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Effective models to describe the dynamics of an open cavity have been extensively discussed in the literature. In many of these models the cavity leakage to the outside is treated as a loss introduced phenomenologically. In contrast to these, we focus here on characterizing the outgoing photon using a novel approach where the outside is treated as part of the system. In such a global system, in order to separately characterize the photon inside and outside cavity, we demonstrate a first-principle derivation of a coherent cavity-reservoir coupling function for cavities with mirrors consisting of a stack of dielectric layers. In particular, we show that due to the effects induced by the multilayer nature of the cavity mirror, even in the standardly defined high-finesse cavity regime, the cavity-reservoir system description might differ from the one where the structure of the mirror is neglected. Based on this, we define a generalized cavity response function and a cavity-reservoir coupling function, which account for the longitudinal geometric structure of the cavity mirror. This allows us to define an effective reflectivity for the cavity with a multilayer mirror as if it was sitting in a well-defined effective mirror plane. We estimate the error of such a definition by considering cavities of different lengths and mirror structures. Finally, we apply this model to characterize the dynamics of a single photon produced in such a cavity and propagating outside.

Quantum optimal control is a set of methods for designing time-varying electromagnetic fields to perform operations in quantum technologies. This tutorial paper introduces the basic elements of this theory based on the Pontryagin maximum principle, in a physicist-friendly way. An analogy with classical Lagrangian and Hamiltonian mechanics is proposed to present the main results used in this field. Emphasis is placed on the different numerical algorithms to solve a quantum optimal control problem. Several examples ranging from the control of two-level quantum systems to that of Bose-Einstein Condensates (BEC) in a one-dimensional optical lattice are studied in detail, using both analytical and numerical methods. Codes based on shooting method and gradient-based algorithms are provided. The connection between optimal processes and the quantum speed limit is also discussed in two-level quantum systems. In the case of BEC, the experimental implementation of optimal control protocols is described, both for two-level and many-level cases, with the current constraints and limitations of such platforms. This presentation is illustrated by the corresponding experimental results., Comment: 51 pages, 15 figures, 272 references

When a photon is sent onto an atomic ensemble, it interacts collectively with the $N$ atoms of the sample and not simply with one of them. This results in measurable modifications in the scattering rate, the emission diagram or the temporal dynamics. Among these collective effects, here, we study in detail the temporal dynamics of the decay of the scattered light after switching off the driving laser. Right after the switch-off, the decay can be faster than for a single atom, whereas at later time, the decay becomes slower. We refer to this behavior as superradiance and subradiance, respectively. We present in this Chapter our investigations of super- and subradiance in disordered cold atomic ensembles, mainly with low-density samples (dilute regime) and a weak excitation (linear-optics regime), but we also studied the first corrections beyond these limiting cases. We emphasize the different possible interpretations of these phenomena, with in particular the presentation of an optical description of these effects, which sheds a new light on cooperative scattering in disordered samples and provides a more intuitive understanding of the physical mechanisms at play.

Using optimal control, we establish and link the ultimate bounds in time (referred to as quantum speed limit) and energy of two- and three-level quantum nonlinear systems which feature 1:2 resonance. Despite the unreachable complete inversion, by using the Pontryagin maximum principle, we determine the optimal time, pulse area, or energy, for a given arbitrary accuracy. We show that the third-order Kerr terms can be absorbed in the detuning in order to lock the dynamics to the resonance. In the two-level problem, we determine the non-linear counterpart of the optimal $\pi$-pulse inversion for a given accuracy. In the three-level problem, we obtain an intuitive pulse sequence similar to the linear counterpart but with different shapes. We prove the (slow) logarithmic increasing of the optimal time as a function of the accuracy.

We investigate the extent to which a two-level quantum system subjected to an external time-dependent drive can be characterized by supervised learning. We apply this approach to the case of bang-bang control and the estimation of the offset and the final distance to a given target state. For any control protocol, the goal is to find the mapping between the offset and the distance. This mapping is interpolated using a neural network. The estimate is global in the sense that no a priori knowledge is required on the relation to be determined. Different neural network algorithms are tested on a series of data sets. We show that the mapping can be reproduced with very high precision in the direct case when the offset is known, while obstacles appear in the indirect case starting from the distance to the target. We point out the limits of the estimation procedure with respect to the properties of the mapping to be interpolated. We discuss the physical relevance of the different results., Comment: 19 pages, 5 figures

