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We propose a theoretical scheme in a cold Rubidium-87 ($^{87}$Rb) 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 ($\mathcal{PT}$) symmetric and parity-time antisymmetric ($\mathcal{APT}$) modulation can be switched by adjusting different relative phases of the applied beams. Both $\mathcal{PT}$ symmetry and $\mathcal{PT}$ 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.

We investigate the light propagation dynamics in ultra-cold Rydberg medium with inverted-Y configuration based on the superatom theory. It is viable to store light information in two types of atomic spin coherence (trivial spin coherence and Rydberg spin coherence), which makes the system a prospective platform for versatile light manipulation. A normal feature is to realize efficient light storage with simultaneous resonant control fields applied. An intriguing feature is to split light into two beams with different intensities and statistical properties if the control fields are applied separately. The beam of light retrieved from the Rydberg spin coherence is severely attenuated and shows anti-bunching character accompanied by the cooperative optical nonlinearity. Moreover, generation and manipulation of beating signal are achievable by applying the non-resonant control fields.

We study the Rydberg excitation of a square atomic lattice driven by a pumping and a coupling fields into the ladder configuration via Monte Carlo simulations based on density matrix equations. Single-atom Rydberg population can be very close to unit benefiting from the formation of a dark state such that the antiferromagnet (AFM) phase has been observed at finite two-photon detunings owing to moderate van der Waals (vdW) interactions. We note in particular that the pumping Rabi frequency is more important than the coupling Rabi frequency in manipulating the AFM phase to occur for specific pumping detunings, coupling detunings, and nearest-neighbor vdW potentials. Moreover, the AFM phase may enter a saturation regime in terms of its parameter region when the boundary effect of vdW interactions is negligible for a large enough lattice size.

We study the parity-time (PT) symmetry characteristics and the applications to nonlinear optics in an optical trimer system consisting of two indirectly coupled standing-mode micro-cavities and a two-level quantum emitter (QE) placed at the intersection of two cavities. We find this trimer system can exhibit analogical phenomena as those in typical $$\mathscr{PT}$$ 𝒫 𝒯 -symmetric dimer systems composed of a passive cavity directly coupled to an active cavity. This system, whose $$\mathscr{PT}$$ 𝒫 𝒯 symmetry is demonstrated by our analytic results, can be transformed between the $$\mathscr{PT}$$ 𝒫 𝒯 -symmetric phase and the $$\mathscr{PT}$$ 𝒫 𝒯 -broken phase by adjusting relevant system parameters. Then, with this system, we observe both the linear and nonlinear parts of the transmission field become remarkably enhanced and can further reach peak values around the $$\mathscr{PT}$$ 𝒫 𝒯 breaking point. In addition, we show the negative correlation between the gain degree of the linear (nonlinear) transmission part and decay rate of the QE. This trimer proposal is feasible for experiments and may provide a promising platform for $$\mathscr{PT}$$ 𝒫 𝒯 -symmetric optics of low-light levels. Moreover, novel phenomena arising from the QE-cavity-coupling induced nonlinearity gain could be explored to fabricate photonic devices and controllable nonlinear optical media for quantum information process and communication of photons.

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.

Fraunhofer light diffraction across a thin two-dimensional lattice of cold atoms subject to transverse hybrid modulations of two standing-wave crossed pump fields is seen to yield lopsided patterns of various degrees of symmetry. We show that one can fully restrain the diffraction of a weak incident probe to two diagonal or adjacent quadrants or even just to a single quadrant, depending on the phases of two standing-wave pumps and on the probe detuning. Different diffraction symmetries with respect to the axes or diagonals of the diffraction plane quadrants are interpreted here in terms of different out-of-phase interplay of absorption and dispersion periodic distributions, resulting from different combinations of Hermitian, $\mathcal{PT}$-symmetric, and non-Hermitian modulations.

We investigate the storage and retrieval of a multiphoton probe field in cold Rydberg atoms with an effective method based on the superatom model. This probe field is found greatly attenuated in light intensity and two-photon correlation yet suffering little temporal broadening as a result of the partial dipole blockade of Rydberg excitation. In particular, the output field energy exhibits an intriguing saturation effect against the input field energy accompanied by an inhomogeneous nonclassical antibunching feature as a manifestation of the dynamic cooperative optical nonlinearity. Our numerical results are qualitatively consistent with those in a recent experiment and could be extended to pursue quantum information applications of nonclassical light fields.

