Nonreciprocal circuit elements form an integral part of modern measurement and communication systems. Mathematically they require breaking of time-reversal symmetry, typically achieved using magnetic materials and more recently using the quantum Hall effect, parametric permittivity modulation or Josephson nonlinearities. Here we demonstrate an on-chip magnetic-free circulator based on reservoir-engineered electromechanic interactions. Directional circulation is achieved with controlled phase-sensitive interference of six distinct electro-mechanical signal conversion paths. The presented circulator is compact, its silicon-on-insulator platform is compatible with both superconducting qubits and silicon photonics, and its noise performance is close to the quantum limit. With a high dynamic range, a tunable bandwidth of up to 30 MHz and an in situ reconfigurability as beam splitter or wavelength converter, it could pave the way for superconducting qubit processors with multiplexed on-chip signal processing and readout.

Mechanical systems facilitate the development of a new generation of hybrid quantum technology comprising electrical, optical, atomic and acoustic degrees of freedom [1]. Entanglement is the essential resource that defines this new paradigm of quantum enabled devices. Continuous variable (CV) entangled fields, known as Einstein-Podolsky-Rosen (EPR) states, are spatially separated two-mode squeezed states that can be used to implement quantum teleportation and quantum communication [2]. In the optical domain, EPR states are typically generated using nondegenerate optical amplifiers [3] and at microwave frequencies Josephson circuits can serve as a nonlinear medium [4][5][6]. It is an outstanding goal to deterministically generate and distribute entangled states with a mechanical oscillator. Here we observe stationary emission of path-entangled microwave radiation from a parametrically driven 30 micrometer long silicon nanostring oscillator, squeezing the joint field operators of two thermal modes by 3.40(37) dB below the vacuum level. This mechanical system correlates up to 50 photons/s/Hz giving rise to a quantum discord that is robust with respect to microwave noise [7]. Such generalized quantum correlations of separable states are important for quantum enhanced detection [8] and provide direct evidence for the non-classical nature of the mechanical oscillator without directly measuring its state [9]. This noninvasive measurement scheme allows to infer information about otherwise inaccessible objects with potential implications in sensing, open system dynamics and fundamental tests of quantum gravity. In the near future, similar on-chip devices can be used to entangle subsystems on vastly different energy scales such as microwave and optical photons. *

Cellulose is the most abundant biopolymer on Earth. Cellulose fibers, such as the one extracted form cotton or woodpulp, have been used by humankind for hundreds of years to make textiles and paper. Here we show how, by engineering light–matter interaction, we can optimize light scattering using exclusively cellulose nanocrystals. The produced material is sustainable, biocompatible, and when compared to ordinary microfiber-based paper, it shows enhanced scattering strength (×4), yielding a transport mean free path as low as 3.5 μm in the visible light range. The experimental results are in a good agreement with the theoretical predictions obtained with a diffusive model for light propagation.

Radiation pressure within engineered structures has recently been used to couple the motion of nanomechanical objects with high sensitivity to optical and microwave electromagnetic fields. Here, we demonstrate a form of electromechanical crystal for coupling microwave photons and hypersonic phonons by embedding the vacuum-gap capacitor of a superconducting resonator within a phononic crystal acoustic cavity. Utilizing a two-photon resonance condition for efficient microwave pumping and a phononic bandgap shield to eliminate acoustic radiation, we demonstrate large cooperative coupling (C ≈ 30) between a pair of electrical resonances at ωr,0 ≈ 10 GHz and an acoustic resonance at ωm/2π = 0.425 GHz. Electrical read-out of the phonon occupancy shows that the hypersonic acoustic mode has an intrinsic energy decay time of 2.3 ms and thermalizes close to its quantum ground-state of motion (occupancy nm = 1.5) at a fridge temperature of T f = 10 mK. Such an electromechanical transducer is envisioned as part of a hybrid quantum circuit architecture, capable of interfacing to both superconducting qubits and optical photons. * These authors contributed equally to this work. † opainter@caltech.edu

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We present a detailed numerical investigation of the tunability of a diffusive random laser when Mie resonances are excited. We solve a multimode diffusion model and calculate multiple light scattering in presence of optical gain which includes dispersion in both scattering and gain, without any assumptions about the β parameter. This allows us to investigate a realistic photonic glass made of latex spheres and rhodamine and to quantify both the lasing wavelength tunability range and the lasing threshold. Beyond what is expected by diffusive monochromatic models, the highest threshold is found when the competition between the lasing modes is strongest and not when the lasing wavelength is furthest from the maximum of the gain curve.Random lasers (RL) are mirror-less lasing systems which have attracted a lot of interest due to their structural simplicity. Nowadays they have been studied in a vast variety of scattering systems ranging from semiconductor powder to biological tissue and biocompatible materials [1]. Random lasing originates from a complex out-of-equilibrium phenomenon with rich multimodes features [2] and surprising statistical features [3]. Despite its potential for practical applications [1], random lasing technology is still in its infancy with pioneering applications such as low coherence light source [4] and biosensing [5]. One of the factors that has limited practical applications is the difficulty of controlling the frequency and directionality of the emission. In conventional lasers the lasing emission can be tuned by engineering the high finesse cavity which provides the feedback and thus defines the lasing mode. Instead, feedback in RL is provided by multiple scattering and the lasing emission properties are determined by the complex interplay between gain and losses. Recent experiments have shown lasing emission controlled by exploiting scattering dispersion via resonant scattering sustained by spherical particles [6,7] or by gain dispersion achieved by artificially increasing absorption in a spectral band [8]. Active tuning of the lasing properties has also been achieved by shaping the pump profile to selectively excite one or a few lasing modes [9][10][11].Different theoretical approaches to model random lasing action have been developed which combine multiple scattering and gain. For uncorrelated random systems in which interference between the scattered waves can be neglected, diffusive models are very accurate even in presence of optical gain [12,13] and they provide the time evolution of the lasing process and a smooth lasing spectrum with no spiking lasing behaviour [14]. The radiative transport model with gain can also be solved for * Corresponding author: michele.gaio@kcl.ac.uk instance with Monte Carlo simulations which consider a random walk of photons [15,16] and in which amplification of single paths can be important in defining the spectral properties [17], and by solving the complete radiative transfer equations [18]. These approaches allow the study of large systems (> 100s...

The inductively shunted transmon (IST) is a superconducting qubit with exponentially suppressed fluxon transitions and a plasmon spectrum approximating that of the transmon. It shares many characteristics with the transmon but offers charge offset insensitivity for all levels and precise flux tunability with quadratic flux noise suppression. In this work we propose and realize IST qubits deep in the transmon limit where the large geometric inductance acts as a mere perturbation. With a flux dispersion of only 5.1 MHz we reach the 'sweet-spot everywhere' regime of a SQUID device with a stable coherence time over a full flux quantum. Close to the flux degeneracy point the device reveals tunneling physics between the two quasi-degenerate ground states with typical observed lifetimes on the order of minutes. In the future, this qubit regime could be used to avoid leakage to unconfined transmon states in high-power read-out or driven-dissipative bosonic qubit realizations. Moreover, the combination of well controllable plasmon transitions together with stable fluxon states in a single device might offer a way forward towards improved qubit encoding schemes.