Nonreciprocal Photon Blockade

Nonreciprocal bipartite and tripartite entanglement in cavity-magnon optomechanics via the Barnett effect

We theoretically propose a scheme for generating nonreciprocal macroscopic bipartite and tripartite entanglement using the Barnett effect in cavity-magnon optomechanics. The system consists of an optomechanical cavity and a rotatable yttrium iron garnet (YIG) sphere. Our results indicate that under appropriate parameter conditions, both bipartite entanglement and genuine tripartite entanglement can be generated between the cavity mode, mechanical mode, and magnon mode. Moreover, when the YIG sphere rotates, adjusting the magnetic field direction can induce a positive or negative Barnett shift, which leads to the nonreciprocity of entanglement, where entanglement exists in one chosen magnetic field direction and disappears in the other. Meanwhile, the macroscopic tripartite entanglement in the system is robust against thermal noise. Our work provides a possible avenue for quantum information processing, quantum chiral device integration, and multi-node quantum networks construction.

Nonreciprocal unconventional photon blockade in a spinning microwave magnomechanical system

We propose a method for realizing the nonreciprocal unconventional photon blockade (NUPB) effect in a spinning microwave magnomechanical system. We determine the optimal parameter conditions for achieving this effect and observe that the numerical solutions are in excellent agreement with the analytical results. Under these optimal conditions, driving the system from the right induces photon antibunching, while driving from the left with identical amplitude leads to photon bunching. This pronounced asymmetry gives rise to NUPB, which arises from the combined effects of destructive quantum interference in two-photon excitation pathways and the Sagnac effect. Furthermore, NUPB can be tuned by adjusting the angular velocity of the microwave resonator. This work provides significant theoretical support for the realization of nonreciprocal single-photon sources and opens new avenues for the design and application of nonreciprocal quantum devices.

Nonreciprocal unconventional magnon blockade induced by Barnett effect and parametric amplification

We propose a scheme to achieve nonreciprocal unconventional magnon blockade (UMB) via the Barnett effect in a spinning ferrimagnetic yttrium-iron-garnet sphere coupled to a microwave cavity that interacts with a parametric amplifier. We show that, with a strong cavity-magnon coupling regime, giant nonreciprocal UMB can emerge by appropriately choosing two sets of parameters in this system, i.e., strong magnon antibunching occurs only from one direction of the magnetic field but not from the other side. This nonreciprocity originates from the fact that the Barnett shift induced by the Barnett effect can be adjusted from positive to negative values by changing the magnetic field direction, resulting in different frequencies of the magnon mode. Moreover, we demonstrate that parametric amplification is an indispensable factor for constructing the pathways of quantum destructive interference to achieve strong UMB. Furthermore, we give analytical parameter conditions to realize strong UMB, which is proven to be in great agreement with numerical results. Interestingly, the nonreciprocity against magnon thermal occupation is remarkably enhanced by increasing the amplitude of the driving field. Notably, the critical temperature for observing nonreciprocal UMB is as high as 133 mK, and the sphere needs to spin at MHz values to achieve the UMB effect. Our work provides an avenue to realize nonreciprocal single-magnon devices and has potential applications in quantum information processing and quantum communication.

Nonreciprocal single-photon band structure in a coupled-spinning-resonator chain

We analyze the single-photon band structure and the transport of a single photon in a one-dimensional coupled-spinning-resonator chain. The time-reversal symmetry of the resonators chain is broken by the spinning of the resonators, instead of external or synthetic magnetic field. Two nonreciprocal single-photon band gaps can be obtained in the coupled-spinning-resonator chain, whose width depends on the angular velocity of the spinning resonator. Based on the nonreciprocal band gaps, we can implement a single photon circulator at multiple frequency windows, and the direction of photon cycling is opposite for different band gaps. In addition, reciprocal single-photon band structures can also be realized in the coupled-spinning-resonator chain when all resonators rotate in the same direction with equal angular velocity. We believe our work opens a new route to achieve, manipulate, and switch nonreciprocal or reciprocal single-photon band structures, and provides new opportunities to realize novel single-photon devices.

Dissipation-induced nonreciprocal magnon entanglement and one-way steering in waveguide electromagnonics

We propose a scheme to generate nonreciprocal entanglement and one-way steering between two distant ferrimagnetic microspheres in waveguide electromagnonics, where the magnon modes of two yttrium iron garnet (YIG) spheres are simultaneously coupled to each other through coherent and dissipative interactions. By matching the coherent interaction with its corresponding dissipative counterpart, unidirectional coupling between two magnon modes can be realized, and then in the presence of significant Kerr nonlinearities, we can obtain strong entanglement and one-way steering. Depending on the direction of the microwave propagation, the long-distance entanglement and steering can be generated nonreciprocally. Our work presents a novel, to the best of our knowledge, approach for generating nonreciprocal quantum correlations, which may find potential applications in chiral quantum networking.

