Optomechanical realization of the bosonic Kitaev chain.

The fermionic Kitaev chain is a canonical model featuring topological Majorana zero modes. We report the experimental realization of its bosonic analogue in a nano-optomechanical network, in which the parametric interactions induce beam-splitter coupling and two-mode squeezing among the nanomechanical modes, analogous to hopping and p-wave pairing in the fermionic case, respectively. This specific structure gives rise to a set of extraordinary phenomena in the bosonic dynamics and transport.

Nonreciprocal Dicke Model.

We investigate the physics of an open two-component Dicke model, where the light field mediates nonreciprocal interactions between two spin species. We show that the model, which we dub nonreciprocal Dicke model, exhibits a discrete parity-time (PT) symmetry and we characterize the emergence of a nonstationary phase, so far explained in terms of dissipation-induced instability, as spontaneous breaking of PT symmetry. We further show that such PT symmetry breaking embodies an instance of a nonreciprocal phase transition, a concept recently introduced by Fruchart et al.

Correspondence between Non-Hermitian Topology and Directional Amplification in the Presence of Disorder.

In order for non-Hermitian (NH) topological effects to be relevant for practical applications, it is necessary to study disordered systems. Without disorder, a class of driven-dissipative cavity arrays displays directional amplification when associated with a nontrivial winding number of the NH dynamic matrix. In this work, we show analytically that the correspondence between NH topology and directional amplification holds also in the presence of disorder.

Classical Prethermal Phases of Matter.

Systems subject to a high-frequency drive can spend an exponentially long time in a prethermal regime, in which novel phases of matter with no equilibrium counterpart can be realized. Because of the notorious computational challenges of quantum many-body systems, numerical investigations in this direction have remained limited to one spatial dimension, in which long-range interactions have been proven a necessity. Here, we show that prethermal nonequilibrium phases of matter are not restricted to the quantum domain.

Higher-order and fractional discrete time crystals in clean long-range interacting systems.

Discrete time crystals are periodically driven systems characterized by a response with periodicity nT, with T the period of the drive and n > 1. Typically, n is an integer and bounded from above by the dimension of the local (or single particle) Hilbert space, the most prominent example being spin-1/2 systems with n restricted to 2. Here, we show that a clean spin-1/2 system in the presence of long-range interactions and transverse field can sustain a huge variety of different 'higher-order' discrete time crystals with integer and, surprisingly, even fractional n > 2.

Bistability and time crystals in long-ranged directed percolation.

Stochastic processes govern the time evolution of a huge variety of realistic systems throughout the sciences. A minimal description of noisy many-particle systems within a Markovian picture and with a notion of spatial dimension is given by probabilistic cellular automata, which typically feature time-independent and short-ranged update rules. Here, we propose a simple cellular automaton with power-law interactions that gives rise to a bistable phase of long-ranged directed percolation whose long-time behaviour is not only dictated by the system dynamics, but also by the initial conditions.

Topological framework for directional amplification in driven-dissipative cavity arrays.

Directional amplification, in which signals are selectively amplified depending on their propagation direction, has attracted much attention as key resource for applications, including quantum information processing. Recently, several, physically very different, directional amplifiers have been proposed and realized in the lab. In this work, we present a unifying framework based on topology to understand non-reciprocity and directional amplification in driven-dissipative cavity arrays.

Period-n Discrete Time Crystals and Quasicrystals with Ultracold Bosons.

We investigate the out-of-equilibrium properties of a system of interacting bosons in a ring lattice. We present a Floquet driving that induces clockwise (counterclockwise) circulation of the particles among the odd (even) sites of the ring which can be mapped to a fully connected model of clocks of two counterrotating species. The clocklike motion of the particles is at the core of a period-n discrete time crystal where L=2n is the number of lattice sites.

Conditional Dynamics of Optomechanical Two-Tone Backaction-Evading Measurements.

Backaction-evading measurements of mechanical motion can achieve precision below the zero-point uncertainty and quantum squeezing, which makes them a resource for quantum metrology and quantum information processing. We provide an exact expression for the conditional state of an optomechanical system in a two-tone backaction-evading measurement beyond the standard adiabatic approximation and perform extensive numerical simulations to go beyond the usual rotating-wave approximation. We predict the simultaneous presence of conditional mechanical squeezing, intracavity squeezing, and optomechanical entanglement.

Topological magnon amplification.

Topology is quickly becoming a cornerstone in our understanding of electronic systems. Like their electronic counterparts, bosonic systems can exhibit a topological band structure, but in real materials it is difficult to ascertain their topological nature, as their ground state is a simple condensate or the vacuum, and one has to rely instead on excited states, for example a characteristic thermal Hall response. Here we propose driving a topological magnon insulator with an electromagnetic field and show that this causes edge mode instabilities and a large non-equilibrium steady-state magnon edge current.

Optical backaction-evading measurement of a mechanical oscillator.

Quantum mechanics imposes a limit on the precision of a continuous position measurement of a harmonic oscillator, due to backaction arising from quantum fluctuations in the measurement field. This standard quantum limit can be surpassed by monitoring only one of the two non-commuting quadratures of the motion, known as backaction-evading measurement. This technique has not been implemented using optical interferometers to date.

Slow Growth of Out-of-Time-Order Correlators and Entanglement Entropy in Integrable Disordered Systems.

We investigate how information spreads in three paradigmatic one-dimensional models with spatial disorder. The models we consider are unitarily related to a system of free fermions and, thus, are manifestly integrable. We demonstrate that out-of-time-order correlators can spread slowly beyond the single-particle localization length, despite the absence of many-body interactions.

Quantum-Limited Directional Amplifiers with Optomechanics.

Directional amplifiers are an important resource in quantum-information processing, as they protect sensitive quantum systems from excess noise. Here, we propose an implementation of phase-preserving and phase-sensitive directional amplifiers for microwave signals in an electromechanical setup comprising two microwave cavities and two mechanical resonators. We show that both can reach their respective quantum limits on added noise.

Quantum Synchronization Blockade: Energy Quantization Hinders Synchronization of Identical Oscillators.

Classically, the tendency towards spontaneous synchronization is strongest if the natural frequencies of the self-oscillators are as close as possible. We show that this wisdom fails in the deep quantum regime, where the uncertainty of amplitude narrows down to the level of single quanta. Under these circumstances identical self-oscillators cannot synchronize and detuning their frequencies can actually help synchronization.

Genuine Quantum Signatures in Synchronization of Anharmonic Self-Oscillators.

We study the synchronization of a Van der Pol self-oscillator with Kerr anharmonicity to an external drive. We demonstrate that the anharmonic, discrete energy spectrum of the quantum oscillator leads to multiple resonances in both phase locking and frequency entrainment not present in the corresponding classical system. Strong driving close to these resonances leads to nonclassical steady-state Wigner distributions.

Quantum synchronization of a driven self-sustained oscillator.

Synchronization is a universal phenomenon that is important both in fundamental studies and in technical applications. Here we investigate synchronization in the simplest quantum-mechanical scenario possible, i.e.

Majorana qubit rotations in microwave cavities.

Majorana bound states have been proposed as building blocks for qubits on which certain operations can be performed in a topologically protected way using braiding. However, the set of these protected operations is not sufficient to realize universal quantum computing. We show that the electric field in a microwave cavity can induce Rabi oscillations between adjacent Majorana bound states.