In this paper, we study steady-state quantum entanglement and steering in an open Dicke model where cavity dissipation and individual atomic decoherence are taken into account. Specifically, we consider that each atom is coupled to independent dephasing and squeezed environments, which makes the widely-adopted Holstein-Primakoff approximation invalid. By discovering the features of quantum phase transition in the presence of the decohering environments, we mainly find that (i) in both normal and superradiant phases, the cavity dissipation and individual atomic decoherence can improve the entanglement and steering between the cavity field and atomic ensemble; (ii) the individual atomic spontaneous emission leads to the appearance of the steering between the cavity field and atomic ensemble but the steering in two directions cannot be simultaneously generated; (iii) the maximal achievable steering in normal phase is stronger than that in superradiant phase; (iv) the entanglement and steering between the cavity output field and the atomic ensemble are much stronger than that with the intracavity, and the steerings in two directions can be achieved even with the same parameters. Our findings reveal unique features of quantum correlations in the open Dicke model in the presence of individual atomic decoherence processes.
In this paper, we study steady-state quantum entanglement and steering in an open Dicke model where cavity dissipation and individual atomic decoherence are taken into account. Specifically, we consider that each atom is coupled to independent dephasing and squeezed environments, which makes the widely-adopted Holstein-Primakoff approximation invalid. By discovering the features of quantum phase transition in the presence of the decohering environments, we mainly find that (i) in both normal and superradiant phases, the cavity dissipation and individual atomic decoherence can improve the entanglement and steering between the cavity field and atomic ensemble; (ii) the individual atomic spontaneous emission leads to the appearance of the steering between the cavity field and atomic ensemble but the steering in two directions cannot be simultaneously generated; (iii) the maximal achievable steering in normal phase is stronger than that in superradiant phase; (iv) the entanglement and steering between the cavity output field and the atomic ensemble are much stronger than that with the intracavity, and the steerings in two directions can be achieved even with the same parameters. Our findings reveal unique features of quantum correlations in the open Dicke model in the presence of individual atomic decoherence processes.
ABSTRACT In this paper, we investigate steady‐state quantum squeezing and entanglement in a generalized Dicke model, which features Jaynes–Cummings (JC) and anti–Jaynes–Cummings (AJC) interactions with different strengths, by taking into account of single‐atom spontaneous emission and continuous homodyne detection of the cavity field. We find that a reduction in the strength of the AJC interaction can lead to atomic squeezing, which is otherwise absent when the strengths of the two interactions are equal. Likewise, cavity‐field squeezing and atom‐field entanglement can be enhanced as the strength of the AJC interaction is reduced. Furthermore, continuous measurement is shown to significantly enhance both the squeezing and entanglement in both normal and superradiant phases. In addition, it is revealed that under certain conditions, single‐atom spontaneous emission can also improve the squeezing and entanglement. Our results reveal distinctive characteristics of quantum correlations in the open Dicke model and suggest a promising route for realizing robust nonclassical states in such systems.
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.
We study Einstein-Podolsky-Rosen (EPR) steering properties of quantum phases in the generalized Dicke model (GDM) generated by a cavity Bose-Einstein condensate (BEC) doped with a single impurity. It is shown that the normal and superradiant phases of the GDM exhibit much rich EPR steerability. In the normal phase, there exist one-way EPR steering from the cavity field (condensed atoms) to condensed atoms (the cavity field). In the superradiant phase, there is either one-way or two-way EPR steering for the cavity field and condensed atoms. It is found that the single impurity can act as a single-atom switch of the EPR steering to control the steering direction of one-way EPR steering and the transition between one-way and two-way EPR steering through switching on or off the impurity-BEC coupling. It is proved that the EPR steering parameters can witness the quantum phase transition (QPT) occurrence through the sudden change of the EPR steering parameters at the critical point of the QPT. Our results open a new way to manipulate macroscopic EPR steering and witness the QPT between the normal phase and the superradiant phase in the GDM through a microscopic impurity atom.
