Anti-reflection structure for perfect transmission through complex media.

The scattering of waves when they propagate through disordered media is an important limitation for a range of applications, including telecommunications1, biomedical imaging2, seismology3 and material engineering4,5. Wavefront shaping techniques can reduce the effect of wave scattering, even in opaque media, by engineering specific modes-termed open transmission eigenchannels-through which waves are funnelled across a disordered medium without any back reflection6-9. However, with such channels being very scarce, one cannot use them to render an opaque sample perfectly transmitting for any incident light field. Here we show that a randomly disordered medium becomes translucent to all incoming light waves when placing a tailored complementary medium in front of it. To this end, the reflection matrices of the two media surfaces facing each other need to satisfy a matrix generalization of the condition for critical coupling. We implement this protocol both numerically and experimentally for the design of electromagnetic waveguides with several dozen scattering elements placed inside them. The translucent scattering media we introduce here also have the promising property of being able to store incident radiation in their interior for remarkably long times.

Observation of chiral state transfer without encircling an exceptional point.

The adiabatic theorem, a corollary of the Schrödinger equation, manifests itself in a profoundly different way in non-Hermitian arrangements, resulting in counterintuitive state transfer schemes that have no counterpart in closed quantum systems. In particular, the dynamical encirclement of exceptional points (EPs) in parameter space has been shown to lead to a chiral phase accumulation, non-adiabatic jumps and topological mode conversion1-8. Recent theoretical studies, however, have shown that contrary to previously established demonstrations, this behaviour is not strictly a result of winding around a non-Hermitian degeneracy9. Instead, it seems to be mostly attributed to the non-trivial landscape of the Riemann surfaces, sometimes because of the presence of an EP in the vicinity9-11. Here, in an effort to bring this counterintuitive aspect of non-Hermitian systems to light and confirm this hypothesis, we provide a set of experiments to directly observe the field evolution and chiral state conversion in an EP-excluding cycle in a slowly varying non-Hermitian system. To do so, a versatile yet unique fibre-based photonic emulator is realized that utilizes the polarization degrees of freedom in a quasi-common-path single-ring arrangement. Our observations may open up new avenues for light manipulation and state conversion, as well as providing a foundation for understanding the intricacies of the adiabatic theorem in non-Hermitian systems.

Random anti-lasing through coherent perfect absorption in a disordered medium.

Non-Hermitian wave engineering is a recent and fast-moving field that examines both fundamental and application-oriented phenomena1-7. One such phenomenon is coherent perfect absorption8-11-an effect commonly referred to as 'anti-lasing' because it corresponds to the time-reversed process of coherent emission of radiation at the lasing threshold (where all radiation losses are exactly balanced by the optical gain). Coherent perfect absorbers (CPAs) have been experimentally realized in several setups10-18, with the notable exception of a CPA in a disordered medium (a medium without engineered structure). Such a 'random CPA' would be the time-reverse of a 'random laser'19,20, in which light is resonantly enhanced by multiple scattering inside a disorder. Because of the complexity of this scattering process, the light field emitted by a random laser is also spatially complex and not focused like a regular laser beam. Realizing a random CPA (or 'random anti-laser') is therefore challenging because it requires the equivalent of time-reversing such a light field in all its degrees of freedom to create coherent radiation that is perfectly absorbed when impinging on a disordered medium. Here we use microwave technology to build a random anti-laser and demonstrate its ability to absorb suitably engineered incoming radiation fields with near-perfect efficiency. Because our approach to determining these field patterns is based solely on far-field measurements of the scattering properties of a disordered medium, it could be suitable for other applications in which waves need to be perfectly focused, routed or absorbed.

Ultrafast Excitation Exchange in a Maxwell Fish-Eye Lens.

The strong coupling of quantum emitters to a cavity mode has been of paramount importance in the development of quantum optics. Recently, also the strong coupling to more than a single mode of an electromagnetic resonator has drawn considerable interest. We investigate how this multimode strong coupling regime can be harnessed to coherently control quantum systems. Specifically, we demonstrate that a Maxwell fish-eye lens can be used to implement a pulsed excitation exchange between two distant quantum emitters. This periodic exchange is mediated by single-photon pulses and can be extended to a photon-exchange between two atomic ensembles, for which the coupling strength is enhanced collectively.

Repetitive transcranial magnetic stimulation (rTMS) triggers dose-dependent homeostatic rewiring in recurrent neuronal networks.

