Metrology with PT-Symmetric Cavities: Enhanced Sensitivity near the PT-Phase Transition

Percolation-Induced PT Symmetry Breaking

We propose a new avenue in which percolation, which has been much associated with critical phase transitions, can also dictate the asymptotic dynamics of non-Hermitian systems by breaking PT symmetry. Central to it is our newly designed mechanism of topologically guided gain, where chiral edge wave packets in a topological system experience non-Hermitian gain or loss based on how they are topologically steered. For sufficiently wide topological islands, this leads to irreversible growth due to positive feedback from interlayer tunneling. As such, a percolation transition that merges small topological islands into larger ones also drives the edge spectrum across a real to complex transition. Our discovery showcases intriguing dynamical consequences from the triple interplay of chiral topology, directed gain, and interlayer tunneling, and suggests new routes for the topology to be harnessed in the control of feedback systems.

Realization of chiral two-mode Lipkin-Meshkov-Glick models via acoustics

Thechirality-controlled two-mode Lipkin-Meshkov-Glick (LMG) modelsare mimicked in a potential hybrid quantum system, involving two ensembles of solid-state spins coupled to a pair of interconnected surface-acoustic-wave cavities. With the assistance of dichromatic classical optical drives featuring chiral designs, it can simulate two-mode LMG-type long-range spin-spin interactions with left-right asymmetry. For applications, this unconventional LMG model can not only engineer both ensembles of collective spins into two-mode spin-squeezed states but also simulate novel quantum critical phenomena and time crystal behaviors, among others. Since this acoustic-based system can generate ion-trap-like interactions without requiring any additional trapping techniques, our work is considered a fresh attempt at realizing chiral quantum manipulation of spin-spin interactions using acoustic hybrid systems.

Homotopy, symmetry, and non-Hermitian band topology

Non-Hermitian matrices are ubiquitous in the description of nature ranging from classical dissipative systems, including optical, electrical, and mechanical metamaterials, to scattering of waves and open quantum many-body systems. Seminal line-gap and point-gap classifications of non-Hermitian systems using K-theory have deepened the understanding of many physical phenomena. However, ample systems remain beyond this description; reference points and lines do not in general distinguish whether multiple non-Hermitian bands exhibit intriguing exceptional points, spectral braids and crossings. To address this we consider two different notions: non-Hermitian band gaps and separation gaps that crucially encompass a broad class of multi-band scenarios, enabling the description of generic band structures with symmetries. With these concepts, we provide a unified and comprehensive classification of both gapped and nodal systems in the presence of physically relevant parity-time (PT) and pseudo-Hermitian symmetries using homotopy theory. This uncovers new stable topology stemming from both eigenvalues and wave functions, and remarkably also implies distinct fragile topological phases. In particular, we reveal different Abelian and non-Abelian phases inPT-symmetric systems, described by frame and braid topology. The corresponding invariants are robust to symmetry-preserving perturbations that do not induce (exceptional) degeneracy, and they also predict the deformation rules of nodal phases. We further demonstrate that spontaneousPTsymmetry breaking is captured by Chern-Euler and Chern-Stiefel-Whitney descriptions, a fingerprint of unprecedented non-Hermitian topology previously overlooked. These results open the door for theoretical and experimental exploration of a rich variety of novel topological phenomena in a wide range of physical platforms.

Enhanced rotation sensing with high-order exceptional points in a multi-mode coupled-ring gyroscope

Exceptional points (EPs) of non-Hermitian systems are sensitive to perturbations and facilitate the development of highly sensitive gyroscopes. We propose a compact multi-mode optical gyroscope protocol that incorporates two coupled rings and exhibits a fourth-order EP, achieving higher sensitivity compared to gyroscopes based on second-order EPs. We show that the gyroscope sensitivity can be further improved by deviating from the fourth-order EP due to the gain dependence on the cavity intensity. Furthermore, our protocol exhibits resilience against backscattering from counter-propagating modes, which leads to a reduced angular random walk (ARW) factor and increased sensitivity. These features make our protocol highly promising for advancing high-performance optical gyroscopes and enhancing angular velocity sensing technologies.

Exceptional-Point Sensors Offer No Fundamental Signal-to-Noise Ratio Enhancement

Exceptional-point (EP) sensors exhibit a square-root resonant frequency bifurcation in response to external perturbations, making them appear attractive for sensing applications. However, there is an open debate as to whether or not this sensitivity advantage is negated by additional noise in the system. We settle this debate by showing that increased fundamental noises of quantum and thermal origin in EP sensors, and in particular self-excited (or PT-symmetric) EP sensors, negate the sensitivity benefit. Accordingly, EP sensing schemes are only beneficial either with further quantum enhancement or if compared to sensors limited by technical noise. As many modern sensors are limited by technical noise, EP sensors may still find practical uses despite their lack of a fundamental advantage. Alternatively, we propose a quantum-enhanced EP sensor that achieves a sensing advantage even when limited by quantum or thermal fluctuations.

Engineering dynamical photon blockade with Liouville exceptional points

We investigate the dynamical blockade in a nonlinear cavity and demonstrate the connection between the correlation function g(2)(t) and system parameters in the entire nonlinear region. Utilizing the Liouville exceptional points (LEPs) and quantum dynamics, a near-perfect single-photon blockade (1PB) can be achieved. By fine-tuning system parameters to approach the second-order LEP (LEP2), we improved single-photon statistics in both weak and strong nonlinearity regimes, including a significant reduction of g(2)(t) and a pronounced increase in the single-photon occupation number. In the strong nonlinearity region, the maximum photon population may correspond to stronger antibunching effect. Simultaneously, the time window and period of blockade can be controlled by selecting detuning based on the LEP2. Furthermore, the 1PB exhibits robustness against parameter fluctuations, and this feature can be generalized to systems for implementing single-photon sources with nonharmonic energy levels.