Experimental realization of on-chip few-photon control around exceptional points

Non-Hermitian physical systems have attracted considerable attention in recent years for their unique properties around exceptional points (EPs), where the eigenvalues and eigenstates of the system coalesce. Phase transitions near exceptional points can lead to various interesting phenomena, such as unidirectional wave transmission. However, most of those studies are in the classical regime and whether these properties can be maintained in the quantum regime is still a subject of ongoing studies. Using a non-Hermitian on-chip superconducting quantum circuit, here we observe a phase transition and the corresponding exceptional point between the two phases. Furthermore, we demonstrate that unidirectional microwave transmission can be achieved even in the few-photon regime within the broken symmetry phase. This result holds some potential applications, such as on-chip few-photon microwave isolators. Our study reveals the possibility of exploring the fundamental physics and practical quantum devices with non-Hermitian systems based on superconducting quantum circuits.

Multi-band enhanced nonreciprocal thermal radiation based on Weyl semimetals

Previous studies manifested that the majority of structures that exhibit nonreciprocal thermal radiation in the mid-infrared are capable of achieving either single-band strong nonreciprocity or multi-band weak nonreciprocity at a large incidence angle. However, few structures can realize multi-band strong nonreciprocity at a small incidence angle. To address such scientific issues, we propose a tunable nonreciprocal thermal emitter based on gallium arsenide (GaAs)/graphene/Weyl semimetal (WSM). This device is capable of achieving strong nonreciprocity at 7.3 μm, 10 μm and 13.6 μm wavelengths at an incidence angle of 25.5°. It is shown that the field enhancement of the GaAs/graphene composite layer can improve the nonreciprocal response of the WSM layer. In addition, by changing the Fermi energy level of graphene and the axial vector b of the Weyl semimetal, tunable nonreciprocal thermal radiation can be realized. What's more, we find that the structure breaks Kirchhoff's law without lithography and an external magnetic field, which reveals the advantages of applying our research in the field of thermal radiation.

Realization of nonreciprocal photon statistics by manipulating the quantum nonlinearity of cold atoms in an asymmetric cavity

In a strongly coupled cavity quantum electrodynamics (QED) system, the second-order correlation function g(2)(τ) of the transmitted probe light from the cavity is determined by the nonlinearity of the atom in the cavity. Therefore, the system provides a platform for controlling the photon statistics by manipulating nonlinearity. In this paper, we experimentally demonstrate nonreciprocal quantum statistics in a cavity QED system with several atoms strongly coupled to an asymmetric optical cavity, which is composed of two mirrors with different transmittivities. When the direction of the probe light is reversed, the intracavity light field alternates to a different level. Distinct photon statistics are then observed due to the quantum nonlinearity associated with strongly coupled atoms. Sub-Poissonian photon-number statistics for forward light and a Poissonian distribution for backward light are then realized. Our work provides an effective approach for realizing nonreciprocal quantum devices, which have potential applications in the unidirectional generation of nonclassical light fields and quantum sensing.

Nonreciprocal Bundle Emissions of Quantum Entangled Pairs

Realizing precise control over multiquanta emission is crucial for quantum information processing, especially when integrated with advanced techniques of manipulating quantum states. Here, by spinning the resonator to induce the Sagnac effect, we can obtain nonreciprocal photon-phonon and photon-magnon super-Rabi oscillations under conditions of optically driving resonance transitions. Opening dissipative channels for such super-Rabi oscillations enables the realization of directional bundle emissions of entangled photon-phonon pairs and photon-magnon pairs by transferring the pure multiquanta state to a bundled multiquanta outside of the system. This nonreciprocal emission is a flexible switch that can be controlled with precision, and simultaneous emissions of different entangled pairs (such as photon-phonon or photon-magnon pairs) can even emerge but in opposite directions by driving the resonator from different directions. This ability to flexibly manipulate the system allows us to achieve directional entangled multiquanta emitters, and has also potential applications for building hybrid quantum networks and on-chip quantum communications.

Enhancement and manipulation of nonreciprocity via dissipative coupling

Classical and quantum nonreciprocity have important applications in information processing due to their special one-way controllability for physical systems. In this paper we investigate the nonreciprocal transmission and quantum correlation by introducing the dissipative coupling into a linear coupling system consisting of two microdisk resonators. Our research results demonstrate that even in the case of a stationary resonator, dissipative coupling can effectively induce nonreciprocity within the system. Moreover, the degree of nonreciprocity increases with the dissipative coupling strength. Importantly, the phase shift between the dissipative coupling and coherent coupling serves as a critical factor for controlling both nonreciprocal transmision and one-way quantum steering. Consequently, the introduction of dissipative coupling not only enhances the nonreciprocal transmission and nonreciprocal quantum correlation but also enables on-demand manipulation of nonreciprocity. This highlights dissipation as an effective means for manipulating classical and quantum nonreciprocity, thus playing a favorable role in chiral quantum networks.

Nonreciprocal routing of microwave photons with broad bandwidth via magnon-cavity chiral coupling

We propose a scheme for realizing nonreciprocal microwave photon routing with two cascaded magnon-cavity coupled systems, which work around the exceptional points of a parity-time (PT)-symmetric Hamiltonian. An almost perfect nonreciprocal transmission can be achieved with a broad bandwidth, where the transmission for a forward-propagating photon can be flexibly controlled with the backpropagating photon being isolated. The transmission or isolated direction can be reversed via simply controlling the magnetic field direction applied to the magnons. The isolation bandwidth is improved by almost three times in comparison with the device based on a single PT-symmetric system. Moreover, the effect of intrinsic cavity loss and added thermal noises is considered, confirming the experimental feasibility of the nonreciprocal device and potential applications in quantum information processing.

