We study a spin-boson chain that exhibits a local ${\mathbb{Z}}_2$ symmetry. We investigate the quantum phase diagram of the model by means of perturbation theory, mean-field theory, and the density matrix renormalization group method. Our calculations show the existence of a first-order phase transition in the region where the boson quantum dynamics is slow compared to the spin-spin interactions. Our model can be implemented with trapped-ion quantum simulators, leading to a realization of minimal models showing local gauge invariance and first-order phase transitions.

The recent observation of the dynamical Casimir effect in a modulated superconducting waveguide, culminating thirty years of worldwide research, empowered the quantum technology community with a tool to create entangled photons on chip. In this work we show how, going beyond the single waveguide paradigm using a scalable array, it is possible to create multipartite nonclassical states, with the possibility to control the long-range quantum correlations of the emitted photons. In particular, our finite-temperature theory shows how maximally entangled NOON states can be engineered in a realistic setup. The results presented here open the way to new kinds of quantum fluids of light, arising from modulated vacuum fluctuations in linear systems.

The Poynting vector in a singular optical field follows a helical path. Hence, it is the presence of a phase singularity that provides the circulating energy flow component to an optical field. These circulations in turn are responsible for the orbital angular momentum of light. This field when diffracted through an isosceles right triangular aperture generates straight line fringes in the far-field diffraction. We have addressed the modifications that happen to the energy circulations and the orbital angular momentum of light due to diffraction. Transverse components of the energy circulations in the diffracted field are studied by the Helmholtz-Hodge decomposition method. Interference experiments are presented to reveal the presence of phase singularities in the diffraction. This paper presents a complete analysis of the phase, phase gradient, and the intensity distributions in the diffraction pattern.

A novel quantum imaging technique has recently been demonstrated in an experiment, where the photon used for illuminating an object is not detected; the image is obtained by interfering two beams, none of which ever interacts with the object. Here we present a detailed theoretical analysis of the experiment. We show that the object information is present only in the interference term and not in the individual intensities of the interfering beams. We also theoretically establish that the magnification of the imaging system depends on two wavelengths: the average wavelength of the photon that illuminates the object and the average wavelength of the photon that is detected. Our analysis affirms that the imaging process is based on the principle that quantum interference occurs when interferometric path information is unavailable.

Spatiospectral properties of twin beams at their transition from low to high intensities are analyzed in parametric and paraxial approximations using decomposition into paired spatial and spectral modes. Intensity auto- and cross-correlation functions are determined and compared in the spectral and temporal domains as well as the transverse wave-vector and crystal output planes. Whereas the spectral, temporal, and transverse wave-vector coherence increases with the increasing pump intensity, coherence in the crystal output plane is almost independent of the pump intensity owing to the mode structure in this plane. The corresponding auto- and cross-correlation functions approach each other for larger pump intensities. The entanglement dimensionality of a twin beam is determined with a comparison of several approaches.

A Gaussian distribution of a quantum state with continuous spectra is known to maximize the Shannon entropy at a fixed variance. Applying it to a pair of canonically conjugate quantum observables $\widehat{x}$ and $\widehat{p}$, the quantum entropic uncertainty relation can take a suggestive form, where the standard deviations ${\sigma }_x$ and ${\sigma }_p$ are featured explicitly. From the construction of the entropic uncertainty relation, it follows in a transparent manner that (i) the entropic uncertainty relation implies the Kennard-Robertson uncertainty relation in a modified form, ${\sigma }_x{\sigma }_p\ge \hslash e^{\mathcal{N}}/2$; (ii) the additional factor $\mathcal{N}$ quantifies the quantum non-Gaussianity of the probability distributions of two observables; and (iii) the lower bound of the entropic uncertainty relation for a non-Gaussian continuous-variable (CV) mixed state becomes stronger with purity. The optimality of specific non-Gaussian CV states for the refined uncertainty relation has been investigated and the existence of a new class of CV quantum state is identified.

