Noise-Induced Network Topologies.

We analyze transport on a graph with multiple constraints and where the weight of the edges connecting the nodes is a dynamical variable. The network dynamics results from the interplay between a nonlinear function of the flow, dissipation, and Gaussian, additive noise. For a given set of parameters and finite noise amplitudes, the network self-organizes into one of several metastable configurations, according to a probability distribution that depends on the noise amplitude α. At a finite value α, we find a resonantlike behavior for which one network topology is the most probable stationary state. This specific topology maximizes the robustness and transport efficiency, it is reached with the maximal convergence rate, and it is not found by the noiseless dynamics. We argue that this behavior is a manifestation of noise-induced resonances in network self-organization. Our findings show that stochastic dynamics can boost transport on a nonlinear network and, further, suggest a change of paradigm about the role of noise in optimization algorithms.

Quantum Critical Behavior of Entanglement in Lattice Bosons with Cavity-Mediated Long-Range Interactions.

We analyze the ground-state entanglement entropy of the extended Bose-Hubbard model with infinite-range interactions. This model describes the low-energy dynamics of ultracold bosons tightly bound to an optical lattice and dispersively coupled to a cavity mode. The competition between on-site repulsion and global cavity-induced interactions leads to a rich phase diagram, which exhibits superfluid, supersolid, and insulating (Mott and checkerboard) phases. We use a slave-boson treatment of harmonic quantum fluctuations around the mean-field solution and calculate the entanglement entropy across the phase transitions. At commensurate filling, the insulator-superfluid transition is signaled by a singularity in the area-law scaling coefficient of the entanglement entropy, which is similar to the one reported for the standard Bose-Hubbard model. Remarkably, at the continuous Z_{2} superfluid-to-supersolid transition we find a critical logarithmic term, regardless of the filling. This behavior originates from the appearance of a roton mode in the excitation and entanglement spectrum, becoming gapless at the critical point, and it is characteristic of collective models.

Lindblad Master Equations for Quantum Systems Coupled to Dissipative Bosonic Modes.

We present a general approach to derive Lindblad master equations for a subsystem whose dynamics is coupled to dissipative bosonic modes. The derivation relies on a Schrieffer-Wolff transformation which allows us to eliminate the bosonic degrees of freedom after self-consistently determining their state as a function of the coupled quantum system. We apply this formalism to the dissipative Dicke model and derive a Lindblad master equation for the atomic spins, which includes the coherent and dissipative interactions mediated by the bosonic mode. This master equation accurately predicts the Dicke phase transition and gives the correct steady state. In addition, we compare the dynamics using exact diagonalization and numerical integration of the master equation with the predictions of semiclassical trajectories. We finally test the performance of our formalism by studying the relaxation of a NOON state and show that the dynamics captures quantum metastability.

Interplay of periodic dynamics and noise: Insights from a simple adaptive system.

We study the dynamics of a simple adaptive system in the presence of noise and periodic damping. The system is composed by two paths connecting a source and a sink, and the dynamics is governed by equations that usually describe food search of the paradigmatic Physarum polycephalum. In this work we assume that the two paths undergo damping whose relative strength is periodically modulated in time, and we analyze the dynamics in the presence of stochastic forces simulating Gaussian noise. We identify different responses depending on the modulation frequency and on the noise amplitude. At frequencies smaller than the mean dissipation rate, the system tends to switch to the path which minimizes dissipation. Synchronous switching occurs at an optimal noise amplitude which depends on the modulation frequency. This behavior disappears at larger frequencies, where the dynamics can be described by the time-averaged equations. Here we find metastable patterns that exhibit the features of noise-induced resonances.

Dynamical Phase Transitions to Optomechanical Superradiance.