Inducing tunable conventional photon blockade and two-photon blockade in a second-order nonlinear system with two-level atoms

We have achieved a conventional photon blockade and two-photon blockade in a second-order nonlinear system with a two-level atom embedded in a high-frequency cavity. The physical mechanisms behind the implementation of both types of photon blockade are explained, and analytical conditions for achieving a conventional photon blockade are derived, which are consistent with the numerical solutions of the master equation in the steady-state limit. By appropriately setting the system parameters, we can achieve simultaneous conventional photon blockade in the high-frequency cavity and two-photon blockade in the low-frequency cavity. The effects of driving factors and environmental temperature on photon blockade are analyzed. The adjustability of the coupling coefficient between the high-frequency cavity and the atom, as well as the nonlinear coupling coefficient between different nanocavities, is discussed in the context of implementing conventional photon blockades. The tunability of these coupling coefficients may significantly reduce the experimental complexity of implementing the system.

Nonreciprocal Topological Phonon Transfer Independent of Both Device Mass and Exceptional-Point Encircling Direction

Imposing topological operations encircling an exceptional point (EP) engenders unconventional one-way topological phonon transfer (TPT), strictly depending on the direction of EP-inclusive control loops and inherently limited to the small-mass regime of practical resonators. We here show how to beat these limitations and predict a mass-free unidirectional TPT by combining topological operations with the Fizeau light-dragging effect, which splits countercirculating optical modes. An efficient TPT happens when light enters from one chosen side of the fiber but not from the other, leading to a unique nonreciprocal TPT, independent of the direction of winding around the EP. Unlike previous proposals naturally sensitive to both mass and quality of quantum devices, our approach is almost immune to these factors. Remarkably, its threshold duration of adiabatic control loops for maintaining an optimal TPT can be easily shortened, yielding a top-speed-tunable perfect TPT that has no counterpart in previous demonstrations. The study paves a quite-general route to exploiting profoundly different chiral topological effects, independent of both EP-encircling direction and device mass.

The manipulation of photon blockade via Newtonian gravity

We theoretically investigate the model of a quadratically coupled optomechanical system with a Newtonian gravitational potential in the weak-driving regime, where the optical cavity is driven by an external laser. The steady state of the whole system is treated in the framework of a few-photon subspace. We find that the conventional single-photon blockade, nonstandard types of single-photon blockade, two-photon blockade, and photon-induced tunneling can be induced by gravity when the quadratic optomechanical coupling strength remains constant. Moreover, we find that gravitational potential energy can compensate for the lack of quadratic optomechanical coupling for observation photon blockade. In particular, the photon stream with super-Poissonian distribution can be converted into a sub-Poissonian, antibunching photon stream by changing the driving detuning when the gravitational potential energy is included. These results show that the gravity has potential for realizing the manipulation of photon blockade in a quadratically coupled optomechanical system.

Chiral photon blockade in the spinning Kerr resonator

We propose how to achieve chiral photon blockade by spinning a nonlinear optical resonator. We show that by driving such a device at a fixed direction, completely different quantum effects can emerge for the counter-propagating optical modes, due to the spinning-induced breaking of time-reversal symmetry, which otherwise is unattainable for the same device in the static regime. Also, we find that in comparison with the static case, robust non-classical correlations against random backscattering losses can be achieved for such a quantum chiral system. Our work, extending previous works on the spontaneous breaking of optical chiral symmetry from the classical to purely quantum regimes, can stimulate more efforts towards making and utilizing various chiral quantum effects, including applications for chiral quantum networks or noise-tolerant quantum sensors.

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.

Nonreciprocal Superradiant Phase Transitions and Multicriticality in a Cavity QED System

We demonstrate the emergence of nonreciprocal superradiant phase transitions and novel multicriticality in a cavity quantum electrodynamics system, where a two-level atom interacts with two counterpropagating modes of a whispering-gallery-mode microcavity. The cavity rotates at a certain angular velocity and is directionally squeezed by a unidirectional parametric pumping χ^{(2)} nonlinearity. The combination of cavity rotation and directional squeezing leads to nonreciprocal first- and second-order superradiant phase transitions. These transitions do not require ultrastrong atom-field couplings and can be easily controlled by the external pump field. Through a full quantum description of the system Hamiltonian, we identify two types of multicritical points in the phase diagram, both of which exhibit controllable nonreciprocity. These results open a new door for all-optical manipulation of superradiant transitions and multicritical behaviors in light-matter systems, with potential applications in engineering various integrated nonreciprocal quantum devices.

