Frustration occurs when a system cannot find a lowest-energy configuration due to conflicting constraints. We show that a frustrated superradiant phase transition occurs when the ground-state superradiance of cavity fields due to local light-matter interactions cannot simultaneously minimize the positive photon hopping energies. We solve the Dicke trimer model on a triangle motif with both negative and positive hopping energies and show that the latter results in a sixfold degenerate ground-state manifold in which the translational symmetry is spontaneously broken. In the frustrated superradiant phase, we find that two sets of diverging time and fluctuation scales coexist, one governed by the mean-field critical exponent and another by a novel critical exponent. The latter is associated with the fluctuation in the difference of local order parameters and gives rise to site-dependent photon number critical exponents, which may serve as an experimental probe for the frustrated superradiant phase. We provide a qualitative explanation for the emergence of unconventional critical scalings and demonstrate that they are generic properties of the frustrated superradiant phase at the hand of a one-dimensional Dicke lattice with an odd number of sites. The mechanism for the frustrated superradiant phase transition discovered here applies to any lattice geometries where the antiferromagnetic ordering of neighboring sites are incompatible and therefore our work paves the way toward the exploration of frustrated phases of coupled light and matter.
Frustration occurs when a system cannot find a lowest-energy configuration due to conflicting constraints. We show that a frustrated superradiant phase transition occurs when the ground-state superradiance of cavity fields due to local light-matter interactions cannot simultaneously minimize the positive photon hopping energies. We solve the Dicke trimer model on a triangle motif with both negative and positive hopping energies and show that the latter results in a sixfold degenerate ground-state manifold in which the translational symmetry is spontaneously broken. In the frustrated superradiant phase, we find that two sets of diverging time and fluctuation scales coexist, one governed by the mean-field critical exponent and another by a novel critical exponent. The latter is associated with the fluctuation in the difference of local order parameters and gives rise to site-dependent photon number critical exponents, which may serve as an experimental probe for the frustrated superradiant phase. We provide a qualitative explanation for the emergence of unconventional critical scalings and demonstrate that they are generic properties of the frustrated superradiant phase at the hand of a one-dimensional Dicke lattice with an odd number of sites. The mechanism for the frustrated superradiant phase transition discovered here applies to any lattice geometries where the antiferromagnetic ordering of neighboring sites are incompatible and therefore our work paves the way toward the exploration of frustrated phases of coupled light and matter.
Understanding how frustration and symmetry breaking shape collective behavior is a central problem in quantum many-body systems. In this work, we investigate this problem in large one- and two-dimensional arrays of coupled Dicke models on a periodic lattice, where strong light-matter coupling gives rise to a superradiant phase and competition between neighboring order parameters induces spontaneous translational symmetry breaking. Such Dicke lattice models constitute a fundamentally new class of quantum many-body systems, as they simultaneously realize the thermodynamic limit associated with the lattice size and an intrinsic thermodynamic limit arising from collective on-site interactions with quantum emitters. We show that frustration drives photonic density-wave ordering, and that the resulting broken periodicity can be predicted from the excitation spectrum of the symmetric phase, without requiring computationally prohibitive thermodynamic energy minimization. Furthermore, we demonstrate that an emergent Nambu-Goldstone mode arises near the critical point in a one-dimensional chain despite the presence of only discrete symmetry, and uncover the mechanism that enables this otherwise forbidden gapless excitation. We also find quasi-periodic ordering in the superradiant phase, reminiscent of quasicrystals, and demonstrate that synthetic magnetic flux provides a powerful knob to control the nature of translational symmetry breaking. Our results establish a new direction in quantum many-body physics where the coexistence of local and global thermodynamic limits gives rise to unconventional symmetry breaking and emergent collective behavior.
We investigate superradiant quantum phase transitions in a Dicke trimer model consisting of two types of hoppings, i.e., photon hoppings and atom hoppings. In the superradiant regime, the system can exist in two distinct phases: normal and frustrated superradiant phases, which are governed by both types of hoppings. Particularly, the interplay between these hoppings gives rise to interesting effects, such as triggering superradiance with much lower coupling strengths when both hoppings exhibit the same tendency. In contrast, with opposite tendencies, the competition between hoppings leads to a first-order phase transition between two different superradiant phases with translational symmetry broken. These findings enable the system to undergo a sequence of transitions across three phases by changing the coupling strength. Our work provides deep insights into competing interactions and quantum phase transitions in multi-cavity systems with geometric structures.
