Non-Hermitian degeneracies and unidirectional reflectionless atomic lattices

Terminal-coupling induced critical eigenspectrum transition in closed non-Hermitian loops

A hallmark feature of non-Hermitian (NH) systems is the non-Hermitian skin effect (NHSE), in which the eigenenergy spectra of the system under open boundary conditions (OBC) and periodic boundary conditions (PBC) differ markedly from each other. In particular, the critical NHSE occurs in systems consisting of multiple non-Hermitian chains coupled in parallel where even an infinitesimally small inter-chain coupling can cause the thermodynamic-limit eigenenergy spectrum of the system to deviate significantly from the OBC spectra of the individual component chains. We overturn the conventional wisdom that multiple chains are required for such critical transitions by showing that such a critical effect can also be induced in a single finite-length non-Hermitian chain where its two ends are connected together by a weak terminal coupling to form a closed loop. An infinitesimally small terminal coupling can induce the thermodynamic-limit energy spectrum of the closed loop to switch from the OBC to the PBC spectrum of the chain. Similar to the critical NHSE, this switch occurs abruptly when the chain length exceeds a critical size limit. We explain analytically the underlying origin of the effect in a Hatano-Nelson chain system, and demonstrate its generality in more complex one-dimensional non-Hermitian chains. Our findings illustrate the generality of critical size-dependent effects in finite NH systems that arise from the interplay between the interfacial boundary conditions and the influence of edge localization.

Spatial susceptibility modulation and controlled unidirectional reflection amplification via four-wave mixing

Control of unidirectional light propagation is of paramount importantance to optical signal processing and optical communication. Especially, the amplified optical signal can isolate noise well that may provide more applications. In this work, we propose a dynamically modulated regime to realize unidirectional reflection amplification in a short and dense uniform atomic medium, and all atoms are driven into four-level double-Λ type by two coupling fields with linearly varied intensities along x direction and two weak probe fields. Based on four-wave mixing resonance and the broken spatial symmetry, the complete nonreciprocal reflection (unidirectional reflection) can be amplified with reflectivity more than 2.0, even to 6.0. In addition, the width, height, and position of the unidirectional reflection bands can be tunable. Thus, our regime is feasible and may inspire further applications in all-optical networks that require controllable unidirectional light amplification.

Discrete dynamics of light in an anti-parity-time symmetric photonic lattice in atomic vapors

We demonstrate the realization of an anti-parity-time (PT)-symmetric photonic lattice in a coherent three-level Λ-type 85Rb atomic system both experimentally and theoretically. Such an instantaneously reconfigurable anti-PT-symmetric photonic lattice is "written" by two one-dimensional coupling fields, which are arranged alternately along the x direction and can modulate the refractive index of the atomic vapor in a spatially periodical manner via controllable atomic coherence. By properly adjusting the relevant atomic parameters, the phase shift between two adjacent lattice channels occurs in the constructed non-Hermitian photonic system. Such a readily reconfigurable anti-PT-symmetric photonic lattice may open the door for demonstrating the discrete characteristics of the optical waves in periodic anti-PT-symmetric photonic systems.

Non-Hermitian Waveguide Cavity QED with Tunable Atomic Mirrors

Optical mirrors determine cavity properties by means of light reflection. Imperfect reflection gives rise to open cavities with photon loss. We study an open cavity made of atom-dimer mirrors with a tunable reflection spectrum. We find that the atomic cavity shows anti-PT symmetry. The anti-PT phase transition controlled by atomic couplings in mirrors indicates the emergence of two degenerate cavity supermodes. Interestingly, a threshold of mirror reflection is identified for realizing strong coherent cavity-atom coupling. This reflection threshold reveals the criterion of atomic mirrors to produce a good cavity. Moreover, cavity quantum electrodynamics with a probe atom shows mirror-tuned properties, including reflection-dependent polaritons formed by the cavity and probe atom. Our Letter presents a non-Hermitian theory of an anti-PT atomic cavity, which may have applications in quantum optics and quantum computation.

Lopsided optical diffraction in a loop electromagnetically induced grating

We propose a theoretical scheme in a cold rubidium-87 (⁸⁷Rb) atomic ensemble with a non-Hermitian optical structure, in which a lopsided optical diffraction grating can be realized just with the combination of single spatially periodic modulation and loop-phase. Parity-time (PT) symmetric and parity-time antisymmetric (APT) modulation can be switched by adjusting different relative phases of the applied beams. Both PT symmetry and PT antisymmetry in our system are robust to the amplitudes of coupling fields, which allows optical response to be modulated precisely without symmetry breaking. Our scheme shows some nontrivial optical properties, such as lopsided diffraction, single-order diffraction, asymmetric Dammam-like diffraction, etc. Our work will benefit the development of versatile non-Hermitian/asymmetric optical devices.

