Nonlinear Cavity Research Articles

Noise switching at a dynamical critical point in a cavity-conductor hybrid

Coupling a mesoscopic conductor to a microwave cavity can lead to fascinating feedback effects which generate strong correlations between the dynamics of photons and charges. We explore the connection between cavity dynamics and charge transport in a model system consisting of a voltage-biased Josephson junction embedded in a high-Q cavity, focussing on the behavior as the system is tuned through a dynamical critical point. On one side of the critical point the noise is strongly suppressed, signalling the existence of a novel regime of highly coherent transport, but on the other side it switches abruptly to a much larger value. Using a semiclassical approach we show that this behavior arises because of the strongly nonlinear cavity drive generated by the Cooper pairs. We also uncover an equivalence between charge and photonic current noise in the system which opens up a route to detecting the critical behavior through straightforward microwave measurements.

Tunable Photon Blockade in Coupled Second-order Nonlinear Cavities

The unconventional photon blockade with weak χ (2) nonlinearity in a system consists of two single-mode cavities driving by two external fields is studied in this paper. The photon statistical properties, described by the second-order correlation function, are discussed, and the exact optimal conditions for strong photon anti-bunching is analytically derived. The optimal frequency detuning and nonlinear interaction strength for the strong photon anti-bunching are also obtained, which are in good agreement with numerical simulations. We find that the unconventional photon blockade effect can be controlled by tuning the relative phase between two complex driving fields when the two cavity modes are driven simultaneously. Our results provide a promising scheme for the coherent manipulation of photon blockade through tuning the relative phase between the two driving fields, which makes the experimental realization more flexible.

All-optical control of ultrahigh-Q silica microcavities with iron oxide nanoparticles.

We propose and experimentally demonstrate, to the best of our knowledge, the first all-optical control scheme of ultrahigh-quality (Q)-factor silica microcavities, which can maintain their Q factors over 108 during the tuning process. For silica microcavities, the resonance tunability is very important and is also challenging for many applications. However, almost all previous works on resonance tuning deteriorate the Q factors of silica microcavities at different levels, and evidently these schemes are not suitable for applications in which ultrahigh Q factors are required. In this work, based on the proposed silica microbottle cavity and iron oxide nanoparticles, we realize all-optical control of the silica microcavity and maintain its Q factor of around 1.2×108 during the tuning process. A tuning range of 85.9GHz (0.68nm) and a tuning sensitivity of 13.6GHz/mW are obtained, and it is possible to realize full tunability by bridging the azimuthal free spectral range using six adjacent q-series modes. Moreover, all-optical control of the reflection spectrum is also carried out. This work will broaden the applications of ultrahigh-Q silica microcavities in nonlinear optics, microwave photonics, cavity optomechanics, and cavity quantum electrodynamics.

Intermode Breather Solitons in Optical Microresonators

The observation of temporal dissipative Kerr solitons in optical microresonators provides, on the applied side, compact sources of coherent optical frequency combs that have already been applied in coherent communications, dual comb spectroscopy and metrology. On a fundamental level, it enables the study of soliton physics in driven nonlinear cavities. Microresonators are commonly multimode and, as a result, inter-mode interactions inherently occur among mode families - a condition referred to as "avoided mode crossings". Avoided mode crossings can cause soliton decay, but can also modify the soliton spectrum, leading to e.g. the formation of dispersive wave and inducing a spectral recoil. Yet, to date, the entailing temporal soliton dynamics from inter-mode interactions has rarely been studied, but is critical to understand regimes of soliton-stability. Here we report the discovery of an inter-mode breather soliton. Such breathing dynamics occurs within a laser detuning range where conventionally stationary dissipative solitons are expected. We demonstrate experimentally the phenomenon in two microresonator platforms (crystalline magnesium fluoride and photonic chip-based silicon nitride microresonators), and theoretically describe the dynamics based on a pair of coupled Lugiato-Lefever equations. We demonstrate experimentally that the breathing is associated with a periodic energy exchange between the soliton and another optical mode family. We further show that inter-mode interactions can be modeled by a response function acting on dissipative solitons. The observation of breathing dynamics in the conventionally stable soliton regime is critical to applications, ranging from low-noise microwave generation, frequency synthesis to spectroscopy. On a fundamental level, our results provide new understandings of the rich dissipative soliton dynamics in multimode nonlinear cavities.

