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On-chip optical nonreciprocal devices are vital components for integrated photonic systems and scalable quantum information processing. Nonlinear optical isolators and circulators have attracted considerable attention because of their fundamental interest and their important advantages in integrated photonic circuits. However, optical nonreciprocal devices based on Kerr or Kerr-like nonlinearity are subject to dynamical reciprocity when the forward and backward signals coexist simultaneously in a nonlinear system. Here, we theoretically propose a method for realizing on-chip nonlinear isolators and circulators with dynamic nonreciprocity. Dynamic nonreciprocity is achieved via the chiral modulation on the resonance frequency due to coexisting self- and cross-Kerr nonlinearities in an optical ring resonator. This work showing dynamic nonreciprocity with a Kerr nonlinear resonator can be an essential step toward integrated optical isolation.

We study a single-photon band structure in a one-dimensional coupled-resonator optical waveguide that chirally couples to an array of two-level quantum emitters (QEs). The chiral interaction between the resonator mode and the QE can break the time-reversal symmetry without the magneto-optical effect and an external or synthetic magnetic field. As a result, nonreciprocal single-photon edge states, band gaps, and flat bands appear. By using such a chiral QE coupled-resonator optical waveguide system, including a finite number of unit cells and working in the nonreciprocal band gap, we achieve frequency-multiplexed single-photon circulators with high fidelity and low insertion loss. The chiral QE-light interaction can also protect one-way propagation of single photons against backscattering. Our work opens a new door for studying unconventional photonic band structures without electronic counterparts in condensed matter and exploring its applications in the quantum regime.

We theoretically propose a scheme for photon blockade in a cavity quantum electrodynamical system consisting of an N-type atomic medium interacting with a single-mode Fabry-Perot cavity. In contrast to inefficient nonlinear-dispersion-induced photon blockade suppressed by a large detuning, the photon blockade in our scheme is induced by a large nonlinear dissipation of the cavity created by the N-type atomic system. A deep photon blockade is manifested with a vanishing equal-time second-order correlation function within the cavity linewidth. This work provides an efficient photon blockade because it work in the near-resonance case.

The optical Kerr nonlinearity can't be used to achieve on-chip optical nonreciprocity because of dynamic reciprocity. Here, we propose a chiral cross-Kerr nonlinearity to bypass dynamic reciprocity and to achieve all-optical nonreciprocity on a chip.

Self-healing of an Airy beam during propagation is of fundamental interest and also promises important applications. Despite many studies of Airy beams in the quantum regime, it is unclear whether an Airy beam only including a single photon can heal after passing an obstacle because the photon may be blocked. Here we experimentally observe self-healing of a heralded single-photon Airy beam. Our observation implies that an Airy wave packet is robust against obstacle caused distortion and can restore even at the single-photon level.

Single photons are at the heart of quantum information processing. The tasks of generating and storing single photons with arbitrary wave-packet shapes are crucial for building quantum networks, but they remain challenging. Here, we present a general machine learning (ML) algorithm with a self-adaptive process to optimize the control of a cavity-atom system for these tasks. This ML algorithm shows high efficiency and fidelity for both generation and storage of single photons. This ML-enhanced single-photon interface may pave the way for building flexible and reliable quantum networks because this ML algorithm can automatically adjust the quantum system according to single-photon wave functions in an ``intelligent'' way.

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 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 quasi-circulator. 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 quasi-circulator, and insertion loss of

All-optical switching increasingly plays an important role in optical information processing. However, simultaneous achievement of ultralow power consumption, broad bandwidth and high extinction ratio remains challenging. We experimentally demonstrate an ultralow-power all-optical switching by exploiting chiral interaction between light and optically active material in a Mach-Zehnder interferometer (MZI). We achieve switching extinction ratio of 20.0(3.8) and 14.7(2.8) dB with power cost of 66.1(0.7) and 1.3(0.1) fJ/bit, respectively. The bandwidth of our all-optical switching is about 4.2 GHz. Our theoretical analysis shows that the switching bandwidth can, in principle, exceed 110 GHz. Moreover, the switching has the potential to be operated at few-photon level. Our all-optical switching exploits a chiral MZI made of linear optical components. It excludes the requisite of high-quality optical cavity or large optical nonlinearity, thus greatly simplifying realization. Our scheme paves the way towards ultralow-power and ultrafast all-optical information processing., 6 figures