Two-color unidirectional reflections by modulating the spatial susceptibility in a homogeneous atomic medium

Non-reciprocal reflections of optical signals are unusual yet fascinating to achieve the imminent applications of non-reciprocal photonic devices and circuits. The complete non-reciprocal reflection (unidirectional reflection) was recently found to be achievable in a homogeneous medium, if the real and imaginary parts of the probe susceptibility satisfy the spatial Kramers-Kronig (KK) relation. We propose a coherent four-level tripod model for realizing dynamically tunable two-color non-reciprocal reflections by applying two control fields with linearly modulated intensities. We found that, the unidirectional reflection can be obtained if the non-reciprocal frequency regions are located in the electromagnetically induced transparency (EIT) windows. This mechanism is to break the spatial symmetry by the spatial modulation of susceptibility to induce unidirectional reflections, the real and imaginary parts of the probe susceptibility are no longer required to satisfy the spatial KK relation.

Optomechanically-induced nonreciprocal conversion between microwave and optical photons

We theoretically propose a scheme of the nonreciprocal conversion device between photons of two arbitrary frequencies in a hybrid cavity optomechanical system, where two optical cavities and two microwave cavities are coupled to two different mechanical resonators via radiation pressure. Two mechanical resonators are coupled together via the Coulomb interaction. We study the nonreciprocal conversions between both the same and different types of frequency photons. The device is based on multichannel quantum interference to break the time-reversal symmetry. Our results show the perfect nonreciprocity conditions. By adjusting the Coulomb interaction and the phase differences, we find that the nonreciprocity can be modulated and even transformed into reciprocity. These results provide new insight into the design of nonreciprocal devices, including isolators, circulators, and routers in quantum information processing and quantum networks.

Double exceptional points in grating coupled metal-insulator-metal heterostructure

In this work we theoretically study the exceptional points and reflection spectra characteristics of a grating coupled metal-insulator-metal heterostructure, which is a non-Hermitian system. Our results show that by selecting suitable geometrical parameters with grating periodicity @150 nm, that satisfy zero reflection condition, double exceptional points appear in a mode bifurcation regime. Furthermore, the thickness of partition metal layer between two cavities plays an important role in controlling the reflection properties of the heterostructure. There is a clear mode splitting when the partition layer allows strong coupling between the two cavity modes. Conversely, in weak coupling regime the mode splitting becomes too close to be distinguished. Moreover, the vanishing of reflection leads to unidirectional reflectionless propagation, which is also known as unidirectional invisibility. With grating periodicity ≥400nm, the transmissions for forward and backward incident directions are no longer the same due to the generation of diffraction. High contrast ratio (≈1) between the two incident directions leads to asymmetric transmission. This work lays the basis for designing double exceptional points and asymmetric transmission in coupled non-Hermitian photonics system. The proposed heterostructure can be a good candidate for new generation optical communications, optical sensing, photo-detection, and nano-photonic devices.

Three-color reflections in one-dimensional ordered and disordered atomic lattices with trapped N-type cold atoms

Investigating and controlling light propagation in one-dimensional (1D) ordered and disordered atomic lattices is critical both fundamentally and for applications. In this study, cold atoms are trapped in 1D optical lattice and driven to the four-level N configuration. In each period, the atoms exhibit a Gaussian density distribution with the average atomic density N₀ (1 + Δ_k). When the random number Δ_k = 0 (the atomic density N_k(z)) corresponding to an ordered 1D atomic lattice, there are three reflection regions of high reflectivity located in two EIT windows and one large detuning range. However, the atomic density may increase (N k+(z) with Δ_k > 0) or decrease (N k-(z) with Δ_k < 0) owing to the imperfect manufacturing process or random distribution of atoms corresponding to a disordered atomic lattice. The results show that the width and height of reflections can be raised (reduced) by the increased (decreased) ratio of N k+(z)/N _k (z) (N k-(z)/N _k (z)) with the random distribution of lattice cells with N k+(z) (N k-(z)). When a cluster of disordered lattice cells with N k+(z) and N k-(z) is located at the front or tail of the atomic lattice, reflection symmetry can be broken. However, the symmetry and robustness can be well preserved with the random fluctuation of the average atomic density in each lattice cell.

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.

