic resonance in a paramagnet

Andrei V. Butashin, S. O. Demokritov, Natalia M. Kreines +1 more

ZhETF Pisma RedaktsiiuNov 1, 19830 citations

Quantum paramagnet and frustrated quantum criticality in a spin-one diamond lattice antiferromagnet

Gang Chen

Motivated by the proposal of a topological quantum paramagnet in the diamond lattice antiferromagnet ${\mathrm{NiRh}}_{2}{\mathrm{O}}_{4}$ , we propose a minimal model to describe the magnetic interaction and properties of the diamond material with spin-one local moments. Our model includes the first- and second-neighbor Heisenberg interactions as well as a local single-ion spin anisotropy that is allowed by the spin-one nature of the local moment and the tetragonal symmetry of the system. We point out that there exists a quantum phase transition from a trivial quantum paramagnet when single-ion spin anisotropy is dominant to the magnetic ordered states when the exchange is dominant. Due to the frustrated spin interaction, the magnetic excitation in the quantum paramagnetic state supports extensively degenerate band minima in the spectra. As the system approaches the transition, extensively degenerate bosonic modes become critical at the criticality, giving rise to unusual magnetic properties. Our phase diagram and experimental predictions for different phases provide a guideline for the identification of the ground state for ${\mathrm{NiRh}}_{2}{\mathrm{O}}_{4}$ . Although our results are fundamentally different from the proposal for topological quantum paramagnets, they represent interesting possibilities for spin-one diamond lattice antiferromagnets.Motivated by the proposal of a topological quantum paramagnet in the diamond lattice antiferromagnet ${\mathrm{NiRh}}_{2}{\mathrm{O}}_{4}$, we propose a minimal model to describe the magnetic interaction and properties of the diamond material with spin-one local moments. Our model includes the first- and second-neighbor Heisenberg interactions as well as a local single-ion spin anisotropy that is allowed by the spin-one nature of the local moment and the tetragonal symmetry of the system. We point out that there exists a quantum phase transition from a trivial quantum paramagnet when single-ion spin anisotropy is dominant to the magnetic ordered states when the exchange is dominant. Due to the frustrated spin interaction, the magnetic excitation in the quantum paramagnetic state supports extensively degenerate band minima in the spectra. As the system approaches the transition, extensively degenerate bosonic modes become critical at the criticality, giving rise to unusual magnetic properties. Our phase diagram and experimental predictions for different phases provide a guideline for the identification of the ground state for ${\mathrm{NiRh}}_{2}{\mathrm{O}}_{4}$. Although our results are fundamentally different from the proposal for topological quantum paramagnets, they represent interesting possibilities for spin-one diamond lattice antiferromagnets.

arXiv:1701.05634Physical review. B./Physical review. BJul 21, 201730 citations

Optical and spin manipulation of non-Kramers ions under a weak magnetic field

Jean Etesse

Aug 7, 20210 citations

Trapping Ions with Light Fields

Leon Karpa

SpringerBriefs in physicsJan 1, 20190 citations

Zeeman polaritons as a platform for probing Dicke physics in condensed matter

T. Elijah Kritzell, Jacques Doumani, Asano, Tobias +11 more

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 Gd $_3$ Ga $_5$ O $_{12}$ . The electron paramagnetic resonance of Gd $^{3+}$ 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.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 Gd$_3$Ga$_5$O$_{12}$. The electron paramagnetic resonance of Gd$^{3+}$ 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.

arXiv:2409.17339Sep 25, 20241 citation

Motivated by the proposal of a topological quantum paramagnet in the diamond lattice antiferromagnet

{\mathrm{NiRh}}_{2}{\mathrm{O}}_{4}

, we propose a minimal model to describe the magnetic interaction and properties of the diamond material with spin-one local moments. Our model includes the first- and second-neighbor Heisenberg interactions as well as a local single-ion spin anisotropy that is allowed by the spin-one nature of the local moment and the tetragonal symmetry of the system. We point out that there exists a quantum phase transition from a trivial quantum paramagnet when single-ion spin anisotropy is dominant to the magnetic ordered states when the exchange is dominant. Due to the frustrated spin interaction, the magnetic excitation in the quantum paramagnetic state supports extensively degenerate band minima in the spectra. As the system approaches the transition, extensively degenerate bosonic modes become critical at the criticality, giving rise to unusual magnetic properties. Our phase diagram and experimental predictions for different phases provide a guideline for the identification of the ground state for

{\mathrm{NiRh}}_{2}{\mathrm{O}}_{4}

. Although our results are fundamentally different from the proposal for topological quantum paramagnets, they represent interesting possibilities for spin-one diamond lattice antiferromagnets.

_3

_5

_{12}

. The electron paramagnetic resonance of Gd

^{3+}

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.