Higher-order exceptional points in parity-time symmetry and the optical gyroscope

The practical application of integrated gyroscopes in engineering has not yet been fully realized due to the linear correlation between the Sagnac effect and dimensions. In recent demonstrations, gyroscopes operating near exceptional points (EPs) under parity-time (PT) symmetry have shown significant potential in enhancing their response to rotational rates. However, constructing higher-order EPs with refined physical properties poses a considerable challenge. Additionally, current methods for constructing higher-order EPs with robustness primarily rely on passive cavities, with almost no reports on constructing robust EPs using PT-symmetric systems that encompass both gain and loss. Here, we propose a robust design for a scalable fabrication of higher-order EP gyroscopes with PT-symmetric structure. We investigate the influence of perturbations on the frequency splitting of the higher-order EP gyroscope and demonstrate that it is possible to achieve a resonance splitting eight orders of magnitude higher than that obtained through the classical Sagnac effect. In comparison to the previously proposed PT-symmetric gyroscope, our solution allows a tunable frequency splitting by adjusting the phase shift, making it more measurable at the output power spectrum.

Toward Heisenberg scaling in non-Hermitian metrology at the quantum regime

Non-Hermitian quantum metrology, an emerging field at the intersection of quantum estimation and non-Hermitian physics, holds promise for revolutionizing precision measurement. Here, we present a comprehensive investigation of non-Hermitian quantum parameter estimation in the quantum regime, with a special focus on achieving Heisenberg scaling. We introduce a concise expression for the quantum Fisher information (QFI) that applies to general non-Hermitian Hamiltonians, enabling the analysis of estimation precision in these systems. Our findings unveil the remarkable potential of non-Hermitian systems to attain the Heisenberg scaling of 1/t, where t represents time. Moreover, we derive optimal measurement conditions based on the proposed QFI expression, demonstrating the attainment of the quantum Cramér-Rao bound. By constructing non-unitary evolutions governed by two non-Hermitian Hamiltonians, one with parity-time symmetry and the other without specific symmetries, we experimentally validate our theoretical analysis. The experimental results affirm the realization of Heisenberg scaling in estimation precision, marking a substantial milestone in non-Hermitian quantum metrology.

Nonlocal Metasurface with Chiral Exceptional Points in the Telecom-Band

The exceptional point (EP) is the critical phase transition point in parity-time (PT) symmetry systems, offering many unique physical phenomena, such as a chiral response. Achieving chiral EP in practical applications has been challenging due to the delicate balance required between gain and loss and complicated fabrication, limiting both working band and device miniaturization. Here, we proposed a nonlocal metasurface featuring orthogonal gold nanorods, where loss modulation is achieved through rod size and lattice pitch. By tuning the coupling strength, we experimentally observed the PT symmetry phase transition and chiral EP in the telecom-band. The experimental and simulated circular conversion dichroism at EP reach 0.79 and 0.99, respectively. We also demonstrated an abrupt phase flip of a specific component near EP theoretically. This work provides a feasible scheme for exploring EP in polarized space within the telecom-band, which may find applications in polarization control, wavelength division multiplexing, ultrasensitive sensing, imaging, etc.

Exceptional Entanglement Phenomena: Non-Hermiticity Meeting Nonclassicality

Non-Hermitian (NH) extension of quantum-mechanical Hamiltonians represents one of the most significant advancements in physics. During the past two decades, numerous captivating NH phenomena have been revealed and demonstrated, but all of which can appear in both quantum and classical systems. This leads to the fundamental question: what NH signature presents a radical departure from classical physics? The solution of this problem is indispensable for exploring genuine NH quantum mechanics, but remains experimentally untouched so far. Here, we resolve this basic issue by unveiling distinct exceptional entanglement phenomena, exemplified by an entanglement transition, occurring at the exceptional point of NH interacting quantum systems. We illustrate and demonstrate such purely quantum-mechanical NH effects with a naturally dissipative light-matter system, engineered in a circuit quantum electrodynamics architecture. Our results lay the foundation for studies of genuinely quantum-mechanical NH physics, signified by exceptional-point-enabled entanglement behaviors.

Higher-order singularities in phase-tracked electromechanical oscillators

Singularities ubiquitously exist in different fields and play a pivotal role in probing the fundamental laws of physics and developing highly sensitive sensors. Nevertheless, achieving higher-order (≥3) singularities, which exhibit superior performance, typically necessitates meticulous tuning of multiple (≥3) coupled degrees of freedom or additional introduction of nonlinear potential energies. Here we propose theoretically and confirm using mechanics experiments, the existence of an unexplored cusp singularity in the phase-tracked (PhT) steady states of a pair of coherently coupled mechanical modes without the need for multiple (≥3) coupled modes or nonlinear potential energies. By manipulating the PhT singularities in an electrostatically tunable micromechanical system, we demonstrate an enhanced cubic-root response to frequency perturbations. This study introduces a new phase-tracking method for studying interacting systems and sheds new light on building and engineering advanced singular devices with simple and well-controllable elements, with potential applications in precision metrology, portable nonreciprocal devices, and on-chip mechanical computing.