Matter-wave gap solitons and vortices in three-dimensional parity-time-symmetric optical lattices

Past decades have witnessed the emergence and increasing expansion of parity-time (PT)-symmetric systems in diverse physical fields and beyond as they manifest entirely all-real spectra, although being non-Hermitian. Nonlinear waves in low-dimensional PT-symmetric non-Hermitian systems have recently been explored broadly; however, understanding these systems in higher dimensions remains abstruse and has yet to be revealed. We survey, theoretically and numerically, matter-wave nonlinear gap modes of Bose-Einstein condensates with repulsive interparticle interactions in three-dimensional PT optical lattices with emphasis on multidimensional gap solitons and vortices. Utilizing direct perturbed simulations, we address the stability and instability areas of both localized modes in the underlying linear band gap spectra. Our study provides deep and consistent understandings of the formation, structural property, and dynamics of coherent localized matter waves supported by PT optical lattices in multidimensional space, thus opening a way for exploring and stabilizing three-dimensional localized gap modes in non-Hermitian systems

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3D parity-time (PT)-symmetric optical lattices are used to overcome the collapse of 3D ultracold atoms.

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3D matter-wave gap solitons and vortices are found in PT-symmetric optical lattices.

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Rich properties and dynamics of 3D matter-wave localized modes are disclosed.

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In-depth soliton physics is provided in 3D non-Hermitian periodic physical systems.

Quantum Squeezing Induced Optical Nonreciprocity

We propose an all-optical approach to achieve optical nonreciprocity on a chip by quantum squeezing one of two coupled resonator modes. By parametric pumping a χ^{(2)}-nonlinear resonator unidirectionally with a classical coherent field, we squeeze the resonator mode in a selective direction due to the phase-matching condition, and induce a chiral photon interaction between two resonators. Based on this chiral interresonator coupling, we achieve an all-optical diode and a three-port quasicirculator. By applying a second squeezed-vacuum field to the squeezed resonator mode, our nonreciprocal device also works for single-photon pulses. We obtain an isolation ratio of >40  dB for the diode and fidelity of >98% for the quasicirculator, and insertion loss of <1  dB for both. We also show that nonreciprocal transmission of strong light can be switched on and off by a relative weak pump light. This achievement implies a nonreciprocal optical transistor. Our protocol opens up a new route to achieve integrable all-optical nonreciprocal devices permitting chip-compatible optical isolation and nonreciporcal quantum information processing.

Optical nonreciprocity and nonreciprocal photonic devices with directional four-wave mixing effect

A scheme for magnetic-free optical nonreciprocity in an ensemble of four-level cold atoms is proposed by exploiting the directional four-wave mixing effect. Using experimentally achievable parameters, the nonreciprocal optical responses of the system can be observed and the conversion on nonreciprocal transmission and nonreciprocal phase shift can be implemented. These nonreciprocal phenomena originate from the directional phase matching, which breaks the time-reversal symmetry and dynamic reciprocity of the cold atomic system. Moreover, by embedding the cold atoms into a Mach-Zehnder interferometer and choosing proper parameters, a two-port optical isolator with an isolation ratio of 79.70 dB and an insertion loss of 0.35 dB and a four-port optical circulator with a fidelity of 0.9985 and a photon survival probability of 0.9278 can be realized, which shows the high performance of isolation and circulation. The proposal may enable a new class of optically controllable cavity-free nonreciprocal devices in optical signal processing at the low light level.

Dynamic manipulation of three-color light reflection in a defective atomic lattice

We extend a recent theoretical work [Phys. Rev. A101, 053856 (2020)10.1103/PhysRevA.101.053856] by replacing disorders characterized by varied atomic densities with defects characterized by vacant lattice cells to evaluate again three-color reflection in a one-dimensional optical lattice filled with cold ⁸⁷Rb atoms. This is based on the consideration that trapped atoms may escape from some lattice cells and effects of vacant cells on light propagation are of major importance from both fundamental and applied research viewpoints. We consider two types of defective atomic lattices where vacant cells are randomly or continuously distributed among filled cells. Numerical results show that the wider reflection band in a large detuning region of negligible off-resonance absorption is quite sensitive to, while the narrower reflection bands in two near-resonant regions of electromagnetically induced transparency are rather robust against, the number of random vacant cells. In contrast, all three reflection bands exhibit strong robustness against the number of continuous vacant cells. Note, however, that both narrower reflection bands may become widened and exhibit a blue shift when continuous vacant cells appear in the front of our atomic lattice due to the joint contributions of Bragg scattering and quantum interference.

Giant and tunable Goos-Hänchen shift with a high reflectance induced by PT-symmetry in atomic vapor

The Goos-Hänchen (GH) shifts of light beams reflected from conventional passive optical systems could be enhanced using the Brewster angle effect or resonance effect, but the maximum GH shift is located at the reflectance minima, which is difficult for experimental detection. In this paper, we present an efficient and flexible scheme to realize complex parity-time (PT)-symmetric periodic optical potentials (complex crystals) in helium atomic vapor. The GH shifts of probe light reflected from the complex crystal are theoretically investigated and large GH shifts could be obtained inside the high-reflection band. When the complex crystal is operated near the coherent perfect absorption-laser point, the maximum GH shift of probe light is exactly located at the reflectance peak. Moreover, the GH shifts could be easily controlled by adjusting the intensity of control light.

