Universal Breakdown of Kibble-Zurek Scaling in Fast Quenches across a Phase Transition.

The crossing of a continuous phase transition gives rise to the formation of topological defects described by the Kibble-Zurek mechanism (KZM) in the limit of slow quenches. The KZM predicts a universal power-law scaling of the defect density as a function of the quench time. We focus on the deviations from KZM experimentally observed in rapid quenches and establish their universality. While KZM scaling holds below a critical quench rate, for faster quenches the defect density and the freeze-out time become independent of the quench rate and exhibit a universal power-law scaling with the final value of the control parameter. These predictions are verified in several paradigmatic scenarios in both the classical and quantum domains.

Stochastic Operator Variance: An Observable to Diagnose Noise and Scrambling.

Noise is ubiquitous in nature, so it is essential to characterize its effects. Considering a fluctuating Hamiltonian, we introduce an observable, the stochastic operator variance (SOV), which measures the spread of different stochastic trajectories in the space of operators. The SOV obeys an uncertainty relation and allows us to find the initial state that minimizes the spread of these trajectories. We show that the dynamics of the SOV is intimately linked to that of out-of-time-order correlators, which define the quantum Lyapunov exponent λ. Our findings are illustrated analytically and numerically in a stochastic Lipkin-Meshkov-Glick Hamiltonian undergoing energy dephasing.

Large Deviations beyond the Kibble-Zurek Mechanism.

The Kibble-Zurek mechanism (KZM) predicts that the average number of topological defects generated upon crossing a continuous or quantum phase transition obeys a universal scaling law with the quench time. Fluctuations in the defect number near equilibrium are approximately of Gaussian form, in agreement with the central limit theorem. Using large deviations theory, we characterize the universality of fluctuations beyond the KZM and report the exact form of the rate function in the transverse-field quantum Ising model. In addition, we characterize the scaling of large deviations in an arbitrary continuous phase transition, building on recent evidence establishing the universality of the defect number distribution.

One-Dimensional Quantum Systems with Ground State of Jastrow Form Are Integrable.

Exchange operator formalism describes many-body integrable systems using phase-space variables involving an exchange operator that acts on any pair of particles. We establish an equivalence between models described by exchange operator formalism and the complete infinite family of parent Hamiltonians describing quantum many-body models with ground states of Jastrow form. This makes it possible to identify the invariants of motion for any model in the family and establish its integrability, even in the presence of an external potential. Using this construction we establish the integrability of the long-range Lieb-Liniger model, describing bosons in a harmonic trap and subject to contact and Coulomb interactions in one dimension. We further identify a variety of models exemplifying the integrability of Hamiltonians in this family.

Spectral Filtering Induced by Non-Hermitian Evolution with Balanced Gain and Loss: Enhancing Quantum Chaos.

The dynamical signatures of quantum chaos in an isolated system are captured by the spectral form factor, which exhibits as a function of time a dip, a ramp, and a plateau, with the ramp being governed by the correlations in the level spacing distribution. While decoherence generally suppresses these dynamical signatures, the nonlinear non-Hermitian evolution with balanced gain and loss (BGL) in an energy-dephasing scenario can enhance manifestations of quantum chaos. In the Sachdev-Ye-Kitaev model and random matrix Hamiltonians, BGL increases the span of the ramp, lowering the dip as well as the value of the plateau, providing an experimentally realizable physical mechanism for spectral filtering. The chaos enhancement due to BGL is optimal over a family of filter functions that can be engineered with fluctuating Hamiltonians.

Variational Principle for Optimal Quantum Controls in Quantum Metrology.

