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We study the steady-state photon distributions in two coupled systems consisting of three or four single-mode cavities. We find that it is viable to realize a single or double dark mode with vanishing photons in one cavity while arbitrary photons in other cavities under specific conditions. Such dark modes arise from perfect destructive interference between different coupling pathways and are in analogy to atomic dark states in the Λ or tripod systems. It is of more interest that a sharp dark-mode dip may be attained in the three-cavity system and two dark modes may interplay to yield a sharp bright-mode peak in the four-cavity system. The flexible tunability of such dips and peaks is beneficial to design sensitive photonic devices of switching or measuring, in a way different from coupled-resonator-induced transparency and absorption.

We propose an efficient scheme for generating and controlling beating stationary light pulses in a five-level atomic sample driven into electromagnetically induced transparency condition. This scheme relies on an asymmetrical procedure of light storage and retrieval tuned by two counter-propagating control fields where an additional coupling field, such as the microwave field, is introduced in the retrieval stage. A quantum probe field, incident upon such an atomic sample, is first transformed into spin coherence excitation of the atoms and then retrieved as beating stationary light pulses exhibiting a series of maxima and minima in intensity due to the alternative constructive and destructive interference. It is convenient to control the beating stationary light pulses just by manipulating the intensity and detuning of the additional microwave field. This interesting phenomenon involves in fact the coherent manipulation of dark-state polaritons and could be explored to achieve the efficient temporal splitting of stationary light pulses and accurate measurement of the microwave intensity.

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.

We study the multistability of fixed points for a dimerized system of Rydberg atoms driven by two laser fields and trapped in a two-dimensional (2D) square lattice. For identical driving fields, the fixed points of this system exhibit stable uniform, unstable uniform, stable nonuniform, or oscillating nonuniform phases in the presence of a bistable region. For different driving fields, however, all (stable, unstable, or oscillating) phases become nonuniform instead, which then results in two islets isolated from the mainland of Rydberg excitation. We also show that a tristable region may stretch out from the (nonuniform) bistable region near the islets, indicating that a richer phase diagram can be attained by tuning the Rabi frequencies and/or detunings of the driving fields. Last but not least, the fixed points can adiabatically evolve from the islets to the mainland but can not inversely evolve from the mainland to the islets.

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 investigate the dual-channel optical nonreciprocity effects of a moving atomic multilayer structure driven into a five-level M-type configuration by two strong coupling fields and two weak probe fields. We find that both the two probe fields propagating along the moving lattice will experience forward–backward asymmetry in transmission. For each one of the two probe fields, two frequency regions with very large nonreciprocity effect may exist and fit within the two AT splitting transparent windows contributed by the two coupling fields, and the degree and position of the nonreciprocity parameter could be controlled by modulating the coupling intensities and frequencies.

We investigate in theory the ultraslow light propagation and reversible light storage in a Pr 3+ : Y 2 SiO 5 crystal driven into the electromagnetically induced transparency regime. By carefully adjusting several critical parameters, we can well recover relevant experimental results in terms of the time delay, the energy loss, the pulse width, and the retrieval efficiency of the transmitted signal. Our results depend on full numerical solutions of the coupled Maxwell–Liouville equations with the inhomogeneous broadenings properly dealt with.

Owing to interference induced by spontaneous emission, the density-matrix equations in a three-level Λ-type system have an additional coherence term, which plays a critical role in modulating the inversionless gain and electromagnetically induced transparency effect. In addition, it is shown that spontaneously generated coherence (SGC) has an effect on the entanglement between an atom and a photon of the coupling laser field by calculating the degree of entanglement (DEM) of the atomic system. In this paper, we investigate the influence of the SGC effect on atom-photon entanglement in a Λ-type system, which generally remains a high entangled state. When an incoherent pump source is introduced, we find that the SGC effect could exert considerable influence on the atom reduced entropy under certain conditions for both transient and steady states. More interestingly, such an incoherent pump field could actively affect the short-time dynamic behaviors of the transient quantum entangled state at a certain range of pump rate as a typical coherent case.

