Intercavity Coupling Research Articles

High-order Autler–Townes splitting in electrically tunable photonic molecules

Whispering gallery mode optical microresonators represent a promising avenue for realizing optical analogs of coherent light–atom interactions, circumventing experimental complexities. All-optical analogs of Autler–Townes splitting have been widely demonstrated, harnessing coupled optical microresonators, also known as photonic molecules, wherein the strong coupling between resonant fields enables energy level splitting. Here, we report the characterizations of Autler–Townes splitting in waveguide-coupled microring dimers featuring mismatched sizes. By exploiting backscattering-induced coupling via Rayleigh and Mie scatterers in individual rings, high-order Autler–Townes splitting has been realized, yielding supermode hybridization in a multi-level system. Upon resonance detuning using an integrated phase shifter, intra-cavity coupling-induced splitting becomes almost indistinguishable at the zero-detuning point where the strong inter-cavity coupling counteracts the imbalance of backscattering strengths in individual rings. Through demonstrations on the maturing silicon photonics platform, our findings establish a framework of electrically tunable photonic molecules for coupling-mediated Autler–Townes splitting, offering promising prospects for on-chip signal generation and processing across classical and quantum regimes.

Single-cavity loss-enabled nanometrology.

Optical monitoring of the position and alignment of objects with a precision of only a few nanometres is key in applications such as smart manufacturing and force sensing. Traditional optical nanometrology requires precise nanostructure fabrication, multibeam interference or complex postprocessing algorithms, sometimes hampering wider adoption of this technology. Here we show a simplified, yet robust, approach to achieve nanometric metrology down to 2 nm resolution that eliminates the need for any reference signal for interferometric measurements. We insert an erbium-doped quartz crystal absorber into a single Fabry-Pérot cavity with a length of 3 cm and then induce exceptional points by matching the optical loss with the intercavity coupling. We experimentally achieve a displacement response enhancement of 86 times compared with lossless methods, and theoretically argue that an enhancement of over 450 times, corresponding to subnanometre resolution, may be achievable. We also show a fivefold enhancement in the signal-to-noise ratio, thus demonstrating that non-Hermitian sensors can lead to improved performances over the Hermitian counterpart.

Engineering the passband shape of coupled-cavity filters for low loss and/or narrow bandwidth.

Emerging applications of photonic integrated circuits are calling for extremely narrowband and/or low-insertion-loss bandpass filters. Both properties are limited by cavity losses or intrinsic quality factors. However, the choice of inter-cavity and bus couplings establishes trade-offs between these two properties and the passband shape, which have been little explored. Using the widely used second-order resonant system as an example, we present new, to the best of our knowledge, classes of filter passband shapes that provide the lowest insertion loss and the narrowest bandwidth for a given loss Q. A normalized design and novel properties based on a temporal coupled-mode theory model are presented, including a design tool to apply these results. These results may benefit loss-sensitive filtering applications such as quantum-correlated photon pair sources and RF-photonic integrated circuits.

Selective active resonance tuning for multi-mode nonlinear photonic cavities

Resonant enhancement of nonlinear photonic processes is critical for the scalability of applications such as long-distance entanglement generation. To implement nonlinear resonant enhancement, multiple resonator modes must be individually tuned onto a precise set of process wavelengths, which requires multiple linearly-independent tuning methods. Using coupled auxiliary resonators to indirectly tune modes in a multi-resonant nonlinear cavity is particularly attractive because it allows the extension of a single physical tuning mechanism, such as thermal tuning, to provide the required independent controls. Here we model and simulate the performance and tradeoffs of a coupled-resonator tuning scheme which uses auxiliary resonators to tune specific modes of a multi-resonant nonlinear process. Our analysis determines the tuning bandwidth for steady-state mode field intensity can significantly exceed the inter-cavity coupling rate g if the total quality factor of the auxiliary resonator is higher than the multi-mode main resonator. Consequently, over-coupling a nonlinear resonator mode to improve the maximum efficiency of a frequency conversion process will simultaneously expand the auxiliary resonator tuning bandwidth for that mode, indicating a natural compatibility with this tuning scheme. We apply the model to an existing small-diameter triply-resonant ring resonator design and find that a tuning bandwidth of 136 GHz ≈ 1.1 nm can be attained for a mode in the telecom band while limiting excess scattering losses to a quality factor of 106. Such range would span the distribution of inhomogeneously broadened quantum emitter ensembles as well as resonator fabrication variations, indicating the potential for the auxiliary resonators to enable not only low-loss telecom conversion but also the generation of indistinguishable photons in a quantum network.

