This Brief Report gives the spectral distribution of the supercontinuum generated from a system of initially partially excited two-level atoms. The expansion in the eigenfunctions of the one-dimensional Liénard-Wiechert kernel which was successful in obtaining previously the results in the linear regime is generalized to the nonlinear regime. The detailed spectral distribution of the emitted radiation is computed without invoking either the phenomenological simplified physical model for the active medium or the mathematical approximations commonly used in treating propagation in absorbing media. The numerical solutions presented are those of the complete set of the coupled Maxwell-Bloch equations.

We demonstrate a fundamental principle of disturbance tradeoff for quantum measurements, along the lines of the celebrated uncertainty principle: The disturbances associated with measurements performed on distinct yet identically prepared ensembles of systems in a pure state cannot all be made arbitrarily small. Indeed, we show that the average of the disturbances associated with a set of projective measurements is strictly greater than zero whenever the associated observables do not have a common eigenvector. For such measurements, we show an equivalence between disturbance tradeoff measured in terms of fidelity and the entropic uncertainty tradeoff formulated in terms of the Tsallis entropy ($T_2$). We also investigate the disturbances associated with the class of nonprojective measurements, where the difference between the disturbance tradeoff and the uncertainty tradeoff manifests quite clearly.

In this paper, using the infinite time-evolving block decimation (iTEBD) algorithm and Bell-type inequalities, we investigate multipartite quantum nonlocality in an infinite one-dimensional quantum spin-$\frac{1}{2} XXZ$ system. High hierarchy of multipartite nonlocality can be observed in the gapless phase of the model, while only the lowest hierarchy of multipartite nonlocality is observed in most regions of the gapped antiferromagnetic phase. Thereby, Bell-type inequalities disclose different correlation structures in the two phases of the system. Furthermore, at the infinite-order quantum phase transition (QPT, or Kosterlitz-Thouless QPT) point of the model, the correlation measures always show a local minimum value, regardless of the length of the subchains. It indicates that relatively low hierarchy of multipartite nonlocality would be observed at the infinite-order QPT point in a Bell-type experiment. The result is in contrast to the existing results of the second-order QPT in the one-dimensional $XY$ model, where multipartite nonlocality with the highest hierarchy has been observed. Thus, multipartite nonlocality provides an alternative perspective to distinguish between these two kinds of QPTs. Reliable clues for the existence of tripartite quantum entanglement have also been found.

We consider parameter estimations with probes being the boundary-driven or dissipated nonequilibrium steady states of $XXZ$ spin-$1/2$ chains. The parameters to be estimated are the dissipation coupling and the anisotropy of the spin-spin interaction. In the weak-coupling regime we compute the scaling of the Fisher information, i.e., the inverse best sensitivity among all estimators, with the number of spins. We find superlinear scalings and transitions between the distinct isotropic and anisotropic phases. We also look at the best relative error, which decreases with the number of particles faster than the shot-noise only for the estimation of anisotropy.

Quantum teleportation is the transfer of quantum information between two locations by the use of shared entanglement. Current teleportation schemes broadly fall under one of two categories, either qubit or continuous-variable teleportation. Spin coherent states on spin ensembles can be teleported under the continuous-variable approximation for states with small deviations from a given polarization. However, for spin-coherent states with large deviations, no convenient teleportation protocol exists. Recently, we introduced a teleportation scheme where a spin-coherent state lying on the equator of the Bloch sphere is teleported between distant parties [A. N. Pyrkov and T. Byrnes, New J. Phys. 16, 073038 (2014)]. Here we generalize the protocol to a spin-coherent state with an arbitrary position on the Bloch sphere. Our proposed scheme breaks classical bounds based on communication in the unconditional case and quantum state estimation with postselection.

Following previous work, we distinguish between genuine $N$-partite entanglement and full $N$-partite inseparability. Accordingly, we derive criteria to detect genuine multipartite entanglement using continuous-variable (position and momentum) measurements. Our criteria are similar but different to those based on the van Loock–Furusawa inequalities, which detect full $N$-partite inseparability. We explain how the criteria can be used to detect the genuine $N$-partite entanglement of continuous variable states generated from squeezed and vacuum state inputs, including the continuous-variable Greenberger-Horne-Zeilinger state, with explicit predictions for up to $N=9$. This makes our work accessible to experiment. For $N=3$, we also present criteria for tripartite Einstein-Podolsky-Rosen (EPR) steering. These criteria provide a means to demonstrate a genuine three-party EPR paradox, in which any single party is steerable by the remaining two parties.

We study the fast transport of a particle or a Bose-Einstein condensate in a harmonic potential. An exact expression for the final excitation energy in terms of the Fourier transform of the trap acceleration is used to engineer optimal transport protocols (with no final excitation) that are robust with respect to spring-constant errors. The same technique provides a way to design the simultaneous and robust transport of a few noninteracting species that experience different harmonic trap frequencies in the same trap.