We theoretically analyze superradiant emission of light from an ultracold gas of bosonic atoms confined in a bad cavity. A metastable dipolar transition of the atoms couples to the cavity field and is incoherently pumped, and the mechanical effects of cavity-atom interactions tend to order the atoms in the periodic cavity potential. By means of a mean-field model we determine the conditions on the cavity parameters and pump rate that lead to the buildup of a stable macroscopic dipole emitting coherent light. We show that this occurs when the superradiant decay rate and the pump rate exceed threshold values of the order of the photon recoil energy. Above these thresholds superradiant emission is accompanied by the formation of stable matter-wave gratings that diffract the emitted photons. Outside of this regime, instead, the optomechanical coupling can give rise to dephasing or chaos, for which the emitted light is respectively incoherent or chaotic. These behaviors exhibit the features of a dynamical phase transitions and emerge from the interplay between global optomechanical interactions, quantum fluctuations, and noise.

Sound of an axon's growth.

Axons are linear structures of nerve cells that can range from a few tens of micrometers up to meters in length. In addition to external cues, the length of an axon is also regulated by unknown internal mechanisms. Molecular motors have been suggested to generate oscillations with an axon-length-dependent frequency that could be used to measure an axon's extension. Here, we present a mechanism for determining the axon length that couples the mechanical properties of an axon to the spectral decomposition of the oscillatory signal.

Dynamical Critical Scaling of Long-Range Interacting Quantum Magnets.

Slow quenches of the magnetic field across the paramagnetic-ferromagnetic phase transition of spin systems produce heat. In systems with short-range interactions the heat exhibits universal power-law scaling as a function of the quench rate, known as Kibble-Zurek scaling. In this work we analyze slow quenches of the magnetic field in the Lipkin-Meshkov-Glick (LMG) model, which describes fully connected quantum spins. We analytically determine the quantum contribution to the residual heat as a function of the quench rate δ by means of a Holstein-Primakoff expansion about the mean-field value. Unlike in the case of short-range interactions, scaling laws in the LMG model are only found for a ramp starting or ending at the critical point. If instead the ramp is symmetric, as in the typical Kibble-Zurek scenario, then the number of excitations exhibits a crossover behavior as a function of δ and tends to a constant in the thermodynamic limit. Previous, and seemingly contradictory, theoretical studies are identified as specific limits of this dynamics. Our results can be tested on several experimental platforms, including quantum gases and trapped ions.

Enhanced Second-Order Nonlinearity for THz Generation by Resonant Interaction of Exciton-Polariton Rabi Oscillations with Optical Phonons.

Semiconductor microcavities in the strong-coupling regime exhibit an energy scale in the terahertz (THz) frequency range, which is fixed by the Rabi splitting between the upper and lower exciton-polariton states. While this range can be tuned by several orders of magnitude using different excitonic media, the transition between both polaritonic states is dipole forbidden. In this work, we show that, in cadmium telluride microcavities, the Rabi-oscillation-driven THz radiation is actually active without the need for any change in the microcavity design. This feature results from the unique resonance condition which is achieved between the Rabi splitting and the phonon-polariton states and leads to a giant enhancement of the second-order nonlinearity.

Dissipation-Assisted Prethermalization in Long-Range Interacting Atomic Ensembles.

We theoretically characterize the semiclassical dynamics of an ensemble of atoms after a sudden quench across a driven-dissipative second-order phase transition. The atoms are driven by a laser and interact via conservative and dissipative long-range forces mediated by the photons of a single-mode cavity. These forces can cool the motion and, above a threshold value of the laser intensity, induce spatial ordering. We show that the relaxation dynamics following the quench exhibits a long prethermalizing behavior which is first dominated by coherent long-range forces and then by their interplay with dissipation. Remarkably, dissipation-assisted prethermalization is orders of magnitude longer than prethermalization due to the coherent dynamics. We show that it is associated with the creation of momentum-position correlations, which remain nonzero for even longer times than mean-field predicts. This implies that cavity cooling of an atomic ensemble into the self-organized phase can require longer time scales than the typical experimental duration. In general, these results demonstrate that noise and dissipation can substantially slow down the onset of thermalization in long-range interacting many-body systems.

Crossover from Classical to Quantum Kibble-Zurek Scaling.