After setting the goal of peaking carbon emissions before 2030 and achieving carbon neutrality before 2060, it has become an irresistible trend for China to decouple carbon emissions from its economic growth. Since cities play a central role in reducing carbon emissions, the issues such as whether and when their carbon dioxide emissions can be decoupled from economic growth have become the focus of attention. Based on the carbon dioxide emissions of 264 prefecture-level cities in China from 2000 to 2017, this paper uses the Tapio decoupling index to measure the decoupling relationship between carbon emissions and economic growth of cities, analyzes the space–time evolution characteristics of carbon emissions and decoupling indexes by stages, and explores the relationship between carbon emissions and socio-economic development characteristics such as per capita GDP and industrial structure. The main conclusions drawn therefrom are as follows: (i) From 2000 to 2017, the city-wide carbon emissions rose from 2.484 billion tons in 2000 to 7.462 billion tons in 2017, registering a total increase of 200.40%. But the growth rate of carbon emissions within cities has been significantly reduced. (ii) As years passed by, the number of cities that achieved strong decoupling saw a significant increase, from zero in the 10th–11th Five-Year Plan period to 14 in the 12th Five-Year Plan period and the first two years of the 13th Five-Year Plan period, accounting for 5.3% of the total number of cities. (iii) There is an inverted U-shaped curve relationship between per capita carbon emissions and per capita GDP, which is consistent with the EKC curve hypothesis, but Chinese cities are still in the growth stage of the quadratic curve currently. The correlation between per capita CO2 emission and the proportion of the secondary industry was positive. The results of this study are expected to provide experience for the low-carbon development of cities in China and other developing countries, and provide references for the formulation and evaluation of policies and measures related to low-carbon economic development based on the decoupling model.

The synchronization of the motion of microresonators has attracted considerable attention. In previous studies, the microresonators for synchronization were studied mostly in the linear regime. While the important problem of synchronizing nonlinear microresonators was rarely explored. Here we present theoretical methods to synchronize the motions of chaotic optical cavity modes in an optomechanical system, where one of the optical modes is strongly driven into chaotic motion and transfers chaos to other weakly driven optical modes via a common mechanical resonator. This mechanical mode works as a common force acting on each optical mode, which, thus, enables the synchronization of states. We find that complete synchronization can be achieved in two identical chaotic cavity modes. For two arbitrary nonidentical chaotic cavity modes, phase synchronization can also be achieved in the strong-coupling small-detuning regime.

Quantum walks are the quantum analogs of classical random walks, which allow for the simulation of large-scale quantum many-body systems and the realization of universal quantum computation without time-dependent control. We experimentally demonstrate quantum walks of one and two strongly correlated microwave photons in a one-dimensional array of 12 superconducting qubits with short-range interactions. First, in one-photon quantum walks, we observed the propagation of the density and correlation of the quasiparticle excitation of the superconducting qubit and quantum entanglement between qubit pairs. Second, when implementing two-photon quantum walks by exciting two superconducting qubits, we observed the fermionization of strongly interacting photons from the measured time-dependent long-range anticorrelations, representing the antibunching of photons with attractive interactions. The demonstration of quantum walks on a quantum processor, using superconducting qubits as artificial atoms and tomographic readout, paves the way to quantum simulation of many-body phenomena and universal quantum computation.

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.

Spontaneous parametric down-conversion (SPDC) in a laser pumped optical nonlinear medium can produce heralded single photons with a high purity but a very low yield. Improving the yield by increasing the pump power in SPDC inevitably reduces the purity due to excitation of multi-photon events. We propose a scheme to overcome this purity-yield trade-off by suppressing multi-photon events in a cavity-enhanced SPDC via the photon blockade effect. By introducing a strong photon-photon interaction into the intracavity medium and increasing the pump power, we can improve the available single-photon yield to larger than $90\%$, while maintaining a high purity of $99\%$, towards on-demand generation of single photons through the SPDC process. Our quasi-on-demand SPDC sources may boost single-photon-based quantum information technology.

We propose a scheme for converting a microwave (mw) single photon in a mw cavity to a flying optical photon. The conversion is realized by using a flying circular Rydberg atom, which plays a role of the “data bus” as an excellent memory to connect the mw and optical cavities. To link the energy levels of atom in optical domain and mw domain, we use fast decircularization method and three-photon Raman transition method. Thank to these low loss processes and the super long lifetime of circular Rydberg states, this scheme can efficiently convert single mw photons into the optical domain. Based on existing experiments and data, the conversion efficiency is simulated as 60%. The theoretical limit of the conversion efficiency is about 87%.