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.

Inverse-design of non-Hermitian potentials for on-demand asymmetric reflectivity

We propose a genetic algorithm-assisted inverse design approach to achieve 'on- demand' light transport in periodic and non-periodic planar structures containing dielectric and gain-loss layers. The optimization algorithm efficiently produces non-Hermitian potentials from any arbitrarily given real (or imaginary) permittivity distribution for the desired frequency selective and broadband asymmetric reflectivity. Indeed, we show that the asymmetric response is directly related to the area occupied by the obtained permittivity distribution in the complex plane. In particular, unidirectional light reflection can be designed in such a way that it switches from left to right (or vice versa) depending on the operating frequency. Moreover, such controllable unidirectional reflectivity is realized using a stack of dielectric layers while keeping the refractive index and gain-loss within realistic values. We believe this proposal will benefit the integrated photonics with frequency selective one-way communication.

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.

All-optical reversible single-photon isolation at room temperature

Nonreciprocal devices operating at the single-photon level are fundamental elements for quantum technologies. Because magneto-optical nonreciprocal devices are incompatible for magnetic-sensitive or on-chip quantum information processing, all-optical nonreciprocal isolation is highly desired, but its realization at the quantum level is yet to be accomplished at room temperature. Here, we propose and experimentally demonstrate two regimes, using electromagnetically induced transparency (EIT) or a Raman transition, for all-optical isolation with warm atoms. We achieve an isolation of 22.52 ± 0.10 dB and an insertion loss of about 1.95 dB for a genuine single photon, with bandwidth up to hundreds of megahertz. The Raman regime realized in the same experimental setup enables us to achieve high isolation and low insertion loss for coherent optical fields with reversed isolation direction. These realizations of single-photon isolation and coherent light isolation at room temperature are promising for simpler reconfiguration of high-speed classical and quantum information processing.

Observation of edge solitons in photonic graphene

Edge states emerge in diverse areas of science, offering promising opportunities for the development of future electronic or optoelectronic devices, sound and light propagation control in acoustics and photonics. Previous experiments on edge states in photonics were carried out mostly in linear regimes, but the current belief is that nonlinearity introduces more striking features into physics of edge states, leading to the formation of edge solitons, optical isolation, making possible stable lasing in such states, to name a few. Here we report the observation of edge solitons at the zigzag edge of a reconfigurable photonic graphene lattice created via the effect of electromagnetically induced transparency in an atomic vapor cell with controllable nonlinearity. To obtain edge solitons, Raman gain is introduced to compensate strong absorption experienced by the edge state during propagation. Our observations may open the way for future experimental exploration of topological photonics on this nonlinear, reconfigurable platform.

Investigation of P T- and P T-antisymmetry in two dimensional (2D) optical lattices

A collection of cold rubidium atoms in three-level configuration trapped in two dimensional (2D) optical lattices is revisited. The trapped atoms are considered in the Gaussian density distribution and we study the realization of P T-, non-P T-, and P T-antisymmetry in 2D optical lattices. Such a fascinating modulation is achieved by spatially modulating the intensity of the driving field. Interestingly, control over P T- to non-P T-symmetry and vice versa in 2D optical lattices is achieved via a single knob such as microwave field, probe field and relative phase of optical and microwave fields. In addition, control over P T-antisymmetry to non-P T-symmetry and vice versa is also achieved via relative phase. The coherent control of P T- non-P T- and P T-antisymmetry in optical susceptibility of 2D atomic lattices can be extended to 2D optical devices including modulators, detectors, and the 2D atomic lattices can also be extended to photonic transistors and diodes.

Reservoir-Mediated Quantum Correlations in Non-Hermitian Optical System

Recent advances in non-Hermitian physical systems have led to numerous novel optical phenomena and applications. Such systems typically involve gain and loss associated with dissipative coupling to the environment, hence interesting quantum phenomena are often washed out, rendering most realizations classical. Here, in contrast, we propose to employ dissipative coupling to enable quantum correlations. In particular, two distant optical channels are judiciously designed to couple to and exchange information with a common reservoir environment, under an anti-parity-time-symmetric setting of hot but coherent atoms. We realize a non-Hermitian nonlinear phase sensitive parametric process, where atomic motion leads to quantum correlations between two distant light beams in the symmetry-unbroken phase. This Letter starts a new route to exploring the non-Hermitian quantum phenomena by bridging the fields of atomic physics, non-Hermitian optics, quantum information, and reservoir engineering. Potential applications include novel quantum light sources, quantum information processing and sensing, and generalization to correlated many-body systems.