The Kibble-Zurek (KZ) hypothesis identifies the relevant time scales in out-of-equilibrium dynamics of critical systems employing concepts valid at equilibrium: It predicts the scaling of the defect formation immediately after quenches across classical and quantum phase transitions as a function of the quench speed. Here, we study the crossover between the scaling dictated by a slow quench, which is ruled by the critical properties of the quantum phase transition, and the excitations due to a faster quench, where the dynamics is often well described by the classical model. We estimate the value of the quench rate that separates the two regimes and support our argument using numerical simulations of the out-of-equilibrium many-body dynamics. For the specific case of a ϕ^{4} model we demonstrate that the two regimes exhibit two different power-law scalings, which are in agreement with the KZ theory when applied to the quantum and classical cases. This result contributes to extending the prediction power of the Kibble-Zurek mechanism and to providing insight into recent experimental observations in systems of cold atoms and ions.

Supercooling of Atoms in an Optical Resonator.

We investigate laser cooling of an ensemble of atoms in an optical cavity. We demonstrate that when atomic dipoles are synchronized in the regime of steady-state superradiance, the motion of the atoms may be subject to a giant frictional force leading to potentially very low temperatures. The ultimate temperature limits are determined by a modified atomic linewidth, which can be orders of magnitude smaller than the cavity linewidth. The cooling rate is enhanced by the superradiant emission into the cavity mode allowing reasonable cooling rates even for dipolar transitions with ultranarrow linewidth.

Nanofriction in Cavity Quantum Electrodynamics.

The dynamics of cold trapped ions in a high-finesse resonator results from the interplay between the long-range Coulomb repulsion and the cavity-induced interactions. The latter are due to multiple scatterings of laser photons inside the cavity and become relevant when the laser pump is sufficiently strong to overcome photon decay. We study the stationary states of ions coupled with a mode of a standing-wave cavity as a function of the cavity and laser parameters, when the typical length scales of the two self-organizing processes, Coulomb crystallization and photon-mediated interactions, are incommensurate. The dynamics are frustrated and in specific limiting cases can be cast in terms of the Frenkel-Kontorova model, which reproduces features of friction in one dimension. We numerically recover the sliding and pinned phases. For strong cavity nonlinearities, they are in general separated by bistable regions where superlubric and stick-slip dynamics coexist. The cavity, moreover, acts as a thermal reservoir and can cool the chain vibrations to temperatures controlled by the cavity parameters and by the ions' phase. These features are imprinted in the radiation emitted by the cavity, which is readily measurable in state-of-the-art setups of cavity quantum electrodynamics.

Dissipative Quantum Control of a Spin Chain.

A protocol is discussed for preparing a spin chain in a generic many-body state in the asymptotic limit of tailored nonunitary dynamics. The dynamics require the spectral resolution of the target state, optimized coherent pulses, engineered dissipation, and feedback. As an example, we discuss the preparation of an entangled antiferromagnetic state, and argue that the procedure can be applied to chains of trapped ions or Rydberg atoms.

Prethermalization of atoms due to photon-mediated long-range interactions.

Atoms can spontaneously form spatially ordered structures in optical resonators when they are transversally driven by lasers. This occurs when the laser intensity exceeds a threshold value and results from the mechanical forces on the atoms associated with superradiant scattering into the cavity mode. We treat the atomic motion semiclassically and show that, while the onset of spatial ordering depends on the intracavity-photon number, the stationary momentum distribution is a Gaussian function whose width is determined by the rate of photon losses. Above threshold, the dynamics is characterized by two time scales: after a violent relaxation, the system slowly reaches the stationary state over time scales exceeding the cavity lifetime by several orders of magnitude. In this transient regime the atomic momenta form non-Gaussian metastable distributions, which emerge from the interplay between the long-range dispersive and dissipative mechanical forces of light. We argue that the dynamics of self-organization of atoms in cavities offers a test bed for studying the statistical mechanics of long-range interacting systems.

Interfacing superconducting qubits and telecom photons via a rare-earth-doped crystal.