Photons are the elementary quantum excitations of the electromagnetic field. Quantization is usually constructed on the basis of an expansion in eigenmodes, in the form of plane waves. Since they form a basis, other electromagnetic configurations can be constructed by linear combinations. In this presentation we discuss a formulation constructed in the general formalism of bosonic Fock space, in which the quantum excitation can be constructed directly on localized pulses of arbitrary shape. Although the two formulations are essentially equivalent, the direct formulation in terms of pulses has some conceptual and practical advantages, which we illustrate with some examples. The first one is the passage of a single photon pulse through a beam splitter. The analysis of this formulation in terms of pulses in Fock space shows that there is no need to introduce "vacuum fluctuations entering through the unused port", as is often done in the literature. Another example is the Hong-Ou-Mandel effect. It is described as a time dependent process in the Schr\"odinger representation in Fock space. The analysis shows explicitly how the two essential ingredients of the Hong-Ou-Mandel effect are the same shape of the pulses and the bosonic nature of photons. This formulation shows that all the phenomena involving linear quantum optical devices can be described and calculated on the basis of the time dependent solution of the corresponding classical Maxwell's equations for pulses, from which the quantum dynamics in Fock space can be immediately constructed., Comment: 26 pages, 3 figures

The ability of pulse-shaping devices to generate accurately quantum optimal control is a strong limitation to the development of quantum technologies. We propose and demonstrate a systematic procedure to design robust digital control processes adapted to such experimental constraints. We show to what extent this digital pulse can be obtained from its continuous-time counterpart. A remarkable efficiency can be achieved even for a limited number of pulse parameters. We experimentally implement the protocols on IBM quantum computers for a single qubit, obtaining an optimal robust transfer in a time T = 382 ns.

Robust time-optimal control is known to feature constant (square) pulses. We analyze fast adiabatic dynamics that preserve robustness by using alternative smooth quasi-square pulses, typically represented by hyper-Gaussian pulses. We here consider the two protocols, robust inverse optimization and time-contracted adiabatic passage, allowing the design of the same pulse shape in both cases. The dynamics and their performance are compared. The superiority of the former protocol is shown.

We apply the inverse geometric optimization technique to generate an optimal and robust stimulated Raman exact passage (STIREP) considering the loss of the upper state as a characterization parameter. Control fields temporal shapes that are optimal with respect to pulse area, energy, and duration, are found to form a simple sequence with a combination of intuitively (near the beginning and the end) and counter-intuitively ordered pulse pairs. The resulting dynamics produces a loss which is about a third of that of the non-robust optimal STIREP. Alternative optimal solutions featuring lower losses, larger pulse areas, and fully counter-intuitive pulse sequences are derived.

Super- and subradiance are usually described in the framework of Dicke collective states, which is an ``atomic picture'' in which the electromagnetic field only provides an effective interaction between the atoms. Here, we discuss a complementary picture, in which we describe the propagation and scattering of light in the atomic medium, which provides a complex susceptibility and scatterers. This ``optical picture'' is valid in the linear-optics regime for disordered samples and is mainly relevant at low density, when the susceptibility and scattering cross-section can be computed from simple textbook formulas. In this picture, superradiance is a dispersion effect due to a single scattering event dressed by an effective refractive index, whereas subradiance is due to multiple scattering. We present numerical and experimental data supporting our interpretation.

Over the last decades, quantum optics has evolved from high quality factor cavities in the early experiments toward new cavity designs involving leaky modes. Despite very reliable models, in the concepts of cavity quantum electrodynamics, photon leakage is most of the time treated phenomenologically. Here, we take a different approach, and starting from first principles, we define an inside-outside representation which is derived from the original true-mode representation, in which one can determine effective Hamiltonian and Poynting vector. Contrary to the phenomenological model, they allow a full description of a leaking single photon produced in the cavity and propagating in free space. This is applied for a laser-driven atom-cavity system. In addition, we propose an atom-cavity non-resonant scheme for single photon generation, and we rigorously analyze the outgoing single photon in time and frequency domains for different coupling regimes. Finally, we introduce a particular coupling regime ensuring adiabatic elimination for which the pulse shape of the outgoing single photon is tailored using a specifically designed driving field envelope.

Quantum teleportation is a very helpful information-theoretic protocol that allows to transfer an unknown arbitrary quantum state from one location to another without having to transmit the quantum system through the intermediate region. Quantum states, quantum channels, and indefinite causal structures are all examples of quantum causal structures that not only enable advanced quantum information processing functions, but can also model causal structures in nonclassical spacetimes. In this letter, we develop quantum teleportation of arbitrary quantum causal structures, as formalized by the process matrix framework. Instead of teleporting all the physical degrees of freedom that implement the causal structure, the central idea is to just teleport the inputs to and outputs from the operations of agents. The communication of outcomes of Bell state measurements, which is necessary for deterministic quantum teleportation, is not possible for all causal structures that one might wish to investigate. To avoid this problem, we propose partially and fully post-selected teleportation protocols. We prove that our partially post-selected teleportation protocol is compatible with all quantum causal structures, including those that involve indefinite causal order., Comment: 5+7 pages, 28 references, 7 figures