We study the effects of quadratic reactive coupling on normal mode splitting in a microdisk-waveguide optomechanical system, whose stability can be determined by the Routh–Hurwitz criterion. We find that the quadratic reactive coupling is important for the mode splitting of a Stokes field only in the presence of a strong pump field. For a large enough pump power, the quadratic reactive coupling will lead to larger and asymmetric frequency shifts for the two Stokes modes, which are however smaller and symmetric when only the linear reactive coupling is considered. Such a unique normal mode splitting happens in an efficient four-wave-mixing process of optomechanical interaction. This is why an anti-Stokes field is seen to arise in the presence of an excited waveguide oscillation. The anti-Stokes field has a much stronger interaction with the lower-frequency Stokes mode because their frequencies and amplitudes change remarkably in a similar way when the quadratic coupling constant is gradually increased.

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 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 and compare the steady and transient optical responses of a four-level system and a three-level system, which are dressed by two and three laser fields, respectively. In the three-level system, a transmissivity window (a reflectivity platform) may be induced on the probe resonance by a traveling-wave (standing-wave) coupling field. In the four-level system, both transmissivity window and reflectivity platform are remarkably modified when a traveling-wave driving field is applied on two-photon resonance with the probe, but change little when the traveling-wave driving field is largely two-photon detuned. This implies that the four-level system can be safely treated as a three-level one in certain frequency regions of interest. Transient behaviors of atomic coherence on the probe resonance are also examined in both three-level and four-level systems to further confirm this conclusion. Our new findings are beneficial to achieve a novel all-optical routing scheme by simultaneously creating a transmissivity window and a reflectivity platform on a single resonance, and may also be used to simplify theoretical treatments in the situations where numerical calculations are complicated and intractable in the presence of at least one standing-wave field.

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 double-cavity optomechanical system where an in-between membrane oscillator is shared by two identical cavities. Two relevant cavity modes experience the optomechanical coupling of same amplitudes but opposite signs when the membrane deviates from its equilibrium position due to radiation pressure. We demonstrate in theory efficient manipulations of optomechanically induced transparency in the weak coupling regime and normal mode splitting in the strong coupling regime via nonlinear wave-mixing processes. It is found that both absorptive and dispersive behaviors of the output probe field can be well controlled to switch between two different steady states by applying a coupling field and a driving field in separate cavities. This optomechanical switching scheme works in both coupling regimes and may be extended to develop new devices of light routing, conversion, delay, and isolation.

We study a double-cavity optomechanical system in which a movable mirror with perfect reflection is inserted between two fixed mirrors with partial transmission. This optomechanical system is driven from both fixed end mirrors in a symmetric scheme by two strong coupling fields and two weak probe fields. We find that three interesting phenomena: coherent perfect absorption (CPA), coherent perfect transmission (CPT), and coherent perfect synthesis (CPS) can be attained within different parameter regimes. That is, we can make two input probe fields totally absorbed by the movable mirror without yielding any energy output from either end mirror (CPA); make an input probe field transmitted from one end mirror to the other end mirror without suffering any energy loss in the two cavities (CPT); make two input probe fields synthesized into one output probe field after undergoing either a perfect transmission or a perfect reflection (CPS). These interesting phenomena originate from the efficient hybrid coupling of optical and mechanical modes and may be all-optically controlled to realize novel photonic devices in quantum information networks.

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 an ensemble of cold atoms driven to the four-level double-$\ensuremath{\Lambda}$ configuration and trapped in the one-dimensional optical lattices for achieving dynamically controlled photonic band gaps (PBGs) via the balanced four-wave mixing interaction. Numerical results show that a pair of PBGs characterized by high platforms of probe reflectivities and reduced density of photonic states are established, simultaneously, on both probe transitions in one symmetric driving scheme. Such two-color PBGs can be easily manipulated in position and width by modulating, e.g., the balanced Rabi frequencies of two coupling fields and the Gaussian widths of atomic density distributions, to change the equal probe detunings fulfilling both Bragg conditions. Each two-color PBG as predicted in the coherent atomic lattices may be explored to attain robust light entanglement, even for single-probe photons, via an efficient frequency conversion during the nonlinearly correlated reflection.

