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Physica Scripta

Quantum phase transitions in a Ξ-type atom-cavity QED system

Leilei Ping, Yongfa Zhu, Shan Huang, Lei Li

Published May 12, 2025• 2 citations
Publisher

Abstract

Abstract We theoretically investigated the influence of an atom’s third energy level on quantum phase transitions in a Ξ-type atom-cavity quantum electrodynamics system driven by a coherent field. Through numerical simulations, we demonstrate that for a resonant two-level atom, the critical driving strength for quantum phase transitions scales linearly with the atom-cavity coupling strength. Analysis of the Wigner function confirms the occurrence of first-order quantum phase transitions, characterized by the emergence of coexistence states and symmetry breaking. Introducing a third atomic energy level under resonant conditions inhibits such phase transitions; however, detuning this level under specific parameters promotes them. By modulating the detuning of the third energy level, one can effectively control the critical conditions for quantum phase transitions in this system. These findings hold potential of applications in optically controlled phase transitions, precision measurements, and laser physics.

DOI
10.1088/1402-4896/add797

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Abstract We theoretically investigated the influence of an atom’s third energy level on quantum phase transitions in a Ξ-type atom-cavity quantum electrodynamics system driven by a coherent field. Through numerical simulations, we demonstrate that for a resonant two-level atom, the critical driving strength for quantum phase transitions scales linearly with the atom-cavity coupling strength. Analysis of the Wigner function confirms the occurrence of first-order quantum phase transitions, characterized by the emergence of coexistence states and symmetry breaking. Introducing a third atomic energy level under resonant conditions inhibits such phase transitions; however, detuning this level under specific parameters promotes them. By modulating the detuning of the third energy level, one can effectively control the critical conditions for quantum phase transitions in this system. These findings hold potential of applications in optically controlled phase transitions, precision measurements, and laser physics.
We theoretically investigate the quantum phase transition in the collective systems of qubits in a high quality cavity, where the cavity field is squeezed via the optical parametric amplification process. We show that the squeezed light induced symmetry breaking can result in quantum phase transition without the ultrastrong coupling requirement. Using the standard mean field theory, we derive the condition of the quantum phase transition. Surprisingly, we show that there exists a tricritical point where the first- and second-order phase transitions meet. With specific atom-cavity coupling strengths, both the first- and second-order phase transition can be controlled by the nonlinear gain coefficient, which is sensitive to the pump field. These features also lead to an optical switching from the normal phase to the superradiant phase by just increasing the pump field intensity. The signature of these phase transitions can be observed by detecting the phase space Wigner function distribution with different profiles controlled by the squeezed light intensity. Such superradiant phase transition can be implemented in various quantum systems, including atoms, quantum dots, and ions in optical cavities as well as the circuit quantum electrodynamics system.
Quantum phase transition in Ξ\XiΞ-configuration Tavis-Cummings model driven by an electromagnetic field for a finite number of atoms
The quantum phase transitions of a three-level Tavis-Cummings model in the \Xi Ξ -configuration driven by a single-mode electromagnetic field in a QED cavity are studied for n_a=1,\,2 n a = 1 , 2 , and 4 4 atoms. Although conventional observables like photon number and energy level populations suffice to locate quantum phase transitions, they often lack sensitivity to finite-size effects. Here, we show that the expectation values of the quadratic Casimir invariants associated with the atomic subsystems offer a more robust measure, exhibiting sharp signatures of criticality that are validated by fidelity calculations. Additionally, the von Neumann entropy is employed to map the entanglement landscape between matter and the quantized field. A key finding is that the external driving field acts as a control parameter that shrinks the normal phase region; as the driving intensity increases, the separable ground state vanishes, leading to the dominance of field-matter entanglement across the parameter space.
Interference-induced photon antibunching is investigated for a three-level system coupled to a cavity mode, in which the level scheme is of a lambda type. One of the transitions is weakly coupled to the cavity mode while the other is driven by a control field. Without the control field, i.e. , in the conventional cavity quantum electrodynamics (QED) scheme in the weak coupling regime, photon antibunching can be achieved by carefully choosing the coupling strength and the detuning. This condition can be alleviated by tuning the strength and the frequency of the control field. The condition for the optimal control field that yields photon blockade is derived, and the effects of changing various parameters are investigated. For a given a set of dissipation rates, the atom-cavity coupling strength g needs to be higher than a certain threshold value, although the whole system still remains in the weak coupling regime. A numerical method for finding the optimal parameter regime is proposed.
We study an atom-cavity system composed of an ensemble of three-level atoms interacting with a high-finesse single-mode optical resonator. Two examples of physical models, the laser-driven $\ensuremath{\Lambda}$-type atomic system and the three-level ladder-type atomic system, are investigated in detail. By altering the collective atom-cavity dynamics via an intracavity optical parametric amplification process, a spin-boson model is realized when the composite system operates in the far-detuning regime. When the number of atoms exceeds a critical value, the quantum system undergoes a superradiant phase transition whose dependence on different experimentally adjustable parameters is explored in detail. The effects of the spontaneous emission of atoms and the cavity loss on the phase transition are considered, and measuring the cavity output field itself gives an experimental probe of the superradiant phase transition.
We propose a cavity quantum electrodynamic system consisting of a five-level atom coupled to a single mode of the cavity electromagnetic field. The study is focused on the regime of strong coupling between the cavity and atom. Pump laser fields and cavity fields connect the split energy levels of the atom. Instead of the well-known two-level Dicke model obtained by adiabatic elimination of the high-energy levels, we consider the pump lasers' detunings to the atomic transitions to be very small such that we can examine the influence of the higher-energy states. We have studied the effect of an external coherent drive and incoherent pumping on these higher-energy levels and observed the enhancement of intracavity photon numbers due to quantum coherence effects. The amplification of intracavity photons is achieved even without a population inversion. However, the effect of the coherent and incoherent drive is negligible for very large detunings when the higher-energy states are adiabatically eliminated. At zero and small detunings, the system reaches the steady state at an earlier instant of time for higher incoherent pumping. We find an almost agreeable steady-state behavior of the system's exact full quantum dynamics model and its semiclassical approximation. Our model tries to accurately simulate the open system by considering the cavity decay, spontaneous decay, and dephasing of the system.
Precise control of criticality in superradiant phase transitions is essential for quantum state engineering and the simulation of nonequilibrium phase transitions. Here, we investigate theoretically multicritical phenomena in a dissipative two-Rydberg-atom cavity--QED system. The intrinisic dipole--dipole interaction between the two Rydberg atoms restructures the energy-level landscape of the atomic subsystem, thereby significantly modifying the boundary of the continuous second-order superradiant phase transition, and shifting both the phase boundary and the multicritical point toward weaker atom--cavity strengths. For sufficiently strong dipole--dipole interactions, the continuous second-order phase transition and the multicritical point both disappear, leaving only a discontinuous first--order phase transition that enables the emergence of a superradiant phase even at arbitrarily weak atom--cavity coupling. This work is of fundamental interest for studying dissipative quantum phase transitions, with potential implications for quantum precision measurement and quantum sensing.