Promising access to high-speed quantum networks relies on the creation of high-dimensional entangled memories that provide quantum communication with higher capacity of noisy quantum channels, thereby reducing the transmission time of information. Yet, the distribution of multidimensional entanglement between remote memory nodes is still faintly investigated. We propose an experimentally feasible protocol of deterministic generation of high-dimensional entanglement between distant multi-level atoms confined in high-finesse optical cavities and driven by laser pulses. Three-dimensional entanglement is generated deterministically between remote atoms by triggering a two-photon wavepacket, which mediates a superposition of states chosen by the laser pulse parameters. The efficient transfer of atomic states between remote nodes allows the construction of a three-dimensional quantum repeater, where the successful creation of entanglement can be verified by a simple method for reliable measurement of atomic ground Zeeman states., Comment: Accepted for publication at PRA. 10 pages, 5 figures

One of the most fundamental open problems in physics is the unification of general relativity and quantum theory to a theory of quantum gravity. An aspect that might become relevant in such a theory is that the dynamical nature of causal structure present in general relativity displays quantum uncertainty. This may lead to a phenomenon known as indefinite or quantum causal structure, as captured by the process matrix formalism. Due to the generality of that framework, however, for many process matrices there is no clear physical interpretation. A popular approach towards a quantum theory of gravity is the Page-Wootters formalism, which associates to time a Hilbert space structure similar to spatial position. By explicitly introducing a quantum clock, it allows to describe time-evolution of systems via correlations between this clock and said systems encoded in history states. In this paper we combine the process matrix framework with a generalization of the Page-Wootters formalism in which one considers several agents, each with their own discrete quantum clock. We describe how to extract process matrices from scenarios involving such agents with quantum clocks, and analyze their properties. The description via a history state with multiple clocks imposes constraints on the implementation of process matrices and on the perspectives of the agents as described via causal reference frames. While it allows for scenarios where different definite causal orders are coherently controlled, we explain why certain noncausal processes might not be implementable within this setting., Comment: New title. Close to published version. Veronika Baumann and Marius Krumm share first authorship of this paper

Guided by the intuition of coherent superposition of causal relations, recent works presented quantum processes without classical common-cause and direct-cause explanation, that is, processes which cannot be written as probabilistic mixtures of quantum common-cause and quantum direct-cause relations (CCDC). In this work, we analyze the minimum requirements for a quantum process to fail to admit a CCDC explanation and present "simple" processes, which we prove to be the most robust ones against general noise. These simple processes can be realized by preparing a maximally entangled state and applying the identity quantum channel, thus not requiring an explicit coherent mixture of common-cause and direct-cause, exploiting the possibility of a process to have both relations simultaneously. We then prove that, although all bipartite direct-cause processes are bipartite separable operators, there exist bipartite separable processes which are not direct-cause. This shows that the problem of deciding weather a process is direct-cause process is not equivalent to entanglement certification and points out the limitations of entanglement methods to detect non-classical CCDC processes. We also present a semi-definite programming hierarchy that can detect and quantify the non-classical CCDC robustnesses of every non-classical CCDC process. Among other results, our numerical methods allow us to show that the simple processes presented here are likely to be also the maximally robust against white noise. Finally, we explore the equivalence between bipartite direct-cause processes and bipartite processes without quantum memory, to present a separable process which cannot be realized as a process without quantum memory., Comment: 24+8 pages, 11 figures. Code available at https://github.com/marcellongvb/non_ccdc_processes

We study numerically the slow (subradiant) decay of the fluorescence of motionless atoms after a weak pulsed excitation. We show that, in the linear-optics regime and for an excitation detuned by several natural linewidths, the slow decay rate can be dominated by close pairs of atoms (dimers) forming superradiant and subradiant states. However, for a large-enough resonant optical depth and at later time, the dynamics is dominated by collective many-body effects. In this regime, we study the polarization and the spectrum of the emitted light, as well as the spatial distribution of excitation inside the sample, as a function of time during the decay dynamics. The behavior of these observables is consistent with what would be expected for radiation trapping of nearly resonant light. This finding sheds light on subradiance in dilute samples by providing an interpretation based on the light behavior of the system (multiple scattering) which is complementary to the more commonly used picture of the collective atomic Dicke state.

Quantum plasmonics extends cavity quantum electrodynamics (cQED) concepts to the nanoscale, taking benefit from the strongly subwavelength confinement of the plasmon modes supported by metal nanostructures. In this work, we describe in detail collective strong coupling to a plasmonic nanocavity. Similarities and differences to cQED are emphasized. We notably observe that the Rabi splitting can strongly deviate from the standard $\sqrt{N_e}\Delta \Omega_1$ law, where $N_e$ is the number of emitters and $\Delta \Omega_1$ the Rabi splitting for a single emitter. In addition, we discuss the collective Lamb shift and the role of quantum corrections to the emission spectra.

