It was recently found that the Lee-Huang-Yang (LHY) correction to the mean-field Hamiltonian of binary atomic boson condensates suppresses the collapse and creates stable localized modes (two-component quantum droplets, QDs) in two and three dimensions (2D and 3D). In particular, the LHY effect modifies the effective Gross-Pitaevskii equation (GPE) in 2D by adding a logarithmic factor to the usual cubic term. In the framework of the accordingly modified two-component GPE system, we construct 2D self-trapped modes in the form of QDs with vorticity $S$ embedded into each component. Because of the effect of the logarithmic factor, the QDs feature a flat-top shape, which expands with the increase of $S$ and norm $N$. An essential finding, produced by a systematic numerical investigation and analytical estimates, is that the vortical QDs are stable (which is a critical issue for vortex solitons in nonlinear models) up to $S=5$, for $N$ exceeding a certain threshold value, which is predicted to scale as $N_{\mathrm{th}}\sim S^4$ for large $S$ (for three-dimensional QDs, the scaling is $N_{\mathrm{th}}\sim S^6$). The prediction is corroborated by numerical findings. Pivots of QDs with $S\ge 2$ are subject to structural instability, as specially selected perturbations can split the single pivot in a set of $S$ or $S+2$ pivots corresponding to unitary vortices; however, the structural instability remains virtually invisible, as it occurs in a broad central “hole” of the vortex soliton, where values of fields are very small, and it does not cause any dynamical instability. In the condensate of ${}^{39}\mathrm{K}$ atoms, in which QDs with $S=0$ and a quasi-2D shape were created recently, the vortical droplets may have radial size $\lesssim 30\mu \mathrm{m}$, with the number of atoms in the range of ${10}^4–{10}^5$. The role of three-body losses is considered too, demonstrating that they do not prevent the creation of the vortex droplets but may produce a noteworthy effect, leading to sudden splitting of “light” droplets. In addition, hidden-vorticity (HV) states in QDs, with topological charges $S_{+}=-S_{-}=1$ in their components, which are prone to strong instability in other settings, have their stability region too. Unstable HV states tend to spontaneously merge into zero-vorticity solitons. Collisions of QDs, which may lead to their merger, and dynamics of elliptically deformed QDs (which form rotating elongated patterns or ones with oscillations of the eccentricity) are briefly considered too.

Reservoir engineering enables the robust and unconditional preparation of pure quantum states in noisy environments. We show how a family of nonclassical states of a mechanical oscillator can be stabilized in a cavity that is parametrically coupled to both the mechanical displacement and the displacement squared. The cavity is driven with three tones, on the red sideband, on the cavity resonance, and on the second blue sideband. The states so stabilized are (squeezed and displaced) superpositions of a finite number of phonons. They show the unique feature of encompassing two prototypes of nonclassicality for bosonic systems: by adjusting the strength of the drives, one can in fact move from a single-phonon- to a Schrödinger-cat-like state. The scheme is deterministic, supersedes the need for measurement-and-feedback loops, and does not require initialization of the oscillator to the ground state.

The propagation of a light ray in a thin layer (film) within geometrical optics is considered. It is assumed that the ray is captured inside the layer due to reflecting walls or total internal reflection (in the case of a dielectric layer). It has been found that for a very thin film (the length scale is imposed by the curvature of the surface at a given point) the equations describing the trajectory of the light beam are reduced to the equation of a geodesic on the limiting curved surface. There have also been found corrections to the trajectory equation resulting from the finite thickness of the film. Numerical calculations performed for a couple of exemplary curved layers (cone, sphere, torus, and catenoid) confirm that for thin layers the light ray which is repeatedly reflected propagates along the curve close to the geodesic but as the layer thickness increases, these trajectories move away from each other. Because the trajectory equations are complicated nonlinear differential equations, their solutions show some chaotic features. Small changes in the initial conditions result in remarkably different trajectories. These chaotic properties become less significant the thinner the layer under consideration.

