We investigate a unique type of zero-index medium with both gain and loss (ZIMGL), whose effective permittivity and permeability are both purely imaginary but of opposite signs. We analytically show that, by using a slab of ZIMGL with equal magnitude of loss and gain, simulation realization of a coherent perfect absorber (CPA) and laser, i.e., the so-called CPA laser, can be achieved. Previously the CPA laser was proposed in parity-time ($PT$) symmetric systems. However, the ZIMGL does not possess the $PT$ symmetry and thus the underlying physics is distinctly different. By designing a photonic crystal (PC) composed of core-shell rods, with loss and gain distributed in either the core or the shell, we have realized such a ZIMGL. The CPA-laser functionality of such a PC is also confirmed in our numerical simulations. Our work provides a different approach for simultaneous realization of CPA and laser besides $PT$-symmetric systems.

Two-photon interference and Hong-Ou-Mandel (HOM) effect are relevant tools for quantum metrology and quantum information processing. In optical coherence tomography, the HOM effect is exploited to achieve high-resolution measurements with the width of the HOM dip being the main parameter. On the other hand, applications like dense coding require high-visibility performance. Here we address high-order dispersion effects in two-photon interference and study, theoretically and experimentally, the dependence of the visibility and the width of the HOM dip on both the pump spectrum and the downconverted photon spectrum. In particular, a spatial light modulator is exploited to experimentally introduce and manipulate a custom phase function to simulate the high-order dispersion effects. Overall, we show that it is possible to effectively introduce high-order dispersion effects on the propagation of photons and also to compensate for such effect. Our results clarify the role of the different dispersion phenomena and pave the way for optimization procedures in quantum technological applications involving PDC photons and optical fibers.

We show that self-organization and synchronization underlie Kerr-cavity-soliton formation in parametric frequency combs. By reducing the Lugiato-Lefever equation to a set of phase equations, we find that self-organization arises from a two-stage process via pump-degenerate and pump-nondegenerate four-wave mixing. The reduced phase equations are akin to the Kuramoto model of coupled oscillators and intuitively explain the origin of the pump phase offset, predict antisymmetrization of the intracavity field before phase synchronization, and clarify the role of chaos in Kerr-cavity-soliton formation in parametric combs.

We propose a compact, fiber-integrated architecture for photon-pair generation by parametric downconversion with unprecedented flexibility in the properties of the photons produced. Our approach is based on a thin-film lithium niobate nanowaveguide, evanescently coupled to a tapered silica microfiber. We demonstrate how controllable mode hybridization between the fiber and waveguide yields control over the joint spectrum of the photon pairs. We also investigate how independent engineering of the linear and nonlinear properties of the structure can be achieved through the addition of a tapered, proton-exchanged layer to the waveguide. This allows further refinement of the joint spectrum through custom profiling of the effective nonlinearity, drastically improving the purity of the heralded photons. We give details of a source design capable of generating heralded single photons in the telecom wavelength range with purity of at least 0.95, and we provide a feasible fabrication methodology.

The structural relation between multipartite entanglement and symmetry is one of the central mysteries of quantum mechanics. In this paper, we study the separability of quantum states in the bosonic system. We show that a mixture of multiqubit Dicke states is separable if and only if its partial transpose is positive semidefinite, which confirms the hypothesis of Wolfe and Yelin [E. Wolfe and S. F. Yelin, Phys. Rev. Lett. 112, 140402 (2014)]. We generalize this result to a class of bosonic states in the $d\otimes d$ system; and for general $d$, we determine its separability is NP-hard although verifiable conditions for separability are easily derived when $d=3,4$.

We show that the decoherence of the atomic center-of-mass induced by spontaneous emission involves interferences corresponding to a single-atom analog of superradiance. We use a decomposition of the stationary decoherence rate as a sum of local and nonlocal contributions obtained to second order in the interaction by the influence functional method. These terms are respectively related to the strength of the coupling between system and environment, and to the quality of the information about the system leaking into the environment. While the local contribution always yields a positive decoherence rate, the nonlocal one may lead to recoherence when only partial information about the system is obtained from the disturbed environment. The nonlocal contribution contains interferences between different quantum amplitudes leading to oscillations of the decoherence rate reminiscent of superradiance. These concepts, illustrated here in the framework of atom interferometry within a trap, may be applied to a variety of quantum systems.