We develop a variational principle to determine the quantum controls and initial state that optimizes the quantum Fisher information, the quantity characterizing the precision in quantum metrology. When the set of available controls is limited, the exact optimal initial state and the optimal controls are, in general, dependent on the probe time, a feature missing in the unrestricted case. Yet, for time-independent Hamiltonians with restricted controls, the problem can be approximately reduced to the unconstrained case via Floquet engineering. In particular, we find for magnetometry with a time-independent spin chain containing three-body interactions, even when the controls are restricted to one- and two-body interaction, that the Heisenberg scaling can still be approximately achieved. Our results open the door to investigate quantum metrology under a limited set of available controls, of relevance to many-body quantum metrology in realistic scenarios.

Micropatterned functional interfaces on elastic substrates fabricated by fixing out of plane deformations.

We report on the preparation of micropatterned functional surfaces produced by inducing an out-of-plane deformation on elastic substrates and fixing these by creating a rigid oxidized top layer. Specifically, the elastic substrate used was Polydimethylsiloxane (PDMS) and the rigid layer on top was created by ozonation of this material. We evidenced that the surface pattern formed is directly dependent on the pressure applied, the mechanical properties of the elastic substrate and on the dimensions and shape of the mask employed to define the exposed and non-exposed areas. In addition to the pattern formed, another interesting aspect is related to the ozone diffusion within the material. Softer PDMS enables more efficient diffusion and produced a thicker oxidized layer in comparison to rigid PDMS. Finally, a simulation was carried out using the distribution of Von Misses stresses of a solid plate to understand the conditions in which the applied force resulted in the rupture of the rigid oxidized layer under a permanent deformation.

Deep-Ultraviolet Emitter: Rare-Earth-Free ZnAl2O4 Nanofibers via a Simple Wet Chemical Route.

Deep-UV (180-280 nm) phosphors have attracted tremendous interest in tri-band-based white light-emitting diode (LED) technology, bio- and photochemistry, as well as various medical fields. However, the application of many UV-emitting materials has been hindered due to their poor thermal or chemical stability, complex synthesis, and environmental harmfulness. A particular concern is posed by the utilization of rare earths affected by rising price and depletion of natural resources. As a consequence, the development of phosphors without rare-earth elements represents an important challenge. In this work, as a potential UV-C phosphor, undoped ZnAl2O4 fibers have been synthesized by a cost-efficient wet chemical route. The rare-earth-free ZnAl2O4 nanofibers exhibit a strong UV emission with two bands peaking at 5.4 eV (230 nm) and 4.75 eV (261 nm). The emission intensity can be controlled by tuning the Zn/Al ratio. A structure-property relationship has been thoroughly studied to understand the origin of the UV emission. For this reason, ZnAl2O4 nanofibers have been analyzed by X-ray absorption near-edge structure (XANES), extended X-ray absorption fine structure (EXAFS), X-ray diffraction (XRD), and Raman spectroscopy techniques showing that a normal spinel structure of the synthesized material is preserved within a wide range of Zn/Al ratios. The experimental evidence of a strong and narrow band at 7.04 eV in the excitation spectrum of the 5.4 eV emission suggests its excitonic nature. Moreover, the 4.75 eV emission is shown to be related to excitons perturbed by lattice defects, presumably oxygen or cation vacancies. These findings shed light on the design of UV-C emission devices for sterilization based on a rare-earth-free phosphor, providing a feasible alternative to the conventional phosphors doped with rare-earth elements.

Probing Quantum Speed Limits with Ultracold Gases.

Quantum speed limits (QSLs) rule the minimum time for a quantum state to evolve into a distinguishable state in an arbitrary physical process. These fundamental results constrain a notion of distance traveled by the quantum state, known as the Bures angle, in terms of the speed of evolution set by nonadiabatic energy fluctuations. I theoretically propose how to measure QSLs in an ultracold quantum gas confined in a time-dependent harmonic trap. In this highly-dimensional system of continuous variables, quantum tomography is prohibited. Yet, QSLs can be probed whenever the dynamics is self-similar by measuring as a function of time the cloud size of the ultracold gas. This makes it possible to determine the Bures angle and energy fluctuations, as I discuss for various ultracold atomic systems.