The generalized sine-Gordon equation is obtained under the theoretical investigation of interaction of few-cycle pulses in a nonlinear medium modeled by a set of four-level atoms. This equation is derived without the use of the slowly varying envelope approximation and is shown to be integrable in the frameworks of the inverse scattering transformation method. Its solutions describing the propagation of the solitons and breathers and their interaction are investigated. In the case of different signs of the parameters of the equation considered, it is revealed, in particular, that the collision of solitons with opposite polarities can lead to an appearance of the short-living pulse having extraordinarily large amplitude, whose dynamics is similar to that of rogue waves. Also, the solitons of “rectangular” form and the breathers with rectangular oscillations exist in the case of the same signs of the parameters.

In a hybrid atom-optomechanical system, the optical coupling of a mechanical mode of a nanomembrane in an optical cavity with a distant interacting atom gas permits highly nonclassical quantum many-body states. We show that the mechanical mode can be squeezed by the backaction of internal excitations of the atoms in the gas. A Bogoliubov approach reveals that these internal excitations form a fluctuating environment of quasiparticle excitations for the mechanical mode with a gaped spectral density. Nanomechanical squeezing arises due to quasiparticle excitations in the interacting atom gas when the mechanical frequency is close to resonance with the internal atomic transitions. Interestingly, nanomechanical squeezing is enhanced by atom-atom interactions.

Isotropy parameters of truly linear ($L^T$) and truly circular ($C^T$) polarization singularities in a three-dimensional monochromatic electromagnetic field are defined. It is demonstrated that these parameters characterize the distribution of polarization ellipses near the singular points in a more detailed way than a topological index. A numerical algorithm which tracks $C^T$ and $L^T$ lines and visualizes the changes of isotropy parameters along the lines is proposed. The algorithm is applied to visualize the polarization singularity lines and their properties in the vicinity of a metallic nanospheroid that is irradiated by a plane elliptically polarized wave. It is shown that both $C^T$ and $L^T$ lines appear close to the surface of the nanoparticle and they are three-dimensional closed loops or arcs that start and end at the surface of the nanospheroid. In most cases the singular lines of different types are topologically linked.

The effect of steering describes a possible action at a distance via measurements but characterizing the quantum states that can be used for this task remains difficult. We provide a method to derive sufficient criteria for steering from entropic uncertainty relations using generalized entropies. We demonstrate that the resulting criteria outperform existing criteria in several scenarios; moreover, they allow one to detect weakly steerable states.

The excitation spectrum of a highly condensed two-dimensional trapped Bose-Einstein condensate (BEC) is investigated within the rotating frame of reference. The rotation is used to transfer high-lying excited states to the low-energy spectrum of the BEC. We employ many-body linear-response theory and show that, once the rotation leads to a quantized vortex in the ground state, already the low-energy part of the excitation spectrum shows substantial many-body effects beyond the realm of mean-field theory. We demonstrate numerically that the many-body effects grow with the vorticity of the ground state, meaning that the rotation enhances them even for very weak repulsion. Furthermore, we explore the impact of the number of bosons $N$ in the condensate on a low-lying single-particle excitation, which is describable within mean-field theory. Our analysis shows deviations between the many-body and mean-field results which clearly persist when $N$ is increased up to the experimentally relevant regime, typically ranging from several thousand up to a million bosons in size. Implications are briefly discussed.

In a previous Letter [A. Grankin et al., Phys. Rev. Lett. 117, 253602 (2016)] we studied the giant optical nonlinearities of a Rydberg atomic medium within an optical cavity, in the Schwinger-Keldysh formalism. In particular, we calculated the nonlinear contributions to the spectrum of the light transmitted through the cavity. In this article we spell out the essential details of this calculation and we show how it can be extended to higher input photon numbers and higher-order correlation functions. As a relevant example, we calculate and discuss the three-photon correlation function of the transmitted light and discuss its physical significance in terms of the polariton energy levels of the Rydberg medium within the optical cavity.

A versatile approach to the design of photonic ultracompact low-pass modal filters is proposed. The idea stems from the shortcut to adiabaticity protocol, originally developed for quantum-mechanical systems and recently introduced in full-wave optics. This method allows one to achieve efficient rejection of higher order modes in a broad wavelength range for any two-dimensional multimode optical waveguide in an ultracompact configuration of the filter. A study case, corroborated by finite-element method numerical simulations, is reported for slab waveguides.