We study the universal relations and normal-phase thermodynamics of a two-component ultracold Fermi gas with coexisting $s$- and $p$-wave interactions. Due to the orthogonality of two-body wave functions of different scattering channels, the universal thermodynamic relations of the system appear to be direct summations of contributions from each partial-wave scattering channel. These universal relations are dictated by a set of contacts, which can be associated with either $s$- or $p$-wave interactions. Interestingly, due to the interplay of $s$- and $p$-wave interactions on the many-body level, the contacts, and hence all the relevant thermodynamic quantities, behave differently from those with only $s$- or $p$-wave interactions. These are manifest in our numerical calculations based on second-order virial expansions for ${}^{40}\mathrm{K}$ atoms under typical experimental parameters. A particularly interesting finding is that, due to the coexistence of $s$- and $p$-wave scatterings, the interaction energy of the repulsive branch features abrupt changes across the $p$-wave resonances. Our results can be readily checked experimentally for ${}^{40}\mathrm{K}$ atoms near the $198\mathrm{G}p$-wave Feshbach resonance, where multiple partial-wave scatterings naturally coexist.

We investigate the real-time evolution of lattice bosons in two spatial dimensions whose dynamics is governed by a Markovian quantum master equation. We employ the Wigner-Weyl phase space quantization and derive the functional integral for open quantum many-body systems that determines the time evolution of the Wigner function. Using the truncated Wigner approximation, in which quantum fluctuations are only taken into account in the initial state whereas the dynamics is governed by classical evolution equations, we study the buildup of long-range correlations due to the action of non-Hermitean quantum jump operators that constitute a mechanism for dissipative cooling. Starting from an initially disordered state corresponding to a vortex condensate, the dissipative process results in the annihilation of vortex-antivortex pairs and the establishment of quasi-long-range order at late times. We observe that a finite vortex density survives the cooling process, which disagrees with the analytically constructed vortex-free Bose-Einstein condensate at asymptotic times. This indicates that quantum fluctuations beyond the truncated Wigner approximation need to be included to fully capture the physics of dissipative Bose-Einstein condensation.

We study an impurity atom trapped by an anharmonic potential, immersed within a cold atomic Fermi gas with attractive interactions that realizes the crossover from a Bardeen-Cooper-Schrieffer superfluid to a Bose-Einstein condensate. Considering the qubit comprising the lowest two vibrational energy eigenstates of the impurity, we demonstrate that its dynamics probes the equilibrium density fluctuations encoded in the dynamic structure factor of the superfluid. Observing the impurity's evolution is thus shown to facilitate nondestructive measurements of the superfluid order parameter and the contact between collective and single-particle excitation spectra. Our setup constitutes a model of an open quantum system interacting with a thermal reservoir, the latter supporting both bosonic and fermionic excitations that are also coupled to each other.

We report on the storage of light via the phenomenon of recoil-induced resonance in a pure two-level system of cold cesium atoms. We use a strong coupling beam and a weak probe beam to couple different external momentum states of the cesium atom via two-photon Raman interaction which leads to the storage of the optical information of the probe beam. We have also measured the probe transmission spectrum, as well as the light storage spectrum which reveals very narrow subnatural resonance features showing absorption and gain. We have demonstrated that this memory presents the unique property of being insensitive to the reading process, which does not destroy the stored information leading to a memory lifetime limited only by the atomic thermal motion.

With an increasing coupling between light and mechanics, nonlinearities begin to play an important role in optomechanics. We solve the quantum dynamics of an optomechanical system in the multiphoton strong-coupling regime retaining nonlinear terms. This is achieved by performing a Schrieffer-Wolff transformation on the Hamiltonian including driving terms. The approach is valid away from the red- and blue-sideband drive. We show that the mechanical resonator displays self-sustained oscillations in regimes where the linear model predicts instabilities and that the amplitude of these oscillations is limited by the nonlinear terms. Related oscillations of the photon number are present due to frequency mixing of the shifted mechanical and cavity frequencies. This leads to additional peaks in the cavity's spectral density. Furthermore, we show that it is possible to create phonon states with sub-Poissonian statistics when the system is red detuned. This result is valid even with strong driving and with initial coherent states.