Controllable unidirectional transport and light trapping using a one-dimensional lattice with non-Hermitian coupling

We propose a one-dimensional tight-binding lattice with special non-Hermitian coupling, the imaginary part of which is modulated by an effective Peierls phase arising from the synthetic magnetic field. Such a non-Hermitian lattice supports robust unidirectional transport that is reflectionless and immune to defects; it thus can serve as a frequency-selectable light filter. To achieve more applications, we further construct two well-designed structures involving this lattice, namely a heterostructure and a sandwich structure. An optical diode can be realized using the heterostructure, while tunable light trapping and reversal can be realized through phase modulations on the sandwich structure. The results in this paper may not only open up a new path for unconventional light transport but also have potential applications for optical communication.

Coherent control of nonreciprocal reflections with spatial modulation coupling in parity-time symmetric atomic lattice

A collection of cold rubidium atoms in three-level configuration trapped in one dimensional (1D) optical lattice is revisited. The trapped atoms are considered in the Gaussian density distribution and study the realization of P T-, non-P T- and P T anti-symmetry in optical susceptibility in 1D atomic lattices in a periodic structure. Such a fascinating modulation is achieved by spatially modulating the intensity of the driving field. Interestingly, a nonreciprocal optical propagation phenomenon is investigated. In this system, we have introduced a microwave that couples to the two ground states, spatial modulation of the coupling field, and the atomic density with Gaussian distribution in practice. With a proper detuning and coupling field Rabi frequencies, we can find the condition of P T-symmetry along with field propagation direction, and the novel properties of transmission and reflections have been discussed. The large difference of field reflections from the two ends of the atomic lattice medium shows strong evidence that the nonreciprocal behavior can be greatly enhanced by increasing the spatial modulation amplitude.

Unidirectional invisibility and enhanced reflection of short pulses in quasi-PT-symmetric media

We consider the interaction of a short optical pulse with a layer with periodically modulated permittivity and a periodic gain-and-loss landscape. It is found that if the medium is quasi-parity-time (PT)-symmetric in the vicinity of the exceptional point, the propagation manifests strong unidirectional reflection and invisibility. Due to strong frequency selectivity, quasi-PT-symmetric periodic layers manifest efficient filtering of back-radiation.

Anti-Parity-Time Symmetric Optical Four-Wave Mixing in Cold Atoms

Non-Hermitian optical systems with parity-time (PT) symmetry have recently revealed many intriguing prospects that outperform conservative structures. The previous works are mostly rooted in complex arrangements with controlled gain-loss interplay. Here, we demonstrate anti-PT symmetry inherent in the nonlinear optical interaction based upon forward optical four-wave mixing in a laser-cooled atomic ensemble with negligible linear gain and loss. We observe that the pair of frequency modes undergo a nontrivial anti-PT phase transition between coherent power oscillation and optical parametric amplification in presence of a large phase mismatch.

Perfectly asymmetric Raman-Nath diffraction in disordered atomic gratings

We investigate the effects of geometrical and structural disorders on perfectly asymmetric diffraction (PAD) in Raman-Nath regime. The two types of disorders are realized by introducing random fluctuations in the position and width of one-dimensional (1D) driven atomic lattices. Raman-Nath diffraction is modified differently with respect to the geometrical and structural disorders. It is shown that the PAD is observed with a certain strength range of geometrical disorder, exceeding which it can be destroyed, while the PAD is rather robust against structural disorder. The different behaviors originate from the disorder-induced random variations of the spatial phase shifts of the standing-wave (SW) coupling field and atomic lattices with Gaussian profile. Furthermore, we find that, in the presence of geometrical disorder, the PAD is more susceptible to correlated disorder than to uncorrelated disorder. Our scheme may be useful for understanding the effects of disorder on the diffraction of light and matter waves in disordered potentials..

Nonreciprocal transmission and fast-slow light effects in a cavity optomechanical system

We study the nonreciprocal transmission and the fast-slow light effects in a cavity optomechanical system, in which the cavity supports a clockwise and a counter-clockwise circulating optical mode; both the modes are driven simultaneously by a strong pump field and a weak signal field. We find that the system reveals a nonreciprocal transmission of the signal fields when the intrinsic photon loss of the cavity is equal to the external coupling loss of the cavity. However, when the intrinsic photon loss is much less than the external coupling loss, the nonreciprocity about the transmission properties almost disappears, the nonreciprocity is shown in the group delay properties of the signal fields, and the system exhibits a nonreciprocal fast-slow light propagation phenomenon.