We perform an experimental study on comparison between the ionization of homonuclear diatomic molecules (${\mathrm{O}}_2$ and ${\mathrm{N}}_2$) and their companion atoms (Xe and Ar) radiated by circularly polarized intense laser fields. We find that the ionization of ${\mathrm{O}}_2$ shows suppression with respect to its companion atom Xe, which exhibits a clear wavelength and intensity dependence similar to that in linearly polarized laser field, while the ionization of ${\mathrm{N}}_2$ behaves like its companion atom Ar. With the help of $S$-matrix theoretical analysis, our observations can be attributed to both the molecular orbital and the two-center interference effect in molecular ionization process.

We compute the output of multimode cavity-enhanced spontaneous parametric down-conversion (SPDC) for subthreshold, but otherwise arbitrary, gain. We find analytic Bogoliubov transformations that allow us to calculate arbitrary field correlation functions, including the second-order intensity correlation function $G^{\left(2\right)}\left(T\right)$. The results show evidence of increased coherence due to stimulated SPDC. We extend an earlier model [Lu and Ou, Phys. Rev. A 62, 033804 (2000)] to arbitrary gain and finesse, and show the extension gives accurate results in most scenarios. The results will allow simple, analytic description of cavity-based nonclassical light sources for quantum networking, quantum-enhanced sensing of atoms, and generation of highly nonclassical field states.

The collective emission from a one-dimensional chain of interacting two-level atoms coupled to a common electromagnetic reservoir is investigated. We derive the system's dissipative few-excitation eigenstates, and analyze its static properties, including the collective dipole moments and branching ratios between different eigenstates. Next, we study the dynamics, and characterize the light emitted or scattered by such a system via different far-field observables. Throughout the analysis, we consider spontaneous emission from an excited state as well as two different pump-field setups, and contrast the two extreme cases of noninteracting and strongly interacting atoms. For the latter case, the two-excitation submanifold contains a two-body bound state, and we find that the two cases lead to different far-field signatures. Finally, we exploit these signatures to characterize the wave functions of the collective eigenstates. For this, we identify a direct relation between the collective branching ratio and the momentum distribution of the collective eigenstates' wave function. This provides a method to prove the existence of certain collective eigenstates and to access their wave function without the need to individually address and/or manipulate single atoms.

By using two-way frequency transfer, we implement a real-time frequency comparison over a uni-directional telecommunication network of 100 km using a pair of parallel fibers with simultaneous digital data transfer. The relative frequency stability is ${10}^{-15}$ at 1-s integration time and reaches $2\times {10}^{-17}$ at 40 000 s, three orders of magnitude below the one-way fiber instability. We also demonstrate ultrahigh-resolution comparison of optical frequencies with a bidirectional scheme using a single fiber. We show that the relative stability at 1-s integration time is $7\times {10}^{-18}$ and scales down to $5\times {10}^{-21}$. The same level of performance is reached when an optical link is implemented with an active compensation of the fiber noise. The fractional uncertainty of the frequency comparisons was evaluated for the best case to $2\times {10}^{-20}$. These results open the way to accurate and high-resolution frequency comparison of optical clocks over intercontinental fiber networks.

We show that, for general probabilistic theories admitting sharp measurements, the exclusivity principle together with two assumptions exactly singles out the Tsirelson bound of the Clauser-Horne-Shimony-Holt Bell inequality.

In the context of (far-field) multislit interferometry we investigate the utility of two formulations of uncertainty in accounting for the complementarity of spatial localization and fringe width. We begin with a characterization of the relevant observables and general considerations regarding the suitability of different types of measures. The detailed analysis shows that both of the discussed uncertainty formulations yield qualitatively similar results, confirming that they correctly capture the relevant tradeoff. One approach, based on an idea of Aharonov and co-workers, is intuitively appealing and relies on a modification of the Heisenberg uncertainty relation. The other approach, developed by Uffink and Hilgevoord for single- and double-slit experiments, is readily applied to multislits. However, it is found that one of the underlying concepts requires generalization and that the choice of the parameters requires more consideration than was known.

Heisenberg's uncertainty principle implies that if one party (Alice) prepares a system and randomly measures one of two incompatible observables, then another party (Bob) cannot perfectly predict the measurement outcomes. This implication assumes that Bob does not possess an additional system that is entangled to the measured one; indeed, the seminal paper of Einstein, Podolsky, and Rosen (EPR) showed that maximal entanglement allows Bob to perfectly win this guessing game. Although not in contradiction, the observations made by EPR and Heisenberg illustrate two extreme cases of the interplay between entanglement and uncertainty. On the one hand, no entanglement means that Bob's predictions must display some uncertainty. Yet on the other hand, maximal entanglement means that there is no more uncertainty at all. Here we follow an operational approach and give an exact relation—an equality—between the amount of uncertainty as measured by the guessing probability and the amount of entanglement as measured by the recoverable entanglement fidelity. From this equality, we deduce a simple criterion for witnessing bipartite entanglement and an entanglement monogamy equality.