Spontaneous symmetry breaking is an important concept in many areas of physics. A fundamentally simple symmetry-breaking mechanism in electrodynamics occurs between counterpropagating electromagnetic waves in ring resonators, mediated by the Kerr nonlinearity. The interaction of counterpropagating light in bidirectionally pumped microresonators finds application in the realization of optical nonreciprocity (for optical diodes), studies of $\mathcal{PT}$-symmetric systems, and the generation of counterpropagating solitons. Here, we present comprehensive analytical and dynamical models for the nonlinear Kerr interaction of counterpropagating light in a dielectric ring resonator. In particular, we study discontinuous behavior in the onset of spontaneous symmetry breaking, indicating divergent sensitivity to small external perturbations. These results can be applied to realize, for example, highly sensitive near-field or rotation sensors. We then generalize to a time-dependent model, which predicts different types of dynamical behavior, including oscillatory regimes that could enable Kerr-nonlinearity-driven all-optical oscillators. The physics of our model can be applied to other systems featuring Kerr-type interaction between two distinct modes, such as for light of opposite circular polarization in nonlinear resonators, which are commonly described by coupled Lugiato-Lefever equations.

A recent experiment by Minev et al., arXiv:1803.00545 demonstrated that in a dissipative (artificial) three-level atom with strongly intermittent dynamics it is possible to “catch and reverse” a quantum jump “midflight”: by the conditional application of a unitary perturbation after a fixed time with no jumps, the system was prevented from getting shelved in the dark state, thus removing the intermittency from the dynamics. Here we offer an interpretation of this phenomenon in terms of the dynamical large deviation formalism for open quantum dynamics. In this approach, intermittency is seen as the first-order coexistence of active and inactive dynamical phases (or more precisely, dynamical regimes in this finite level system). Dark periods are thus like time bubbles of the inactive regime in the active one. Here we consider a controlled dynamics via the (single—as in the experiment—or multiple) application of a unitary control pulse during no-jump periods. By considering the large deviation statistics of the emissions, we show that appropriate choice of the control allows one to stabilize a desired dynamical regime and remove the intermittency. In the thermodynamic analogy, the effect of the control is to prick bubbles, thus preventing the fluctuations that manifest phase coexistence. We discuss similar controlled dynamics in broader settings.

We can only perform finite rounds of measurements in protocols with local operations and classical communication (LOCC). In this paper, we propose a set of product states that require infinite rounds of measurements in order to distinguish this given set of states perfectly by LOCC. Therefore, we can conclude that these sets of states are locally indistinguishable. More accurately, given any multipartite LOCC indistinguishable set where every local system cannot start with a nontrivial measurement, then after appending these states with arbitrarily choosing two nonorthogonal states, we obtain another LOCC indistinguishable set. It can be seen that some parties can perform some nontrivial measurements. Hence, these sets are quite different from those constructed before. This result broadens the knowledge of nonlocality without entanglement to a certain extent.

A complete classification of single-mode bosonic Gaussian channels on the basis of being quantum-limited or entanglement breaking under $n$-fold composition is obtained. Parametric forms for all single-mode bosonic Gaussian channels that remain quantum-limited under $n$-fold composition is obtained. It is shown that the obtained parametric forms of quantum-limited amplifier, attenuator, and singular noise channels are entanglement saving, i.e., they do not break entanglement under finite $n$-fold composition. All other single-mode bosonic Gaussian channels, quantum limited or not, are shown to be eventually entanglement breaking. Nonclassicality breaking under multiple composition of a single-mode bosonic Gaussian channel is also studied. We outline a family of single-mode bosonic Gaussian channels that are eventually entanglement breaking, but asymptotically nonclassicality saving. We illustrate examples of channels that are eventually nonclassicality breaking, asymptotically nonclassicality breaking, and asymptotically nonclassicality saving.

Quantum information processing relies on unitary transformations applied to specific qubits. In most cases, these gate operations are driven by alternating electromagnetic fields that are near resonant with specific transitions between eigenstates of the system Hamiltonian. For single-qubit gate operations, they should implement the operation on the target qubit, while all other qubits should be left invariant. It is typically assumed that this goal can be achieved if the amplitude of the control field is small compared to the frequency difference between the field and the transition frequency of the passive qubits. However, in many cases, even qubits whose energy-level differences are very far from the frequency of the applied control field can be affected by nonresonant effects, which are normally nonlinear in the amplitude of the control field. A typical example is the effect known as Bloch-Siegert shift. Unless these shifts are accounted for and, if possible, compensated, they can completely destroy the information contained in the quantum register. Therefore, we study this effect quantitatively in the important example of the nitrogen vacancy center in diamond and demonstrate how it can be eliminated.