Transport properties of the non-Hermitian T-shaped quantum router

In this study, we design a T-shaped quantum router that comprises two-level systems (TLSs), an infinite coupled resonator waveguide (CRW), and a semi-infinite CRW. The loss (absorption) and gain (amplification) of the energy levels of the TLSs can be considered as energy exchange between the system and its environment. Considering loss in the ground state and gain in the excited state of the TLSs and loss of cavities, the system is non-energy-conserving and non-Hermitian. Loss in the system consists of loss of cavities and TLSs. The total transmission probabilities (TPs) of photons in the system are equal to 1 or lower when the system has loss only. Loss causes a bounce-back phenomenon in the TPs. The TPs have a divergent point when the TLSs have gain, and we obtain this divergent condition. The reflection probability has a minimal point only when photons are incident from the semi-infinite CRW and the system has loss. The TPs of the non-Hermitian router are increased by gain, decreased by loss, and conserved under certain conditions.

Lop-sided Raman-Nath diffraction in PT-antisymmetric atomic lattices

Two-dimensional (2D) optical lattices of driven cold atoms can provide a useful platform to construct 2D electromagnetically induced grating (EIG) with parity-time (PT) antisymmetry. This atomic grating is achieved by the spatial modulations of the atomic density and frequency detunings in the four-level double-Λ atomic system. Gain-assisted PT antisymmetry allows us to realize lop-sided Raman-Nath diffraction with high diffraction efficiency at the exception point. It is shown that the nontrivial phenomenon originates from non-Hermitian degeneracy of PT antisymmetry. Our scheme may provide the possibility for active all-optical control and conversion of the spatial beam in optics.

Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms

Open physical systems with balanced loss and gain, described by non-Hermitian parity-time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {{\cal P}{\cal T}} \right)$$\end{document}PT reflection symmetric Hamiltonians, exhibit a transition which could engender modes that exponentially decay or grow with time, and thus spontaneously breaks the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal P}{\cal T}$$\end{document}PT-symmetry. Such \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal P}{\cal T}$$\end{document}PT-symmetry-breaking transitions have attracted many interests because of their extraordinary behaviors and functionalities absent in closed systems. Here we report on the observation of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal P}{\cal T}$$\end{document}PT-symmetry-breaking transitions by engineering time-periodic dissipation and coupling, which are realized through state-dependent atom loss in an optical dipole trap of ultracold ⁶Li atoms. Comparing with a single transition appearing for static dissipation, the time-periodic counterpart undergoes \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal P}{\cal T}$$\end{document}PT-symmetry breaking and restoring transitions at vanishingly small dissipation strength in both single and multiphoton transition domains, revealing rich phase structures associated to a Floquet open system. The results enable ultracold atoms to be a versatile tool for studying \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal P}{\cal T}$$\end{document}PT-symmetric quantum systems.

Ultracold atoms provide controllable platforms to study many quantum mechanical phenomena. Here the authors use noninteracting fermions of ultracold Li atoms with tunable time‐periodic dissipation or coupling to demonstrate the breaking and restoration of parity‐time symmetry.

Experimental Observation of Momentum-Space Chiral Edge Currents in Room-Temperature Atoms

Chiral edge currents play an important role in characterizing topological matter. In atoms, they have been observed at such a low temperature that the atomic motion can be measured. Here we report the first experimental observation of chiral edge currents in atoms at room temperature. Staggered magnetic fluxes are induced by the spatial phase difference between two standing-wave light fields, which couple atoms to form a momentum-space zigzag superradiance lattice. The chiral edge currents are measured by comparing the directional superradiant emissions of two timed Dicke states in the lattice. Our results pave the way for simulating topological physics in hot atoms.

Intrinsic link of asymmetric reflection and diffraction in non-Hermitian gratings

Asymmetric reflection in Bragg gratings and asymmetric diffraction in diffraction gratings are both linked to parity-time (PT) symmetry in non-Hermitian optics, but their direct relation has not been examined. To fill this gap, we first consider a PT-symmetric sinusoidal grating to compare the contrast of forward and backward reflectivities and the ratio of ±1-order diffraction efficiencies. Analytical and numerical results show that they change with identical tendencies and peaks at same positions in a wide parameter space, indicating thus an intrinsic link in both PT symmetric and PT broken phases. The underlying physics is found to be that the unbalanced coupling strengths between forward and backward reflected waves are identical to those between 0-order and ±1-order diffracted waves. We then consider a non-Hermitian grating dynamically induced in cold atomic lattices to include higher-order diffractions and corresponding reflections.Full numerical calculations show that the aforementioned findings hold also true in this complicated but practical grating, even in more general non-Hermitian cases beyond the exact PT symmetry.

