Phase transitions are paradigmatic examples of emergent phenomena, in which symmetries present at the microscopic level can be spontaneously broken in the thermodynamic limit. Two primary physical mechanisms can drive this symmetry breaking: thermal fluctuations in classical phase transitions and quantum fluctuations in quantum critical phenomena. Here, we introduce $nonlocal$ $quantum$ $fluctuations$ as a new fundamental mechanism to drive phase transitions. We show that entanglement shared between environmental modes can induce a correlated symmetry breaking in remote systems, independent of their spatial separation. Using the framework of driven-dissipative phase transitions, we theoretically investigate a system composed of two nonlinear quantum resonators placed at arbitrarily large spatial separations, each coupled to independent local Markovian baths. We consider the regime in which remote environmental modes are prepared in broadband entangled states. We show that near the critical point, where the susceptibility to weak perturbations diverges, quantum correlations in the environments govern the system critical behavior. While these correlations manifest locally only as effective thermal fluctuations, at the global level they give rise to an emergent nonlocal phase transition, marked by the spontaneous symmetry breaking of a collective mode shared by the two remote systems.
Phase transitions are paradigmatic examples of emergent phenomena, in which symmetries present at the microscopic level can be spontaneously broken in the thermodynamic limit. Two primary physical mechanisms can drive this symmetry breaking: thermal fluctuations in classical phase transitions and quantum fluctuations in quantum critical phenomena. Here, we introduce nonlocalquantumfluctuations as a new fundamental mechanism to drive phase transitions. We show that entanglement shared between environmental modes can induce a correlated symmetry breaking in remote systems, independent of their spatial separation. Using the framework of driven-dissipative phase transitions, we theoretically investigate a system composed of two nonlinear quantum resonators placed at arbitrarily large spatial separations, each coupled to independent local Markovian baths. We consider the regime in which remote environmental modes are prepared in broadband entangled states. We show that near the critical point, where the susceptibility to weak perturbations diverges, quantum correlations in the environments govern the system critical behavior. While these correlations manifest locally only as effective thermal fluctuations, at the global level they give rise to an emergent nonlocal phase transition, marked by the spontaneous symmetry breaking of a collective mode shared by the two remote systems.
Quantum mechanics is fundamentally governed by the Schrödinger equation, which is linear in the wave function. Nevertheless, quantum systems can exhibit highly nonlinear behavior in their observable dynamics. Such nonlinearities can emerge from many-body interactions, nonlinear coupling mechanisms, or the interplay between coherent evolution and dissipation. In the collective limit, microscopic quantum interactions can give rise to qualitatively new macroscopic behavior. Open quantum systems provide a rich setting for such phenomena, as environmental coupling introduces dissipation and fluctuations that compete with coherent dynamics and can alter the steady states and dynamical phases of a system. Combined with nonlinear interactions, this competition can produce behavior with no direct counterpart in conventional linear light--matter systems. In this thesis, I investigate such collective phenomena through nonlinear two-photon light--matter interactions and engineered quantum reservoirs. I first investigate the driven--dissipative two-photon Dicke model and demonstrate the emergence of a dissipative superradiant phase transition. The quadratic light--matter interaction introduces distinct stability requirements in the presence of dissipation. In particular, two-photon loss stabilizes the superradiant phase, allowing its steady states and critical behavior to be characterized. I next investigate photon blockade and transient quadrature-squeezed radiation in the two-photon Tavis--Cummings model. I show that two-photon interactions collectively enhance photon blockade and squeezing, in contrast to the conventional one-photon model, where the effective nonlinearity diminishes in the collective limit. Finally, I consider collective behavior induced by reservoir engineering. Two spatially separated open quantum systems without direct coherent interaction can undergo a nonlocal quantum phase transition when coupled to correlated quantum reservoirs. Remarkably, the transition is hidden from local observables and emerges only through nonlocal correlations and collective observables. Together, these results demonstrate how nonlinear interactions and engineered dissipation can reshape collective behavior in open quantum systems.
In a quantum many-body system coupled to the environment, its steady state can exhibit spontaneous symmetry breaking when a control parameter exceeds a critical value. In this study, we consider spontaneous symmetry breaking in nonsteady modes of an open quantum many-body system. Assuming that the time evolution of the density matrix of the system is described by a Markovian master equation, the dynamics of the system is fully characterized by the eigenmodes and spectrum of the corresponding time evolution superoperator. Among the nonsteady eigenmodes with finite lifetimes, we focus on the eigenmodes with the highest frequency, which we call the most coherent mode. For a dissipative spin model, it is shown that the most coherent mode exhibits a transition from a disordered phase to a symmetry-broken ordered phase, even if the steady state does not show singular behavior. We further argue that the phase transition of the most coherent mode induces a qualitative change in the decoherence dynamics of highly entangled states, i.e., the Schr\"odinger's cat states.