The notorious Wigner's friend thought experiment (and modifications thereof) has in recent years received renewed interest especially due to new arguments that force us to question some of the fundamental assumptions of quantum theory. In this paper, we formulate a no-go theorem for the persistent reality of Wigner's friend's perception, which allows us to conclude that the perceptions that the friend has of her own measurement outcomes at different times cannot "share the same reality", if seemingly natural quantum mechanical assumptions are met. More formally, this means that, in a Wigner's friend scenario, there is no joint probability distribution for the friend's perceived measurement outcomes at two different times, that depends linearly on the initial state of the measured system and whose marginals reproduce the predictions of unitary quantum theory. This theorem entails that one must either (1) propose a nonlinear modification of the Born rule for two-time predictions, (2) sometimes prohibit the use of present information to predict the future -- thereby reducing the predictive power of quantum theory -- or (3) deny that unitary quantum mechanics makes valid single-time predictions for all observers. We briefly discuss which of the theorem's assumptions are more likely to be dropped within various popular interpretations of quantum mechanics., Comment: 7 pages. New proof of the main result. Very close to published version

We evaluate the exact dipole coupling strength between a single emitter and the radiation field within an optical cavity, taking into account the effects of multilayer dielectric mirrors. Our model allows one to freely vary the resonance frequency of the cavity, the frequency of light or atomic transition addressing it and the design wavelength of the dielectric mirror. The coupling strength is derived for an open system with unbound frequency modes. For very short cavities, the effective length used to determine their mode volume and the lengths defining their resonances are different, and also found to diverge appreciably from their geometric length, with the radiation field being strongest within the dielectric mirror itself. Only for cavities much longer than their resonant wavelength does the mode volume asymptotically approach that normally assumed from their geometric length., Comment: 17 pages, 5 figures, 1 table

Dipole-dipole interactions are at the origin of long-lived collective atomic states, often called subradiant, which are explored for their potential use in novel photonic devices or in quantum protocols. Here, we study subradiance beyond linear optics and experimentally demonstrate a two hundred-fold increase in the population of these modes, as the saturation parameter of the driving field is increased. We attribute this enhancement to a mechanism similar to optical pumping through the well-coupled superradiant states. The lifetimes are unaffected by the pump strength, as the system is ultimately driven toward the single-excitation sector.

We compare the field-field g(1)(\tau), intensity-field g(3/2)(\tau), and intensity-intensity g(2)(\tau) correlation functions for models that are of relevance in astrophysics. We obtain expressions for the general case of a chaotic radiation, where the amplitude is Rician based on a model with an ensemble of harmonic oscillators in Brownian motion. We obtain the signal to noise ratios for two methods of measurement. The intensity-field correlation function signal to noise ratio scales with the first power of |g(1)(\tau)|. This is in contrast with the well-established result of g(2)(\tau) which goes as the square of |g(1)(\tau)|., Comment: 23 pages, 2 figures, 3 Tables

In quantum communication networks, wires represent well-defined trajectories along which quantum systems are transmitted. In spite of this, trajectories can be used as a quantum control to govern the order of different noisy communication channels, and such a control has been shown to enable the transmission of information even when quantum communication protocols through well-defined trajectories fail. This result has motivated further investigations on the role of the superposition of trajectories in enhancing communication, which revealed that the use of quantum control of parallel communication channels, or of channels in series with quantum-controlled operations, can also lead to communication advantages. Building upon these findings, here we experimentally and numerically compare different ways in which two trajectories through a pair of noisy channels can be superposed. We observe that, within the framework of quantum interferometry, the use of channels in series with quantum-controlled operations generally yields the largest advantages. Our results contribute to clarify the nature of these advantages in experimental quantum-optical scenarios, and showcase the benefit of an extension of the quantum communication paradigm in which both the information exchanged and the trajectory of the information carriers are quantum., Comment: 20 pages, 11 figures. Accepted version

Adiabatic passage is a standard tool for achieving robust transfer in quantum systems. We show that, in the context of driven nonlinear Hamiltonian systems, adiabatic passage becomes highly non-robust when the target is unstable. We show this result for a generic (1:2) resonance, for which the complete transfer corresponds to a hyperbolic fixed point in the classical phase space featuring an adiabatic connectivity strongly sensitive to small perturbations of the model. By inverse engineering, we devise high-fidelity and robust partially non-adiabatic trajectories. They localize at the approach of the target near the stable manifold of the separatrix, which drives the dynamics towards the target in a robust way. These results can be applicable to atom-molecule Bose-Einstein condensate conversion and to nonlinear optics., Comment: 5 pages, 4 figures