García-Pintos, Hamma, and del Campo Reply.

We acknowledge that a derivation reported in Phys. Rev. Lett. 125, 040601 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.040601 is incorrect as pointed out by Cusumano and Rudnicki. We respond by giving a correct proof of the claim "fluctuations in the free energy operator upper bound the charging power of a quantum battery" that we made in the Letter.

Influence of chemical and electronic inhomogeneities of graphene/copper on the growth of oxide thin films: the ZnO/graphene/copper case.

The interaction of graphene with metal oxides is essential for understanding and controlling new devices' fabrication based on these materials. The growth of metal oxides on graphene/substrate systems constitutes a challenging task due to the graphene surface's hydrophobic nature. In general, different pre-treatments should be performed before deposition to ensure a homogenous growth depending on the deposition technique, the metal oxide, and the surface's specific nature. Among these factors, the initial state and interaction of graphene with its substrate is the most important. Therefore, it is imperative to study the initial local state of graphene and relate it to the early stages of metal oxides' growth characteristics. Taking as initial samples graphene grown by chemical vapor deposition on polycrystalline Cu sheets and then exposed to ambient conditions, this article presents a local study of the inhomogeneities of this air-exposed graphene and how they influence on the subsequent ZnO growth. Firstly, by spatially correlating Raman and x-ray photoemission spectroscopies at the micro and nanoscales, it is shown how chemical species present in air intercalate inhomogeneously between Graphene and Cu. The reason for this is precisely the polycrystalline nature of the Cu support. Moreover, these local inhomogeneities also affect the oxidation level of the uppermost layer of Cu and, consequently, the electronic coupling between graphene and the metallic substrate. In second place, through the same characterization techniques, it is shown how the initial state of graphene/Cu sheets influences the local inhomogeneities of the ZnO deposit during the early stages of growth in terms of both, stoichiometry and morphology. Finally, as a proof of concept, it is shown how altering the initial chemical state and interaction of Graphene with Cu can be used to control the properties of the ZnO deposits.

Limits to Perception by Quantum Monitoring with Finite Efficiency.

We formulate limits to perception under continuous quantum measurements by comparing the quantum states assigned by agents that have partial access to measurement outcomes. To this end, we provide bounds on the trace distance and the relative entropy between the assigned state and the actual state of the system. These bounds are expressed solely in terms of the purity and von Neumann entropy of the state assigned by the agent, and are shown to characterize how an agent's perception of the system is altered by access to additional information. We apply our results to Gaussian states and to the dynamics of a system embedded in an environment illustrated on a quantum Ising chain.

Fluctuations in Extractable Work Bound the Charging Power of Quantum Batteries.

We study the connection between the charging power of quantum batteries and the fluctuations of the extractable work. We prove that in order to have a nonzero rate of change of the extractable work, the state ρ_{W} of the battery cannot be an eigenstate of a "free energy operator," defined by F≡H_{W}+ß^{-1}log(ρ_{W}), where H_{W} is the Hamiltonian of the battery and ß is the inverse temperature of a reference thermal bath with respect to which the extractable work is calculated. We do so by proving that fluctuations in the free energy operator upper bound the charging power of a quantum battery. Our findings also suggest that quantum coherence in the battery enhances the charging process, which we illustrate on a toy model of a heat engine.

Full Counting Statistics of Topological Defects after Crossing a Phase Transition.

We consider the number distribution of topological defects resulting from the finite-time crossing of a continuous phase transition and identify signatures of universality beyond the mean value, predicted by the Kibble-Zurek mechanism. Statistics of defects follows a binomial distribution with N Bernouilli trials associated with the probability of forming a topological defect at the locations where multiple domains merge. All cumulants of the distribution are predicted to exhibit a common universal power-law scaling with the quench time in which the transition is crossed. Knowledge of the distribution is used to discuss the onset of adiabatic dynamics and bound rare events associated with large deviations.