Photon blockade with high photon occupation via cavity electromagnetically induced transparency

Photon blockade (PB) is one of the effective methods to generate single-photon sources. In general, both the PB effect with the significant sub-Poissonian statistics and a large mean photon number are desired to guarantee the brightness and the purity of single-photon sources. Here, we propose to obtain the PB effect at the cavity dark-state polariton (DSP) using a cavity Λ-type electromagnetically induced transparency (EIT) system with and without the two-photon dissipation (TPD). In the Raman resonance case, the PB effect at the DSP could by realized by using the TPD process in the weak or intermediate coupling regime, which accompanies with near unity transmission, i.e., very high photon occupation. In the slightly detuned Raman resonance case, the excited state is induced into the components of the DSP, and the atomic dissipation path is added into the two-photon excitation paths. Thus, the PB effect at the DSP can be obtained due to the quantum destructive interference (QDI) in the strong coupling regime, which can be further enhanced using the TPD process. Due to the slight detuning, the PB effect still remains high photon occupation and has highly tunability. This work provides an alternative way to manipulate the photon statistics by the PB effect and has potential applications in generating single-photon sources with high brightness and purity.

Quantum nonlinear effect in a dissipatively coupled optomechanical system

A full-quantum approach is used to study the quantum nonlinear properties of a compound Michelson-Sagnac interferometer optomechanical system. By deriving the effective Hamiltonian, we find that the reduced system exhibits a Kerr nonlinear term with a complex coefficient, entirely induced by the dissipative and dispersive couplings. Unexpectedly, the nonlinearities resulting from the dissipative coupling possess non-Hermitian Hamiltonian-like properties preserving the quantum nature of the dispersive coupling beyond the traditional system dissipation. This protective mechanism allows the system to exhibit strong quantum nonlinear effects when the detuning (the compound cavity detuning Δc and the auxiliary cavity detuning Δe) and the tunneling coupling strength (J) of two cavities satisfy the relation J2 = ΔcΔe. Moreover, the additive effects of dispersive and dissipative couplings can produce strong anti-bunching effects, which exist in both strong and weak coupling conditions. Our work may provide a new way to study and produce strong quantum nonlinear effects in dissipatively coupled optomechanical systems.

Passive magnetic-free broadband optical isolator based on unidirectional self-induced transparency

Achieving a broadband nonreciprocal device without gain and any external bias is very challenging and highly desirable for modern photonic technologies and quantum networks. Here we theoretically propose a passive and magnetic-free all-optical isolator for a femtosecond laser pulse by exploiting a new mechanism of unidirectional self-induced transparency, obtained with a nonlinear medium followed by a normal absorbing medium at one side. The transmission contrast between the forward and backward directions can reach 14.3 dB for a 2π - 5 fs laser pulse. The 20 dB bandwidth is about 56 nm, already comparable with a magneto-optical isolator. This work provides a new mechanism which may benefit non-magnetic isolation of ultrashort laser pulses.

Nonreciprocal P T-symmetric magnon laser in spinning cavity optomagnonics

We propose a scheme to achieve nonreciprocal parity-time (P T)-symmetric magnon laser in a P T-symmetric cavity optomagnonical system. The system consists of active and passive optical spinning resonators. We demonstrate that the Fizeau light-dragging effect induced by the spinning of a resonator results in significant variations in magnon gain and stimulated emitted magnon numbers for different driving directions. We find that utilizing the Fizeau light-dragging effect allows the system to operate at ultra-low thresholds even without reaching gain-loss balance. A one-way magnon laser can also be realized across a range of parameters. High tunability of the magnon laser is achieved by changing the spinning speed of the resonators and driving direction. Our work provides a new way to explore various nonreciprocal effects in non-Hermitian magnonic systems, which may be applied to manipulate photons and magnons in multi-body non-Hermitian coupled systems.

Photon blockade induced by two-photon absorption in cavity quantum electrodynamics

Photon blockade (PB) is an important quantum phenomenon in cavity quantum electrodynamics (QED). Here, we investigate the PB effect in the simplest cavity QED systems (one cavity containing first a single atom and then two atoms), where only the atoms are weakly driven. Via the analytical calculation and numerical simulation, we show that the strong PB can be generated even with the weak-coupling regime at the total resonance. This blockade is ascribed to the two-photon absorption, which is fundamentally different from the conventional and unconventional blockade mechanisms. Therefore, our study provides an alternative approach to produce the PB in the atom-driven cavity QED system.

Nonreciprocal magnon blockade via the Barnett effect

We propose a scheme to achieve nonreciprocal magnon blockade via the Barnett effect in a magnon-based hybrid system. Due to the rotating yttrium iron garnet (YIG) sphere, the Barnett shift induced by the Barnett effect can be tuned from positive to negative via controlling magnetic field direction, leading to nonreciprocity. We show that a nonreciprocal unconventional magnon blockade (UMB) can emerge only from one magnetic field direction but not from the other side. Particularly, by further tuning system parameters, we simultaneously observe a nonreciprocal conventional magnon blockade (CMB) and a nonreciprocal UMB. This result achieves a switch between efficiency (UMB) and purity (CMB) of a single-magnon blockade. Interestingly, stronger UMB can be reached under stronger qubit-magnon coupling, even the strong coupling regime. Moreover, the nonreciprocity of the magnon blockade is sensitive to temperature. This work opens up a way for achieving quantum nonreciprocal magnetic devices and chiral magnon communications.