We study the nonequilibrium steady states of an open anisotropic quantum Rabi trimer. Combining semiclassical and quantum mechanical treatments, we map out the system's phase diagram and elucidate the critical phenomena induced by anisotropic light-matter coupling, cavity dissipation, and complex photon hopping, which give rise to abundant multistable phases. Counterintuitively, the frustrated superradiant phase (FSP) can be stabilized by both positive and negative photon hopping, a feature absent in closed Rabi and Dicke trimers. We further uncover two independent dissipation thresholds for the normal superradiant phase and the FSP. Unlike isotropic open quantum Rabi trimers, both phases are suppressed once the dissipation exceeds their respective critical values. The rotating and counter-rotating interaction terms exhibit mutually reciprocal effects on the quantum phase transitions. By analyzing universal scaling behaviors with quantum fluctuations incorporated, we reveal an unprecedented finite-fluctuation critical exponent for the FSP. Moreover, the critical exponents of individual phases are coupling-strength dependent. The multistability and FSP can be tuned by anisotropy and dissipation. Our results broaden the scope of nonequilibrium quantum phase physics in few-body systems and hold promising applications for quantum state engineering and cavity/circuit quantum electrodynamics.
We investigate the emergence of frustrated quantum phases in a Jaynes-Cummings (JC) trimer with complex hopping amplitudes between the cavities, which represents the smallest frustrated unit in light-matter systems. The complex hopping amplitudes that can be engineered via synthetic gauge fields introduce chiral effects and geometric frustration into the system.We obtain analytic solutions in the semiclassical limit and map out the phase diagram of this model, featuring one normal and three distinct superradiant phases. Among these phases, a chirally frustrated superradiant phase emerges, characterized by broken chiral and translational symmetries and unidirectional photon flow. These results reveal how frustration and symmetry breaking can arise in JC systems with synthetic gauge fields and ultrastrong coupling.
The emergence of multiple superradiant phases in Dicke lattice models has attracted considerable attention in the quantum optics community. However, a unified understanding of the origin of multistability and its relation to different superradiant phases is still lacking. Here, we develop a configuration-based understanding to classify the superradiant phases in Dicke lattices. We show that photon hopping naturally organizes the possible superradiant configurations according to the lattice symmetry, providing a unified interpretation of the nonequilibrium phase diagram and the emergence of multistability. For the dissipative four-site Dicke lattice, we obtain the complete phase diagram and identify the coexistence of up to four stable superradiant phases. The proposed classification is further extended to five- and six-site lattices. Moreover, we demonstrate that the same configuration-based understanding also applies to the closed Dicke lattice, where the ground state uniquely selects one of the allowed configurations. Finally, we show that different configurations may belong to either same or distinct nonequilibrium universality classes in the dissipative Dicke lattice, while they share the same equilibrium universality class in the closed Dicke lattice. Our results provide a unified picture for understanding equilibrium and nonequilibrium superradiant phase transitions in Dicke lattices.
The quantum fluctuations of a quantum Rabi triangle are investigated using an analytical method that goes beyond mean-field theory. An artificial magnetic field applied in three cavities leads to the breaking of time-reversal symmetry, which is evident in the directional transfer of photons. In contrast to previous studies, we focus on the scaling exponents of quantum fluctuations of the local photon number and the position variance near the critical point. Specifically, the fluctuations of photons do not diverge as the coupling strength approaches the critical value from below for the chiral superradiant phase transition. Attributing to geometric frustration, two distinct scaling laws arise for the frustrated cavity and the remaining cavities. Specifically, in the frustrated cavity, the scaling exponent in the chiral superradiant phase differs from that without an artificial magnetic field for the frustrated antiferromagnetic superradiant phase. The unusual scaling exponents indicate distinct universality classes in contrast to the single-cavity Rabi one. We suggest that accurate critical exponents in few-body systems are useful for identifying exotic quantum phase transitions in light-matter coupling systems.