In the vicinity of ground-state phase transitions quantum correlations can display nonanalytic behavior and critical scaling. This signature of emergent collective effects has been widely investigated within a broad range of equilibrium settings. However, under nonequilibrium conditions, as found in open quantum many-body systems, characterizing quantum correlations near phase transitions is challenging. Moreover, the impact of local and collective dissipative processes on quantum correlations is not broadly understood. Here we consider as a paradigmatic setting the superradiant phase transition of the open quantum Dicke model and characterize quantum and classical correlations across the phase diagram. We develop an approach to quantum fluctuations which allows us to show that local dissipation, which cannot be treated within the commonly employed Holstein-Primakoff approximation, rather unexpectedly leads to an enhancement of collective quantum correlations, and to the emergence of a nonequilibrium superradiant phase in which the bosonic and spin degrees of freedom of the Dicke model are entangled.
Quantum entanglement is commonly assumed to be fragile at ambient temperature and over macroscopic distances, where thermal noise and dissipation are expected to rapidly suppress nonclassical correlations. Here we show that this intuition fails for collective quantum modes whose dynamics is governed by reduced open-system channels rather than by microscopic thermal equilibrium. For two spatially separated collective modes, we derive an exact entanglement boundary based on the positivity of the partial transpose, valid in the symmetric resonant limit. From this result we obtain an explicit minimum collective fluctuation amplitude, expressed entirely in measurable noise, bandwidth, dissipation, and distance-dependent coupling parameters, required to sustain steady-state entanglement at finite temperature. We further show that large collective occupation suppresses but does not eliminate quantum phase diffusion, so the steady state remains phase symmetric and does not collapse to a classical mean-field despite macroscopic signal amplitudes. Stochastic simulations of the reduced open-system dynamics, together with matched classical correlated-noise null models analyzed through an identical pipeline, confirm that entanglement witnesses are violated only in the quantum regime. Our results establish a minimal, platform-independent framework connecting collective-mode dynamics, noise injection, distance, and operational certification of macroscopic entanglement.
Abstract Quantum entanglement is commonly assumed to be fragile at ambient temperature and over macroscopic distances, where thermal noise and dissipation are expected to rapidly suppress nonclassical correlations. Here we show that this intuition fails for collective quantum modes whose dynamics is governed by reduced open-system channels rather than by microscopic thermal equilibrium. For two spatially separated collective modes, we derive an exact entanglement boundary based on the positivity of the partial transpose, valid in the symmetric resonant limit. From this result we obtain an explicit minimum collective fluctuation amplitude, expressed entirely in measurable noise, bandwidth, dissipation, and distance-dependent coupling parameters, required to sustain steady-state entanglement at finite temperature. We further show that large collective occupation suppresses but does not eliminate quantum phase diffusion, so the steady state remains phase symmetric and does not collapse to a classical mean-field despite macroscopic signal amplitudes. Stochastic simulations of the reduced open-system dynamics, together with matched classical correlated-noise null models analyzed through an identical pipeline, confirm that entanglement witnesses are violated only in the quantum regime. Our results establish a minimal, platform-independent framework connecting collective-mode dynamics, noise injection, distance, and operational certification of macroscopic entanglement.
Quantum phase transitions manifest as an abrupt change in the ground state of a many-body system; yet it is an open question whether this sudden change necessarily precludes a continuous dynamical connection between the two phases. We introduce a classification of quantum phase transitions based on this geometric aspect of the ground-state manifold, that differs from known classifications. By leveraging the framework of counterdiabatic driving, we explicitly construct schedules that dynamically connect one phase to another. This strategy allows us to uncover a large class of quantum phase transitions, where the states on both sides are separated only by a finite geometric distance in the thermodynamic limit. We term such transitions traversable, since exact counterdiabatic driving links the two phases via a finite dynamical protocol in the thermodynamic limit. We show that multiple known transitions fall into this class -- e.g., symmetry-breaking transitions obeying hyperscaling and discontinuous transitions with an enhanced continuous symmetry. We further show the existence of quantum phase transitions that cannot be crossed dynamically even with the help of nonlocal counterdiabatic driving, as they would require divergent amplitudes and frequencies. Geometrically, these nontraversable transitions correspond to an infinite distance separating the two phases of matter; we show that the class comprises continuous transitions exhibiting mean-field universality, and discontinuous transitions arising from the competition between metastable minima. Our geometric classification goes beyond the known taxonomy, is independent of local order parameters and renormalization group fixed points, and has direct implications for the complexity of state preparation and adiabatic quantum computation.