Nonreciprocal strong mechanical squeezing based on the Sagnac effect and two-tone driving

We propose a scheme for generating nonreciprocal strong mechanical squeezing by using two-tone lasers to drive a spinning optomechanical system. For given driving frequencies, strong mechanical squeezing of the breathing mode in the spinning resonator can be achieved in a chosen driving direction but not in the other. The nonreciprocity originates from the Sagnac effect caused by the resonator's spinning. We also find the classical nonreciprocity and the quantum nonreciprocity can be switched by simply changing the angular velocity of the spinning resonator. We show that the scheme is robust to the system's dissipations and the mechanical thermal noise. This work may be meaningful for the study of nonreciprocal device and quantum precision measurement.

Controllable nonreciprocal phonon laser in a hybrid photonic molecule based on directional quantum squeezing

Here, a scheme for a controllable nonreciprocal phonon laser is proposed in a hybrid photonic molecule system consisting of a whispering-gallery mode (WGM) optomechanical resonator and a χ(2)-nonlinear WGM resonator, by directionally quantum squeezing one of two coupled resonator modes. The directional quantum squeezing results in a chiral photon interaction between the resonators and a frequency shift of the squeezed resonator mode with respect to the unsqueezed bare mode. We show that the directional quantum squeezing can modify the effective optomechanical coupling in the optomechanical resonator, and analyze the impacts of driving direction and squeezing extent on the phonon laser action in detail. Our analytical and numerical results indicate that the controllable nonreciprocal phonon laser action can be effectively realized in this system. The proposed scheme uses an all-optical and chip-compatible approach without spinning resonators, which may be more beneficial for integrating and packaging of the system on a chip. Our proposal may provide a new route to realize integratable phonon devices for on-chip nonreciprocal phonon manipulations, which may be used in chiral quantum acoustics, topological phononics, and acoustical information processing.

Magnetic-free polarization rotation in an atomic vapor cell

Magnetic-free nonreciprocal optical devices have attracted great attention in recent years. Here, we investigated the magnetic-free polarization rotation of light in an atom vapor cell. Two mechanisms of magnetic-free nonreciprocity have been realized in ensembles of hot atoms, including electromagnetically induced transparency and optically-induced magnetization. For a linearly polarized input probe light, a rotation angle up to 86.4° has been realized with external control and pump laser powers of 10 mW and is mainly attributed to the optically-induced magnetization effect. Our demonstration offers a new approach to realize nonreciprocal devices, which can be applied to solid-state atom ensembles and may be useful in photonic integrated circuits.

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.

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.

Photon blockade with a trapped Λ-type three-level atom in asymmetrical cavity

We propose a scheme to manipulate strong and nonreciprocal photon blockades in asymmetrical Fabry-Perot cavity with a Λ-type three-level atom. Utilizing the mechanisms of both conventional and unconventional blockade, the strong photon blockade is achieved by the anharmonic eigenenergy spectrum brought by Λ-type atom and the destructive quantum interference effect induced by a microwave field. By optimizing the system parameters, the manipulation of strong photon blockade over a wide range of cavity detuning can be realized. Using spatial symmetry breaking introduced by the asymmetry of cavity, the direction-dependent nonreciprocal photon blockade can be achieved, and the nonreciprocity can reach the maximum at optimal cavity detuning. In particular, manipulating the occurring position of nonreciprocal photon blockade can be implemented by simply adjusting the cavity detuning. Our scheme provides feasible access for generating high-quality nonreciprocal single-photon sources.

Magnon-photon cross-correlations via optical nonlinearity in cavity magnonical system

We propose an alternative scheme to achieve the cross-correlations between magnon and photon in a hybrid nonlinear system including two microwave cavities and one yttrium iron garnet (YIG) sphere, where two cavities nonlinearly interact and meanwhile one of cavities couples to magnon representing the collective excitation in YIG sphere via magnetic dipole interaction. Based on dispersive couplings between two cavities and between one cavity and magnon with the larger detunings, the nonlinear interaction occurs between the other cavity and magnon, which plays a crucial role in generating quantum correlations. By analyzing the second-order correlation functions via numerical simulations and analytical calculations, the remarkable nonclassical correlations are existent in such a system, where the magnon blockade and photon antibunching could be obtainable on demand. The scheme we present is focused on the magnon-photon cross-correlations in the weak coupling regime and relaxes the requirements of experimental conditions, which may have potential applications in quantum information processing in the hybrid system.

Squeezing-induced nonreciprocal photon blockade in an optomechanical microresonator

We propose a scheme to generate nonreciprocal photon blockade in a stationary whispering gallery microresonator system based on two physical mechanisms. One of the two mechanisms is inspired by recent work [Phys. Rev. Lett.128, 083604 (2022)10.1103/PhysRevLett.128.083604], where the quantum squeezing caused by parametric interaction not only shifts the optical frequency of propagating mode but also enhances its optomechanical coupling, resulting in a nonreciprocal conventional photon blockade phenomenon. On the other hand, we also give another mechanism to generate stronger nonreciprocity of photon correlation according to the destructive quantum interference. Comparing these two strategies, the required nonlinear strength of parametric interaction in the second one is smaller, and the broadband squeezed vacuum field used to eliminate thermalization noise is no longer needed. All analyses and optimal parameter relations are further verified by numerically simulating the quantum master equation. Our proposed scheme opens a new avenue for achieving the nonreciprocal single photon source without stringent requirements, which may have critical applications in quantum communication, quantum information processing, and topological photonics.