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 investigate the interaction of an open (N + 1)-level extended V-type atomic system (i.e. a closed (N + 2)-level atomic system) with N coherent laser fields and one incoherent pumping field through both analytical and numerical calculations. Our results show that the system can exhibit multiple resonant gain suppressions via perfect quantum destructive interference, which is usually believed to be absent in closed three-level V system and its extended versions involving more atomic levels, with at most N – 1 transparency windows associated with very steep anomalous dispersions occurring in the system. The superluminal group velocity of the probe-laser pulse with at most N – 1 negative values can also be generated and controlled with little gain or absorption.

We study a five-level double-tripod system of cold atoms for efficiently manipulating the dynamic propagation and evolution of a quantum probe field by modulating four classical control fields. Our numerical results show that it is viable to transform the quantum probe field into a pair of two-color stationary light pulses mutually coupled through two wave packets of atomic spin coherence. The pair of stationary light pulses can be released either from the sample entrance and exit synchronously or just from the sample exit with a controlled time delay. In addition, the two-color stationary light pulses are immune to the fast decay originating from the higher-order Fourier components of atomic spin and optical coherence, and may exhibit the quantum limited beating signals with their characteristic frequency determined by detunings of the four classical control fields. These results could be explored to design novel photonic devices, such as optical routing, beam splitter, and beat generator, for manipulating a quantum light field.

We study a dilute sample of cold atoms to achieve efficient population transfer from a ground state to a Rydberg state. This sample is approximately divided into many independent microspheres containing only two atoms. Each pair of atoms in a microsphere may become quantum correlated via the dipole-dipole interaction characterized by a van der Waals potential. Our numerical results show that, by modulating detunings of a pump pulse and a Stokes pulse applied in the counterintuitive order, we can drive the dilute sample either into the blockade regime or into the antiblockade regime. In the blockade regime, only one atom is allowed to be coherently transferred into the Rydberg state in a microsphere, which then results in a maximal entangled state. In the antiblockade regime, however, both atoms in a microsphere can be efficiently excited into the Rydberg state, which is not accompanied by quantum entanglement. A second maximal entangled state may also be generated if we work between the blockade regime and the antiblockade regime. Note that the existence of a quasidark state is essential for exciting both atoms in a microsphere into the Rydberg state when the van der Waals potential is nonzero.

We study a cold atomic sample coherently driven into the five-level triple-$\ensuremath{\Lambda}$ configuration for attaining a dynamically controlled triple photonic band-gap structure. Our numerical calculations show that three photonic band gaps with homogeneous reflectivities up to $92%$ can be induced on demand around the probe resonance by a standing-wave driving field in the presence of spontaneously generated coherence. All these photonic band gaps are severely malformed with probe reflectivities declining rapidly to very low values when spontaneously generated coherence is gradually weakened. The triple photonic band-gap structure can also be attained in a five-level chain-$\ensuremath{\Lambda}$ system of cold atoms in the absence of spontaneously generated coherence, which however requires two additional traveling-wave fields to couple relevant levels.

We study both steady and dynamic optical responses of three samples with the same amounts of cold atoms but very different density functions. These samples are driven into the regime of electromagnetically induced transparency by a probe and a coupling in the Lambda configuration. When the coupling is in the traveling-wave pattern, all samples have the same transmission spectra and therefore identical transmitted pulses at the sample exits. In the case of a standing-wave coupling, however, very different reflection and transmission spectra are found for the three samples. Accordingly, reflected pulses at the sample entrances and transmitted pulses at the sample exits are quite sensitive to the spatial inhomogeneity of cold atoms. These interesting phenomena are qualitatively analyzed in terms of constructive and destructive interference between forward and backward probe photons scattered by a standing-wave atomic grating.