Recently some alternatives to the measurement-device-independent (MDI) quantum key distribution (QKD) based on the single-photon Bell-state measurement (SBSM) were proposed. Although these alternatives are not precisely as secure as the MDI QKD, they possess the advantage of a high key rate of the traditional BB84-like protocol and avoid the technical complexity of two-photon interference required in the MDI QKD. However, the setups of these proposed schemes are rather complicated compared to commonly used BB84 systems. Here we propose a simple implementation of SBSM-based QKD that is directly built on the existing realization of the BB84 QKD. Our proposal exhibits the hidden connection between the SBSM-based QKD and traditional phase-encoding QKD protocols. This finding discloses the physics behind these two different types of QKD protocols. In addition, we experimentally demonstrate the feasibility of our protocol.

We study a recently demonstrated design for a high-performance tunable coupler suitable for superconducting Xmon and planar transmon qubits [Y. Chen et al., Phys. Rev. Lett. 113, 220502 (2014)]. The coupler circuit uses a single flux-biased Josephson junction and acts as a tunable current divider. We calculate the effective qubit-qubit interaction Hamiltonian by treating the nonlinearity of the qubit and coupler junctions perturbatively. We find that the qubit nonlinearity has two principal effects: The first is to suppress the magnitude of the transverse ${\sigma }^x\otimes {\sigma }^x$ coupling from that obtained in the harmonic approximation by about 15%, assuming typical qubit parameters. The second is to induce a small diagonal ${\sigma }^z\otimes {\sigma }^z$ coupling. The effects of the coupler junction nonlinearity are negligible in the parameter regime considered. The approach used here can be applied to other complex nonlinear circuits arising in the design of superconducting hardware for quantum information processing.

We show how to reliably encode quantum information and send it between two arbitrary general-relativistic observers without a shared reference frame. Information stored in a quantum field will inevitably be destroyed by an unknown Bogoliubov transformation relating the observers. However, certain quantum correlations between different, independent fields will be preserved, no matter what transformation is applied. We show how to efficiently use these correlations in communication between arbitrary observers.

We derive quantum electrodynamics corrections to the fine structure in three-electron atomic systems at $m{\alpha }^6$ and $m{\alpha }^{7}ln\alpha$ orders and present their numerical evaluations for the Li atom and ${\mathrm{Be}}^{+}$ ion.

We measure photoelectron energy distributions from single ionization of xenon atoms by a linearly polarized laser pulse $(800\mathrm{nm},25\mathrm{fs})$ with successively varying the laser intensity within the region of $1.4-7.0\times {10}^{13}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$. By measuring the photoelectron energy shifted with the ponderomotive potential, we have calibrated the laser peak intensity precisely with an uncertainty less than $5\%$. Employing the quantum trajectory Monte Carlo theory, we simulate the photoelectron energy spectra with respect to the laser intensity. By comparison between the measurement and the simulation, we are able to identify resonant structures from photoelectron energy spectra in the low-energy region, which do not shift with the laser intensity. Inspecting the momentum distribution along the laser propagation axis, we have further shown that the quantum interference effect has a significant effect on the width of the momentum distribution perpendicular to the laser polarization direction beside the Coulomb focusing effect.

We consider a hybrid system consisting of a cavity optomechanical device with nonlinear quadratic radiation pressure coupled to an atomic ensemble. By considering the collective excitation, we show that this system supports nontrivial, nonlinear dark states. The coupling strength can be tuned via the lasers that ensure the population transfer adiabatically between the mechanical modes and the collective atomic excitations in a controlled way. In addition, we show how to detect the dark-state resonance by calculating the single-photon spectrum of the output fields and the transmission of the probe beam based on two-phonon optomechanically induced transparency. Possible application and extension of the dark states are also discussed.

Skolianos et al. [Phys. Rev. A 89, 033818 (2014)] recently published a derivation of the thermal phase noise in a Fabry-Pérot resonator. We point out that the thermally driven noise properties of an optical resonator can only be understood from the derivation of the signal-to-noise ratio and not from consideration of phase noise alone. The differences in expressions for the thermal phase noise given in the published literature (e.g., Ref. [5] of Skolianos et al. 2014) and those derived by Skolianos et al. [Phys. Rev. A 89, 033818 (2014)] arise only from differences in definition of optical phase and do not result in incorrect calculation of thermodynamically driven cavity length fluctuations.