The interplay between many-body interactions and controlled dissipation provides a rich setting for nonequilibrium quantum phases. We explore the superradiant phase transitions in a Rydberg-interacting open Dicke model with cavity loss and local dissipation. We find that the nonlinear feedback from atomic interactions stabilizes the atomic collective excited state and induces resonant collective motion, which can be further converted into robust superradiant oscillations with the inclusion of local dissipation. Beyond the mean-field approximation, we prove this system can support the finite-size local dissipative temporal order, i.e., continuous time crystal, from evidences of the decreasing damping of a finite-frequency Liouvillian mode and the linear-size scaling of quantum fluctuations. The correlation between the atomic colletive dynamics and the cavity photon number makes our findings easy to detect from output optical signal. By bridging interacting atomic matter and driven-dissipative cavity QED, our Rydberg-interacting Dicke model provides a unique spin-1/2 platform for exploring dynamical phase transitions and macroscopic temporal order in open quantum matter.
Abstract Quantum technologies critically rely on maintaining coherence and controllable correlations in open systems, yet these resources are fragile under dissipation and noise. To address this challenge, we investigate a hybrid platform composed of two identical three-level atoms in a V-type configuration coupled to a single-mode cavity field prepared in a squeezed coherent state. Using the Lindblad master equation, we numerically simulate the system dynamics, allowing a rigorous treatment of coherent atom–field interactions, interatomic couplings, and cavity losses. Our analysis reveals that squeezing introduces nonclassical correlations that enhance field coherence and support the generation of entanglement under specific regimes. Strong interatomic coupling stabilizes entanglement, while squeezing mitigates decoherence-induced losses. Conversely, large photon amplitudes and cavity dissipation degrade both coherence and bipartite correlations. Quantum steering emerges as the most fragile correlation, yet its persistence can be moderately extended through squeezing. These results identify squeezing and interatomic interactions as complementary resources for optimizing coherence, entanglement, and steering, offering practical strategies for robust quantum communication, information processing, and engineered nonclassical states.
Dicke model describes a collective interaction between the two-level atoms and the light cavity and has been predicted to show a peculiar quantum phase transition, which is a second-order phase transition from a normal phase (in a weak-coupling strength) to a superradiant phase (in a strong-coupling strength). The model plays an important role in illustrating the quantum ground-state properties of many-body macroscopic quantum states. In the experiment, Dicke quantum phase transition in an open system could be formed by a Bose-Einstein condensate coupled to a high-finesse optical cavity. This experiment on the Bose-Einstein condensate trapped in the optical cavity have opened new frontiers, which could combine the cold atoms with quantum optics and makes it possible to enter into the strongly coupled regime of cavity quantum electrodynamics. In strong coupled regime, the atoms exchange the photons many times before spontaneous emission and cavity losses set in. It has become a hot research topic in recent years and plays an important role in many fields of modern physics, such as condensed matter physics, nuclear physics, etc. It can be applied to the manipulation of the geometric phase and entanglement in quantum information and computing. Quantum phase transition has been widely studied for the Dicke model as a typical example. Many different research methods about the mean-field approximation have been used to analyze the ground state properties of the Dicke model. In this paper, we study the ground state properties of two-component Bose-Einstein condensate in a single-mode cavity. Meanwhile, the associated quantum phase transition is described by the spin-coherent-state variational method, whose advantage is that the ground state energy and wave function can be obtained without the thermodynamic limit. By taking the average in the boson coherent state, we obtain an equivalent effective pesudospin Hamiltonian, which will be diagonalized by using the spin coherent state. Finally, we can obtain the energy functional, which is the basics of the variation to obtain the numerical solution of photon number and the expression of the atomic number and the ground state energy. This paper presents a rich phase diagram, which can be manipulated by changing the atom-field coupling imbalance between two components and the atom-field frequency detuning. While in the single-mode Dicke model there exist only the normal phase and the superradiation phase. When the frequency of one component atom is zero or the frequency of the two component atoms are equal in optical cavity, the system returns to the standard Dicke model, in which there occurs the second-order phase transition from the normal phase to the superradiant phase by adjusting the atom-field coupling. In conclusion, we discover that the stimulated radiation comes from the collective state of atomic population inversion, which does not exist in the single-mode Dicke model. Meanwhile, the new stimulated-radiation state S and S, which can only be produced by one component of the atom, are observed in the two-component Bose-Einstein condensates in the single-mode optical cavity. By adjusting the atom-field coupling imbalance and the atom-field frequency detuning (the blue or red detuning), the order of the superradiation state and the stimulated-radiation states can be exchanged between the two components of the atom.