Molecules with deep vibrational potential wells provide optical intervals sensitive to variation in the proton-electron mass ratio ($\mu$). On one hand, polar molecules are of interest since optical state preparation techniques have been demonstrated for such species. On the other hand, it might be assumed that polar species are unfavorable candidates, because typical molecule-frame dipole moments reduce vibrational state lifetimes and cause large polarizabilities and associated Stark shifts. Here, we consider single-photon spectroscopy on a vibrational overtone transition of the polar species ${\mathrm{TeH}}^{+}$, which is of practical interest because its diagonal Franck-Condon factors should allow rapid state preparation by optical pumping. We point out that all but the ground rotational state obtains a vanishing low-frequency scalar polarizability from coupling with adjacent rotational states, because of a fortuitous relationship between rigid rotor spacings and dipole matrix elements. We project that, for good choices of spectroscopy states, demonstrated levels of field control should make possible uncertainties of order $1\times {10}^{-18}$, similar to those of leading atomic ion clocks. If fast state preparation can be achieved, the moderately long-lived vibrational states of ${\mathrm{TeH}}^{+}$ make possible a frequency uncertainty approaching $1\times {10}^{-17}$ with one day of averaging for a single trapped ion. Observation over one year could probe for variation of $\mu$ with a sensitivity approaching the $1\times {10}^{-18}/\mathrm{yr}$ level.

Superexcited states of ${\mathrm{H}}_2\mathrm{S}$ have been investigated with determining the cross sections for emission of dispersed and nondispersed atomic fluorescence against the incident photon energy in the range 11–40 eV to address the ionization and excitation of the valence electrons. This method enables us to extract the discrete electronic state from the superposition with continuous electronic states. The cross sections for H($2p$) formation have been put on an absolute scale. Ten superexcited states have been found, two in the range 13–15 eV are singly excited $2b_2^{-1}$(mo) states with a single configuration and the other eight states in the range 16–25 eV are doubly excited states with multiple configurations. State-resolved dipole oscillator strengths for H($2p$) formation in the photoexcitation of ${\mathrm{H}}_2\mathrm{S}$ have been determined. Similar experiments have been performed for ${\mathrm{H}}_2\mathrm{O}$. The state-resolved dipole oscillator strengths for H($2p$) formation in the photoexcitation of ${\mathrm{H}}_2\mathrm{S}$ are $\sim {10}^{-3}$, whereas those in the photoexcitation of ${\mathrm{H}}_2\mathrm{O}$ range from $\sim {10}^{-3}$ to $\sim {10}^{-2}$. It is found that major fragment atoms are H($2p$) atoms in the photoexcitation of ${\mathrm{H}}_2\mathrm{O}$ and ${\mathrm{S}}^{*}$ in the photoexcitation of ${\mathrm{H}}_2\mathrm{S}$. The superexcited states of ${\mathrm{H}}_2\mathrm{O}$ and ${\mathrm{H}}_2\mathrm{S}$ are compared based on the similarity and difference of the electronic structures. It turns out from the comparison that (i) the smaller values of the dipole oscillator strengths for H($2p$) formation in the photoexcitation of ${\mathrm{H}}_2\mathrm{S}$ are related to the change of the major fragment atoms and (ii) the energy splitting of the doubly excited “$4a_1^{-1}\left({\text{mo}}^{\prime }\right)$” states of ${\mathrm{H}}_2\mathrm{S}$ is enhanced in comparison with that of the doubly excited “$2a_1^{-1}\left({\text{mo}}^{\prime }\right)$” states of ${\mathrm{H}}_2\mathrm{O}$. This enhancement is caused by the stronger electron correlation in ${\mathrm{H}}_2\mathrm{S}$ than in ${\mathrm{H}}_2\mathrm{O}$. The similarity in shape is indicated between the inner valence band and inner shell band in the fluorescence cross sections against the incident photon energy for ${\mathrm{H}}_2\mathrm{S}$ and ${\mathrm{H}}_2\mathrm{O}$.