A tripod atomic system driven by two standing-wave fields (a coupling and a driving) is explored to generate tunable double photonic bandgaps in the regime of electromagnetically induced transparency. Both photonic bandgaps depend critically on frequency detunings, spatial periodicities, and initial phases of the two standing-wave fields. When the coupling and driving detunings are very close, a small fluctuation of one standing-wave field may demolish both photonic bandgaps. If the two detunings are greatly different, however, each standing-wave field determines only one photonic bandgap in a less sensitive way. Dynamic generation and elimination of a pair of photonic bandgaps shown here may be exploited toward the end of simultaneous manipulation of two weak light signals even at the single-photon level.

We study a four-level double-Lambda system with spontaneously generated coherence driven by a standing-wave coupling field. It is found that two well-developed photonic bandgaps with reflectivities of about 90% can be generated on the probe resonance in the presence of maximal spontaneously generated coherence. The induced double photonic bandgaps become, however, severely malformed when spontaneously generated coherence vanishes. Dynamic control of the double photonic bandgaps may be exploited to achieve a novel two-port double-channel routing scheme for weak light signals in quantum networks.

By investigating the steady optical response of a cold atomic ensemble, we find that one high-reflection band gap and one high-transmission region with comparable widths may be dynamically induced and well controlled around the probe resonance by a traveling-wave coupling field and a standing-wave grating field. The high-reflection band gap and the high-transmission region are then applied to devise a scheme for all-optical routing of two different light signals toward either the opposite or the same directions. This all-optical routing scheme is very efficient because both reflected and transmitted signals experience little loss and deformation, and thus it may have important applications in quantum information networks.

We theoretically study the coherent interaction of a tripod-type atomic system with three laser fields, i.e., one probe and two coupling, or two probe and one coupling field. Our analytical and numerical results show that, when all three fields are on two-photon resonance, in addition to the Rabi frequencies of the coupling fields, the probe group velocities also depend on the spontaneous decay rates and the initial population distribution. So we can manipulate the probe pulses to achieve controllable ultraslow group velocities by preparing different initial atomic states. With an incoherent pump field applied, a narrow transparent window accompanied by abnormal dispersion may occur in the probe absorption spectrum, which then allows us to switch a probe pulse from ultraslow to superluminal propagation.

We study both dynamical and steady responses of a coherently driven four-level tripod-type atomic system, which may be either open or closed. With all three driving fields being on Raman resonance, this tripod system can quickly evolve into a complicated steady dark state decoupled from both coherent and dissipative interactions. In the open model, this tripod system is sensitive to all parameters in its dynamical evolution while the steady dark state only depends on the initial population distribution and the relative Rabi frequency values. In the closed model, however, relative values of spontaneous decay rates also play an important role in generating the steady dark state. Analytical results based on the quantum jump theory show that the steady dark state is always multiple (from twofold to sixfold) degenerate and usually comes into existence through both coherent and incoherent superpositions.

We study a three-mode double-cavity optomechanical system in which an oscillating membrane of perfect reflection is inserted between two fixed mirrors of partial transmission. We find that electromagnetically induced transparency (EIT) can be realized and controlled in this optomechanical system by adjusting the relative intensity and the relative phase between left-hand and right-hand input (probe and coupling) fields. In particular, one perfect EIT window is seen to occur when the two probe fields are exactly out of phase and the EIT window's width is very sensitive to the relative intensity of two coupling fields. Our numerical findings may be extended to achieve optomechanical storage and switching schemes applicable in quantum information processing.

In order to identify special information from a light pulse sequence, we propose a few viable schemes for marking a desired slow light signal with a fast optical precursor in a Λ-type and N-type atomic system. The fast optical precursor is characterized by transient beating patterns originating from the temporal discontinuity of the marking pulse at the sharp rising or falling edge. Compared with the schemes in the Λ system, the one in the N system has the advantage of flexibility in situations in which we are not the sender of the original probe signals. Besides, there is no disturbance to the probe signals nor an undesired main pulse coming from the marking field.