Photon blockade in the Jaynes-Cummings model with two-photon dissipation

We propose a scheme to generate a single-photon source based on photon blockade in the Jaynes-Cummings (J-C) model with a two-photon dissipation (TPD) process. We present the optimal conditions for conventional/unconventional photon blockade via the wave function method with an effective Hamiltonian involving TPD. The results show that the second-order correlation function for the J-C model with TPD is considerably less than that of the J-C model with single-photon dissipation. Additionally, the average photon number can reach 0.5 in the large atomic detuning regime. This feature makes the J-C model with TPD a high-quality single photon source.

Few-photon isolation in a one-dimensional waveguide using chiral quantum coupling

We investigated the transmission of single and two photons in a one-dimensional waveguide that is coupled with a Kerr micro-ring resonator and a polarized quantum emitter. In both cases, a phase shift occurs, and the non-reciprocal behavior of the system is attributed to the unbalanced coupling between the quantum emitter and the resonator. Our analytical solutions and numerical simulations demonstrate that the nonlinear resonator scattering causes the energy redistribution of the two photons through the bound state. When the system is in the two-photon resonance state, the polarization of the correlated two photons is locked to their propagation direction, leading to non-reciprocity. As a result, our configuration can act as an optical diode.

Strong antibunching effect under the combination of conventional and unconventional photon blockade

Photon blockade (PB), an effective method of generating antibunching effect, is a critical way to construct a single photon source. The PB effect can be divided into conventional PB effect (CPB) and unconventional PB effect (UPB). Most studies focus on designing systems to successfully enhance CPB or UPB effect individually. However, CPB extremely depends on the nonlinearity strength of the Kerr materials to achieve strong antibunching effect while UPB relies on quantum interference beset with the high probability of the vacuum state. Here, we propose a method to utilize the relevance and complementarity of CPB and UPB to realize these two types simultaneously. We employ a hybrid Kerr nonlinearity two-cavity system. Because of the mutual assistance of two cavities, CPB and UPB can coexist in the system under certain states. In this way, for the same Kerr material, we reduce the value of the second-order correlation function due to CPB by three orders of magnitude without losing the mean photon number due to the presence of UPB, so the advantages of both PB effects are fully reflected in our system, which is a huge performance boost for single photons.

Optical noise-resistant nonreciprocal phonon blockade in a spinning optomechanical resonator

A scheme of nonreciprocal conventional phonon blockade (PB) is proposed in a spinning optomechanical resonator coupled with a two-level atom. The coherent coupling between the atom and breathing mode is mediated by the optical mode with a large detuning. Due to the Fizeau shift caused by the spinning resonator, the PB can be implemented in a nonreciprocal way. Specifically, when the spinning resonator is driven from one direction, the single-phonon (1PB) and two-phonon blockade (2PB) can be achieved by adjusting both the amplitude and frequency of the mechanical drive field, while phonon-induced tunneling (PIT) occurs when the spinning resonator is driven from the opposite direction. The PB effects are insensitive to cavity decay because of the adiabatic elimination of the optical mode, thus making the scheme more robust to the optical noise and still feasible even in a low-Q cavity. Our scheme provides a flexible method for engineering a unidirectional phonon source with external control, which is expected to be used as a chiral quantum device in quantum computing networks.

Multiple-photon bundle emission in the n-photon Jaynes-Cummings model

We study the multiple-photon bundle emission in the n-photon Jaynes-Cummings model composed of a two-level system coupled to a single-mode optical field via the n-photon exciting process. Here, the two-level system is strongly driven by a near-resonant monochromatic field, and hence the system can work in the Mollow regime, in which a super-Rabi oscillation between the zero-photon state and the n-photon state can take place under proper resonant conditions. We calculate the photon number populations and the standard equal-time high-order correlation functions, and find that the multiple-photon bundle emission can occur in this system. The multiple-photon bundle emission is also confirmed by investigating the quantum trajectories of the state populations and both the standard and generalized time-delay second-order correlation functions for multiple-photon bundle. Our work paves the way towards the study of multiple-photon quantum coherent devices, with potential application in quantum information sciences and technologies.

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.

Nonreciprocal photon blockade in a spinning optomechanical system with nonreciprocal coupling

A scheme is presented to achieve quantum nonreciprocity by manipulating the statistical properties of the photons in a composite device consisting of a double-cavity optomechanical system with a spinning resonator and nonreciprocal coupling. It can be found that the photon blockade can emerge when the spinning device is driven from one side but not from the other side with the same driving amplitude. Under the weak driving limit, to achieve the perfect nonreciprocal photon blockade, two sets of optimal nonreciprocal coupling strengths are analytically obtained under different optical detunings based on the destructive quantum interference between different paths, which are in good agreement with the results obtained from numerical simulations. Moreover, the photon blockade exhibits thoroughly different behaviors as the nonreciprocal coupling is altered, and the perfect nonreciprocal photon blockade can be achieved even with weak nonlinear and linear couplings, which breaks the orthodox perception.

