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Advanced Quantum Technologies

Squeezed Displaced Cat States: A Signature of the PT‐Symmetry Phase Transition

Yuetao Chen, G.S. Chen, Shoukang Chang, Jing Wang, Ma Qiang, Shaoyan GAO

Published Apr 1, 2026• 1 citation
Publisher

Abstract

ABSTRACT Harnessing parity–time symmetry with balanced gain and loss profiles has created a variety of opportunities in an electronic system from wireless energy transfer to telemetry sensing and topological defect engineering. However, it is difficult to capture the ‐symmetry phase transition in an electronic system due to the limitation of probing the virtual energy spectrum. Here, we proposed a scheme to probe the ‐symmetry phase transition in an Non‐Hermitian (NH) Su–Schrieffer–Heeger (SSH) electronic chain coupled to a cavity. We show that, when ‐symmetry is broken, the cavity ground state is a Squeezed Displaced Schrödinger cat (SDSc) state, which immediately disappears when the symmetry recovers. Thus, our proposal provides a platform for capturing ‐symmetry phase transition based on cavity ground state. Furthermore, we demonstrate that the generation of the SDSc state in our scheme is related to spontaneous symmetry breaking mechanism. Besides, we exploit the cavity ground state to estimate the phase in the optical interferometer, and show that the quantum Fisher information and nonclassicality will sharply decline when symmetry recovers. This suggests that the phase estimation is preferably performed in the broken PT‐symmetry phase near the exceptional‐points. Our proposal offers a scheme not only to manipulate but also to probe the properties of electronic materials based on quantum Floquet engineering, and improve the utilization of cavity ground states in quantum metrology.

DOI
10.1002/qute.202500905

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Squeezed Displaced Schrödinger-cat state as a signature of the PT-symmetry phase transition

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Parity-time (PT ) symmetric systems are gain-loss systems whose dynamics are governed by non-Hermitian Hamiltonians with degeneracies at exceptional-points (EPs) and has been studied in various photonic, electrical, mechanical systems, and so on. However, it is still an open question how to capture PT symmetry phase transition in electronic system where the transport properties of electron will be dramatically effected. Fortunately, the hybridization between photon and electron offers a novel way not only to control but also probe material properties. Here, we investigate a cavity coupled to a non-Hermitian Su-Schrieffer-Heeger (SSH) chain within mean-field ansatzs. We find that Squeezed Displaced Schrodinger cat (SDSc) will emerge with high fidelity in cavity ground state when PT -symmetry is broken and the fidelity will experience a sharp drop from almost 1 to 0 as PT symmetry recovers. Additionally, in semiclassical limit, we find that there exists local extrema at two sides of $x=0$ in semiclassical photon Hamiltonian $H_{\rm eff}(x, p)$, a clear signature of the emergence of SDSc state in cavity ground state. Thus, the appearance of SDSc state can be used to capture PT-symmetry phase transition which can not be modified by cavity mode. Besides, we exploit the cavity ground state to estimate the phase in the optical interferometer, and show that the quantum Fisher information and nonclassicality will sharply decline at EPs. This reveals that PT-symmetry breaking in electronic materials can also be captured by the quantum Fisher information and nonclassicality in phase estimation.