Fundamental Sensitivity Limits for Non-Hermitian Quantum Sensors

Considering non-Hermitian systems implemented by utilizing enlarged quantum systems, we determine the fundamental limits for the sensitivity of non-Hermitian sensors from the perspective of quantum information. We prove that non-Hermitian sensors do not outperform their Hermitian counterparts (directly couple to the parameter) in the performance of sensitivity, due to the invariance of the quantum information about the parameter. By scrutinizing two concrete non-Hermitian sensing proposals, which are implemented using full quantum systems, we demonstrate that the sensitivity of these sensors is in agreement with our predictions. Our theory offers a comprehensive and model-independent framework for understanding the fundamental limits of non-Hermitian quantum sensors and builds the bridge over the gap between non-Hermitian physics and quantum metrology.

Entanglement enhancement and EPR steering based on a PT-symmetric-like cavity-opto-magnomechanical hybrid system

We investigate the enhancement of entanglement and EPR steering in a parity-time(PT-) symmetric-like cavity-opto-magnomechanical system. The system consists of an optical cavity, a magnon mode in a ferromagnetic crystal, a phonon mode, and a microwave cavity. Our findings demonstrate that microwave-cavity gain significantly boosts distant quantum entanglement and greatly improves the robustness of bipartite entanglement against environment temperature. Additionally, we observe an enhancement of tripartite entanglement within the system and uncover the phenomenon of entanglement transfer. Notably, we also achieve one-way steering and two-way asymmetric steering in the system. This study offers insights into the integration of traditional optomechanics and cavity magnomechanics, presenting a novel approach to manipulate asymmetric quantum steering between two distant macroscopic objects. The implications of our research extend to the fields of quantum state preparation and quantum information.

Electromagnetically unclonable functions generated by non-Hermitian absorber-emitter

Physically unclonable functions (PUFs) are a class of hardware-specific security primitives based on secret keys extracted from integrated circuits, which can protect important information against cyberattacks and reverse engineering. Here, we put forward an emerging type of PUF in the electromagnetic domain by virtue of the self-dual absorber-emitter singularity that uniquely exists in the non-Hermitian parity-time (PT)-symmetric structures. At this self-dual singular point, the reconfigurable emissive and absorptive properties with order-of-magnitude differences in scattered power can respond sensitively to admittance or phase perturbations caused by, for example, manufacturing imperfectness. Consequently, the entropy sourced from inevitable manufacturing variations can be amplified, yielding excellent PUF security metrics in terms of randomness and uniqueness. We show that this electromagnetic PUF can be robust against machine learning-assisted attacks based on the Fourier regression and generative adversarial network. Moreover, the proposed PUF concept is wavelength-scalable in radio frequency, terahertz, infrared, and optical systems, paving a promising avenue toward applications of cryptography and encryption.

Experimentally Realizable PT Phase Transitions in Reflectionless Quantum Scattering

Above-barrier quantum scattering with truncated real potentials V(x)=-|x|^{p} provides an experimentally accessible platform that exhibits spontaneous parity-time symmetry breaking as p is varied. The unbroken phase has reflectionless states that correspond to bound states in the continuum of the nontruncated potentials at arbitrarily high discrete real energies. In the fully broken phase there are no bound states. There is a mixed phase in which exceptional points occur at specific energies and values of p. These effects should be observable in cold-atom scattering experiments.

Theoretical investigation of dynamics and concurrence of entangled [Formula: see text] and anti-[Formula: see text] symmetric polarized photons

Non-Hermitian systems with parity-time [Formula: see text] symmetry and anti-parity-time [Formula: see text] symmetry have exceptional points (EPs) resulting from eigenvector co-coalescence with exceptional properties. In the quantum and classical domains, higher-order EPs for [Formula: see text] symmetry and [Formula: see text]-symmetry systems have been proposed and realized. Both two-qubits [Formula: see text]-[Formula: see text] and [Formula: see text]-[Formula: see text] symmetric systems have seen an increase in recent years, especially in the dynamics of quantum entanglement. However, to our knowledge, neither theoretical nor experimental investigations have been conducted for the dynamics of two-qubits entanglement in the [Formula: see text]-[Formula: see text] symmetric system. We investigate the [Formula: see text]-[Formula: see text] dynamics for the first time. Moreover, we examine the impact of different initial Bell-state conditions on entanglement dynamics in [Formula: see text]-[Formula: see text], [Formula: see text]-[Formula: see text] and [Formula: see text]-[Formula: see text] symmetric systems. Additionally, we conduct a comparative study of entanglement dynamics in the [Formula: see text]-[Formula: see text] symmetrical system, [Formula: see text]-[Formula: see text] symmetrical system, and [Formula: see text]-[Formula: see text] symmetrical systems in order to learn more about non-Hermitian quantum systems and their environments. Entangled qubits evolve in a [Formula: see text]-[Formula: see text] symmetric unbroken regime, the entanglement oscillates with two different oscillation frequencies, and the entanglement is well preserved for a long period of time for the case when non-Hermitian parts of both qubits are taken quite away from the exceptional points.