Phase transition and dynamics of qubits in coupled-cavity arrays with nonlinear topological photonics

The topological properties of a coupled-cavity array corresponding to a Su–Schrieffer–Heeger (SSH) model have been investigated through the evolution of a edge cavity, with the Kerr-like nonlinearities added to the inter-cavity coupling strengths. In the topological phase, the state distribution is more localized at the first cavity with the nonlinearities enhanced. The phase transition occurs with the enhancement of nonlinearities after the system evolving for long time when the SSH model is initially at the phase-transition point or in the trivial phase. The entanglement dynamics of two atoms placed in the two edge cavities is explored, and it is found the coupled-cavity array with nonlinearities is more robust against the disturbance of the frequency of each cavity. Moreover, the dynamics and phase transition of a 2-dimensional kagome lattice with the Kerr-like nonlinearities is also discussed through the probability amplitude of the first site after evolving for long time.

Enlarging the spectral accessibility of photonic zero-modes in coupled Photonic Crystal cavities through "image barrier" engineering

Photonic modes resistant to imperfections or perturbations are of paramount importance in many photonic applications. In this context, zero-modes have several advantages. Unfortunately, they are often difficult to observe. In this work, focusing on coupled photonic crystal cavities, we propose and demonstrate a technique that allows control of inter-cavity coupling without introducing concomitant frequency mismatch, thus allowing observation of zero-modes in a non-Hermitian system and testing of their robustness against asymmetries of coupling. This is done through an original "image barrier" engineering approach.

A Fourth-order Dielectric Narrow-band Bandpass Filter Using Coaxial Resonator

In this paper, a compact fourth-order dielectric bandpass filter is proposed. The filter adopts the mode of linear coupling and is composed of four coaxial resonators and two coupling slots, which are fed by two probes, and the four coaxial resonators are resonated to form a passband. The resonant frequency can be controlled by the radius and height of the resonators, and the inter-cavity coupling is controlled by the width of the coupling windows formed by the coupling slots. At last, the simulation results of the filter show that the filter has narrow bandwidth and good in-band matching performance and out-of-band suppression.

Imaginary couplings in non-Hermitian coupled-mode theory: Effects on exceptional points of optical resonators

Exceptional point (EP) degeneracies in coupled cavities with gain and loss provide on-chip photonic devices with unconventional features and performance. However, such systems with realistic structures often miss the exact EPs even in simulation, and the mechanism of this EP disruption has yet to be thoroughly identified. Here, we extend the coupled-mode theory of one-dimensional non-Hermitian resonator arrays to study the effects of the imaginary part of the inter-cavity coupling, which is a second-order term and attributed to material amplification, absorption, and radiation. By taking an appropriate gauge for the model, we clarify that the imaginary coupling components have a symmetric form in the effective Hamiltonian and hence represent non-Hermiticity. These additional factors can lift the gain- and loss-based EP degeneracies. However, they are proportional to the sum of the imaginary permittivities for involved cavity pairs. Thus, when the amplification and absorption of adjacent cavities are balanced, their contribution to the imaginary coupling is canceled, and the EP singularity can be restored. Radiation-induced imaginary couplings measure the change in net radiation loss by the interference between cavity modes. Their impact on the EP can also be counteracted by small cavity resonance detuning even in loss-biased cases. We show and analyze eligible simulation examples based on photonic crystal nanocavities, and highlight design of an ideal EP degeneracy that is protected by generalized PT symmetry and induced by radiation.

Inter-Cavity Coupling Strength Control in Metal/Insulator Multilayers for Hydrogen Sensing

Hydrogen (H2) sensing is crucial for modern energy storage technology, which looks to hydrogen as the most promising alternative to fossil fuels. In this respect, magnesium (Mg) offers unique possibilities, since magnesium and hydrogen easily undergo a reversible hydrogenation reaction where Mg reversibly converts into MgH2. From an optical point of view, this process produces an abrupt refractive index change, which can be exploited for sensing applications. To maximize this opportunity, we envision an architecture composed of two Ag/ITO/Mg metal/dielectric resonators facing each other and displaced by 200 nm of vacuum. This structure forms a so-called Epsilon-Near-Zero (ENZ) multi-cavity resonator, in which the two internal Mg layers, used as tunneling coupling metals, are accessible to environmental agents. We demonstrate that the hydrogenation of the two Mg layers leads to substantial changes in the strong coupling between the cavities composing the entire resonator, with a consequent abrupt modification of the spectral response, thus enabling the sensing mechanism. One of the main advantages of the proposed system with respect to previous research is that the proposed multilayered architecture avoids the need for lithographic processes. This feature makes the proposed architecture inexpensive and wafer-to-chip scalable, considering that each kind of substrate from common glass to silicon can be used. Therefore, our sensing architecture offers great promise for applications in embedded H2 sensors.