In a standard interferometry experiment, one measures the phase difference between two paths by recombining the two wave packets on a beam-splitter. However, it has been recently recognized that the phase can also be estimated via local measurements, by using an ancillary particle in a known superposition state. In this work, we further analyse these protocols for different types of particles (bosons or fermions, charged or uncharged), with a particular emphasis on the subtleties that arise when the phase is due to the coupling to an abelian gauge field. In that case, we show that the measurable quantities are spacetime loop integrals of the 4-vector potential, enclosed by two identical particles or by a particle-antiparticle pair. Furthermore, we generalize our considerations to scenarios involving an arbitrary number of parties performing local measurements on a general charged fermionic state. Finally, as a concrete application, we analyse a recent proposal by Marletto and Vedral (arXiv:1906.03440) involving the time-dependent Aharonov-Bohm effect., Comment: 6 pages and 3 figures (main text), plus 3 appendices. Revised version

Uncertainty relations in quantum mechanics express bounds on our ability to simultaneously obtain knowledge about expectation values of non-commuting observables of a quantum system. They quantify trade-offs in accuracy between complementary pieces of information about the system. In Quantum multiparameter estimation, such trade-offs occur for the precision achievable for different parameters characterizing a density matrix: an uncertainty relation emerges between the achievable variances of the different estimators. This is in contrast to classical multiparameter estimation, where simultaneous optimal precision is attainable in the asymptotic limit. We study trade-off relations that follow from known tight bounds in quantum multiparameter estimation. We compute trade-off curves and surfaces from Cram\'er--Rao type bounds which provide a compelling graphical representation of the information encoded in such bounds, and argue that bounds on simultaneously achievable precision in quantum multiparameter estimation should be regarded as measurement uncertainty relations. From the state-dependent bounds on the expected cost in parameter estimation, we derive a state independent uncertainty relation between the parameters of a qubit system.

The Siegert relation relates the electric field and intensity correlations of light, under given assumptions. After a brief history of intensity correlations, we give a derivation of the relation. Then we present an experiment, which can be easily adapted for an undergraduate setup, and that allows measuring both field and intensity correlations at the same time, thus providing a direct test of the Siegert relation. As a conclusion, we discuss typical situations where the relation fails.

We provide a critical analysis of some of the commonly used theoretical models to describe quantum plasmons. We summarize the standard approach based on a Fano diagonalization and we show explicit discrepancies in the obtained results by taking the limit of vanishing coupling between the electromagnetic field and the material medium. We then discuss the derivation of spontaneous emission in a plasmonic environment, which usually relies on a Green tensor and is based on an incomplete identity. The effect of the missing terms is calculated in a one-dimensional model.

This is an updated version of supplementary information to accompany "Quantum supremacy using a programmable superconducting processor", an article published in the October 24, 2019 issue of Nature. The main article is freely available at https://www.nature.com/articles/s41586-019-1666-5. Summary of changes since arXiv:1910.11333v1 (submitted 23 Oct 2019): added URL for qFlex source code; added Erratum section; added Figure S41 comparing statistical and total uncertainty for log and linear XEB; new References [1,65]; miscellaneous updates for clarity and style consistency; miscellaneous typographical and formatting corrections., Comment: 67 pages, 51 figures

We developed single-shot shaped pulses for ultra high fidelity (UH-fidelity) population transfer on a 3-level quantum system in lambda configuration. To ensure high fidelity, we use the Lewis-Riesenfeld (L-R) method to derive a family of solutions leading to an exact transfer, where the solutions follow a single dynamical mode of the L-R invariant. Among this family, we identify a tracking solution with a single parameter to control simultaneously the fidelity of the transfer, the population of the excited state, and robustness. We define a measure of the robustness of an UH-fidelity transfer as the minimum percentile deviation on the pulse areas at which the infidelity rises above $10^{-4}$. The robustness of our shaped pulses is found superior to that of Gaussian and adiabatically-optimized pulses for moderate pulse areas.

We study the paradigmatic model of a qubit interacting with a structured environment and driven by an external field by means of a microscopic and a phenomenological model. The validity of the so-called fixed-dissipator (FD) assumption, where the dissipation is taken as the one of the undriven qubit is discussed. In the limit of a flat spectrum, the FD model and the microscopic one remarkably practically coincide. For a structured reservoir, we show in the secular limit that steady states can be different from those determined from the FD model, opening the possibility for exploiting reservoir engineering. We explore it as a function of the control field parameters, of the characteristics of the spectral density and of the environment temperature. The observed widening of the family of target states by reservoir engineering suggests new possibilities in quantum control protocols., Comment: 9 pages, 5 figures

Subradiance is the cooperative inhibition of the radiation by several emitters coupled to the same electromagnetic modes. It was predicted by Dicke in 1954 and only recently observed in cold atomic vapors. Here we address the question to what extent this cooperative effect survives outside the limit of frozen two-level systems by studying the subradiant decay in an ensemble of cold atoms as a function of the temperature. Experimentally, we observe only a slight decrease of the subradiant decay time when increasing the temperature up to several millikelvins, and in particular we measure subradiant decay rates that are much smaller than the Doppler broadening. This demonstrates that subradiance is surprisingly robust against thermal decoherence. The numerical simulations are in good agreement and allow us to extrapolate the behavior of subradiance at higher temperatures.