Parity-time symmetry breaking optical nanocircuit

Gain and loss balanced parity-time (PT) inversion symmetry has been achieved across multiple platforms including acoustics, electronics, and photonics. Tunable subwavelength asymmetric transmission based on PT symmetry breaking has attracted great interest. However, due to the diffraction limit, the geometric size of an optical PT symmetric system is much larger than the resonant wavelength, which limits the device miniaturization. Here, we theoretically studied a subwavelength optical PT symmetry breaking nanocircuit based on the similarity between a plasmonic system and an RLC circuit. Firstly, the asymmetric coupling of an input signal is observed by varying the coupling strength and gain-loss ratio between the nanocircuits. Furthermore, a subwavelength modulator is proposed by modulating the gain of the amplified nanocircuit. Notably, the modulation effect near the exceptional point is remarkable. Finally, we introduce a four-level atomic model modified by the Pauli exclusion principle to simulate the nonlinear dynamics of a PT symmetry broken laser. The asymmetric emission of a coherent laser is realized by full-wave simulation with a contrast of about 50. This subwavelength optical nanocircuit with broken PT symmetry is of great significance for realizing directional guided light, modulator and asymmetric-emission laser at subwavelength scales.

P T symmetry in a superconducting hybrid quantum system with longitudinal coupling

We propose a scheme consisting of coupled nanomechanical cantilever resonators and superconducting flux qubits to engineer a parity-time- (P T-) symmetric phononic system formed by active and passive modes. The effective gain (loss) of the phonon mode is achieved by the longitudinal coupling of the resonator and the fast dissipative superconducting qubit with a blue-sideband driving (red-sideband driving). A P T-symmetric to broken-P T-symmetric phase transition can be observed in both balanced gain-to-loss and unbalanced gain-to-loss cases. Applying a resonant weak probe field to the dissipative resonator, we find that (i) for balanced gain and loss, the acoustic signal absorption to amplification can be tuned by changing the coupling strength between resonators; (ii) for unbalanced gain and loss, both acoustically induced transparency and anomalous dispersion can be observed around Δ = 0, where the maximum group delay is also located at this point. Our work provides an experimentally feasible scheme to design P T-symmetric phononic systems and a powerful platform for controllable acoustic signal transmission in a hybrid quantum system.

Stable Atomic Magnetometer in Parity-Time Symmetry Broken Phase

Random motion of spins is usually detrimental in magnetic resonance experiments. The spin diffusion in nonuniform magnetic fields causes broadening of the resonance and limits the sensitivity and the spectral resolution in applications like magnetic resonance spectroscopy. Here, by observation of the parity-time (PT) phase transition of diffusive spins in gradient magnetic fields, we show that the spatial degrees of freedom of atoms could become a resource, rather than harmful, for high-precision measurement of weak signals. In the normal phase with zero or low gradient fields, the diffusion results in dissipation of spin precession. However, by increasing the field gradient, the spin system undergoes a PT transition, and enters the PT symmetry broken phase. In this novel phase, the spin precession frequency splits due to spatial localization of the eigenmodes. We demonstrate that, using these spatial-motion-induced split frequencies, the spin system can serve as a stable magnetometer, whose output is insensitive to the inevitable long-term drift of control parameters. This opens a door to detect extremely weak signals in imperfectly controlled environments.

Harnessing Dynamical Encircling of an Exceptional Point in Anti-PT-Symmetric Integrated Photonic Systems

Dynamically encircling an exceptional point in a non-Hermitian system can lead to chiral behaviors, but this process is difficult for on-chip PT-symmetric devices which require accurate control of gain and loss rates. Here, we experimentally demonstrated encircling an exceptional point with a fixed loss rate in a compact anti-PT-symmetric integrated photonic system, where chiral mode switching was achieved within a length that is an order of magnitude shorter than that of a PT-symmetric system. Based on the experimental demonstration, we proposed a topologically protected mode (de)multiplexer that is robust against fabrication errors with a wide operating wavelength range. With the advantages of simplified fabrication and characterization processes, the demonstrated system can be used for studying higher-order exceptional points and for exotic light manipulation.

Exceptional Precision of a Nonlinear Optical Sensor at a Square-Root Singularity

Exceptional points (EPs)-spectral singularities of non-Hermitian linear systems-have recently attracted interest for sensing. While initial proposals and experiments focused on enhanced sensitivities neglecting noise, subsequent studies revealed issues with EP sensors in noisy environments. Here we propose a single-mode Kerr-nonlinear resonator for exceptional sensing in noisy environments. Based on the resonator's dynamic hysteresis, we define a signal that displays a square-root singularity reminiscent of an EP. However, our sensor has crucial fundamental and practical advantages over EP sensors: the signal-to-noise ratio increases with the measurement speed, the square-root singularity is easily detected through intensity measurements, and both sensing precision and information content of the signal are enhanced around the singularity. Our sensor also overcomes the fundamental trade-off between precision and averaging time characterizing all linear sensors. All these unconventional features open up new opportunities for fast and precise sensing using hysteretic resonators.

Quantum Squeezing and Sensing with Pseudo-Anti-Parity-Time Symmetry

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.

A new type of non-Hermitian phase transition in open systems far from thermal equilibrium

We demonstrate a new type of non-Hermitian phase transition in open systems far from thermal equilibrium, which can have place in the absence of an exceptional point. This transition takes place in coupled systems interacting with reservoirs at different temperatures. We show that the spectrum of energy flow through the system caused by the temperature gradient is determined by the [Formula: see text]-potential. Meanwhile, the frequency of the maximum in the spectrum plays the role of the order parameter. The phase transition manifests itself in the frequency splitting of the spectrum of energy flow at a critical point, the value of which is determined by the relaxation rates and the coupling strength. Near the critical point, fluctuations of the order parameter diverge according to a power law with the critical exponent that depends only on the ratio of reservoirs temperatures. The phase transition at the critical point has the non-equilibrium nature and leads to the change in the energy flow between the reservoirs. Our results pave the way to manipulate the heat energy transfer in the coupled out-of-equilibrium systems.

