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arXiv:2412.08123 · Physical Review A

Robustness of entanglement in a non-Hermitian cavity-optomechanical system even away from exceptional points

Jia-Jia Wang, Yu-Hong He, Chang-Geng Liao, Rongxin Chen, Jacob Dunningham

Published Jun 16, 2025• 5 citations
arXivHTMLPDF

Abstract

Quantum physics can be extended into the complex domain by considering non-Hermitian Hamiltonians that are $\mathcal{PT}$-symmetric. These exhibit exceptional points (EPs) where the eigenspectrum changes from purely real to purely imaginary values and have useful properties enabling applications such as accelerated entanglement generation and the delay of the sudden death of entanglement in noisy systems. An interesting question is whether similar beneficial effects can be achieved away from EPs, since this would extend the available parameter space and make experiments more accessible. We investigate this by considering a $\mathcal{PT}$-symmetric optomechanical system but also consider what happens when two-mode squeezing interactions are included, taking us into the pseudo-Hermitian regime. The addition of squeezing is motivated by an attempt to extend the lifetime of the system's entanglement. While this does not prove to be the case, rich dynamics are nonetheless observed in both the pseudo-Hermitian and $\mathcal{PT}$-symmetric systems, including the sudden death and revival of entanglement under certain conditions. In both cases, we find that the sudden disappearance of entanglement can be mitigated at EPs, and also show that the revival of entanglement is quite robust to thermal noise in a group of parameters away from the EPs. This investigation extends our understanding of non-Hermitian systems and opens a new perspective for the development of quantum devices in non-Hermitian systems even away from EPs.