In dense atomic gases the interaction between transition dipoles and photons leads to the formation of many-body states with collective dissipation and long-ranged forces. Despite decades of research, a full understanding of this paradigmatic many-body problem is still lacking. Here, we put forward and explore a scenario in which a dense atomic gas is weakly excited by an off-resonant laser field. We develop the theory for describing such dressed many-body ensembles and show that collective excitations are responsible for the emergence of many-body interactions, i.e. effective potentials that cannot be represented as a sum of binary terms. We illustrate how interaction effects may be probed through microwave spectroscopy via the analysis of time-dependent line-shifts, and show that these signals are sensitive to the phase pattern of the dressing laser. Our study offers a new perspective on dense atomic ensembles interacting with light and promotes this platform as a setting for the exploration of rich non-equilibrium many-body physics.

In a recent series of works [Ebler et al. Phys. Rev. Lett. 120, 120502 (2018); arXiv:1809.06655v2; arXiv:1810.10457v2], it has been proposed that the quantum superposition of causal order -- the quantum switch -- may offer an enhancement of classical and quantum channel capacity through noisy channels, a phenomena that was coined `causal activation'. In this paper we attempt to clarify the nature of the purported advantage, by comparing the quantum switch to a class of processes that can be interpreted as quantum superposition of processes with the same causal order. We show that some of these processes can match or even outperform the quantum switch at enhancing classical and quantum channel capacity, and argue that they require the same resources as the switch. We conclude, in agreement with Abbott et al. [arXiv:1810.09826v1], that the aforementioned advantages appear to be attributable to the ability to coherently control quantum operations, and not to indefinite causal order per se., Comment: 8 pages, 1 figure. Published version

Plasmonic superradiance originates from the plasmon mediated strong correlation that builds up between dipolar emitters coupled to a metal nanoparticle. This leads to a fast burst of emission so that plasmonic superradiance constitutes ultrafast and extremely bright optical nanosources of strong interest for integrated quantum nano-optics platforms. We elucidate the superradiance effect by establishing the dynamics of the system, including all features like the orientation of the dipoles, their distance to the particle and the number of active plasmon modes. We determine an optimal configuration for Purcell enhanced superradiance. We also show superradiance blockade at small distances.

The quantization of plasmons has been analyzed mostly under the assumption of an infinite-sized bulk medium interacting with the electromagnetic field. We reformulate it for finite-size media, such as metallic or dielectric nano-structures, highlighting sharp differences. By diagonalizing the Hamiltonian by means of a Lippmann-Schwinger equation, we show the contribution of two sets of bosonic operators, one stemming from medium fluctuations, and one from the electromagnetic field. The results apply to general models including dissipative and dispersive responses.

We report investigation of near-resonance light scattering from a cold and dense atomic gas of $^{87}$Rb atoms. Measurements are made for probe frequencies tuned near the $F=2\to F'=3$ nearly closed hyperfine transition, with particular attention paid to the dependence of the scattered light intensity on detuning from resonance, the number of atoms in the sample, and atomic sample size. We find that, over a wide range of experimental variables, the optical depth of the atomic sample serves as an effective single scaling parameter which describes well all the experimental data.

Area laws are a far-reaching consequence of the locality of physical interactions, and they are relevant in a range of systems, from black holes to quantum many-body systems. Typically, these laws concern the entanglement entropy or the quantum mutual information of a subsystem at a single time. However, when considering information propagating in spacetime, while carried by a physical system with local interactions, it is intuitive to expect area laws to hold for spacetime regions; in this work, we prove such a law in the case of quantum lattice systems. We consider a sequence of local quantum operations performed at discrete times on a spin-lattice, such that each operation is associated to a point in spacetime. In the time between operations, the time evolution of the spins is governed by a finite range Hamiltonian. By considering a purification of the quantum instruments and analyzing the quantum mutual information between the ancillas used in the purification, we obtain a spacetime area law bound for the correlations between the measurement outcomes inside a spacetime region, and those outside of it.