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arXiv:2405.12080•Advanced Quantum Technologies•Aug 4, 2024•11 citations
ABSTRACT Harnessing parity–time symmetry with balanced gain and loss profiles has created a variety of opportunities in an electronic system from wireless energy transfer to telemetry sensing and topological defect engineering. However, it is difficult to capture the ‐symmetry phase transition in an electronic system due to the limitation of probing the virtual energy spectrum. Here, we proposed a scheme to probe the ‐symmetry phase transition in an Non‐Hermitian (NH) Su–Schrieffer–Heeger (SSH) electronic chain coupled to a cavity. We show that, when ‐symmetry is broken, the cavity ground state is a Squeezed Displaced Schrödinger cat (SDSc) state, which immediately disappears when the symmetry recovers. Thus, our proposal provides a platform for capturing ‐symmetry phase transition based on cavity ground state. Furthermore, we demonstrate that the generation of the SDSc state in our scheme is related to spontaneous symmetry breaking mechanism. Besides, we exploit the cavity ground state to estimate the phase in the optical interferometer, and show that the quantum Fisher information and nonclassicality will sharply decline when symmetry recovers. This suggests that the phase estimation is preferably performed in the broken PT‐symmetry phase near the exceptional‐points. Our proposal offers a scheme not only to manipulate but also to probe the properties of electronic materials based on quantum Floquet engineering, and improve the utilization of cavity ground states in quantum metrology.
Parity-time (PT ) symmetric systems are gain-loss systems whose dynamics are governed by non-Hermitian Hamiltonians with degeneracies at exceptional-points (EPs) and has been studied in various photonic, electrical, mechanical systems, and so on. However, it is still an open question how to capture PT symmetry phase transition in electronic system where the transport properties of electron will be dramatically effected. Fortunately, the hybridization between photon and electron offers a novel way not only to control but also probe material properties. Here, we investigate a cavity coupled to a non-Hermitian Su-Schrieffer-Heeger (SSH) chain within mean-field ansatzs. We find that Squeezed Displaced Schrodinger cat (SDSc) will emerge with high fidelity in cavity ground state when PT -symmetry is broken and the fidelity will experience a sharp drop from almost 1 to 0 as PT symmetry recovers. Additionally, in semiclassical limit, we find that there exists local extrema at two sides of x=0x=0x=0 in semiclassical photon Hamiltonian Heff(x,p)H_{\rm eff}(x, p)Heff​(x,p), a clear signature of the emergence of SDSc state in cavity ground state. Thus, the appearance of SDSc state can be used to capture PT-symmetry phase transition which can not be modified by cavity mode. Besides, we exploit the cavity ground state to estimate the phase in the optical interferometer, and show that the quantum Fisher information and nonclassicality will sharply decline at EPs. This reveals that PT-symmetry breaking in electronic materials can also be captured by the quantum Fisher information and nonclassicality in phase estimation.
Abstract While gain-loss-coupled photonic platforms have achieved significant success in studying classical parity-time (PT) symmetry, they encounter challenges in demonstrating pure quantum effects due to incompatible operator transformations and Langevin noise. Here, we present compelling evidence that a non-Hermitian (NH) twin-beam system, undergoing phase-sensitive amplification and balanced loss, not only enables observing the usual eigenvalue-associated PT phase transition but also exhibits distinctive features absent in classical NH or traditional Hermitian quantum scenarios, encompassing quadrature PT symmetry, anomalous loss-induced quadrature squeezing, and classical-to-quantum (C2Q) transitions in noise fluctuations. Furthermore, our proposed bipartite open system promises optimal sensing for various quantum observable measurements, showcasing an improved signal-to-noise ratio and sensitivity, constrained by quantum Cramér–Rao bound or Fisher information. These findings deepen the comprehension of authentic quantum optical PT symmetry involving both gain and loss, addressing contentious issues and illuminating new facets of the subject.
The emergence of parity-time (PT) symmetry has greatly enriched our study of symmetry-enabled non-Hermitian physics, but the realization of quantum PT symmetry faces an intrinsic issue of unavoidable symmetry-breaking Langevin noises. Here we construct a quantum pseudo-anti-PT (pseudo-APT) symmetry in a two-mode bosonic system without involving Langevin noises. We show that the spontaneous pseudo-APT symmetry breaking leads to an exceptional point, across which there is a transition between different types of quantum squeezing dynamics; i.e., the squeezing factor increases exponentially (oscillates periodically) with time in the pseudo-APT-symmetric (broken) region. Such dramatic changes of squeezing factors and quantum dynamics near the exceptional point are utilized for ultraprecision quantum sensing. These exotic quantum phenomena and sensing applications can be experimentally observed in two physical systems: spontaneous wave mixing nonlinear optics and atomic Bose-Einstein condensates. Our Letter offers a physical platform for investigating exciting APT symmetry physics in the quantum realm, paving the way for exploring fundamental quantum non-Hermitian effects and their quantum technological applications.
Pure dephasing is the dominant leak mechanism in photonic cat qubits because its phase errors disrupt the parity protection, rendering the qubit vulnerable to energy relaxation. In this manuscript, we reveal that this dephasing mechanism conceals an interesting physical phenomenon: it induces \textit{asymmetric leakage} from the cat-state subspace, where even- and odd-parity cat states decay at different rates. This leak asymmetry enables the dynamics of the system to be described by a non-Hermitian Hamiltonian, thereby transforming the cat qubit into a platform with controllable gain and loss for probing non-Hermitian physics. Within this platform, we demonstrate the possibility to control the parity-time symmetry phase transition in a single cat qubit by adjusting its amplitude. Moreover, we couple two cat qubits to realize an entanglement phase transition induced by the exceptional point. Our work constructs a controllable non-Hermitian system simulator, overturning the conventional paradigm that treats dephasing as harmful noise.
Abstract Parity‐time (PT) symmetric systems with gain‐loss balanced structures can have entirely real eigenenergy spectra despite their non‐Hermitian nature, leading to peculiar discoveries such as single‐mode lasers, wireless power transfer, and non‐reciprocal light propagation. Recently, the study of PT‐symmetry has extended to the quantum realm, inspiring a search for PT‐symmetric quantum effects as well as their unique applications. Here, quantum entanglement and sensing with a PT‐symmetric system of two qubits are studied with Ising‐type interaction. It is shown that exceptional points (EPs) can induce exceptional entanglement phenomena such as collapse‐revival and steady‐state entanglement on the two sides of EPs. The entanglement in the PT‐symmetric system is also found to be generated more quickly than that in the Hermitian counterpart. In addition, a scheme for realizing EP‐enhanced quantum sensing is proposed by calculating the quantum Fisher information to estimate the parameters of the system. The work provides new insights into EP‐engineered quantum effects and can benefit a wide range of applications based on non‐Hermitian quantum devices.
Abstract Light‐matter interactions provide an ideal testground for interplay of critical phenomena, topological transitions, quantum metrology, and non‐Hermitian physics with high controllability and tunability. The present work considers two fundamental non‐Hermitian Jaynes‐Cummings models in light‐matter interactions that possess real energy spectra in parity‐time (PT) symmetry and anti‐PT symmetry. The quantum Fisher information is shown to be critical around the transitions at the exceptional points and exhibit a super universality, with respect to different parameters, all energy levels, both models, symmetric phases, and symmetry‐broken phases, which guarantees a universally high measurement precision in quantum metrology. In particular, the transitions are found to be both symmetry‐breaking Landau‐class transitions (LCTs) and symmetry‐protected topological‐class transitions (TCTs), thus realizing a simultaneous occurrence of critical LCTs and TCTs that are conventionally incompatible due to contrary symmetry requirements. Besides establishing a paradigmatic case to break the incompatibility of the LCTs and the TCTs in non‐Hermitian systems, the both availabilities of the sensitive critical feature and the robust topological feature can also provide more potential for designing quantum devices or sensors.