We investigate the single-photon transport problem in the system of a Whispering-Gallery mode microresonator directionally coupled with a two-level quantum emitter (QE). This QE-microresonator coupling system can usually be studied by cavity quantum electrodynamics and the single-photon transport methods. However, we find that if we treat a two-level QE as a single-photon phase-amplitude modulator, we can also deal with such systems using the transfer matrix method. Further, in theory, we prove that these three methods are equivalent. The corresponding relations of respective parameters among these approaches are precisely deduced. Our work can be extended to a multiple-resonator system interacting with two-level QEs in a chiral way. Therefore, the transfer matrix method may provide a convenient and intuitive form for exploring more complex chiral QE-resonator interaction systems.

Optical isolation is important for protecting a laser from damage due to the detrimental back reflection of light. It typically relies on breaking Lorentz reciprocity and normally is achieved via the Faraday magneto-optical effect, requiring a strong external magnetic field. Single-photon isolation, the quantum counterpart of optical isolation, is the key functional component in quantum information processing, but its realization is challenging. In this chapter, we present all-optical schemes for isolating the backscattering from single photons. In the first scheme, we show the single-photon isolation can be realized by using a chiral quantum optical system, in which a quantum emitter asymmetrically couples to nanowaveguide modes or whispering-gallery modes with high optical chirality. Secondly, we propose a chiral optical Kerr nonlinearity to bypass the so-called dynamical reciprocity in nonlinear optics and then achieve room-temperature photon isolation with low insertion loss. The concepts we present may pave the way for quantum information processing in an unconventional way.

Magnetic-free optical nonreciprocity has been experimentally demonstrated for a genuine single photon 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.

Photon blockade via a giant self-Kerr nonlinearity in an optical resonator induced by an N-type quantum system is one of the main routines towards photon-based quantum information processing. However, such an N-type system for phonons is lacking. We propose an effective N-type quantum system for phonons, forming from a superconducting transmon qubit and a microwave resonator. In the absence of any external driving, the quantum vacuum-qubit interaction causes the surface acoustic wave (SAW) phonon blockade. Such a vacuum-induced phonon blockade paves the way to prepare single SAW phonons from a weak coherent phononic state for SAW accessible superconducting quantum computation.

Optical nonreciprocity is an essential property for a wide range of applications, such as building nonreciprocal optical devices that include isolators and circulators. The realization of optical nonreciprocity relies on breaking the symmetry associated with Lorentz reciprocity, which typically requires stringent conditions such as introducing a strong magnetic field or a high-finesse cavity with nonreciprocal coupling geometry. Here we discover that the collision effect of thermal atoms, which is undesirable for most studies, can induce broadband optical nonreciprocity. By exploiting the thermal atomic collision, we experimentally observe magnet-free and cavity-free optical nonreciprocity, which possesses a high isolation ratio, ultrabroad bandwidth, and low insertion loss simultaneously. The maximum isolation ratio is close to 40 dB, while the insertion loss is less than 1 dB. The bandwidth for an isolation ratio exceeding 20 dB is over 1.2 GHz, which is 2 orders of magnitude broader than typical resonance-enhanced optical isolators. Our work paves the way for the realization of high-performance optical nonreciprocal devices and provides opportunities for applications in integrated optics and quantum networks.

Vector vortex beams simultaneously carrying spin and orbital angular momentum of light promise additional degrees of freedom for modern optics and emerging resources for both classical and quantum information technologies. The inherently infinite dimensions can be exploited to enhance data capacity for sustaining the unprecedented growth in big data and internet traffic, and can be encoded to build quantum computing machines in high-dimensional Hilbert space. So far much progress has been made in the emission of vector vortex beams from a chip surface into free space, however, the generation of vector vortex beams inside a photonic chip hasn't been realized yet. Here, we demonstrate the first vector vortex beam emitter embedded in a photonic chip by using femtosecond laser direct writing. We achieve a conversion of vector vortex beams with an efficiency up to 30% and scalar vortex beams with an efficiency up to 74% from Gaussian beams. We also present an expanded coupled-mode model for understanding the mode conversion and the influence of the imperfection in fabrication. The fashion of embedded generation makes vector vortex beams directly ready for further transmission, manipulation and emission without any additional interconnection. Together with the ability to be integrated as an array, our results may enable vector vortex beams become accessible inside a photonic chip for high-capacity communication and high-dimensional quantum information processing., 20 pages, 7 figures