Quantum Statistical Enhancement of the Collective Performance of Multiple Bosonic Engines.

We consider an ensemble of indistinguishable quantum machines and show that quantum statistical effects can give rise to a genuine quantum enhancement of the collective thermodynamic performance. When multiple indistinguishable bosonic work resources are coupled to an external system, the internal energy change of the external system exhibits an enhancement arising from permutation symmetry in the ensemble, which is absent when the latter consists of distinguishable work resources.

Nonadiabatic Energy Fluctuations of Scale-Invariant Quantum Systems in a Time-Dependent Trap.

We consider the nonadiabatic energy fluctuations of a many-body system in a time-dependent harmonic trap. In the presence of scale-invariance, the dynamics becomes self-similar and the nondiabatic energy fluctuations can be found in terms of the initial expectation values of the second moments of the Hamiltonian, square position, and squeezing operators. Nonadiabatic features are expressed in terms of the scaling factor governing the size of the atomic cloud, which can be extracted from time-of-flight images. We apply this exact relation to a number of examples: the single-particle harmonic oscillator, the one-dimensional Calogero-Sutherland model, describing bosons with inverse-square interactions that includes the non-interacting Bose gas and the Tonks-Girdardeau gas as limiting cases, and the unitary Fermi gas. We illustrate these results for various expansion protocols involving sudden quenches of the trap frequency, linear ramps and shortcuts to adiabaticity. Our results pave the way to the experimental study of nonadiabatic energy fluctuations in driven quantum fluids.

Probing the Full Distribution of Many-Body Observables By Single-Qubit Interferometry.

We present an experimental scheme to measure the full distribution of many-body observables in spin systems, both in and out of equilibrium, using an auxiliary qubit as a probe. We focus on the determination of the magnetization and the kink number statistics at thermal equilibrium. The corresponding characteristic functions are related to the analytically continued partition function. Thus, both distributions can be directly extracted from experimental measurements of the coherence of a probe qubit that is coupled to an Ising-type bath, as reported in [X. Peng et al., Phys. Rev. Lett. 114, 010601 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.010601] for the detection of Lee-Yang zeros.

Spontaneous Symmetry Breaking Induced by Quantum Monitoring.

Spontaneous symmetry breaking (SSB) is responsible for structure formation in scenarios ranging from condensed matter to cosmology. SSB is broadly understood in terms of perturbations to the Hamiltonian governing the dynamics or to the state of the system. We study SSB due to quantum monitoring of a system via continuous quantum measurements. The acquisition of information during the measurement process induces a measurement backaction that seeds SSB. In this setting, by monitoring different observables, an observer can tailor the topology of the vacuum manifold, the pattern of symmetry breaking, and the nature of the resulting domains and topological defects.

Extreme Decoherence and Quantum Chaos.

We study the ultimate limits to the decoherence rate associated with dephasing processes. Fluctuating chaotic quantum systems are shown to exhibit extreme decoherence, with a rate that scales exponentially with the particle number, thus exceeding the polynomial dependence of systems with fluctuating k-body interactions. Our findings suggest the use of quantum chaotic systems as a natural test bed for spontaneous wave function collapse models. We further discuss the implications on the decoherence of AdS/CFT black holes resulting from the unitarity loss associated with energy dephasing.

Universal Statistics of Topological Defects Formed in a Quantum Phase Transition.

When a quantum phase transition is crossed in finite time, critical slowing down leads to the breakdown of adiabatic dynamics and the formation of topological defects. The average density of defects scales with the quench rate following a universal power law predicted by the Kibble-Zurek mechanism. We analyze the full counting statistics of kinks and report the exact kink number distribution in the transverse-field quantum Ising model. Kink statistics is described by the Poisson binomial distribution with all cumulants exhibiting a universal power law scaling with the quench rate. In the absence of finite-size effects, the distribution approaches a normal one, a feature that is expected to apply broadly in systems described by the Kibble-Zurek mechanism.