Realization of simultaneously parity-time-symmetric and parity-time-antisymmetric susceptibilities along the longitudinal direction in atomic systems with all optical controls

We propose an all-optical-control scheme to simultaneously realize parity-time (𝒫𝒯)-symmetric and 𝒫𝒯-antisymmetric susceptibilities along the propagation direction of light by applying an external magnetic field. Through the light-atom interaction within a double-Λ configuration, the resulting position-dependent susceptibilities for the interacting fields can be manipulated through the relative phase between them. In particular, for the probe field, one can switch its refractive index from the 𝒫𝒯-symmetry to 𝒫𝒯-antisymmetry by just varying the phase. Based on the quantum interference among transition channels in a closed loop, analytical formulas are also derived to illustrate the conditions for 𝒫𝒯-symmetry and 𝒫𝒯-antisymmetry.

PT symmetry and antisymmetry by anti-Hermitian wave coupling and nonlinear optical interactions

Light propagation in systems with anti-Hermitian coupling, described by a spinor-like wave equation, provides a general route for the observation of antiparity-time (PT) symmetry in optics. Remarkably, under a different definition of parity operator, a PT symmetry can be found as well in such systems. Such symmetries are ubiquitous in nonlinear optical interactions and are exemplified by considering modulation instability in optical fibers and optical parametric amplification.

Understanding and overcoming fundamental limits of asymmetric light-light switches

The interplay between interference and absorption leads to interesting phenomena like coherent perfect absorption and coherent perfect transparency (CPA and CPT), which can be exploited for fully optical modulation. While it is known that it is possible to harness CPA and CPT for switching a strong signal beam with a weak control beam, it is not immediate that this process suffers from a fundamental compromise between the device efficiency (quantified by device loss and modulation depth) and the asymmetry between signal and control intensity desired for operation. This article quantifies this compromise and outlines a possible way to overcome it by means of a combination of optical gain and loss in the same photonic component. A general formulation and a specific device realization are both discussed.

𝒫𝒯 symmetric phase transition and photonic transmission in an optical trimer system

Parity-time (𝒫𝒯) symmetric structures have exhibited potential applications in developing various robust quantum devices. In an optical trimer with balanced loss and gain, we analytically study the 𝒫𝒯 symmetric phase transition by investigating the spontaneous symmetric breaking. We also illustrate the asymmetric photonic transmission behaviors in both of the 𝒫𝒯 symmetric and 𝒫𝒯 symmetry broken phases. We find (i) the non-periodical dynamics of photonic transmission in the 𝒫𝒯 symmetry broken phase instead of 𝒫𝒯 symmetric phase can be regarded as a signature of phase transition; and (ii) it shows asymmetric photonic transmission behavior in both of the phases but comes from different underlying physical mechanisms. The obtained results may be useful to implement the photonic devices based on coupled-cavity system.

Detecting topological exceptional points in a parity-time symmetric system with cold atoms

We reveal a novel topological property of the exceptional points in a two-level parity-time symmetric system and then propose a scheme to detect the topological exceptional points in the system, which is embedded in a larger Hilbert space constructed by a four-level cold atomic system. We show that a tunable parameter in the presented system for simulating the non-Hermitian Hamiltonian can be tuned to sweep the eigenstates through the exceptional points in parameter space. The non-trivial Berry phases of the eigenstates obtained in this loop from the exceptional points can be measured by the atomic interferometry. Since the proposed operations and detection are experimentally feasible, our scheme may pave a promising way to explore the novel properties of non-Hermitian systems.

Nonparaxial self-accelerating beams in an atomic vapor with electromagnetically induced transparency

We theoretically and numerically investigate the nonparaxial self-accelerating beams in a Λ-type three-level energy system of rubidium atomic vapor in the electromagnetically induced transparency (EIT) window. In the EIT window, the absorption of the atomic vapor is small, and robust nonparaxial self-accelerating beams can be generated. The reason is that the energy of the tail transfers to the main lobe, which then maintains its shape, owing to the self-healing effect. Media with large absorption would demand large energy to compensate, and the tail would be lifted too high to maintain the profile of an accelerating beam, so that self-accelerating beams cannot be obtained any longer. An atomic vapor with small absorption is the ideal medium to produce such self-accelerating beams and, in return, self-accelerating beams may inspire new ideas in the research associated with atomic vapors and atomic-like ensembles.