The previous Comment clarifies a few key points that were unclear in an earlier paper by its authors, in particular their definitions of phase and of phase noise. We now agree that this earlier paper was modeling the resonance-frequency fluctuations of a Fabry-Perot resonator, whereas our article [Phys. Rev. A 89, 033818 (2014)] was modeling the noise in the phase of the resonator's output field. In light of the Comment, the two pictures are indeed consistent. The resonance-frequency fluctuations are independent of group index, whereas the phase noise in the output field is proportional to group index. This important dependence was pointed out in our paper [Phys. Rev. A 89, 033818 (2014)]. From a more physical standpoint, we argue that phase noise can be described without resorting to the concept of signal-to-noise ratio and that, although the phase noise is of course in part a property of the fiber itself, its group-index dependence is introduced solely by the resonator.

In this work we generalize the Bochner criterion addressing the characteristic function, i.e., the Fourier transform, of the Glauber-Sudarshan phase-space function. For this purpose we extend the Bochner theorem by including derivatives of the characteristic function. The resulting necessary and sufficient nonclassicality criteria unify previously known moment-based criteria with those based on the characteristic function. For applications of the generalized nonclassicality probes, we provide direct sampling formulas for balanced homodyne detection. A squeezed vacuum state is experimentally realized and characterized with our method. This complete framework—theoretical unification, sampling approach, and experimental implementation—presents an efficient toolbox to characterize quantum states of light for applications in quantum technology.

We study the detection capability of the weak-value amplification on the basis of the statistical hypothesis testing. We propose a reasonable testing method in the physical and statistical senses to find that the weak measurement with the large weak value has the advantage to increase the detection power and to reduce the possibility of missing the presence of interaction. We enhance the physical understanding of the weak value and mathematically establish the significance of the weak-value amplification. Our present work overcomes the critical dilemma of the weak-value amplification that the larger the amplification is, the smaller the number of data becomes, because the statistical hypothesis testing works even for a small number of data. This is contrasted with the parameter estimation by the weak-value amplification in the literature which requires a large number of data.

In 1952 Dyson put forward a simple and powerful argument indicating that the perturbative expansions of QED are asymptotic. His argument can be related to Chandrasekhar's limit on the mass of a star for stability against gravitational collapse. Combining these two arguments, we estimate the optimal number of terms of the QED series to be $3.1{\left(137\right)}^{3/2}\approx 5000$. For condensed-matter manifestations of QED in narrow-band-gap semiconductors and Weyl semimetals the optimal number of terms is around 80, while in graphene the utility of the perturbation theory is severely limited.

I theoretically investigate how the entanglement properties of a two-mode squeezed vacuum state (TMSVS) can be enhanced by operating quantum-optical catalysis on each mode of the TMSVS. The quantum-optical catalysis is simply mixing one photon at the beam splitter and post-select the beam-splitter (BS) output based on detection of one photon, first proposed by Lvovsky and Mlynek [Phys. Rev. Lett. 88, 250401 (2002)]. I find that there exists some enhancement in the entanglement properties (namely, entanglement entropy, second-order Einstein-Podolsky-Rosen correlation, and the fidelity of quantum teleportation) in certain parameter ranges spanned by the low transmissivities of the BSs and the small squeezing parameter of the input TMSVS.

Postulated by Pauli to explain the electronic structure of atoms and molecules, the exclusion principle establishes an upper bound of 1 for fermionic natural occupation numbers $\left\{n_i\right\}$. A recent analysis of the pure $N$-representability problem provides a wide set of inequalities for the $\left\{n_i\right\}$, leading to constraints on these numbers. This has a strong potential impact on reduced density matrix functional theory as we know it. In this work we continue our study of the nature of these inequalities for some atomic and molecular systems. The results indicate that (quasi)saturation of some of them leads to selection rules for the dominant configurations in configuration interaction expansions, in favorable cases providing means for significantly reducing their computational requirements.