We study the dynamic processes of reversible dual-channel light memory in a double-tripod atomic system by modulating only a pair of counterpropagating control fields in time. We find that two pairs of stationary light pulses (SLPs) can be simultaneously generated when we switch on both control fields after storage. Two incident signal fields in two channels can be released either simultaneously from the same surface of the sample, or at different times from the same or different surfaces of the sample, depending on the time modulation of the two control fields, the time sequence of the input signal fields, and the group velocities of the signal fields propagating in medium, which could be successfully manipulated in each channel. Comparing with the light storage in spin-wave excitations, the SLPs may suffer a little space-dependent diffusion but maintain optical components required for nonlinear optical interactions. These results could be used to study the enhanced low-noises nonlinear interaction between dual-channel SLPs, which can maximize the interaction time. Besides, this scheme could also be explored to design synchronous multitasking information processing during light memory processes at low-light even below single-photon level.

We propose a scheme for realizing electromagnetically induced grating via the giant Kerr nonlinearity in a coherently driven four-level system with spontaneously generated coherence. In the presence of spontaneously generated coherence, Kerr nonlinearity can be enhanced with vanishing linear absorption. Thus, with a standing-wave coupling field, one can achieve a pure absorption grating, which leads the probe field to gather the zero-order direction when the detuning of the coupling field is on resonance. Moreover, we can obtain a pure phase grating, which diffracts a weak probe light into the first-order direction and the second-order direction when the detuning of the coupling field is off resonance.

We propose an efficient scheme for the dynamic generation and manipulation of beating signals in a sample of cold atoms driven into the four-level quasi-Λ configuration. This scheme relies on a procedure of light storage and retrieval controlled by a classical coupling field with a microwave field introduced only in the retrieval stage. One quantum probe field, incident upon this atomic sample, is transformed into a collective excitation of atomic spin coherence and then into two optical components characterized by different time-dependent phases. Consequently the retrieved quantum probe field exhibits a series of maxima and minima (beating signals) in intensity due to the alternative constructive and destructive interference. This interesting phenomenon, in fact, involves the coherent conversion between single-mode and two-mode dark-state polaritons and could be explored to measure the microwave intensity with high-precision beating signals.

We demonstrate efficient four-wave mixing with an intensity conversion efficiency of nearly 100% in theory without considering the Doppler-broadening effect in a four-level double-Λ system of hot 87Rb gas. The corresponding experimental value of about 73% was reported in our earlier work under the same conditions. This dramatic efficiency is critically dependent on the constructive interference between two four-wave mixing processes relevant to the internally generated four-wave mixing signal.

We investigate the steady optical properties of a three-level open V system (i.e. a four-level closed atomic system) through both analytical and numerical calculations. Our results show that the resonant probe gain can be greatly suppressed to generate a narrow and deep transparency window associated with very steep abnormal dispersion. The underlying physics is identified as the perfect quantum destructive interference between a pair of dressed state transition pathways, which is usually believed to be absent in three-level closed V systems. In addition, we show that the transparency window and its associated abnormal dispersion can be used to realize a striking propagation dynamics where a light pulse may have a negative group velocity of small absolute values and experience little gain or absorption.

We propose an efficient scheme for the robust and controlled generation of beating signals in a sample of stationary atoms driven into the tripod configuration. This scheme relies on an asymmetric procedure of light storage and retrieval where the two classical coupling fields have equal detunings in the storage stage but opposite detunings in the retrieval stage. A quantum probe field, incident upon such an atomic sample, is first transformed into two spin coherence wave-packets and then retrieved with two optical components characterized by different time-dependent phases. Therefore the retrieved quantum probe field exhibits a series of maxima and minima (beating signals) in intensity due to the alternative constructive and destructive interference. This interesting phenomenon involves in fact the coherent manipulation of two dark-state polaritons and may be explored to achieve the fast quantum limited measurement.