Repetitive transcranial magnetic stimulation (rTMS) is a non-invasive brain stimulation technique used to induce neuronal plasticity in healthy individuals and patients. Designing effective and reproducible rTMS protocols poses a major challenge in the field as the underlying biomechanisms of long-term effects remain elusive. Current clinical protocol designs are often based on studies reporting rTMS-induced long-term potentiation or depression of synaptic transmission. Herein, we employed computational modeling to explore the effects of rTMS on long-term structural plasticity and changes in network connectivity. We simulated a recurrent neuronal network with homeostatic structural plasticity among excitatory neurons, and demonstrated that this mechanism was sensitive to specific parameters of the stimulation protocol (i.e., frequency, intensity, and duration of stimulation). Particularly, the feedback-inhibition initiated by network stimulation influenced the net stimulation outcome and hindered the rTMS-induced structural reorganization, highlighting the role of inhibitory networks. These findings suggest a novel mechanism for the lasting effects of rTMS, i.e., rTMS-induced homeostatic structural plasticity, and highlight the importance of network inhibition in careful protocol design, standardization, and optimization of stimulation.

Graph model for multiple scattering in lithium niobate on insulator integrated photonic networks.

We present a graph-based model for multiple scattering of light in integrated lithium niobate on insulator (LNOI) networks, which describes an open network of single-mode integrated waveguides with tunable scattering at the network nodes. We first validate the model at small scale with experimental LNOI resonator devices and show consistent agreement between simulated and measured spectral data. Then, the model is used to demonstrate a novel platform for on-chip multiple scattering in large-scale optical networks up to few hundred nodes, with tunable scattering behaviour and tailored disorder. Combining our simple graph-based model with material properties of LNOI, this platform creates new opportunities to control randomness in large optical networks.

Certifying Multimode Light-Matter Interaction in Lossy Resonators.

Quantum models based on few-mode master equations have been a central tool in the study of resonator quantum electrodynamics, extending the seminal single-mode Jaynes-Cummings model to include loss and multiple modes. Despite their broad application range, previous approaches within this framework have either relied on a Markov approximation or a fitting procedure. By combining ideas from pseudomode and quasinormal mode theory, we develop a certification criterion for multi-mode effects in lossy resonators. It is based on a witness observable, and neither requires a fitting procedure nor a Markov approximation. Using the resulting criterion, we demonstrate that such multi-mode effects are important for understanding previous experiments in x-ray cavity QED with Mössbauer nuclei and that they allow one to tune the nuclear ensemble properties.

Optimal Cooling of Multiple Levitated Particles through Far-Field Wavefront Shaping.

Light forces can be harnessed to levitate mesoscopic objects and cool them down toward their motional quantum ground state. Roadblocks on the way to scale up levitation from a single to multiple particles in close proximity are the requirements to constantly monitor the particles' positions as well as to engineer light fields that react fast and appropriately to their movements. Here, we present an approach that solves both problems at once. By exploiting the information stored in a time-dependent scattering matrix, we introduce a formalism enabling the identification of spatially modulated wavefronts, which simultaneously cool down multiple objects of arbitrary shapes. An experimental implementation is suggested based on stroboscopic scattering-matrix measurements and time-adaptive injections of modulated light fields.

Triggered Superradiance and Spin Inversion Storage in a Hybrid Quantum System.

We study the superradiant emission of an inverted spin ensemble strongly coupled to a superconducting cavity. After fast inversion, we detune the spins from the cavity and store the inversion for tens of milliseconds, during which the remaining transverse spin components disappear. Switching back on resonance enables us to study the onset of superradiance. A weak trigger pulse of a few hundred photons shifts the superradiant burst to earlier times and imprints its phase onto the emitted radiation. For long hold times, the inversion decreases below the threshold for spontaneous superradiance. There, the energy stored in the ensemble can be used to amplify microwave pulses passing through the cavity.

Homeostatic control of synaptic rewiring in recurrent networks induces the formation of stable memory engrams.