Cold atoms trapped in one-dimensional optical lattices and driven to the four-level N configuration are exploited for achieving an electromagnetically induced grating with parity-time-symmetry. This nontrivial grating exhibits unidirectional diffraction patterns, e.g., with incident probe photons diffracted into either negative or positive angles, depending on the sign relation between spatially modulated absorption and dispersion coefficients. Such asymmetric light diffraction is a result of the out-of-phase interplay of amplitude and phase modulations of transmission function and can be easily tuned via optical depth, probe detuning, pump Rabi frequencies, etc.

We study the transmitted intensity and correlation properties of a probe field propagating through a sample of cold interacting 87 Rb atoms driven into the Y level configuration with single Rydberg state. We find two electromagnetically induced transparency (EIT) windows in the transmission spectrum. One window is linear since it is immune to the incident probe field. The other window depth is sensitive to the incident probe intensity, exhibiting cooperative nonlinearity. Meanwhile, the linear window is low but the transmissivity at the nonlinear window can reach nearly 100% in case of the weak probe intensity. When two EIT windows overlap, the cooperative optical nonlinearity plays a leading role in the degenerate window. In addition, the probe propagation is affected by its two-photon correlation which is suppressed at the center of nonlinear window and is enhanced near the boundaries of two windows. The two-photon correlation is also sensitive to the probe field, and that means we can attain the strongest photon bunching (anti-bunching) effect by controlling the probe and coupling fields.

We study the dynamic control of stationary light pulses generated in a sample of cold atoms driven into the double- Λ configuration with two ground levels coupled by a weak microwave field. This microwave field can modify the spin coherence of two ground levels through its phase and amplitude, and then increase or decrease the intensity of a stationary light pulse generated from this spin coherence. Such phase-modulation technique is essential to maximize the effective interaction time between light and matter in photonic information processing and therefore facilitate the achievement of enhanced optical nonlinearities at low-light levels.

We theoretically investigate the slow and fast light effects of a probe laser in an optomechanical double-ended cavity filled with a bunch of identical two-level cold 87Rb atoms. It is shown that the presence of atoms can transfer the optomechanically induced transparency (OMIT) window into the steeper Fano shapes and the broader normal-mode splitting shapes. We find that the transmission group delay related to the Fano resonance is much greater than that of the OMIT and normal-mode splitting at the resonances, meanwhile, with the growing of the atomic number, the slow light becomes increasingly significant. The value of reflection group delay related to the OMIT and normal-mode splitting is positive, while the value related to the Fano resonance is significantly negative. This indicates that the reflection parts of output field contain both slow light and fast light. Therefore, via changing the atomic number and detuning, we can realize not only the manipulation of the magnitudes of the group delay and advance, but also a tunable switch from slow light to fast light.

We study the optical response of a double optomechanical cavity system assisted by two Rydberg atoms. The target atom is only coupled with one side cavity by a single cavity mode, and gate one is outside the cavities. It has been realized that a long-range manipulation of optical properties of a hybrid system, by controlling the Rydberg atom decoupled with the optomechanical cavity. Switching on the coupling between atoms and cavity mode, the original spatial inversion symmetry of the double cavity structure has been broken. Combining the controllable optical non-reciprocity with the coherent perfect absorption/transmission/synthesis effect (CPA/CPT/CPS reported by [ X.-B. Yan Opt. Express22, 4886 (2014)], we put forward the theoretical schemes of an all-optical transistor which contains functions such as a controllable diode, rectifier, and amplifier by controlling a single gate photon.

We study in theory the single-photon Rydberg excitation in an ensemble of two-level cold atoms at finite low temperatures. Rydberg population plotted against laser detuning may exhibit a nonlinear bistable behavior arising from the dipole–dipole interactions manifested as a van der Waals (vdW) potential. We find that Doppler broadening can result in a remarkable reduction of the bistable region, which may disappear as the atomic temperature increases to a certain value, of the order of tens to hundreds of μK. This special temperature, depending critically on the vdW potential, can be largely raised by partially eliminating the Doppler effect, when a double-photon excitation scheme is used to replace the single-photon excitation scheme.

