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arXiv:2301.05511 · Quantum Science and Technology

Quadrature-PT symmetry: classical-to-quantum transition in noise fluctuations

Wencong Wang, Yanhua Zhai, Dongmei Liu, Xiaoshun Jiang, Saeid Vashahri-Ghamsari, Jianming Wen

Published Jan 24, 2025• 7 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/2058-9565/adae2e

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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.
Our recent research on type-I quadrature parity-time (PT) symmetry, utilizing an open twin-beam system, not only enables observing genuine quantum photonic PT symmetry amid phase-sensitive amplification (PSA) and loss in the presence of Langevin noise but also reveals an additional classical-to-quantum (C2Q) transition in noise fluctuations. In contrast to the previous setup, our exploration of an alternative system assuming no loss involves a type-II PSA-only scheme. This scheme facilitates dual opposing quadrature-PT symmetry, offering a comprehensive and complementary comprehension of C2Q transitions and PT-enhanced quantum sensing with optimal performance in the symmetry unbroken region. Furthermore, our investigation into the quantum correlation with the Einstein-Podolsky-Rosen criteria uncovers previously unexplored connections between PT symmetry and nonclassicality, as well as quantum entanglement within the continuous-variable framework.
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Quantum Langevin noise makes the observation of quantum-optical parity-time (PT) symmetry in an open system with both gain and loss elusive. Here, we challenge this problem by exploiting twin beams produced from a nonlinear parametric process, one undergoing phase-sensitive linear quantum amplification (PSA) and the other engaging balanced loss merely. Unlike previous studies involving phase-insensitive linear quantum amplification (PIA), our PSA-loss scheme enables only one pair of quadratures to evolve PT-symmetrically with variances transiting from periodic oscillations to exponential growths when crossing an exceptional point (EP), while tailors the conjugate pair with PT-adjusted quadrature squeezing. We further investigate such asymmetric PT-quadrature squeezing for quantum sensing by evaluating the quantum Cramer–Rao bound with distinct features beyond existing protocols. The proposed quadrature PT sheds new light on continuous-variable based quantum information and technology.
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.
On-chip non-Hermitian dynamic systems based on dissipative engineering have achieved remarkable results, but intrinsic losses and Langevin noise limit the further development of on-chip non-Hermitian devices. In this article, we propose a simple and feasible on-chip gain-gain coupling fully quantum non-Hermitian sensing model based on quasi-phase-matched second-order degenerate parametric downconversion in periodically poled LiNbO 3 waveguides and demonstrate the feasibility of the theory through finite element simulations. Our theory suggests that this model exhibits hidden quadrature pseudo-PT (parity-time) symmetry behavior and gives rise to the phenomenon of competitive amplification between downconverted photons. Additionally, based on quantum Fisher information, our proposed scheme can achieve quantum-sensing enhancement in the full PT-symmetric domain and super-Heisenberg scaling close to the exceptional point (EP). For detuning disturbances, our system exhibits excellent robustness in the nonspecial EP region. These findings will introduce a new perspective for the development of on-chip non-Hermitian technologies and promote the development of non-Hermitian quantum-sensing theories.
Quasi-parametric amplification (QPA) is a nonlinear interaction in which the idler wave is depleted through a loss mechanism. QPA plays an important role in signal amplification in ultrafast photonics and quantum light generation. In this report, we explore the generalized features characterized by non-Hermitian parity-time ( PT ) symmetry in the QPA process and uncover multiple PT -symmetric phase transitions in such a QPA process in which transitions are ultrasensitive to external parameters. In particular, we demonstrate the feasibility of detection of 10 –11 inhomogeneities of the doped absorber, which is several orders of magnitude more sensitive than similar measurements performed in a linear absorption regime. In doing so, we reveal a family of PT -symmetric phase transitions appearing in the QPA process and provide a distinctive nonlinear optical sensing mechanism for precise optical measurements.