Nonlinear cavity feeding and unconventional photon statistics in solid-state cavity QED revealed by many-level real-time path-integral calculations

The generation of photons in a microcavity coupled to a laser-driven quantum dot interacting with longitudinal acoustic (LA) phonons is studied in the regime of simultaneously strong driving and strong dot-cavity coupling. The stationary cavity photon number is found to depend in a non-trivial way on the detuning between the laser and the exciton transition in the dot. In particular, the maximal efficiency of the cavity feeding is obtained for detunings corresponding to transition energies between cavity-dressed states with excitation numbers larger than one. Phonons significantly enhance the cavity feeding at large detunings. In the strong-driving, strong-coupling limit, the photon statistics is highly non-Poissonian. While without phonons a double-peaked structure in the photon distribution is predicted, phonons make the photon statistics thermal-like with very high effective temperatures $\sim 10^5$ K, even for low phonon temperatures $\sim 4$ K. These results were obtained by numerical calculations where the driving, the dot-cavity coupling and the dot-phonon interactions are taken into account without approximations. This is achieved by a reformulation of an exact iterative path-integral scheme which is applicable for a large class of quantum-dissipative systems and which in our case reduces the numerical demands by 15 orders of magnitude.

Bose-Hubbard hopping due to resonant Rayleigh scattering.

We show theoretically that dynamic behavior of light confined in the modes of a nonlinear optical ring cavity characterized by resonant Rayleigh scattering can be described using the Bose-Hubbard model. Nonlinear interaction between clockwise and counterclockwise optical modes results in instability and intermode hopping occurring at a rate defined by the frequency separation of the Rayleigh doublet harmonics. Hopping may lead to an instability and breathing behavior of a Kerr frequency comb observed in the cavity.

An ultra-compact all optical full adder based on nonlinear photonic crystal resonant cavities

In this paper we are going to propose and design an all optical full adder based on photonic crystal. For realizing the proposed structure we will use four nonlinear resonant cavities inside a two dimensional photonic crystal. Nonlinear resonant cavities will be created by replacing the ordinary rods via defect rod made of nonlinear material such as doped glass. The simulation results show that the worst cases for logics 0 (the maximum normalized power in OFF state) and 1 (the minimum normalized power in ON state) are 3% and 53% for SUM port and they are 10% and 100% for CARRY port respectively. Also the maximum delay time for the proposed device is about 8 ps.

Generation and spectroscopic signatures of a fractional quantum Hall liquid of photons in an incoherently pumped optical cavity

We theoretically investigate a driven-dissipative model of strongly interacting photons in a nonlinear optical cavity in the presence of a synthetic magnetic field. We show the possibility of using a frequency-dependent incoherent pump to create a strongly-correlated $\nu = 1/2$ bosonic Laughlin state of light: thanks to the incompressibility of the Laughlin state, fluctuations in the total particle number and excitation of edge modes can be tamed by imposing a suitable external potential profile for photons. We further propose angular momentum-selective spectroscopy of the emitted light as a tool to obtain unambiguous signatures of the microscopic physics of the quantum Hall liquid of light.

Nonequilibrium photonic transport and phase transition in an array of optical cavities

We characterize photonic transport in a boundary driven array of nonlinear optical cavities. We find that the output field suddenly drops when the chain length is increased beyond a threshold. After this threshold a highly chaotic and unstable regime emerges, which marks the onset of a super-diffusive photonic transport. We show the scaling of the threshold with pump intensity and nonlinearity. Finally, we address the competition of disorder and nonlinearity presenting a diffusive-insulator phase transition.