We present efficient protocols for creating multipartite Greenberger-Horne-Zeilinger (GHZ) and W states of distant stationary qubits. The system nonuniformity and/or the non-ideal single-photon scattering usually limit the performance of entanglement creation, and result in the decrease of the fidelity and the efficiency in practical quantum information processing. By using linear optical elements, errors caused by the system nonuniformity and non-ideal photon scattering can be converted into heralded loss in our protocols. Thus, the fidelity of generated multipartite entangled states keeps unchanged and only the efficiency decreases. The GHZ state of distant stationary qubits is created in a parallel way that its generation efficiency considerably increases. In the protocol for creating the W state of N distant stationary qubits, an input single photon is prepared in a superposition state and sent into N paths parallelly. We use the two-spatial-mode interferences to eliminate the “which path” single-photon scattering “knowledge”. As a result, the efficiency of creating the N-qubit W state is independent of the number of stationary qubits rather than exponentially decreases.

Magnetic-free optical non-reciprocal components, such as isolators and circulators, are highly desirable for on-chip optical signal processing1,2 and quantum networks3,4. However, their realization presents a fundamental difficulty due to the Lorentz reciprocity in most optical devices5. In this study, we propose and experimentally realize optical non-reciprocity with atoms embedded in a ring cavity at room temperature. Random thermal motion of atoms, in the presence of a unidirectional control field, creates susceptibility–momentum locking, and subsequently a new type of chiral quantum optical system. Furthermore, we demonstrate strong non-reciprocity based on this chiral quantum system in the regime of collectively strong atom–cavity coupling. Our scheme provides a new routine towards the realization of chiral quantum optics and chip-compatible, non-magnetic optical non-reciprocity. Optical non-reciprocity is experimentally realized with Rb atoms embedded in a ring cavity at room temperature. Random thermal motion of the atoms causes the probe-direction-dependent response assisted by a unidirectional control laser field.

Here, we present a novel optical medium with chiral cross-Kerr nonlinearity to bypass the so-called “dynamic reciprocity” in nonlinear optics, allowing us to perform the optical isolators and circulators without applying external magnetic fields. © 2019 The Author(s)

Nonreciprocal light propagation plays an important role in modern optical systems, from photonic networks to integrated photonics. We propose a nonreciprocal system based on a resonance-frequency-tunable cavity and intensity-adaptive feedback control. Because the feedback-induced Kerr nonlinearity in the cavity is dependent on the incident direction of light, the system exhibits nonreciprocal transmission with a transmission contrast of 0.99 and an insertion loss of 1.5 dB. By utilizing intensity-adaptive feedback control, the operating intensity range of the nonreciprocal system is broadened to 20 dB, which relaxes the limitation of the operating intensity range for nonlinear nonreciprocal systems. Our protocol paves the way to realize high-performance nonreciprocal propagation in optical systems and can also be extended to microwave systems.

Vector vortex beams (VVBs) have attracted significant attention in both classical and quantum optics. Liquid crystal (LC), beyond its applications in information display, has emerged as a versatile tool for manipulating VVBs. In this review, we focus on the functions and applications of typical LC devices in recent studies on controlling the space-variant polarized vortex light. Manipulation of VVBs through patterned nematic LC optical elements, patterned cholesteric LC optical elements, self-assembled defects, and LC spatial light modulators is discussed separately. Moreover, LC-based novel optical applications in the field of quantum information are reviewed.

We fabricate a microscale electromechanical system, in which a suspended superconducting membrane, treated as a mechanical oscillator, capacitively couples to a superconducting microwave resonator. As the microwave driving power increases, nonmonotonic dependence of the resonance frequency of the mechanical oscillator on the driving power has been observed. We also demonstrate the optical switching of the resonance frequency of the mechanical oscillator. Theoretical models for qualitative understanding of our experimental observations are presented. Our experiment may pave the way for the application of a mechanical oscillator with its resonance frequency controlled by the electromagnetic and/or optical fields, such as a microwave-optical interface and a controllable element in a superqubit-mechanical oscillator hybrid system., 8 pages,4 figures

Optical nonlinearity has been widely used to try to produce optical isolators. However, this is very difficult to achieve due to dynamical reciprocity. Here, we show the use of the chiral cross-Kerr nonlinearity of atoms at room temperature to realize optical isolation, circumventing dynamical reciprocity. In our approach, the chiral cross-Kerr nonlinearity is induced by the thermal motion of $N$-type atoms. The resulting cross phase shift and absorption of a weak probe field are dependent on its propagation direction. This proposed optical isolator can achieve more than 30 dB of isolation ratio, with a low loss of less than 1 dB. By inserting this atomic medium in a Mach-Zehnder interferometer, we further propose a four-port optical circulator with a fidelity larger than 0.9 and an average insertion loss less than 1.6 dB. Using atomic vapor embedded in an on-chip waveguide, our method may provide chip-compatible optical isolation at the single-photon level of a probe field.