We derive effective Hamiltonians for a single dipolar emitter coupled to a metal nanoparticle (MNP) with particular attention devoted to the role of losses. For small particles sizes, absorption dominates and a non hermitian effective Hamiltonian describes the dynamics of the hybrid emitter-MNP nanosource. We discuss the coupled system dynamics in the weak and strong coupling regimes offering a simple understanding of the energy exchange, including radiative and non radiative processes. We define the plasmon Purcell factors for each mode. For large particle sizes, radiative leakages can significantly perturbate the coupling process. We propose an effective Fano Hamiltonian including plasmon leakages and discuss the link with the quasi-normal mode description. We also propose Lindblad equations for each situation and introduce a collective dissipator for describing the Fano behaviour.

A quantum process encodes the causal structure that relates quantum operations performed in local laboratories. The process matrix formalism includes as special cases quantum mechanics on a fixed background space-time, but also allows for more general causal structures. Motivated by the interpretation of processes as a resource for quantum information processing shared by two (or more) parties, with advantages recently demonstrated both for computation and communication tasks, we investigate the notion of composition of processes. We show that under very basic assumptions such a composition rule does not exist. While the availability of multiple independent copies of a resource, e.g. quantum states or channels, is the starting point for defining information-theoretic notions such as entropy (both in classical and quantum Shannon theory), our no-go result means that a Shannon theory of general quantum processes will not possess a natural rule for the composition of resources., Comment: 9 pages, 3 figures. Published version

In general relativity, the causal structure between events is dynamical, but it is definite and observer-independent; events are point-like and the membership of an event A in the future or past light-cone of an event B is an observer-independent statement. When events are defined with respect to quantum systems however, nothing guarantees that the causal relationship between A and B is definite. We propose to associate a causal reference frame corresponding to each event, which can be interpreted as an observer-dependent time according to which an observer describes the evolution of quantum systems. In the causal reference frame of one event, this particular event is always localised, but other events can be "smeared out" in the future and in the past. We do not impose a predefined causal order between the events, but only require that descriptions from different reference frames obey a global consistency condition. We show that our new formalism is equivalent to the pure process matrix formalism. The latter is known to predict certain multipartite correlations, which are incompatible with the assumption of a causal ordering of the events -- these correlations violate causal inequalities. We show how the causal reference frame description can be used to gain insight into the question of realisability of such strongly non-causal processes in laboratory experiments. As another application, we use causal reference frames to revisit a thought experiment where the gravitational time dilation due to a massive object in a quantum superposition of positions leads to a superposition of the causal ordering of two events., Comment: 20 + 5 pages, 3 figures. Corrected equations (53)-(56)

We construct mode-selective effective models describing the interaction of N quantum emitters (QEs) with the localised surface plasmon polaritons (LSPs) supported by a spherical metal nanoparticle (MNP) in an arbitrary geometric arrangement of the QEs. We develop a general formulation in which the field response in the presence of the nanosystem can be decomposed into orthogonal modes with the spherical symmetry as an example. We apply the model in the context of quantum information, investigating on the possibility of using the LSPs as mediators of an efficient control of population transfer between two QEs. We show that a Stimulated Raman Adiabatic Passage configuration allows such a transfer via a decoherence-free dark state when the QEs are located on the same side of the MNP and very closed to it, whereas the transfer is blocked when the emitters are positioned at the opposite sides of the MNP. We explain this blockade by the destructive superposition of all the interacting plasmonic modes.

We report the first intensity correlation measured with star light since Hanbury Brown and Twiss' historical experiments. The photon bunching $g^{(2)}(\tau, r=0)$, obtained in the photon counting regime, was measured for 3 bright stars, $\alpha$ Boo, $\alpha$ CMi, and $\beta$ Gem. The light was collected at the focal plane of a 1~m optical telescope, was transported by a multi-mode optical fiber, split into two avalanche photodiodes and digitally correlated in real-time. For total exposure times of a few hours, we obtained contrast values around $2\times10^{-3}$, in agreement with the expectation for chaotic sources, given the optical and electronic bandwidths of our setup. Comparing our results with the measurement of Hanbury Brown et al. on $\alpha$ CMi, we argue for the timely opportunity to extend our experiments to measuring the spatial correlation function over existing and/or foreseen arrays of optical telescopes diluted over several kilometers. This would enable $\mu$as long-baseline interferometry in the optical, especially in the visible wavelengths with a limiting magnitude of 10., Comment: Accepted for publication in Mon. Not. Roy. Astron. Soc