Coherent perfect absorption in one-sided reflectionless media

In optical experiments one-sided reflectionless (ORL) and coherent perfect absorption (CPA) are unusual scattering properties yet fascinating for their fundamental aspects and for their practical interest. Although these two concepts have so far remained separated from each other, we prove that the two phenomena are indeed strictly connected. We show that a CPA–ORL connection exists between pairs of points lying along lines close to each other in the 3D space-parameters of a realistic lossy atomic photonic crystal. The connection is expected to be a generic feature of wave scattering in non-Hermitian optical media encompassing, as a particular case, wave scattering in parity-time (PT) symmetric media.

Unidirectional transport of wave packets through tilted discrete breathers in nonlinear lattices with asymmetric defects

We consider the transfer of lattice wave packets through a tilted discrete breather (TDB) in opposite directions in the discrete nonlinear Schrödinger model with asymmetric defects, which may be realized as a Bose-Einstein condensate trapped in a deep optical lattice, or as optical beams in a waveguide array. A unidirectional transport mode is found, in which the incident wave packets, whose energy belongs to a certain interval between full reflection and full passage regions, pass the TDB only in one direction, while in the absence of the TDB, the same lattice admits bidirectional propagation. The operation of this mode is accurately explained by an analytical consideration of the respective energy barriers. The results suggest that the TDB may emulate the unidirectional propagation of atomic and optical beams in various settings. In the case of the passage of the incident wave packet, the scattering TDB typically shifts by one lattice unit in the direction from which the wave packet arrives, which is an example of the tractor-beam effect, provided by the same system, in addition to the rectification of incident waves.

Observation of Parity-Time Symmetry in Optically Induced Atomic Lattices

We experimentally demonstrate PT-symmetric optical lattices with periodical gain and loss profiles in a coherently prepared four-level N-type atomic system. By appropriately tuning the pertinent atomic parameters, the onset of PT-symmetry breaking is observed through measuring an abrupt phase-shift jump between adjacent gain and loss waveguides. The experimental realization of such a readily reconfigurable and effectively controllable PT-symmetric waveguide array structure sets a new stage for further exploiting and better understanding the peculiar physical properties of these non-Hermitian systems in atomic settings.

Optical PT-symmetry and PT-antisymmetry in coherently driven atomic lattices

We study an ensemble of ultracold atoms trapped in the one-dimensional optical lattices under the N level configuration to examine the absorption and dispersion properties modulated into different ways along the lattice direction z. We find these trapped atoms with a Gaussian density distribution in each period may exhibit either symmetry χp(z)=χp*(-z) or antisymmetry χp(z)=-χp*(-z) of parity-time (PT) in terms of the probe susceptibility. Such intriguing twofold modulations of real (χ'p) and imaginary (χ″p) susceptibilities with a π/2 phase shift are attained by spatially modulating intensities or frequencies of one driving field in a suitable way. The PT-symmetric or PT-antisymmetric atomic lattices correspond in fact to complex photonic crystals and may be extended to develop functional devices like photonic diodes and transistors, a task impossible for real photonic crystals.

Unidirectional reflectionless propagation in plasmonic waveguide-cavity systems at exceptional points

We design a non-parity-time-symmetric plasmonic waveguide-cavity system, consisting of two metal-dielectric-metal stub resonators side coupled to a metal-dielectric-metal waveguide, to form an exceptional point, and realize unidirectional reflectionless propagation at the optical communication wavelength. The contrast ratio between the forward and backward reflection almost reaches unity. We show that the presence of material loss in the metal is critical for the realization of the unidirectional reflectionlessness in this plasmonic system. We investigate the realized exceptional point, as well as the associated physical effects of level repulsion, crossing and phase transition. We also show that, by periodically cascading the unidirectional reflectionless plasmonic waveguide-cavity system, we can design a wavelength-scale unidirectional plasmonic waveguide perfect absorber. Our results could be potentially important for developing a new generation of highly compact unidirectional integrated nanoplasmonic devices.

Analogy of transistor function with modulating photonic band gap in electromagnetically induced grating

Optical transistor is a device used to amplify and switch optical signals. Many researchers focus on replacing current computer components with optical equivalents, resulting in an optical digital computer system processing binary data. Electronic transistor is the fundamental building block of modern electronic devices. To replace electronic components with optical ones, an equivalent optical transistor is required. Here we compare the behavior of an optical transistor with the reflection from a photonic band gap structure in an electromagnetically induced transparency medium. A control signal is used to modulate the photonic band gap structure. Power variation of the control signal is used to provide an analogy between the reflection behavior caused by modulating the photonic band gap structure and the shifting of Q-point (Operation point) as well as amplification function of optical transistor. By means of the control signal, the switching function of optical transistor has also been realized. Such experimental schemes could have potential applications in making optical diode and optical transistor used in quantum information processing.