We study a hybrid system of coupled cavities, with or without two-level atoms doped inside. By employing a building-block construction facilitated by nonlinear Stark coupling, we identify a manifold of exact many-body eigenstates that remain analytically tractable across arbitrary lattice geometries and atom distributions. We demonstrate that these exact states exhibit a dual physical nature depending on their spectral positioning: when embedded within the chaotic many-body spectrum, they manifest as quantum scars that violate the eigenstate thermalization hypothesis and undergo weak ergodicity breaking; conversely, as ground states within fixed-total-excitation sectors, they exhibit off-diagonal long-range order and form polariton condensates. Furthermore, numerical calculations of local excitation-number fluctuations suggest that negative Stark coupling shifts the Mott-insulator to superfluid transition toward weaker inter-cavity hopping. Our findings provide a versatile framework for engineering both coherent quantum phases and non-thermalizing states in diverse light-matter architectures.
We study a hybrid system of coupled cavities, with or without two-level atoms doped inside. By employing a building-block construction facilitated by nonlinear Stark coupling, we identify a manifold of exact many-body eigenstates that remain analytically tractable across arbitrary lattice geometries and atom distributions. We demonstrate that these exact states exhibit a dual physical nature depending on their spectral positioning: when embedded within the chaotic many-body spectrum, they manifest as quantum scars that violate the eigenstate thermalization hypothesis and undergo weak ergodicity breaking; conversely, as ground states within fixed-total-excitation sectors, they exhibit off-diagonal long-range order and form polariton condensates. Furthermore, numerical calculations of local excitation-number fluctuations suggest that negative Stark coupling shifts the Mott-insulator to superfluid transition toward weaker inter-cavity hopping. Our findings provide a versatile framework for engineering both coherent quantum phases and non-thermalizing states in diverse light-matter architectures.
Microcavity exciton-polaritons have emerged as an excellent platform for realizing quantum phases of matter, owing to their ability to undergo non-equilibrium Bose-Einstein condensation. Here, we show that the interplay between multiple quantized levels in microcavities and polariton nonlinearity drives the emergence of unconventional phases. Specifically, we demonstrate that intra-site quantization in microcavity polariton lattices—manifested as multiple energy levels in strongly confined sites—provides a route to manipulating these phases. We show that nonlinear interactions transfer population into excited onsite energy levels, acting as an intrinsic dynamical channel that controls coherence across the lattice. While weak nonlinearity confines polaritons to the lowest mode, yielding a robust superfluid phase with broken U(1) symmetry, strong nonlinearity induces phase diffusion through inter-level mixing. This dynamically generated fluctuation suppresses global phase coherence and drives the system into a dynamical Bose-insulating phase. Transitions between these phases occur either as a non-equilibrium phase transition or a sharp crossover. This study investigates the destruction of global order in a non-equilibrium condensate within a lattice featuring onsite quantized energy levels. Long-range fluctuations suppress superfluid stiffness and the condensate fraction, while persistent local order reveals a dynamical Bose-insulating state.
The unitary transformation method is used to study the properties of the polaritonic states and Bose-Einstein condensation in the Rabi lattice model, where the on-site two-level systems (TLSs) are coupled with the intersite hopping photons. It is shown that the counter-rotating coupling (CRC) between TLS and photon, which breaks down the conservation of the excitation numbers, may induce a long-range Ising-like interaction among intersite TLSs. We have shown that the coupled TLSs and photons are hybridized to form the polaritonic states, and the corresponding ground state and polaritonic excitation spectra are calculated by diagonalizing our transformed Hamiltonian. When the photon hopping J is weak, the excitation spectrum is gapped. But the gap decreases with increasing J, and at critical value J=Jc the gap becomes zero at the $\mathrm{\ensuremath{\Gamma}}$ point and the ground state becomes instable. Thus, Jc is the phase transition point where the polaritons are condensed at the $\mathrm{\ensuremath{\Gamma}}$ point to form the delocalized superradiant phase. The results show that the larger detuning between TLS and photon favors the disorder insulator phase, which requires the stronger Jc to get the long-range order phase. The phase diagram of the delocalized superradiant phase transition has been obtained where there are no Mott lobes since the CRC breaks down the number conservation. The ground state and the excitation spectra of the delocalized superradiant phase are also calculated. It is shown that in the delocalized superradiant state the order parameter is the nonzero ground-state average of the photon annihilation operator. The polaritonic excitation has a finite excitation gap because the CRC breaks down the number conservation but leaves only a discrete symmetry, the parity conservation.