Noncritical generation of nonclassical frequency combs via spontaneous rotational symmetry breaking

Synchronously pumped optical parametric oscillators (SPOPOs) are optical cavities containing a nonlinear crystal capable of down-converting a frequency comb to lower frequencies. These have received a lot of attention lately, because their intrinsic multimode nature makes them compact sources of quantum correlated light with promising applications in modern quantum information technologies. In this work we show that SPOPOs are also capable of accessing the challenging but interesting regime where spontaneous symmetry breaking plays a crucial role in the quantum properties of the emitted light, difficult to access with any other nonlinear optical cavity. Apart from opening the possibility of studying experimentally this elusive regime of dissipative phase transitions, our predictions will have a practical impact, since we show that spontaneous symmetry breaking provides a specific spatiotemporal mode with perfect squeezing for any value of the system parameters, turning SPOPOs into robust sources of highly nonclassical light above threshold.

Period-Doubling and Quadrupling Bifurcation of Vector Soliton Bunches in a Graphene Mode Locked Fiber Laser

Period-doubling bifurcation and period-quadrupling bifurcation of vector soliton pulses in a graphene mode locked fiber laser is experimentally observed and investigated. Not only single vector soliton but also vector soliton bunches as a unity are found to exhibit period-doubling and period-quadrupling bifurcation. The experimental results suggest that period-doubling and quadrupling bifurcation are intrinsic features of the pulses circulating in a nonlinear ring cavity, which are independent of the properties of the mode-locker in the fiber lasers.

All optical half adder based on photonic crystal resonant cavities

In this paper, we are going to propose and design an all optical half adder based on photonic crystal structures. For realizing the proposed structure, we will use two nonlinear resonant cavities inside a two-dimensional photonic crystal structure. Nonlinear resonant cavities will be created by replacing the ordinary rods via defect rod made of nonlinear material such as doped glass. Plane-wave expansion and finite difference time domain methods will be used for simulating the proposed structure. For the proposed structure, the maximum delay time is about 3 ps.

Quantum dynamics of a Josephson junction driven cavity mode system in the presence of voltage bias noise

We give a semiclassical analysis of the average photon number as well as photon number variance (Fano factor $F$) for a Josephson-junction (JJ) embedded microwave cavity system, where the JJ is subject to a fluctuating (i.e. noisy) bias voltage with finite dc average. Through the ac Josephson effect, the dc voltage bias drives the effectively nonlinear microwave cavity mode into an amplitude squeezed state ($F<1$), as has been established previously [A. D. Armour, et al., Phys. Rev. Lett. 111, 247001 (2013)], but bias noise acts to degrade this squeezing. We find that the sensitivity of the Fano factor to bias voltage noise depends qualitatively on which stable fixed point regime the system is in for the corresponding classical nonlinear steady state dynamics. Furthermore, we show that the impact of voltage bias noise is most significant when the cavity is excited to states with large average photon number.

Coexistence of Multiple Nonlinear States in a Tristable Passive Kerr Resonator

Passive Kerr cavities driven by coherent laser fields display a rich landscape of nonlinear physics, including bistability, pattern formation, and localised dissipative structures (solitons). Their conceptual simplicity has for several decades offered an unprecedented window into nonlinear cavity dynamics, providing insights into numerous systems and applications ranging from all-optical memory devices to microresonator frequency combs. Yet despite the decades of study, a recent theoretical study has surprisingly alluded to an entirely new and unexplored paradigm in the regime where nonlinearly tilted cavity resonances overlap with one another [T. Hansson and S. Wabnitz, J. Opt. Soc. Am. B 32, 1259 (2015)]. We have used synchronously driven fiber ring resonators to experimentally access this regime, and observed the rise of new nonlinear dissipative states. Specifically, we have observed, for the first time to the best of our knowledge, the stable coexistence of dissipative (cavity) solitons and extended modulation instability (Turing) patterns, and performed real time measurements that unveil the dynamics of the ensuing nonlinear structures. When operating in the regime of continuous wave tristability, we have further observed the coexistence of two distinct cavity soliton states, one of which can be identified as a "super" cavity soliton as predicted by Hansson and Wabnitz. Our experimental findings are in excellent agreement with theoretical analyses and numerical simulations of the infinite-dimensional Ikeda map that governs the cavity dynamics. The results from our work reveal that experimental systems can support complex combinations of distinct nonlinear states, and they could have practical implications to future microresonator-based frequency comb sources.