Wireless Power Transfer and Telemetry for Implantable Bioelectronics

Implantable bioelectronic devices are becoming useful and prospective solutions for various diseases owing to their ability to monitor or manipulate body functions. However, conventional implantable devices (e.g., pacemaker and neurostimulator) are still bulky and rigid, which is mostly due to the energy storage component. In addition to mechanical mismatch between the bulky and rigid implantable device and the soft human tissue, another significant drawback is that the entire device should be surgically replaced once the initially stored energy is exhausted. Besides, retrieving physiological information across a closed epidermis is a tricky procedure. However, wireless interfaces for power and data transfer utilizing radio frequency (RF) microwave offer a promising solution for resolving such issues. While the RF interfacing devices for power and data transfer are extensively investigated and developed using conventional electronics, their application to implantable bioelectronics is still a challenge owing to the constraints and requirements of in vivo environments, such as mechanical softness, small module size, tissue attenuation, and biocompatibility. This work elucidates the recent advances in RF-based power transfer and telemetry for implantable bioelectronics to tackle such challenges.

Gain-Free Parity-Time Symmetry for Evanescent Fields

Parity-time (PT) symmetry, satisfied when a system commutes under combined parity and time-reversal operations, enables extreme optical responses in non-Hermitian systems with balanced distributions of gain and loss. In this Letter, we propose a different path for PT symmetry utilizing the evanescent field excitation of anti-PT-symmetric structures, which anticommute with the PT operator and do not necessarily require gain. Beyond offering a robust platform to explore PT symmetry, our study showcases an important link between non-Hermitian physics and near-field interactions, with implications in nanophotonics, plasmonics, and acoustics for nanoimaging, sensing, and communications.

Nonlinear-dissipation-induced nonreciprocal exceptional points

Exceptional points (EPs) have revealed a lot of fundamental physics and promise many important applications. The effect of system nonlinearity on the property of EPs is yet to be well studied. Here, we propose an optical system with nonlinear dissipation to achieve a nonreciprocal EP. Our system consists of a linear whispering-gallery-mode microresonator (WGMR) coupling to a WGMR with nonlinear dissipation. In our system, the condition of EP appearance is dependent on the field intensity in the nonlinear WGMR. Due to the chirality of intracavity field intensity, the EPs and the transmission of the system can be nonreciprocal. Our work may pave the way to exploit nonreciprocal EP for optical information processing.

Dynamically Encircling an Exceptional Point in a Real Quantum System

The exceptional point, known as the non-Hermitian degeneracy, has special topological structure, leading to various counterintuitive phenomena and novel applications, which are refreshing our cognition of quantum physics. One particularly intriguing behavior is the mode switch phenomenon induced by dynamically encircling an exceptional point in the parameter space. While these mode switches have been explored in classical systems, the experimental investigation in the quantum regime remains elusive due to the difficulty of constructing time-dependent non-Hermitian Hamiltonians in a real quantum system. Here we experimentally demonstrate dynamically encircling the exceptional point with a single nitrogen-vacancy center in diamond. The time-dependent non-Hermitian Hamiltonians are realized utilizing a dilation method. Both the asymmetric and symmetric mode switches have been observed. Our Letter reveals the topological structure of the exceptional point and paves the way to comprehensively explore the exotic properties of non-Hermitian Hamiltonians in the quantum regime.

Enhanced optomechanically induced transparency via atomic ensemble in optomechanical system

We investigate the optomechanically induced transparency phenomena assisted through cavity optomechanical system. The system consists of an optical cavity system filled with the two-level atomic ensemble and driven by a weak probe laser as well as a strong coupling fields. Under different driving conditions, the system can exhibit the phenomena of optomechanical induced transparency dip. Specifically, the width of the transparency window increases with an increase in the coupling constant, while decreasing with an increase in atomic decay rate. Furthermore, the induced transparency phenomena are strongly affected by the number of atoms, coupling, and the decay rate. It is found that the larger the number of atoms, the wider the window of induced transparency, and therefore enhance the depth of transparency window. These results may have spectacular applications for slowing and on-chip storage of light pulses by the use of a micro-fabricated optomechanical array.

Universal quantum simulation of single-qubit nonunitary operators using duality quantum algorithm

Quantum information processing enhances human’s power to simulate nature in quantum level and solve complex problem efficiently. During the process, a series of operators is performed to evolve the system or undertake a computing task. In recent year, research interest in non-Hermitian quantum systems, dissipative-quantum systems and new quantum algorithms has greatly increased, which nonunitary operators take an important role in. In this work, we utilize the linear combination of unitaries technique for nonunitary dynamics on a single qubit to give explicit decompositions of the necessary unitaries, and simulate arbitrary time-dependent single-qubit nonunitary operator F(t) using duality quantum algorithm. We find that the successful probability is not only decided by F(t) and the initial state, but also is inversely proportional to the dimensions of the used ancillary Hilbert subspace. In a general case, the simulation can be achieved in both eight- and six-dimensional Hilbert spaces. In phase matching conditions, F(t) can be simulated by only two qubits. We illustrate our method by simulating typical non-Hermitian systems and single-qubit measurements. Our method can be extended to high-dimensional case, such as Abrams–Lloyd’s two-qubit gate. By discussing the practicability, we expect applications and experimental implementations in the near future.