Brain networks store new memories using functional and structural synaptic plasticity. Memory formation is generally attributed to Hebbian plasticity, while homeostatic plasticity is thought to have an ancillary role in stabilizing network dynamics. Here we report that homeostatic plasticity alone can also lead to the formation of stable memories. We analyze this phenomenon using a new theory of network remodeling, combined with numerical simulations of recurrent spiking neural networks that exhibit structural plasticity based on firing rate homeostasis. These networks are able to store repeatedly presented patterns and recall them upon the presentation of incomplete cues. Storage is fast, governed by the homeostatic drift. In contrast, forgetting is slow, driven by a diffusion process. Joint stimulation of neurons induces the growth of associative connections between them, leading to the formation of memory engrams. These memories are stored in a distributed fashion throughout connectivity matrix, and individual synaptic connections have only a small influence. Although memory-specific connections are increased in number, the total number of inputs and outputs of neurons undergo only small changes during stimulation. We find that homeostatic structural plasticity induces a specific type of "silent memories", different from conventional attractor states.

Time Course of Homeostatic Structural Plasticity in Response to Optogenetic Stimulation in Mouse Anterior Cingulate Cortex.

Plasticity is the mechanistic basis of development, aging, learning, and memory, both in healthy and pathological brains. Structural plasticity is rarely accounted for in computational network models due to a lack of insight into the underlying neuronal mechanisms and processes. Little is known about how the rewiring of networks is dynamically regulated. To inform such models, we characterized the time course of neural activity, the expression of synaptic proteins, and neural morphology employing an in vivo optogenetic mouse model. We stimulated pyramidal neurons in the anterior cingulate cortex of mice and harvested their brains at 1.5 h, 24 h, and $48\,\mathrm{h}$ after stimulation. Stimulus-induced cortical hyperactivity persisted up to 1.5 h and decayed to baseline after $24\,\mathrm{h}$ indicated by c-Fos expression. The synaptic proteins VGLUT1 and PSD-95, in contrast, were upregulated at $24\,\mathrm{h}$ and downregulated at $48\,\mathrm{h}$, respectively. Spine density and spine head volume were also increased at $24\,\mathrm{h}$ and decreased at $48\,\mathrm{h}$. This specific sequence of events reflects a continuous joint evolution of activity and connectivity that is characteristic of the model of homeostatic structural plasticity. Our computer simulations thus corroborate the observed empirical evidence from our animal experiments.

Transforming Space with Non-Hermitian Dielectrics.

Coordinate transformations are a versatile tool to mold the flow of light, enabling a host of astonishing phenomena such as optical cloaking with metamaterials. Moving away from the usual restriction that links isotropic materials with conformal transformations, we show how nonconformal distortions of optical space are intimately connected to the complex refractive index distribution of an isotropic non-Hermitian medium. Remarkably, this insight can be used to circumvent the material requirement of working with refractive indices below unity, which limits the applications of transformation optics. We apply our approach to design a broadband unidirectional dielectric cloak, which relies on nonconformal coordinate transformations to tailor the non-Hermitian refractive index profile around a cloaked object. Our insights bridge the fields of two-dimensional transformation optics and non-Hermitian photonics.

Dynamically encircling an exceptional point for asymmetric mode switching.

Physical systems with loss or gain have resonant modes that decay or grow exponentially with time. Whenever two such modes coalesce both in their resonant frequency and their rate of decay or growth, an 'exceptional point' occurs, giving rise to fascinating phenomena that defy our physical intuition. Particularly intriguing behaviour is predicted to appear when an exceptional point is encircled sufficiently slowly, such as a state-flip or the accumulation of a geometric phase. The topological structure of exceptional points has been experimentally explored, but a full dynamical encircling of such a point and the associated breakdown of adiabaticity have remained out of reach of measurement. Here we demonstrate that a dynamical encircling of an exceptional point is analogous to the scattering through a two-mode waveguide with suitably designed boundaries and losses. We present experimental results from a corresponding waveguide structure that steers incoming waves around an exceptional point during the transmission process. In this way, mode transitions are induced that transform this device into a robust and asymmetric switch between different waveguide modes. This work will enable the exploration of exceptional point physics in system control and state transfer schemes at the crossroads between fundamental research and practical applications.

Shaping the branched flow of light through disordered media.

Electronic matter waves traveling through the weak and smoothly varying disorder potential of a semiconductor show a characteristic branching behavior instead of a smooth spreading of flow. By transferring this phenomenon to optics, we demonstrate numerically how the branched flow of light can be controlled to propagate along a single branch rather than along many of them at the same time. Our method is based on shaping the incoming wavefront and only requires partial knowledge of the system's transmission matrix. We show that the light flowing along a single branch has a broadband frequency stability such that one can even steer pulses along selected branches-a prospect with many interesting possibilities for wave control in disordered environments.

Basal ganglia and cortical control of thalamic rebound spikes.