Quantum switching between nonclassical correlated single photons and two-photon bundles in a two-photon Jaynes-Cummings model

We propose a scheme to realize a two-photon Jaynes-Cummings model for a single atom inside an optical cavity. It is shown that the interplay of a laser detuning and atom (cavity) pump (driven) field gives rise to the strong single photon blockade, two-photon bundles, and photon-induced tunneling. With the cavity driven field, strong photon blockade occurs in the weak coupling regime, and switching between single photon blockade and photon-induced tunneling at two-photon resonance are achievable via increasing the driven strength. By turning on the atom pump field, quantum switching between two-photon bundles and photon-induced tunneling at four-photon resonance are realized. More interestingly, the high-quality quantum switching between single photon blockade, two-photon bundles, and photon-induced tunneling at three-photon resonance is achieved with combining the atom pump and cavity driven fields simultaneously. In contrast to the standard two-level Jaynes-Cummings model, our scheme with generating a two-photon (multi-photon) Jaynes-Cummings model reveals a prominent strategy to engineer a series of special nonclassical quantum states, which may pave the way for investigating basic quantum devices to implement in quantum information processing and quantum networks.

Auxiliary-Cavity-Assisted Slow and Fast Light in a Photonic Molecule Spinning Optomechanical System

We investigate the coherent optical propagation in a photonic molecule spinning optomechanical system consisting of two whispering gallery microcavities in which one of the optical cavities is a spinning optomechanical cavity and the other one is an ordinary auxiliary optical cavity. As the optomechanical cavity is spinning along the clockwise or counterclockwise direction, the cavity field can undergo different Sagnac effects, which accompanies the auxiliary optical cavity, together influencing the process of the evolution of optomechanically induced transparency and its related propagation properties, such as fast and slow light effects. The numerical results indicate that the enhanced slow and fast light and the conversion from fast to slow light (or slow to fast light) are determined by the spinning direction of the optomechanical cavity and the coupling of the two optical cavities. The study affords further insight into the photonic molecule spinning optomechanical systems and also indicates promising applications in quantum information processing.

Nonreciprocal sideband responses in a spinning microwave magnomechanical system

Nonreciprocal sideband responses in a spinning microwave magnomechanical system consists of a spinning resonator coupled with a yttrium iron garnet sphere are proposed. We show that the efficiency of sideband generation can be enhanced in one driving direction but restrained in the opposite. This nonreciprocity results from Sagnac effect induced by the spinning resonator, leading to asymmetric magnonic responses in two different driving directions. Beyond the conventional linearized description, the properties of nonreciprocal two-color second-order sideband are demonstrated. By adjusting Sagnac-Fizeau shift and the power of control field, the degree of asymmetric magnonic responses can be strengthened, therefore causing stronger nonreciprocity of sideband. Especially, for the case of strong Sagnac-Fizeau shift and the control field, high level of efficiency and isolation ratio of sideband are achieved simultaneously and the operational bandwidth of strong nonreciprocity can be expanded. Our proposal provides an effective avenue for the manipulation of the nonreciprocity of sideband and has potentially practical applications in on-chip microwave isolation devices and magnon-based precision measurement.

Nonreciprocal Frequency Conversion and Mode Routing in a Microresonator

The transportation of photons and phonons typically obeys the principle of reciprocity. Breaking reciprocity of these bosonic excitations will enable the corresponding nonreciprocal devices, such as isolators and circulators. Here, we use two optical modes and two mechanical modes in a microresonator to form a four-mode plaquette via radiation pressure force. The phase-controlled nonreciprocal routing between any two modes with completely different frequencies is demonstrated, including the routing of phonon to phonon (megahertz to megahertz), photon to phonon (terahertz to megahertz), and especially photon to photon with frequency difference of around 80 THz for the first time. In addition, one more mechanical mode is introduced to this plaquette to realize a phononic circulator in such single microresonator. The nonreciprocity is derived from interference between multimode transfer processes involving optomechanical interactions in an optomechanical resonator. It not only demonstrates the nonreciprocal routing of photons and phonons in a single resonator but also realizes the nonreciprocal frequency conversion for photons and circulation for phonons, laying a foundation for studying directional routing and thermal management in an optomechanical hybrid network.

Phase-controlled photon blockade in optomechanical systems

The manipulation of photons is a key technology for obtaining optical quantum information. In this study, we present a phase-modulated optomechanical system comprising two coupled cavity resonators and illustrate the phase-controlled photon blockade in the system. The coupling phase of the cavities reveals the interference of photons and introduces an unconventional photon-blockade effect. We also study the influence of the energy level fineness on the photon blockade and resonant frequency of the mechanical mode. Numerical simulations demonstrate that photon blockade can occur over a wide range of system parameters. These results have several implications for understanding the role of the state phase in quantum cavity optomechanics and provide a promising method for the realization of optomechanical quantum devices using photon blockade.