Exceptional points enhance sum sideband generation in a mechanical PT-symmetric system

Systems exhibiting parity-time (PT) symmetry are, in general, non-Hermitian systems, in which exceptional points (EPs) emerge when the system transits from the PT-symmetric phase to the broken-PT-symmetric phase. Based on the abnormal exponential amplification effect in EPs, it is often used to generate, control and transmit light in non-Hermitian systems. In this paper, we theoretically analyze the generation of the frequency components at the sum sideband by considering the nonlinear terms of the optomechanical dynamics in a double-probe-field-driven mechanical PT-symmetric system. Using experimentally achievable parameters, we demonstrate that the efficiency of sum sideband generation (SSG) can be significantly enhanced in EPs, even that the efficiency of SSG can be raised by three orders of magnitude compared to the general optomechanical system by adjusting the appropriate system parameters. These results are beneficial to explore the transmission and conversion of light in chip-scale optical communications.

Color-detuning-dynamics-based quantum sensing with dressed states driving

Exploring quantum technology to precisely measure physical quantities is a meaningful task for practical scientific researches. Here, we propose a novel quantum sensing model based on color detuning dynamics with dressed states driving (DSD) in stimulated Raman adiabatic passage. The model is valid for sensing different physical quantities, such as magnetic field, mass, rotation and so on. For different sensors, the used systems can range from macroscopic scale, e.g. optomechanical systems, to microscopic nanoscale, e.g. solid spin systems. The dynamics of color detuning of DSD passage indicates the sensitivity of sensors can be enhanced by tuning system with more adiabatic or accelerated processes in different color detuning regimes. To show application examples, we apply our approach to build optomechanical mass sensor and solid spin magnetometer with practical parameters.

Rotation-time symmetry in bosonic systems and the existence of exceptional points in the absence of [Formula: see text] symmetry

We study symmetries of open bosonic systems in the presence of laser pumping. Non-Hermitian Hamiltonians describing these systems can be parity-time ([Formula: see text]) symmetric in special cases only. Systems exhibiting this symmetry are characterised by real-valued energy spectra and can display exceptional points, where a symmetry-breaking transition occurs. We demonstrate that there is a more general type of symmetry, i.e., rotation-time ([Formula: see text]) symmetry. We observe that [Formula: see text]-symmetric non-Hermitian Hamiltonians exhibit real-valued energy spectra which can be made singular by symmetry breaking. To calculate the spectra of the studied bosonic non-diagonalisable Hamiltonians we apply diagonalisation methods based on bosonic algebra. Finally, we list a versatile set rules allowing to immediately identifying or constructing [Formula: see text]-symmetric Hamiltonians. We believe that our results on the [Formula: see text]-symmetric class of bosonic systems and their spectral singularities can lead to new applications inspired by those of the [Formula: see text]-symmetric systems.

Efficient Quantum Simulation of an Anti-P-Pseudo-Hermitian Two-Level System

Besides Hermitian systems, quantum simulation has become a strong tool to investigate non-Hermitian systems, such as PT-symmetric, anti-PT-symmetric, and pseudo-Hermitian systems. In this work, we theoretically investigate quantum simulation of an anti-P-pseudo-Hermitian two-level system in different dimensional Hilbert spaces. In an arbitrary phase, we find that six dimensions are the minimum to construct the anti-P-pseudo-Hermitian two-level subsystem, and it has a higher success probability than using eight dimensions. We find that the dimensions can be reduced further to four or two when the system is in the anti-PT-symmetric or Hermitian phase, respectively. Both qubit-qudit hybrid and pure-qubit systems are able to realize the simulation, enabling experimental implementations in the near future.

Observing Information Backflow from Controllable Non-Markovian Multichannels in Diamond

The unavoidable interaction of a quantum open system with its environment leads to the dissipation of quantum coherence and correlations, making its dynamical behavior a key role in many quantum technologies. In this Letter, we demonstrate the engineering of multiple dissipative channels by controlling the adjacent nuclear spins of a nitrogen-vacancy center in diamond. With a controllable non-Markovian dynamics of this open system, we observe that the quantum Fisher information flows to and from the environment using different noisy channels. Our work contributes to the developments of both noisy quantum metrology and quantum open systems from the viewpoints of metrologically useful entanglement.

Equivalence of Effective Non-Hermitian Hamiltonians in the Context of Open Quantum Systems and Strongly Correlated Electron Systems

Recently, it has become clear that non-Hermitian phenomena can be observed not only in open quantum systems experiencing gain and loss but also in equilibrium single-particle properties of strongly correlated systems. However, the circumstances and requirements for the emergence of non-Hermitian phenomena in each field are entirely different. While the implementation of postselection is a significant obstacle to observe the dynamics governed by a non-Hermitian Hamiltonian in open quantum systems, it is unnecessary in strongly correlated systems. Until now, a relation between both descriptions of non-Hermitian phenomena has not been revealed. In this Letter, we close this gap and demonstrate that the non-Hermitian Hamiltonians emerging in both fields are identical, and we clarify the conditions for the emergence of a non-Hermitian Hamiltonian in strongly correlated materials. Using this knowledge, we propose a method to analyze non-Hermitian properties without the necessity of postselection by studying specific response functions of open quantum systems and strongly correlated systems.

Petermann-factor sensitivity limit near an exceptional point in a Brillouin ring laser gyroscope

Exceptional points are singularities of open systems, and among their many remarkable properties, they provide a way to enhance the responsivity of sensors. Here we show that the improved responsivity of a laser gyroscope caused by operation near an exceptional point is precisely compensated by increasing laser noise. The noise, of fundamental origin, is enhanced because the laser mode spectrum loses the oft-assumed property of orthogonality. This occurs as system eigenvectors coalesce near the exceptional point and a bi-orthogonal analysis confirms experimental observations. While the results do not preclude other possible advantages of the exceptional-point-enhanced responsivity, they do show that the fundamental sensitivity limit of the gyroscope is not improved through this form of operation. Besides being important to the physics of microcavities and non-Hermitian photonics, these results help clarify fundamental sensitivity limits in a specific class of exceptional-point sensor.