Rogue waves with multiple compression points in nonlinear optical cavities

In this paper, we use the similarity transformation method to investigate the generation and the control of rogue wave solutions in nonlinear optical cavities described by a (2 + 1) -dimensional Lugiato-Lefever equation with varying coefficients. For a periodic distribution of the diffraction parameter, first-order and second-order rogue wave solutions with multiple compression points are generated. Our results reveal that multiple compression points depend on the values of the modulation amplitude of the diffraction parameter and are independent of the spatial distribution in the cavities.

On the robustness of strongly correlated multi-photon states in frustrated driven-dissipative cavity lattices

We present a theoretical study on the robustness of multi-photon states in a frustrated lattice of coupled nonlinear optical cavities, which are described by a driven-dissipative Bose-Hubbard model. In particular, we focus here on a Lieb lattice with two elementary cells and periodic boundary conditions. Due to the geometric frustration of the lattice, the non-equilibrium steady state can exhibit dark sites with low photon density and strong correlations, ascribable to the population of multi-photon modes. We explore the sensitivity of such strong correlations on the random inhomogeneity of the lattice parameters. We show that the correlations are more sensitive to the inhomogeneity of the cavity frequencies than to the random fluctuations of the hopping strength.

Dual square-wave pulse passively mode-locked fiber laser.

We study a passively mode-locked square-wave pulse (SWP) fiber laser with a nonlinear amplifying loop mirror in the cavity. The net dispersion of the cavity is about 0.68 ps2 and the SWP mode-locked fiber laser can be realized. The peak power of the SWP hardly varies and the pulse duration gets expanded with the increasing pump power. SWPs breaking in the low nonlinear cavity can be observed and the stable dual SWP can be achieved in the experiment. When the total pump power stays at 800 mW, the interval of dual pulses is 41 ns. The widths of dual SWPs are both 1.5 ns. The output power rises linearly with the increasing of the pump power, while the interval of dual SWPs is almost constant. Then, the physical mechanism of the SWP breaking and vector nature of the pulse are analyzed.

Spatiotemporal chaos and two-dimensional dissipative rogue waves in Lugiato-Lefever model

Driven nonlinear optical cavities can exhibit complex spatiotemporal dynamics. We consider the paradigmatic Lugiato-Lefever model describing driven nonlinear optical resonator. This model is one of the most-studied nonlinear equations in optics. It describes a large spectrum of nonlinear phenomena from bistability, to periodic patterns, localized structures, self-pulsating localized structures and to a complex spatiotemporal behavior. The model is considered also as prototype model to describe several optical nonlinear devices such as Kerr media, liquid crystals, left handed materials, nonlinear fiber cavity, and frequency comb generation. We focus our analysis on a spatiotemporal chaotic dynamics in one-dimension. We identify a route to spatiotemporal chaos through an extended quasiperiodicity. We have estimated the Kaplan-Yorke dimension that provides a measure of the strange attractor complexity. Likewise, we show that the Lugiato-Leferver equation supports rogues waves in two-dimensional settings. We characterize rogue-wave formation by computing the probability distribution of the pulse height.

Topological edge states of bound photon pairs

We predict the existence of interaction-driven edge states of bound two-photon quasiparticles in a dimer periodic array of nonlinear optical cavities. Energy spectrum of photon pairs is dramatically richer than in the noninteracting case or in a simple lattice, featuring collapse and revival of multiple edge and bulk modes as well as edge states in continuum. Despite the unexpected breakdown of the Zak phase technique and the edge mixing of internal and center-of-mass motion we link the edge state existence to the two-photon quantum walk graph connectivity, thus uncovering the topological nature of the many-body problem in complex lattices.

Topological Quantum Phase Transition and Local Topological Order in a Strongly Interacting Light-Matter System

An attempt is made to understand the topological quantum phase transition, emergence of relativistic modes and local topological order of light in a strongly interacting light-matter system. We study this system, in a one dimensional array of nonlinear cavities. Topological quantum phase transition occurs with massless excitation only for the finite detuning process. We present a few results based on the exact analytical calculations along with the physical explanations. We observe the emergence of massive Majorana fermion mode at the topological state, massless Majorana-Weyl fermion mode during the topological quantum phase transition and Dirac fermion mode for the non-topological state. Finally, we study the quantized Berry phase (topological order) and its connection to the topological number (winding number).