We consider soliton propagation in two parallel optical waveguides, in the presence of a linear nondispersive coupling and in the few-cycle regime. The numerical analysis is based on a set of two coupled modified Korteweg–de Vries equations. The evidenced few-cycle vector solitons are optical breathers. In addition to the usual breathing due to carrier-envelope velocity mismatch, we observe, and describe in detail, spatial oscillations of soliton's amplitude and energy.

The problem of constructing physically and mathematically well-defined Wigner functions for the canonical pair angle $\theta$ and angular momentum $p$ is solved. While a key element for the construction of Wigner functions for the planar phase space $\{(q,p)\in {\mathbb{R}}^2\}$ is the Heisenberg-Weyl group, the corresponding group for the cylindrical phase space $\{(\theta ,p)\in S^1\times \mathbb{R}\}$ is the Euclidean group $E\left(2\right)$ of the plane and its unitary representations. Here the angle $\theta$ is replaced by the pair $(cos\theta ,sin\theta )$, which corresponds uniquely to the points on the unit circle. The main structural properties of the Wigner functions for the planar and the cylindrical phase spaces are strikingly similar. A crucial role is played by the $sinc$ function, which provides the interpolation for the discontinuous quantized angular momenta in terms of the continuous classical ones, in accordance with the famous Whittaker cardinal function well known from interpolation and sampling theories. The quantum mechanical marginal distributions for the angle (continuous) and angular momentum (discontinuous) are, as usual, uniquely obtained by appropriate integrations of the $(\theta ,p)$ Wigner function. Among the examples discussed is an elementary system of simple cat states.

Quantum teleportation (QT) is a fundamentally remarkable communication protocol that also finds many important applications for quantum informatics. Given a quantum entangled resource, it is crucial to know to what extent one can accomplish the QT. This is usually assessed in terms of output fidelity, which can also be regarded as an operational measure of entanglement. In the case of multipartite communication when each communicator possesses a part of an $N$-partite entangled state, not all pairs of communicators can achieve a high fidelity due to the monogamy property of quantum entanglement. We here investigate how such a monogamy relation arises in multipartite continuous-variable (CV) teleportation, particularly when using a Gaussian entangled state. We show a strict monogamy relation, i.e., a sender cannot achieve a fidelity higher than optimal cloning limit with more than one receiver. While this seems rather natural owing to the no-cloning theorem, a strict monogamy relation still holds even if the sender is allowed to individually manipulate the reduced state in collaboration with each receiver to improve fidelity. The local operations are further extended to non-Gaussian operations such as photon subtraction and addition, and we demonstrate that the Gaussian cloning bound cannot be beaten by more than one pair of communicators. Furthermore, we investigate a quantitative form of monogamy relation in terms of teleportation capability, for which we show that a faithful monogamy inequality does not exist.

We analyze the entanglement properties for the not-completely-permutation-symmetric states of quantum systems composed of two subsystems with an equal but arbitrary finite local Hilbert space dimension. We investigate both pure and mixed states with such a symmetry obtained by relaxing the symmetry requirement of the axisymmetric states. For such states we discuss the entanglement classification with respect to stochastic local operations and classical communication and establish the entanglement quantitatively by means of concurrence and negativity. In particular, we determine the separability criterion in the frame of various methods, including the $k$-positive map witness, optimal Schmidt-number witnesses, and entanglement measures.

We present a precise calculation of the Lamb shift $(2P_{1/2}-2S_{1/2})$ in muonic ions ${\left({\mu }_3^6\text{Li}\right)}^{2+},{\left({\mu }_3^7\text{Li}\right)}^{2+}, {\left({\mu }_4^9\text{Be}\right)}^{3+},{\left({\mu }_4^{10}\text{Be}\right)}^{3+}, {\left({\mu }_5^{10}\text{B}\right)}^{4+},{\left({\mu }_5^{11}\text{B}\right)}^{4+}$. The contributions of orders ${\alpha }^3÷{\alpha }^6$ to the vacuum polarization, nuclear structure and recoil, and relativistic effects are taken into account. Our numerical results are consistent with previous calculations and improved by additional corrections. The obtained results can be used for the comparison with future experimental data, and extraction more accurate values of nuclear charge radii.