Summary form only given. Bosons can populate quantum states macroscopically, forming various kinds of thermal-equilibrium, and quasi-equilibrium condensates, which exhibit a wide range of collective phenomena including superfluidity and macroscopic coherence in matter. Interferometry has been employed to demonstrate long-range off-diagonal order in cold-atom systems, and, recently, in the rapidly developing field of exciton-polariton condensates. However, all such interferometric measurements have been performed on steady-state condensates, unable to access the temporal off-diagonal order and non-equilibrium dynamics. Moreover, in solid-state systems, interference between two separate condensates has not been observed before. Here we use optical injection to resonantly generate two dynamic exciton-polariton condensates with distinct momenta and at different times. We characterize the interference between condensates, demonstrating their long-range temporal order. We show that the build-up of the temporal long-range order strongly depends on the strength of polariton interactions, as well as the temperature and particle density. Moreover, polariton interactions yield a blue shift of the dynamic condensate energy, acting as an extremely large optical nonlinearity. These results provide direct evidence of temporal long-range order in dynamic condensates as well as demonstrate a new approach for probing the ultrafast coherent dynamics of exciton-polaritons, opening new directions in the fundamental study of coherence in matter as well as in practical applications such as quantum information processing and ultrafast logic.
The ultrafast nonlinear optical response of molecular ensembles is fundamentally altered under strong light-matter coupling. To rigorously isolate the genuine many-body contributions, an exact time-domain field-subtraction protocol is developed within a fully non-perturbative Maxwell-Liouville framework explicitly incorporating the two-exciton manifold in real space and time. This approach reveals that while collective cavity delocalization drives the macroscopic nonlinear signal toward a severe harmonic cancellation (an effect termed "spectral starvation"), intrinsic many-body molecular interactions robustly resurrect genuine polaritonic double-quantum coherences (DQCs). This many-body resurrection is governed by a universal two-photon matching rule, ΔB+4J=ΩR, linking molecular anharmonicity (ΔB) to the macroscopic Rabi splitting (ΩR) and excitonic coupling (J). Crucially, this resonance exploits the spatial mismatch between macroscopic polaritons and localized two-exciton pairs to break harmonic cancellation. For J-aggregates (J<0), this condition uniquely isolates the resonant many-body state below the dense manifold of localized dark states, protecting the macroscopic coherence from spatial fragmentation. This predictive framework establishes a direct phase diagram to engineer and protect optical nonlinearities across diverse strongly coupled platforms.
The typical mechanisms of ergodicity breaking in isolated interacting quantum systems, such as many-body localization and quantum many-body scars, originate from the nonthermal nature of the underlying eigenstates. Here, in the absence of nonthermal eigenstates, we identify a mechanism for collective revivals of multiparticle Wannier states (MWSs) associated with nearly linear bands in a spatially modulated Bose-Hubbard lattice. The MWSs, as superpositions of multiparticle Bloch states within individual energy bands, give rise to band-resolved Wannier-sector fragmentation. The key idea is that spatially periodic modulation folds and separates energy bands of a simple lattice into several sub-bands, among which nearly linear sub-bands inherit the linear segments of the original bands. Although multiparticle Bloch states satisfy the eigenstate thermalization hypothesis (ETH), the MWSs in the nearly linear band still exhibit long-lived collective revivals, due to emergent equally spaced energy levels. Our work provides a route to weak ergodicity breaking in which long-lived revivals arise from spectral phase coherence among ETH-satisfying eigenstates rather than from scar-like nonthermal eigenstates.
We construct exact eigenstates of multicomponent Hubbard models in arbitrary dimensions by generalizing the η -pairing mechanism. Our models include the SU ( N ) Hubbard model as a special case. Unlike the conventional two-component case, the generalized η -pairing mechanism permits the construction of eigenstates that feature off-diagonal long-range order and magnetic long-range order. These states form fragmented fermionic condensates due to a simultaneous condensation of multicomponent η pairs. While the η -pairing states in the SU(2) Hubbard model are based on the η -pairing symmetry, the exact eigenstates in the N -component system with N ≥ 3 arise not from symmetry of the Hamiltonian but from a spectrum generating algebra defined in a restricted Hilbert space. We exploit this fact to show that the generalized η -pairing eigenstates do not satisfy the eigenstate thermalization hypothesis and serve as quantum many-body scar states. This result indicates a weak breakdown of ergodicity in the N -component Hubbard models for N ≥ 3 . Furthermore, we show that these exact eigenstates constitute integrable subsectors in which the Hubbard Hamiltonian effectively reduces to a noninteracting model. This partial integrability causes various multicomponent Hubbard models to weakly break ergodicity. We propose a method of harnessing dissipation to distill the integrable part of the dynamics and elucidate a mechanism of nonthermalization caused by dissipation. This work establishes the coexistence of off-diagonal long-range order and SU ( N ) magnetism in excited eigenstates of the multicomponent Hubbard models, which presents a possibility of novel out-of-equilibrium pairing states of multicomponent fermions. These models unveil a unique feature of quantum thermalization of multicomponent fermions, which can experimentally be tested with cold-atom quantum simulators. Published by the American Physical Society 2024