We propose a scheme to couple short single photon pulses to superconducting qubits. An optical photon is first absorbed into an inhomogeneously broadened rare-earth doped crystal using controlled reversible inhomogeneous broadening. The optical excitation is then mapped into a spin state using a series of π pulses and subsequently transferred to a superconducting qubit via a microwave cavity. To overcome the intrinsic and engineered inhomogeneous broadening of the optical and spin transitions in rare-earth doped crystals, we make use of a special transfer protocol using staggered π pulses. We predict total transfer efficiencies on the order of 90%.

Bose-Glass phases of ultracold atoms due to cavity backaction.

We determine the quantum ground-state properties of ultracold bosonic atoms interacting with the mode of a high-finesse resonator. The atoms are confined by an external optical lattice, whose period is incommensurate with the cavity mode wavelength, and are driven by a transverse laser, which is resonant with the cavity mode. While for pointlike atoms photon scattering into the cavity is suppressed, for sufficiently strong lasers quantum fluctuations can support the buildup of an intracavity field, which in turn amplifies quantum fluctuations. The dynamics is described by a Bose-Hubbard model where the coefficients due to the cavity field depend on the atomic density at all lattice sites. Quantum Monte Carlo simulations and mean-field calculations show that, for large parameter regions, cavity backaction forces the atoms into clusters with a checkerboard density distribution. Here, the ground state lacks superfluidity and possesses finite compressibility, typical of a Bose glass. This system constitutes a novel setting where quantum fluctuations give rise to effects usually associated with disorder.

Structural transitions of ion strings in quantum potentials.

We analyze the stability and dynamics of an ion chain confined inside a high-finesse optical resonator. When the dipolar transition of the ions strongly couples to one cavity mode, the mechanical effects of light modify the chain properties close to a structural transition. We focus on the linear chain close to the zigzag instability and show that linear and zigzag arrays are bistable for certain strengths of the laser pumping the cavity. For these regimes the chain is cooled into one of the configurations by cavity-enhanced photon scattering. The excitations of these structures mix photonic and vibrational fluctuations, which can be entangled at steady state. These features are signaled by Fano-like resonances in the spectrum of light at the cavity output.

Quantum zigzag transition in ion chains.

A string of trapped ions at zero temperature exhibits a structural phase transition to a zigzag structure, tuned by reducing the transverse trap potential or the interparticle distance. The transition is driven by transverse, short wavelength vibrational modes. We argue that this is a quantum phase transition, which can be experimentally realized and probed. Indeed, by means of a mapping to the Ising model in a transverse field, we estimate the quantum critical point in terms of the system parameters, and find a finite, measurable deviation from the critical point predicted by the classical theory. A measurement procedure is suggested which can probe the effects of quantum fluctuations at criticality. These results can be extended to describe the transverse instability of ultracold polar molecules in a one-dimensional optical lattice.

Structural defects in ion chains by quenching the external potential: the inhomogeneous Kibble-Zurek mechanism.

The nonequilibrium dynamics of an ion chain in a highly anisotropic trap is studied when the transverse trap frequency is quenched across the value at which the chain undergoes a continuous phase transition from a linear to a zigzag structure. Within Landau theory, an equation for the order parameter, corresponding to the transverse size of the zigzag structure, is determined when the vibrational motion is damped via laser cooling. The number of structural defects produced during a linear quench of the transverse trapping frequency is predicted and verified numerically. It is shown to obey the scaling predicted by the Kibble-Zurek mechanism, when extended to take into account the spatial inhomogeneities of the ion chain in a linear Paul trap.

Cooling carbon nanotubes to the phononic ground state with a constant electron current.

We present a quantum theory of cooling of a mechanical resonator using back action with a constant electron current. The resonator device is based on a doubly clamped nanotube, which mechanically vibrates and acts as a double quantum dot for electron transport. Mechanical vibrations and electrons are coupled electrostatically using an external gate. The fundamental eigenmode is cooled by absorbing phonons when electrons tunnel through the double quantum dot. We identify the regimes in which ground-state cooling can be achieved for realistic experimental parameters.