Operating a laser gyroscope near an exceptional point has been shown to enhance its responsivity. However, here the authors demonstrate in theory and experiment that the enhanced responsivity is exactly compensated by increased noise that is inherent to this system near the exceptional point.

Enhanced four-wave mixing in P T-symmetric optomechanical systems

We investigate the enhanced four-wave mixing (FWM) process in a parity-time (P T)-symmetric optomechanical system, where an active cavity is coupled to a passive cavity supporting a mechanical mode. The passive cavity is optically driven by a strong control field and a weak probe field, and the mechanical mode is excited by a weak coherent driving field. By tuning the coupling strength between the two cavities with balanced gain and loss, we find that the FWM intensity can be significantly enhanced near the exceptional points (EPs) at low control power, which is about 12 orders of magnitude higher than that of the single-cavity case. Due to the interference effect induced by the optical and mechanical driving field, it is shown that the FWM intensity can be further enhanced or suppressed by tuning the amplitude and phase of the mechanical driving field. Moreover, the dependence of the FWM intensity on the frequency and power of the control field is also discussed. Our work provides a route to enhance the four-wave mixing process in a flexible way.

Vector Exceptional Points with Strong Superchiral Fields

Exceptional points (EPs), branch points of complex energy surfaces at which eigenvalues and eigenvectors coalesce, are ubiquitous in non-Hermitian systems. Many novel properties and applications have been proposed around the EPs. One of the important applications is to enhance the detection sensitivity. However, due to the lack of single-handed superchiral fields, all of the proposed EP-based sensing mechanisms are only useful for the nonchiral discrimination. Here, we propose theoretically and demonstrate experimentally a new type of EP, which is called a radiation vector EP, to fulfill the homogeneous superchiral fields for chiral sensing. This type of EP is realized by suitably tuning the coupling strength and radiation losses for a pair of orthogonal polarization modes in the photonic crystal slab. Based on the unique modal-coupling property at the vector EP, we demonstrate that the uniform superchiral fields can be generated with two beams of lights illuminating the photonic crystal slab from opposite directions. Thus, the designed photonic crystal slab, which supports the vector EP, can be used to perform surface-enhanced chiral detection. Our findings provide a new strategy for ultrasensitive characterization and quantification of molecular chirality, a key aspect for various bioscience and biomedicine applications.

Quantum Sensing with a Single-Qubit Pseudo-Hermitian System

Quantum sensing exploits the fundamental features of a quantum system to achieve highly efficient measurement of physical quantities. Here, we propose a strategy to realize a single-qubit pseudo-Hermitian sensor from a dilated two-qubit Hermitian system. The pseudo-Hermitian sensor exhibits divergent susceptibility in a dynamical evolution that does not necessarily involve an exceptional point. We demonstrate its potential advantages to overcome noises that cannot be averaged out by repetitive measurements. The proposal is feasible with the state-of-art experimental capability in a variety of qubit systems, and represents a step towards the application of non-Hermitian physics in quantum sensing.

Observation of Critical Phenomena in Parity-Time-Symmetric Quantum Dynamics

We experimentally simulate nonunitary quantum dynamics using a single-photon interferometric network and study the information flow between a parity-time- (PT-)symmetric non-Hermitian system and its environment. We observe oscillations of quantum-state distinguishability and complete information retrieval in the PT-symmetry-unbroken regime. We then characterize in detail critical phenomena of the information flow near the exceptional point separating the PT-unbroken and PT-broken regimes, and demonstrate power-law behavior in key quantities such as the distinguishability and the recurrence time. We also reveal how the critical phenomena are affected by symmetry and initial conditions. Finally, introducing an ancilla as an environment and probing quantum entanglement between the system and the environment, we confirm that the observed information retrieval is induced by a finite-dimensional entanglement partner in the environment. Our work constitutes the first experimental characterization of critical phenomena in PT-symmetric nonunitary quantum dynamics.

Parity-time-symmetry-breaking gyroscopes: lasing without gain and subthreshold regimes

We show that the lasing threshold for two coupled resonators (CRs) corresponds to lasing without gain (LWG), a phenomenon analogous to lasing without inversion in atomic systems, when parity-time (PT) symmetry is broken. The use of LWG for gyroscopes may resolve some of the difficulties associated with PT-symmetric gyroscopes. In particular, we find that PT-symmetric systems suffer from undamped Rabi oscillations, whereas LWG systems are overdamped. In addition, observation of enhanced sensitivity should be more straightforward in LWG gyros because the enhancement remains above unity even at couplings far from the exceptional point (EP). Finally, LWG gyros operate more like conventional laser gyroscopes with one frequency for each output direction, and therefore there is no ambiguity in the direction of rotation. Gain saturation in CR systems is found to dramatically boost the size of the sensitivity enhancement, eliminate the Rabi oscillations, and enlarge the parameter space around the EP over which the enhancement is expected to occur. A second situation with broken symmetry is also examined: CR systems below threshold. Whereas the pole in sensitivity coincides with the EP at threshold, the pole can occur far away from the EP for subthreshold systems. Our analysis also puts previous results on passive and active fast-light cavities using atomic vapor cells into the context of EP-enhanced sensing with non-Hermitian Hamiltonians.