One way to study the physical plausibility of closed timelike curves (CTCs) is to examine their computational power. This has been done for Deutschian CTCs (D-CTCs) and post-selection CTCs (P-CTCs), with the result that they allow for the efficient solution of problems in PSPACE and PP, respectively. Since these are extremely powerful complexity classes, which are not expected to be solvable in reality, this can be taken as evidence that these models for CTCs are pathological. This problem is closely related to the nonlinearity of this models, which also allows for example cloning quantum states, in the case of D-CTCs, or distinguishing non-orthogonal quantum states, in the case of P-CTCs. In contrast, the process matrix formalism allows one to model indefinite causal structures in a linear way, getting rid of these effects, and raising the possibility that its computational power is rather tame. In this paper we show that process matrices correspond to a linear particular case of P-CTCs, and therefore that its computational power is upperbounded by that of PP. We show, furthermore, a family of processes that can violate causal inequalities but nevertheless can be simulated by a causally ordered quantum circuit with only a constant overhead, showing that indefinite causality is not necessarily hard to simulate., Comment: 11 + 5 pages, no figures, 16 circuits. Corrected equations (33)-(36)

We develop the method of adiabatic tracking for photo- and magneto-association of Bose-Einstein atomic condensates with models that include Kerr type nonlinearities. We show that the inclusion of these terms can produce qualitatively important modifications in the adiabatic dynamics, like the appearance of bifurcations, in which the trajectory that is being tracked loses its stability. As a consequence the adiabatic theorem does not apply and the adiabatic transfer can be strongly degraded. This degradation can be compensated by using fields that are strong enough compared with the values of the Kerr terms. The main result is that, despite these potentially detrimental features, there is always a choice of the detuning that leads to an efficient adiabatic tracking, even for relatively weak fields.

We propose and demonstrate a robust control scheme by ultrafast nonadiabatic chirped laser pulse, designed for targeting coherent superpositions of two-level systems. Robustness against power fluctuation is proved by our numerical study and a proof-of-principle experiment performed with femtosecond laser interaction on cold atoms. They exhibit for the final driven dynamics a cusp on the Bloch sphere, corresponding to a zero curvature of fidelity. This solution is particularly simple and thus applicable to a wide range of potential applications., Comment: 5 pages. 4 figures

Hybrid molecular-plasmonic nanostructures have demonstrated their potential for surface enhanced spectroscopies, sensing or quantum control at the nanoscale. In this work, we investigate the strong coupling regime and explicitly describe the hybridization between the localized plasmons of a metal nanoparticle and the excited state of a quantum emitter, offering a simple and precise understanding of the energy exchange in full analogy with cavity quantum electrodynamics treatment and dressed atom picture. Both near field emission and far field radiation are discussed, revealing the richness of such optical nanosources.

In communication complexity, a number of distant parties have the task of calculating a distributed function of their inputs, while minimizing the amount of communication between them. It is known that with quantum resources, such as entanglement and quantum channels, one can obtain significant reductions in the communication complexity of some tasks. In this work, we study the role of the quantum superposition of the direction of communication as a resource for communication complexity. We present a tripartite communication task for which such a superposition allows for an exponential saving in communication, compared to one-way quantum (or classical) communication; the advantage also holds when we allow for protocols with bounded error probability., Comment: 5 pages, 2 figures. Published version

Since Dicke's seminal paper on coherence in spontaneous radiation by atomic ensembles, superradiance has been extensively studied. Subradiance, on the contrary, has remained elusive, mainly because subradiant states are weakly coupled to the environment and are very sensitive to nonradiative decoherence processes.Here we report the experimental observation of subradiance in an extended and dilute cold-atom sample containing a large number of particles. We use a far detuned laser to avoid multiple scattering and observe the temporal decay after a sudden switch-off of the laser beam. After the fast decay of most of the fluorescence, we detect a very slow decay, with time constants as long as 100 times the natural lifetime of the excited state of individual atoms. This subradiant time constant scales linearly with the cooperativity parameter, corresponding to the on-resonance optical depth of the sample, and is independent of the laser detuning, as expected from a coupled-dipole model.

We propose an exactly solvable multisite interaction spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice for the rigorous studies of chaotic entanglement. By making use of the generalized star-triangle transformation, we map the initial model onto an effective Ising one on a Husimi lattice, which we solve then exactly by applying the recursive method. Expressing the entanglement of the Heisenberg spins, that we quantify by means of the concurrence, in terms of the magnetic quantities of the system, we demonstrate its bifurcation and chaotic behavior. Furthermore, we show that the underlying chaos may slightly enhance the amount of the entanglement, and present on the phase diagram the transition lines from the uniform to periodic and from the periodic to chaotic regimes., Comment: 12 pages, 7 figures. Updated version for publication

We propose a mechanism to produce a superposition of atomic and molecular states by a train of ultrashort laser pulses combined with weak control fields. By adjusting the repetition rate of the pump pulses and the intensity of the coupling laser, one can suppress a transition while simultaneously enhancing the desired transitions. As an example, various superpositions of vibrational states of the $K_2$ molecule are shown., Comment: 7 pages, 6 figures