Controllable frequency conversion in the coupled time-modulated cavities with phase delay

By introducing the phase delay in time-modulated photonic structure, the outgoing waves can acquire a dispersionless phase shift regardless of incident angle and polarization. Here, we present a mechanism to control the frequency conversion using a system of two coupled time-modulated cavities with phase delay. The frequency conversion efficiency of structure can be finely controlled by tuning the modulation phase of cavities. The asymmetric frequency conversion to a single sideband can be achieved at the reflection port of structure by changing the intercavity coupling and the modulation phase. The corresponding physical mechanisms are described by a simple three-frequency model. The controllable frequency conversion achieved by the modulation phase in the time-modulated photonic structure can significantly enhance the tunability and the possible functionalities of photonic elements.

Non-Markovian entanglement transfer to distant atoms in a coupled superconducting resonator**Project supported by the Fundamental Research Funds for the Central Universities, China (Grant No. 2018MS056) and the National Natural Science Foundation of China (Grant Nos. 11605055 and 11974108).

We investigate the non-Markovian effects on the entanglement transfer to the distant non-interacting atom qubits, which are embedded in a coupled superconducting resonator. The master equation governing the dynamics of the system is derived by the non-Markovian quantum state diffusion (NMQSD) method. Based on the solution, we show that the memory effect of the environment can lead to higher entanglement revival and make the entanglement last for a longer time. That is to say, the non-Markovian environment can enhance the entanglement transfer. It is also found that the maximum entanglement transferred to distant atoms can be modified by appropriately selecting the frequency of the modulated inter-cavity coupling. Moreover, with the initial anti-correlated state, the entanglement between the cavity fields can be almost completely transferred to the separated atoms. Lastly, we show that the memory effect has a significant impact on the generation of entanglement from the initial non-entangled states.

Single-photon quantum router based on asymmetric intercavity couplings

As a special quantum node in a quantum network, the quantum router plays an important role in storing and transferring quantum information. In this paper, we propose a quantum router scheme based on asymmetric intercavity couplings and a three-level Λ-type atomic system. This scheme implements the quantum routing capability very well. It can perfectly transfer quantum information from one quantum channel to another. Compared with the previous quantum routing scheme, our proposed scheme can achieve the transfer rate of single photons from one quantum channel to another quantum channel reaching 100%, the high transfer rate is located in the almost quadrant regions with negative values of the two variables λa and λb, and their maximum values emerge in the center point λa = λb = −1. Therefore, it is possibly feasible to efficiently enhance the routing capability of the single photons between two channels by adjusting the inter-resonator couplings, and the asymmetric intercavity coupling provides a new method for achieving high-fidelity quantum routers.

Scheme for realizing quantum dense coding via entanglement swapping

Quantum dense coding is a protocol for transmitting two classical bits of information from a sender (Alice) to a remote receiver (Bob) by sending only one quantum bit (qubit). In this article, we propose an experimentally feasible scheme to realize quantum dense coding via entanglement swapping in a cavity array containing a certain number of two-level atoms. Proper choice of system parameters such as atom–cavity and inter-cavity couplings allows perfect transfer of information. A high fidelity transfer of information is shown to be possible by using recently achieved experimental values in the context of photonic crystal cavities and superconducting resonators. To mimic experimental imperfections, disorder in both the coupling strengths and resonance frequencies is considered.

Double-passage mechanical cooling in a coupled optomechanical system**Project supported by the Fundamental Research Funds for the Central Universities, China (Grant No. 2018MS056) and the National Natural Science Foundation of China (Grant Nos. 11605055 and 11574082).

We consider a three-mode optomechanical system where two cavity modes are coupled to a common mechanical oscillator. We focus on the resolved sideband limit and illustrate the relation between the significant parameters of the system and the instantaneous-state mean phonon number of the oscillator cooled to the ground state, particularly at the early stage of the evolution. It is worth noting that the optical coupling sets up a correlation between the two cavity modes, which has significant effect on the cooling process. Using numerical solutions, we find that the inter-cavity coupling will decrease the cooling effect when both cavities have the same effective optomechanical coupling. However, when the effective optomechanical couplings are different, the cooling effect will be strongly improved by selecting appropriate range of inter-cavity coupling.

Selective frequency conversion with coupled time-modulated cavities

Time dependence in photonic structures leads to a number of intriguing and useful phenomena such as optical isolation, topological states of light, and frequency conversion. Here we present a mechanism to achieve efficient and selective frequency conversion using a system of two time-modulated cavities. This setup allows us to fine-tune the conversion process by controlling important parameters such as the intercavity coupling and the external excitation frequency. Both symmetric and asymmetric (up- or down-conversion) outputs can be targeted at will. We describe the processes extensively, with for example a leading role for the dynamic modes of the coupled system, the Floquet modes.