Quantum key distribution (QKD) enables participants to exchange secret information over long distances with unconditional security. However, the performance of today's QKD systems is subject to hardware limitations, such as those of available nonclassical-light sources and single-photon detectors. By encoding photons in high-dimensional states, the rate of generating secure information under these technical constraints can be maximized. Here, we demonstrate a complete time-energy entanglement-based QKD system with proven security against the broad class of arbitrary collective attacks. The security of the system is based on nonlocal dispersion cancellation between two time-energy entangled photons. This resource-efficient QKD system is implemented at telecommunications wavelength, is suitable for optical fiber and free-space links, and is compatible with wavelength-division multiplexing.

Achieving individual qubit readout is a major challenge in the development of scalable superconducting quantum processors. We have implemented the multiplexed readout of a four transmon qubit circuit using nonlinear resonators operated as Josephson bifurcation amplifiers. We demonstrate the simultaneous measurement of Rabi oscillations of the four transmons. We find that multiplexed Josephson bifurcation is a high-fidelity readout method, the scalability of which is not limited by the need of a large-bandwidth, nearly quantum-limited amplifier as is the case with linear readout resonators.

Due to the experimental time constraints of state of the art quantum simulations, the direct preparation of the ground state by adiabatically ramping the field of a transverse-field Ising model becomes more and more difficult as the number of particles increase. We propose a spectroscopy protocol that intentionally creates excitations through diabatic ramping and measures a low-noise observable as a function of time for a constant Hamiltonian to reveal the structure of the coherent dynamics of the resulting many-body states. To simulate experimental data, noise from counting statistics and decoherence error are added. Compressive sensing is then applied to Fourier transform the simulated data into the frequency domain and extract the low-lying energy excitation spectrum. By using compressive sensing, the amount of data in time needed to extract this energy spectrum is sharply reduced, making such experiments feasible with current technology in, for example, ion trap quantum simulators.

We demonstrate the transfer of a single atom in a ring optical lattice with the aid of an auxiliary moving tweezer and investigate the influences on fidelity of the qubit encoded in the atom. When the tweezer has deeper trap depth and moves across the lattice, it is observed that an atom in one site follows the movement. The transfer efficiency of one atom to the destination site reaches up to 95%. This scheme is suitable for scalable quantum registers because of no influence on the other sites. We obtain atomic qubit fidelity during the transfer process by using quantum state tomography. Extracted fidelity indicates that the eigenstate is well preserved, while the superposition state is influenced. In combination with spin-echo measurement, dephasing mechanisms in this process are analyzed and discussed in detail. Loss of qubit fidelity is found to result from heating effects induced by this process and pointing instabilities of the trap laser. Our results pave the way for quantum computation with single atoms trapped in a scalable optical lattice.

The time-dependent nonlinear refractive index $n_4$ is calculated for a series of noble gases (helium, neon, krypton, and xenon) in the nonresonant regime using the coupled cluster singles and doubles method to account for electron correlation. Second-order polynomial fitting of dc Kerr ${\gamma }_{\lambda \mu \nu \rho }^{\left(2\right)}(-\omega ;\omega ,0,0)$, electric-field-induced second-harmonic generation ${\gamma }_{\lambda \mu \nu \rho }^{\left(2\right)}(-2\omega ;\omega ,\omega ,0)$, degenerate four-wave mixing (DFWM) ${\gamma }_{\lambda \mu \nu \rho }^{\left(2\right)}(-\omega ;\omega ,-\omega ,\omega )$, and static second-order hyperpolarizability ${\gamma }_{\lambda \mu \nu \rho }^{\left(2\right)}(0;0,0,0)$ is performed to obtain the corresponding fourth-order optical properties. An expression involving static, dc Kerr, DFWM fourth-order hyperpolarizability is employed to calculate the degenerate six-wave mixing ${\gamma }_{\lambda \mu \nu \rho \varphi \theta }^{\left(4\right)}(-\omega ;\omega ,-\omega ,\omega ,-\omega ,\omega )$ optical process. The calculated higher-order nonlinear refractive indices $n_4$ for He, Ne, Kr, and Xe atoms are positive over the wavelengths 250–2000 nm. The quartic nonlinear refractive index calculated for xenon is about four orders of magnitude larger than that for helium in the infrared regime.

In orbital-free density functional theory, only a Schrödinger-like equation has to be solved for the square root of the electron density. In this equation, however, there is an extra potential in addition to the Kohn-Sham potential, the so-called Pauli potential. Cusp relations are now presented for this Pauli potential for spherically symmetric systems.