Movement-related decreases in firing rate have been observed in basal ganglia output neurons. They may transmit motor signals to the thalamus, but the effect of these firing rate decreases on downstream neurons in the motor thalamus is not known. One possibility is that they lead to thalamic post-inhibitory rebound spikes. However, it has also been argued that the physiological conditions permitting rebound spiking are pathological, and primarily present in Parkinson's disease. As in Parkinson's disease neural activity becomes pathologically correlated, we investigated the impact of correlations in basal ganglia output on the transmission of motor signals using a Hodgkin-Huxley model of thalamocortical neurons. We found that such correlations disrupt the transmission of motor signals via rebound spikes by decreasing the signal-to-noise ratio and increasing the trial-to-trial variability. We further examined the role of sensory responses in basal ganglia output neurons and the effect of cortical excitation of motor thalamus in modulating rebound spiking. Interestingly, both could either promote or suppress the generation of rebound spikes depending on their timing relative to the motor signal. Finally, we determined parameter regimes, such as levels of excitation, under which rebound spiking is feasible in the model, and confirmed that the conditions for rebound spiking are primarily given in pathological regimes. However, we also identified specific conditions in the model that would allow rebound spiking to occur in healthy animals in a small subset of thalamic neurons. Overall, our model provides novel insights into differences between normal and pathological transmission of motor signals.

Invariance Property of the Fisher Information in Scattering Media.

Determining the ultimate precision limit for measurements on a subwavelength particle with coherent laser light is a goal with applications in areas as diverse as biophysics and nanotechnology. Here, we demonstrate that surrounding such a particle with a complex scattering environment does, on average, not have any influence on the mean quantum Fisher information associated with measurements on the particle. As a remarkable consequence, the average precision that can be achieved when estimating the particle's properties is the same in the ballistic and in the diffusive scattering regime, independently of the particle's position within its nonabsorbing environment. This invariance law breaks down only in the regime of Anderson localization, due to increased C_{0}-speckle correlations. Finally, we show how these results connect to the mean quantum Fisher information achievable with spatially optimized input fields.

Optimal Control of Coherent Light Scattering for Binary Decision Problems.

Because of quantum noise fluctuations, the rate of error achievable in decision problems involving several possible configurations of a scattering system is subject to a fundamental limit known as the Helstrom bound. Here, we present a general framework to calculate and minimize this bound using coherent probe fields with tailored spatial distributions. As an example, we experimentally study a target located in between two disordered scattering media. We first show that the optimal field distribution can be directly identified using a general approach based on scattering matrix measurements. We then demonstrate that this optimal light field successfully probes the presence of the target with a number of photons that is reduced by more than 2 orders of magnitude as compared to unoptimized fields.

Speckle Engineering through Singular Value Decomposition of the Transmission Matrix.

Speckle patterns are ubiquitous in optics and have multiple applications for which the control of their spatial correlations is essential. Here, we report on a method to engineer speckle correlations behind a scattering medium through the singular value decomposition of the transmission matrix. We not only demonstrate control over the speckle grain size and shape but also realize patterns with nonlocal correlations. Moreover, we show that the reach of our method extends also along the axial dimension, allowing volumetric speckle engineering behind scattering layers.

Periodic Cavity State Revivals from Atomic Frequency Combs.

Spin ensembles with a comb-shaped spectrum have shown exciting properties as efficient quantum memories. Here, we present a rigorous theoretical study of such atomic frequency combs in the strong coupling limit of cavity QED, based on a full quantum treatment using tensor-network methods. Our results demonstrate that arbitrary multiphoton states in the cavity are almost perfectly absorbed by the spin ensemble and reemitted as parity-flipped states at periodic time intervals. Fidelity values near unity are achieved in these revived states by compensating for energy shifts induced by the strong spin-cavity coupling through adjustments of individual coupling values of the teeth in the atomic frequency comb.

Echo Trains in Pulsed Electron Spin Resonance of a Strongly Coupled Spin Ensemble.

We report on a novel dynamical phenomenon in electron spin resonance experiments of phosphorus donors. When strongly coupling the paramagnetic ensemble to a superconducting lumped element resonator, the coherent exchange between these two subsystems leads to a train of periodic, self-stimulated echoes after a conventional Hahn echo pulse sequence. The presence of these multiecho signatures is explained using a simple model based on spins rotating on the Bloch sphere, backed up by numerical calculations using the inhomogeneous Tavis-Cummings Hamiltonian.