The electronic structure of the diatomic VO anion was explored by combining the photoelectron-imaging spectroscopy and high-level theoretical calculations. The electron affinity (EA) of VO is determined to be 1.244 ± 0.025 eV from the vibrationally resolved photoelectron spectrum acquired at 532 nm. The anisotropy parameter (β) for the EA defined peak is measured to be 1.59 ± 0.02, indicating that it is the 9σ electron attachment leading to the formation of the ground state of $\mathrm{V}{\mathrm{O}}^{-}$. The present imaging experiment provides direct evidence that the ground state of $\mathrm{V}{\mathrm{O}}^{-}$ is $X{}^3{\mathrm{\Sigma }}^{-}$ with a ${\left(3\pi \right)}^4{\left(8\sigma \right)}^2{\left(9\sigma \right)}^2{\left(1\delta \right)}^2$ electron configuration, which resolves the significant discrepancy in previous experiment and theory. In addition, the molecular orbitals and bonding involved in the anionic VO cluster are also examined based on the present high-level theoretical calculations.

We report the frequency measurements of the $2{}^{3}P\to 3{}^{3}D$ transitions in ${}^{3,4}\mathrm{He}$ at 588 nm using an optical frequency comb stabilized laser system. The Doppler-free spectra of the $2{}^{3}P\to 3{}^{3}D$ transitions are demonstrated in an rf discharged sealed-off helium cell using intermodulated fluorescence spectroscopy. The measured absolute frequency of the ${}^4\mathrm{He}2{{}^{3}P}_0\to 3{{}^{3}D}_1$ transition is 510 059 755.352(28) MHz, which is more precise than the previous measurement by two orders of magnitude. The ionization energies of the ${}^4\mathrm{He}2{{}^{3}P}_0$ and $2{{}^{3}S}_1$ states can be derived from our result and agree very well with the previous experimental values. More importantly, the Lamb shift of the $2{{}^{3}S}_1$ state can be deduced to be 4057.086(34) MHz, which is two times more precise than the previous result. In addition, the absolute frequencies of the $2{{}^{3}P}_{0,1/2}\to 3{{}^{3}D}_{1,3/2}, 2{{}^{3}P}_{0,1/2}\to 3{{}^{3}D}_{1,1/2}$, and $2{{}^{3}P}_{0,1/2}\to 3{{}^{3}D}_{2,3/2}$ transitions in ${}^3\mathrm{He}$ are measured. Our precision surpasses the theoretical calculations by more than one to two orders of magnitude. The hyperfine separations of the $3{}^{3}D$ states in ${}^3\mathrm{He}$ and the frequency differences between ${}^4\mathrm{He}$ and ${}^3\mathrm{He}$ transitions are also presented.

The internal degrees of freedom provided by ultracold atoms provide a route for realizing higher dimensional physics in systems with limited spatial dimensions. Nonspatial degrees of freedom in these systems are dubbed “synthetic dimensions.” This connection is useful from an experimental standpoint but complicated by the fact that interactions alter the condensate ground state. Here we use the Gross-Pitaevskii equation to study the ground-state properties of a spin-1 Bose gas under the combined influence of an optical lattice, spatially varying spin-orbit coupling, and interactions at the mean-field level. The associated phases depend on the sign of the spin-dependent interaction parameter and the strength of the spin-orbit field. We find “charge”- and spin-density-wave phases which are directly related to helical spin order in real space and affect the behavior of edge currents in the synthetic dimension. We determine the resulting phase diagram as a function of the spin-orbit coupling and spin-dependent interaction strength, considering both attractive (ferromagnetic) and repulsive (polar) spin-dependent interactions, and we provide a direct comparison of our results with the noninteracting case. Our findings are applicable to current and future experiments, specifically with ${}^{87}\mathrm{Rb}, {}^7\mathrm{Li}, {}^{41}\mathrm{K}$, and ${}^{23}\mathrm{Na}$.