DOI
10.1103/f8pm-7z7r

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Quantum physics can be extended into the complex domain by considering non-Hermitian Hamiltonians that are PT\mathcal{PT}PT-symmetric. These exhibit exceptional points (EPs) where the eigenspectrum changes from purely real to purely imaginary values and have useful properties enabling applications such as accelerated entanglement generation and the delay of the sudden death of entanglement in noisy systems. An interesting question is whether similar beneficial effects can be achieved away from EPs, since this would extend the available parameter space and make experiments more accessible. We investigate this by considering a PT\mathcal{PT}PT-symmetric optomechanical system but also consider what happens when two-mode squeezing interactions are included, taking us into the pseudo-Hermitian regime. The addition of squeezing is motivated by an attempt to extend the lifetime of the system's entanglement. While this does not prove to be the case, rich dynamics are nonetheless observed in both the pseudo-Hermitian and PT\mathcal{PT}PT-symmetric systems, including the sudden death and revival of entanglement under certain conditions. In both cases, we find that the sudden disappearance of entanglement can be mitigated at EPs, and also show that the revival of entanglement is quite robust to thermal noise in a group of parameters away from the EPs. This investigation extends our understanding of non-Hermitian systems and opens a new perspective for the development of quantum devices in non-Hermitian systems even away from EPs.
Although non-Hermitian dynamics near exceptional points (EPs) provide a route to accelerated entanglement generation, entanglement can also be generated far from EPs at comparable or even higher rates. However, the behavior of such entanglement in open systems remains largely unexplored, rendering it highly susceptible to environmental noise. Here, we study entanglement dynamics in two coupled qubits described by a non-Hermitian Hamiltonian, where the dissipative rates are subject to stochastic noise. We focus on the regime away from EPs. Our approach demonstrates that, even in the presence of classical noise, rich dynamical control can be achieved, enabling highly efficient entanglement generation with a timescale that is significantly shorter than that of both Hermitian systems and EP-based non-Hermitian protocols. Additionally, the timescale is independent of the number of qubits, highlighting favorable scalability for multipartite entanglement generation and facilitating integration into future photonic quantum processors.
Higher-order exceptional points (EPs), resulting from non-Hermitian degeneracies, have shown greater advantages in sensitive enhancement than second-order EPs (EP2s). Therefore, seeking higher-order EPs in various quantum systems is important for quantum information science. Here we propose a benchmark cavity optomechanical (COM) system consisting of a mechanical resonator coupled to two cavities via radiation pressure for predicting the third-order exceptional point (EP3). We first give the pseudo-Hermitian condition for the non-Hermitian COM system by taking the bath effects into account. Then we consider the mechanical gain effect, and we find that the pseudo-Hermitian COM system without PT\mathcal{PT}PT symmetry can host both EP3 and EP2 for symmetric and asymmetric cavities. In the symmetric case, only EP3 or EP2 can be predicted in the parameter space, but EP3 and EP2 can be transformed into each other by tuning the optomechanical coupling strength in the asymmetric case. We further consider the case of one cavity with gain. For this case, the pseudo-Hermitian COM system is PT\mathcal{PT}PT symmetric and can also host EP3 or EP2. The influence of system parameters on them is discussed. Our proposal provides a potential way to realize sensitive detection and study other physical phenomena around higher-order EPs in non-Hermitian COM systems.
Higher-order exceptional points (EPs) in non-Hermitian systems have attracted great interest due to their advantages in sensitive enhancement and distinct topological features. However, realization of such EPs is still a challenge because more fine-tuning parameters are generically required in quantum systems, compared to the second-order EP (EP2). Here, we propose a non-Hermitian three-mode optomechanical system in the blue-sideband regime for predicting the third-order EP (EP3). By deriving the pseudo-Hermitian condition for the proposed system, one cavity with loss and the other with gain must be required. Then we show that EP3 or EP2 can be observed when the mechanical resonator (MR) is neutral, loss, or gain. For the neutral MR, we find that two degenerate or two nondegenerate EP3s can be predicted by tuning system parameters in the parameter space, while four nondegenerate EP2s can be observed when the system parameters deviate from EP3s, which is distinguished from the previous study in the red-detuned optomechanical system. For the gain (loss) MR, we find that only two degenerate EP3s or EP2s can be predicted by tuning enhanced coupling strength. Our proposal provides a potential way to predict higher-order EPs or multiple EP2s and study multimode quantum squeezing around EPs using blue-detuned non-Hermitian optomechanical systems.
The exploration of the effect of non-Hermitian (NH) in quantum systems is gaining renewed momentum as a result of the recent progress in experiments. It has been indicated that the ability to engineer the orders of exceptional points (EPs) can be fundamental to its applications in quantum control, such as accelerating entanglement generation; however, an initial survey of the interactions between different orders of EPs is still missing. In this work, we try to partially address this issue by employing a non-reciprocally coupled cavity system which can be experimentally realizable with a two-dimensional reconfigurable NH gauged laser array. With deliberate design, our systems display both second and third orders of EPs. The sign of a novel, purely quantum continuous entanglement phase transition is observed, which reveals how multi-EP interactions alter entanglement dynamics across different regimes while maintaining accelerated generation. Our findings reveil the genuinely quantum NH physics of higher-order EPs, which has opened up a new avenue for future investigations of the higher-order degeneracy application and the dynamic phase transitions of quantum systems.
Non-Hermitian quantum systems have attracted significant interest in recent years due to the presence of unique spectral singularities in which eigenvalues and eigenvectors coalesce. Those singularities are known as exceptional points (EPs). The drastic changes of the non-Hermitian systems around their EPs have led to unique entanglement dynamics, which remained elusive until quite recently. In this work, we theoretically investigate the robustness of multipartite entanglement induced by EPs of the passive PT -symmetric non-Hermitian superconducting qubits, both in stand-alone configurations and hybrid setups with Hermitian qubits. In particular, we consider the qubits with both all-to-all and nearest-neighbor couplings under uniform and nonuniform coupling strengths. Our results reveal that non-Hermitian qubits with all-to-all coupling generate GHZ states, while those with nearest-neighbor interactions produce W states. These entangled states are resilient to nonuniform couplings, off-resonant driving fields, and decoherence effects. Moreover, the hybrid configurations combining Hermitian and non-Hermitian qubits indicate the necessity of EPs for rapidly generating and maintaining genuine multipartite entanglement. Additionally, driving the PT -symmetric qubits with a strong Rabi frequency can help sustain the entanglement over time by countering losses, while strong interqubit coupling favors the entangled states in the low dissipation regime. We also demonstrate that increasing the number of non-Hermitian qubits speeds up multipartite entanglement generation due to enhanced collective interactions. These findings reveal that exploiting non-Hermitian systems and their associated EPs is beneficial for generating robust and genuine entangled states which are useful for both fundamental studies and quantum technologies.
We investigate higher-order exceptional points and quantum squeezing of exciton polaritons in a pseudo-Hermitian semiconductor optomechanical system. We show that a third-order exceptional point (EP3) can emerge from the tripartite coupling among photons, excitons, and phonons under pseudo-Hermitian conditions. A pronounced two-mode quantum squeezing of exciton polaritons is revealed, and we demonstrate that this squeezing is significantly enhanced in the vicinity of the EP3. Furthermore, we find that in the PT-symmetric phase, the squeezing dynamics produce a frequency comb of exciton polaritons, whereas the squeezing remains constant over time in the PT-symmetry broken phase and exactly at the EP3. The sudden change in quantum squeezing dynamics can be used to probe the phase transition and the EP3. Our work opens a pathway to manipulate quantum squeezing in semiconductor optomechanical platforms, offering potential advantages for quantum sensing and metrology.