We propose a resource-efficient error-rejecting entangled-state analyzer for polarization-encoded multiphoton systems. Our analyzer is based on two single-photon quantum-nondemolition detectors, where each of them is implemented with a four-level emitter (e.g., a quantum dot) coupled to a one-dimensional system (such as a micropillar cavity or a photonic nanocrystal waveguide). The analyzer works in a passive way and can completely distinguish $2^n$ Greenberger-Horne-Zeilinger~(GHZ) states of $n$ photons without using any active operation or fast switching. The efficiency and fidelity of the GHZ-state analysis can, in principle, be close to unity, when an ideal single-photon scattering condition is fulfilled. For a nonideal scattering, which typically reduces the fidelity of a GHZ-state analysis, we introduce a passively error-rejecting circuit to enable a near-perfect fidelity at the expense of a slight decrease of its efficiency. Furthermore, the protocol can be directly used to perform a two-photon Bell-state analysis. This passive, resource-efficient, and error-rejecting protocol can, therefore, be useful for practical quantum networks., 15 pages, 5 figures

Controlling the spectrum of light with a phase has received intensive interest of researchers recently. Here, we study the phase control of the spectral line shape of the output from an optical March-Zehncler interferometer (MZI) with one arm involving a high quality Fabry-Perot cavity. Due to the interaction of the narrow-band light transmitted through the cavity with the broadband light, the spectrum can be tuned from Lorentzian to Fano-like profile with a phase shifter in MZI. (C) 2015 Elsevier B.V. All rights reserved

Using four-wave mixing in a 1D medium, we present a scheme without using cavities for achieving a conditional π phase shift between two traveling single photons. Our proposal provides a way for cavity-free quantum information processing.

Chiral quantum systems have received intensive attention in fundamental physics and applications in quantum information processing including optical isolation and photon unidirectional emission. Here, we design an on-chip emitter-resonator system with strong chiral light-matter interaction for a chiral single-photon interface. The system includes a microring resonator with a strong evanescent field and a near-unity optical chirality along both of the whole outside and inside walls, allowing a strong and chiral coupling of the Whispering-Gallery mode to a quantum emitter. By initializing a quantum dot in a specific spin ground state or shifting the transition energy with a polarization-selective optical Stark effect, we show a broadband optical isolation at the single-photon level over several GHz. Furthermore, a quantum emitter chirally coupling to the microring resonator can emit single photons unidirectionally. Our protocol paves a way to realize multifunctional chiral single-photon interface in on-chip quantum information processing and quantum networks., Comment: 15 pages, 11 figures

Anti-Stokes one-photon luminescence from a single gold nanorod is experimentally investigated. The anti-Stokes emission of gold nanorods is enhanced and strongly modulated by localized surface plasmon resonance (LSPR). It is found that the polarization dependence of the anti-Stokes emission is in strong correlation with that of the Stokes emission. Further experiments provide evidence that LSPR significantly enhanced both excitation and emission processes. Moreover, the line shape of the anti-Stokes emission is dependent on the surface temperature, which is related to the distribution of free electrons near the Fermi level. This discovery provides an effective method in principle to probe localized temperature at nanoscale dimension. Here, the reported results about the anti-Stokes emission provide more understanding for the photoemission process from the plasmonic nanostructures.

Luminescence quantum yields (QYs) of gold nanoparticles including nanorods, nanobipyramids and nanospheres are measured elaborately at single nanoparticle level with different excitation wavelengths. It is found that the QYs of the nanostructures are essentially dependent on the excitation wavelength. The QY is higher when the excitation wavelength is blue-detuned and close to the nanoparticles’ surface plasmon resonant peak. A phenomenological model based on plasmonic resonator concept is proposed to understand the experimental findings. The excitation wavelength dependent of QY is attributed to the wavelength dependent coupling efficiency between the free electrons oscillation and the intrinsic plasmon resonant radiative mode. These studies should contribute to the understanding of one-photon luminescence from metallic nanostructures and plasmonic surface enhanced spectroscopy.