We study both the steady and the dynamic optical response of cold atoms trapped in an optical lattice and driven to the three-level $\mathrm{\ensuremath{\Lambda}}$ configuration. These atoms are found to exhibit gain without population inversion when an incoherent pump is applied to activate spontaneously generated coherence. Gain-assisted double photonic band gaps characterized by reflectivities over 100% then grow up near the probe resonance due to the periodic distribution of the atomic density. These band gaps along with the neighboring allowed bands of transmissivities over 100% can be tuned by modulating the control field in amplitude, frequency, and, especially, phase. Consequently it is viable to realize a reflector, an amplifier, or a splitter when a weak incident light pulse is totally reflected in the photonic band gaps, totally transmitted in the allowed bands, or equally reflected and transmitted in the intersecting regions. Our results have potential applications in all-optical networks with respect to fabricating dynamically switchable devices for manipulating photon flows at low-light levels.

Utilizing dipole blockade of Rydberg excitations, we study an ensemble of stationary atoms driven into the four-level N configuration for achieving a new kind of electromagnetically induced grating in the presence of a traveling-wave and a standing-wave classical control fields. This grating shows cooperative optical nonlinearities as manifested by the sensitivity of output diffraction patterns to input light intensities (photon correlations) of a quantum probe field, promising then an essential opportunity for distinguishing weaker and stronger (bunched and anti-bunched) light fields.

We study the adiabatic passage for a pair of interacting cold atoms driven into the ladder configuration with one ground state and two Rydberg states. We find, with proper single-photon and two-photon detunings, that it is viable to (i) achieve efficient population transfer from the ground state to either Rydberg state by fully overcoming the dipole blockade effect and (ii) implement maximal entangled states by partially overcoming the dipole blockade effect. These entangled atomic states are very stable and have purities and fidelities approaching 100%, among which one is of particular interest since it involves the simultaneous excitation of two different Rydberg states.

We study a heterojunction cavity with one vacuum gap inserted between two dielectric slabs with conjugate complex refractive indices, i.e., of balanced gain and loss. This cavity is found to exhibit a multiple parity-time (PT) symmetry characterized by alternating symmetric and broken phases, when examined in terms of both of the eigenvalues of the scattering matrix. Scattering behaviors, including reflection and transmission, however, should be classified into three distinct types because a transition region may exist between the symmetric and broken phases. It is of particular interest that vanishing reflectance could occur for light waves input from both the left and right sides, though of different wave vectors, in the symmetric phases. Moreover, it is viable to attain unidirectional invisibility for light waves only input from the left side and simultaneously realize coherent perfect absorption and lasing for a given wave vector in the transition regions. These unique scattering behaviors can be easily tuned to suit a wide range of wave vectors by adjusting the gap width.

We propose a feasible and flexible scheme to realize all-optical photon switching, router and amplifier by using a passive-active optomechanical system consisting of a passive cavity, an active cavity and a common movable membrane oscillator. Due to the cooperation between the gain effect of the active cavity and the interference effect between the probe fields, some novel phenomena arise, such as the frequency-independent perfect reflection first proposed in this paper, controllable photon routing, tunable fast and slow lights and so on. Based on the results, a photon switching of absorption-amplification and fast-slow-light transitions, and a photon router with controllable direction and intensity can be realized by adjusting relevant parameters such as the strengths of control fields and the relative phase between probe fields. Such a scheme may provide a promising platform for controllable photon transport and photonic device fabrication.

We investigate the stationary entanglement properties in a hybrid system consisting of an optical cavity, a mechanical resonator, a charged object, and an atomic ensemble. Numerical results show that this hybrid system exhibits three kinds of controllable bipartite entanglements in an experimentally accessible parameter regime with the help of the charged object. More importantly, it is viable to enhance on demand each bipartite entanglement at the expense of reducing others by modulating the Coulomb coupling strength. Last but not least, these bipartite entanglements seem more robust against on the environmental temperature for the positive Coulomb interaction.

We study the steady optical responses of a cold atomic ensemble driven into the three-level ladder configuration involving a Rydberg state at finite temperatures. By improving the superatom model with thermal movement included, we calculate relevant atomic coherence effects and find that the residual Doppler broadening at the mK–K temperatures will weaken the nonclassical properties of transmitted probe photons. Furthermore, propagation directions of the probe and coupling fields have a great influence on various properties related to electromagnetically induced transparency. That is, the residual Doppler effect is more destructive to relevant atomic coherence effects in the co-propagation case but can be partially eliminated in the counter-propagation case.