Quantum Noise Theory of Exceptional Point Amplifying Sensors

Open quantum systems can have exceptional points (EPs), degeneracies where both eigenvalues and eigenvectors coalesce. Recently, it has been proposed and demonstrated that EPs can enhance the performance of sensors in terms of amplification of a detected signal. However, typically amplification of signals also increases the system noise, and it has not yet been shown that an EP sensor can have improved signal-to-noise performance. We develop a quantum noise theory to calculate the signal-to-noise performance of an EP sensor. We use the quantum Fisher information to extract a lower bound for the signal-to-noise ratio (SNR) and show that parametrically improved SNR is possible. Finally, we construct a specific experimental protocol for sensing using an EP amplifier near its lasing threshold and heterodyne signal detection that achieves the optimal scaling predicted by the Fisher bound. Our results can be generalized to higher order EPs for any bosonic non-Hermitian system with linear interactions.

Quantum Transducer Using a Parametric Driven-Dissipative Phase Transition

We study a dissipative Kerr resonator subject to both single- and two-photon detuned drives. Beyond a critical detuning threshold, the Kerr resonator exhibits a semiclassical first-order dissipative phase transition between two different steady states that are characterized by a π phase switch of the cavity field. This transition is shown to persist deep into the quantum limit of low photon numbers. Remarkably, the detuning frequency at which this transition occurs depends almost linearly on the amplitude of the single-photon drive. Based on this phase-switching feature, we devise a sensitive quantum transducer that translates the observed frequency of the parametric quantum phase transition to the detected single-photon amplitude signal. The effects of noise and temperature on the corresponding sensing protocol are addressed, and a realistic circuit-QED implementation is discussed.

Temperature-resistant generation of robust entanglement with blue-detuning driving and mechanical gain

We present a proposal to generate robust optomechanical entanglement induced by the blue-detuning laser and the mechanical gain in a double-cavity optomechanical system. We show that the stability of the system can be obtained by introducing a cavity mode driven by the red-detuning laser in the blue-detuning regime. In contrast to the red-detuning regime, we find that the entanglement in the blue-detuning regime is extremely robust to temperature. The cavity mode driven by the blue-detuning laser can control indirectly the optomechanical entanglement between mechanical resonator and cavity mode driven by the red-detuning laser. Moreover, the entanglement between two cavity modes without direct coupling can also be achieved in our system. Although the entanglement is weak, it is robust to temperature, and meanwhile, the optomechanical entanglement is hardly affected by the temperature when the damping rate of the mechanical oscillator is close to zero. Furthermore, the entanglement amplification at high temperature can be achieved by adjusting the mechanical gain appropriately. Our proposal provides an efficient way to achieve robust optomechanical entanglement in the blue-detuning regime and entanglement amplification in optomechanical system with mechanical gain.

Mechanical switch of photon blockade and photon-induced tunneling

We propose how to mechanically control photon blockade (PB) and photon-induced tunneling (PIT) in an optomechanical system. We show that single-photon blockade (1PB) and two-photon blockade (2PB) can emerge by tuning mechanical driving parameters. Moreover, by varying the strength of mechanical driving, PIT can be converted into 1PB or 2PB, or vice versa, with the constant optical frequency. We refer to this effect as PIT-1PB or PIT-2PB switch. In addition, the switch between 1PB and 2PB can also be realized with this strategy. This mechanical engineering of quantum optical effects can be understood from the shifts of energy levels induced by external mechanical pumping. Our results not only pave the way towards devising new schemes for quantum light switch but also, on a more fundamental level, could shed light on the nonclassicality of the few-photon states.

Classification of Exceptional Points and Non-Hermitian Topological Semimetals

Exceptional points are universal level degeneracies induced by non-Hermiticity. Whereas past decades witnessed their new physics, the unified understanding has yet to be obtained. Here we present the complete classification of generic topologically stable exceptional points according to two types of complex-energy gaps and fundamental symmetries of charge conjugation, parity, and time reversal. This classification reveals unique non-Hermitian gapless structures with no Hermitian analogs and systematically predicts unknown non-Hermitian semimetals and nodal superconductors; a topological dumbbell of exceptional points in three dimensions is constructed as an illustration. Our work paves the way toward richer phenomena and functionalities of exceptional points and non-Hermitian topological semimetals.

Quantum Behavior of a PT-Symmetric Two-Mode System with Cross-Kerr Nonlinearity

Quantum behavior of two oscillator modes, with mutually balanced gain and loss and coupled via linear coupling (including energy conserving as well as energy non-conserving terms) and nonlinear cross-Kerr effect, is investigated. Stationary states are found and their stability analysis is given. Exceptional points for PT -symmetric cases are identified. Quantum dynamics treated by the model of linear operator corrections to a classical solution reveals nonclassical properties of individual modes (squeezing) as well as their entanglement.

Berry phase in an anti-PT symmetric metal-semiconductor complex system

Berry phase can be used to generate quantum state which is robust to environmental noises in quantum information processing. Recently, the relationship between Berry phase and quantum phase transition attracts great attention in the research about topological states of matter. Here, we investigate the behavior of Berry phase in an anti parity-time symmetric system consisting of a metal nanoparticle and semiconductor quantum dot. The change of Berry phase undergoes a sudden death around exceptional point, i.e., Berry phase keeps unchanged in symmetry unbroken region, while it can be well adjusted through changing the strength and frequency of input light in symmetry broken region. The result demonstrated in this paper may be of significant importance in quantum computation and topological physics.