Cavity optomechanical chaos

Cavity optomechanics provides a powerful platform for observing many interesting classical and quantum nonlinear phenomena due to the radiation-pressure coupling between its optical and mechanical modes. In particular, the chaos induced by optomechanical nonlinearity has been of great concern because of its importance both in fundamental physics and potential applications ranging from secret information processing to optical communications. This review focuses on the chaotic dynamics in optomechanical systems. The basic theory of general nonlinear dynamics and the fundamental properties of chaos are introduced. Several nonlinear dynamical effects in optomechanical systems are demonstrated. Moreover, recent remarkable theoretical and experimental efforts in manipulating optomechanical chaotic motions are addressed. Future perspectives of chaos in hybrid systems are also discussed.

Parity-dependent unidirectional and chiral photon transfer in reversed-dissipation cavity optomechanics

Nonreciprocal elements, such as isolators and circulators, play an important role in classical and quantum information processing. Recently, strong nonreciprocal effects have been experimentally demonstrated in cavity optomechanical systems. In these approaches, the bandwidth of the nonreciprocal photon transmission is limited by the mechanical resonator linewidth, which is arguably much smaller than the linewidths of the cavity modes in most electromechanical or optomechanical devices. In this work, we demonstrate broadband nonreciprocal photon transmission in the reversed-dissipation regime, where the mechanical mode with a large decay rate can be adiabatically eliminated while mediating anti- PT -symmetric dissipative coupling with two kinds of phase factors. Adjusting the relative phases allows the observation of periodic Riemann-sheet structures with distributed exceptional points (Eps). At the Eps, destructive quantum interference breaks both the T - and P -inversion symmetry, resulting in unidirectional and chiral photon transmissions. In the reversed-dissipation regime, the nonreciprocal bandwidth is no longer limited by the mechanical mode linewidth but is improved to the linewidth of the cavity resonance. Furthermore, we find that the direction of the unidirectional and chiral energy transfer could be reversed by changing the parity of the Eps. Extending non-Hermitian couplings to a three-cavity model, the broken anti- PT -symmetry allows us to observe high-order Eps, at which a parity-dependent chiral circulator is demonstrated. The driving-phase controlled periodical Riemann sheets allow observation of the parity-dependent unidirectional and chiral energy transfer and thus provide a useful cell for building up nonreciprocal array and realizing topological, e.g., isolators, circulators, or amplifiers.

Hybrid photon-phonon blockade

We describe a novel type of blockade in a hybrid mode generated by linear coupling of photonic and phononic modes. We refer to this effect as hybrid photon-phonon blockade and show how it can be generated and detected in a driven nonlinear optomechanical superconducting system. Thus, we study boson-number correlations in the photon, phonon, and hybrid modes in linearly coupled microwave and mechanical resonators with a superconducting qubit inserted in one of them. We find such system parameters for which we observe eight types of different combinations of either blockade or tunnelling effects (defined via the sub- and super-Poissonian statistics, respectively) for photons, phonons, and hybrid bosons. In particular, we find that the hybrid photon-phonon blockade can be generated by mixing the photonic and phononic modes which do not exhibit blockade.

Single-photon nonlinearities and blockade from a strongly driven photonic molecule

Achieving the regime of single-photon nonlinearities in photonic devices by just exploiting the intrinsic high-order susceptibilities of conventional materials would open the door to practical semiconductor-based quantum photonic technologies. Here we show that this regime can be achieved in a triply resonant integrated photonic device made of two coupled ring resonators, in a material platform displaying an intrinsic third-order nonlinearity. By strongly driving one of the three resonances of the system, a weak coherent probe at one of the others results in a strongly suppressed two-photon probability at the output, evidenced by an antibunched second-order correlation function at zero-time delay under continuous wave driving.

Optical tomography dynamics induced by qubit-resonator interaction under intrinsic decoherence

A superconducting circuit with a qubit and a resonator coupled via a two-photon interaction is considered. When the resonator is initially in a superposition of coherent states, optical tomography and quantum coherence dynamics are examined in the context of intrinsic decoherence. The results reveal that optical tomography is a good quantifier of the quantum coherence produced by the qubit-resonator interaction. The effects of qubit-resonator detuning and intrinsic decoherence on the dynamics of optical tomography distributions for coherent and even coherent states are investigated. The dynamics of optical tomography distributions are highly dependent on detuning and intrinsic decoherence. Our numerical simulations reveal that there is a relation between the optical tomography and the generated quantum coherence. When the qubit-resonator detuning and intrinsic decoherence are augmented, the amplitude and intensity, as well as the structure of the optical tomography, change substantially.

Few-photon optical diode in a chiral waveguide

We study the coherent transport of one or two photons in a one-dimensional waveguide chirally coupled to a nonlinear resonator. Analytic solutions of the one-photon and two-photon scattering is derived. Although the resonator acts as a non-reciprocal phase shifter, light transmission is reciprocal at one-photon level. However, the forward and reverse transmitted probabilities for two photons incident from either the left side or the right side of the nonlinear resonator are nonreciprocal due to the energy redistribution of the two-photon bound state. Hence, the nonlinear resonator acts as an optical diode at two-photon level.