We study the optical response of cold rubidium atoms driven into the four-level Y configuration exhibiting two high Rydberg levels in the regime of electromagnetically induced transparency (EIT). Atoms excited to either Rydberg level interact with each other just via self-blockade potentials (I) or also via cross blockade potentials (II). Numerical results show a few interesting quantum phenomena on the transmitted properties of a weak probe field owing to controlled single and double Rydberg blockade. In case (I), it is viable to switch between single-photon outputs with vanishing (invariable) two-photon (three-photon) correlation and photon-pair outputs with vanishing (invariable) three-photon (two-photon) correlation. Such output switch can be easily done by modulating frequencies and intensities of two strong coupling fields to create a degenerate EIT window or two separated EIT windows. In case (II), we find that two-photon and three-photon correlations decrease together at a degenerate EIT window center while increasing together between two separated EIT windows. Such consistent changes are observed because both correlations are modified by the identical polarizability degradation though depending on single and double Rydberg blockade, respectively.

We study a five-level $\text{quasi}\ensuremath{-}\ensuremath{\Lambda}$ system of cold atoms for achieving high-order photonic band gaps (PBGs) probed by an ultraviolet field in two cases where either an infrared or a visible control field works in the standing-wave configuration to induce one atomic grating. Transfer-matrix calculations for appropriate rubidium levels demonstrate that three fifth-order band gaps or two second-order band gaps can be generated near the probe resonance when the standing-wave control field is modulated to satisfy relevant Bragg conditions in the regime of electromagnetically induced transparency. These high-order PBGs, as characterized by homogeneous high reflectivities, can be dynamically tuned in positions and widths on demand and may be extended to develop efficient devices (like diodes and reflectors) for manipulating weak high-frequency light with strong low-frequency light.

We present an improved superatom model for examining nonlinear optical responses of cold Rydberg atoms in the regime of electromagnetically induced transparency (EIT). By going beyond the weak-probe approximation, we find that several higher-order collective states should be included to correctly describe the coherent Rydberg excitation of superatoms. Otherwise, numerical results based on the simple ladder system of superatoms will contribute wrong predictions on light intensity and photon correlation of the transmitted probe field. In particular, a great photon-bunching effect will be improperly expected somewhere out of the EIT window in one dilute atomic sample. The essence of this improved superatom model lies in that it can provide reliable predictions on the nonlinear Rydberg-EIT phenomena even in dense atomic samples and may be extended to realize lossless conditional light interactions in appropriate multilevel systems exhibiting dipole blockade.

We study the transmission properties of a probe field passing through a sample of $N$-type cold atoms possessing a high Rydberg state. Due to the conditioned dipole blockade of Rydberg excitation, this atomic sample might exhibit a nonlinear optical response in terms of electromagnetically induced transparency (EIT) as manifested by the sensitivity of the transmitted probe intensity and correlation to input probe intensity and correlation. It is of particular interest that the nonlinear EIT response can be opposite (either normal or abnormal) in two different regions of probe detuning, which is a striking feature of the four-level N system of interacting atoms. The realization of both normal and abnormal nonlinear EIT effects in one atomic sample is expected to have wider applications in manipulation of photonic statistics of weak light signals, e.g., to attain prominent photonic bunching and/or antibunching in a dynamic quantum delay or memory process.

We study the transmitted intensity and correlation properties of a probe field traveling through a sample of interacting cold ${}^{87}$Rb atoms driven into the inverted $\mathsf{Y}$ configuration. Two windows of electromagnetically induced transparency are found in the transmission spectrum, which are either sensitive or immune to the input probe intensity. This means that one window is accompanied by cooperative optical nonlinearity while the other is a result of a linear optical response. Moreover, we find sufficiently suppressed two-photon correlation within the nonlinear window and greatly enhanced two-photon correlation between the linear and nonlinear windows. In the case of the degenerate window, however, it is viable to conceal the cooperative optical nonlinearity behind the linear optical response. This then allows us considerable flexibility to manipulate the propagation and evolution of a quantum light field.