Scully-Lamb quantum laser model for parity-time-symmetric whispering-gallery microcavities: Gain saturation effects and nonreciprocity

We use a non-Lindbladian master equation of the Scully-Lamb laser model for the analysis of light propagation in a parity-time symmetric photonic system composed of coupled active and passive whispering-gallery microresonators. Performing the semiclassical approximation, we obtain a set of two nonlinear coupled differential equations describing the time evolution of intracavity fields. These coupled equations are able to explain the experimentally-observed light non-reciprocity [Peng {\em et al.}, Nature Physics {\bf 10}, 394 (2014), Chang {\em et al.}, Nature Photonics {\bf 8}, 524 (2014)]. We show that this effect arises from the interplay between gain saturation in the active microcavity, intercavity coupling, and losses in the cavities. Additionally, using this approach, we study the effect of the gain saturation on exceptional points, i.e., exotic degeneracies in non-Hermitian systems. Namely, we demonstrate that the inclusion of gain saturation leads to a modification of the exceptional points in the presence of intense intracavity fields. The Scully-Lamb master equation for systems of coupled optical structures, as proposed and applied here, constitutes a promising tool for the study of quantum optical effects in coupled systems with losses, gain, and gain saturation.

Robust lasing modes in coupled colloidal quantum dot microdisk pairs using a non-Hermitian exceptional point

Evanescently coupled pairs of microdisk lasers have emerged as a useful platform for studying the non-Hermitian physics of exceptional points. It remains an open question how scalable and versatile such phenomena can be when carried over to other designs. Here we have studied the effect of gain/loss modulation in an evanescently coupled pair of microdisk optical resonators fabricated from solution-processed colloidal quantum dots. The emission spectra of these structures are sensitive to small imperfections, which cause frequency-splitting of the whispering gallery modes. Despite this inherent disorder, we found that when spatially modulating the optical pump to vary the gain differential between the coupled microdisks, the coupling drives the split parasitic intra-cavity modes into coalescence at an exceptional point of the resulting three-mode system. This unusual behavior is rationalized via a Hamiltonian that incorporates the intra-cavity coupling as well as the anisotropic inter-cavity coupling between modes in the microdisk pair.

Tunable quantum routing via asymmetric intercavity couplings

Routing efficiently the photon signals between different channels is essential in an optical quantum network. Recent chiral waveguide–emitter coupling techniques are widely applied to improve the routing capabilities in waveguide systems. As a possible alternative, we put forward a proposal to control the quantum routing of photons by adjusting asymmetric intercavity couplings on both sides of a cross-cavity in an X-shaped coupled-resonator waveguide. With the robust and tunable intercavity couplings, high transfer rate between quantum channels and expected probability distributions of two ports in the same output channel can be easily implemented. The asymmetric intercavity coupling may be utilized as a new handle to efficiently control the single-photon routing.

Microscopic–macroscopic entanglement transfer in optomechanical system: Non-Markovian effects

In this paper, we investigate the entanglement transfer in two coupled optomechanical systems. A master equation governing the dynamics of the optomechanical systems is derived beyond the Markov approximation. Based on the master equation, we investigate the entanglement transfer from microscopic objects (electromagnetic cavities) to macroscopic objects (mechanical resonators). We show the memory effect of the environment can enhance the entanglement transfer between cavities and resonators. The non-Markovian feedback results in a stronger entanglement transfer, and it also leads to an entanglement revival in the resonators which can make the entanglement last for a longer time. Besides, we also show that in order to achieve higher entanglement transfer, some crucial system parameters such as the inter-cavity coupling should be properly chosen based on the strength of the memory effect. It is our hope that our research is helpful for future studies about entanglement transfer between microscopic and macroscopic objects, particularly for the impact from the environment.

Coherence enhanced quantum metrology in a nonequilibrium optical molecule

We explore the quantum metrology in an optical molecular system coupled to two environments with different temperatures, using a quantum master equation beyond secular approximation. We discover that the steady-state coherence originating from and sustained by the nonequilibrium condition can enhance quantum metrology. We also study the quantitative measures of the nonequilibrium condition in terms of the curl flux, heat current and entropy production at the steady state. They are found to grow with temperature difference. However, an apparent paradox arises considering the contrary behaviors of the steady-state coherence and the nonequilibrium measures in relation to the inter-cavity coupling strength. This paradox is resolved by decomposing the heat current into a population part and a coherence part. Only the latter, the coherence part of the heat current, is tightly connected to the steady-state coherence and behaves similarly with respect to the inter-cavity coupling strength. Interestingly, the coherence part of the heat current flows from the low-temperature reservoir to the high-temperature reservoir, opposite to the direction of the population heat current. Our work offers a viable way to enhance quantum metrology for open quantum systems through steady-state coherence sustained by the nonequilibrium condition, which can be controlled and manipulated to maximize its utility. The potential applications go beyond quantum metrology and extend to areas such as device designing, quantum computation and quantum technology in general.