We introduce a class of systems holding parity-time ($\mathcal{PT}$) symmetry locally, whereas being globally $\mathcal{P}$ symmetric. The potential, $U=U\left(\right|r\left|\right)$, fulfills $\mathcal{PT}$ symmetry with respect to periodically distributed points $r_0:U\left(\right|r_0+r\left|\right)=U^{*}\left(\right|r_0-r\left|\right)$ being $r_0\ne 0$. We show that such systems hold unusual properties arising from the merging of the two different symmetries, leading to a strong field localization and enhancement at the double-symmetry center, $r=0$, when the coupling of outward to inward propagating waves is favored. We explore such general potentials in one and two dimensions, which could have actual realizations combining gain-loss and index modulations in nanophotonic structures. In particular, we show how to render a broad aperture vertical-cavity surface-emitting laser into a bright and narrow beam source, as a direct application.

We present the exact analytical solution of the explicitly time-periodic quantum Langevin equation describing the dual-beam backaction-evading measurement of a single mechanical oscillator quadrature due to V. B. Braginsky, Y. I. Vorontsov, and K. S. Thorne [Science 209, 547 (1980)] beyond the commonly used rotating-wave approximation. We show that counterrotating terms lead to extra sidebands in the optical and mechanical spectra and to a modification of the main peak. Physically, the backaction of the measurement is due to periodic coupling of the mechanical resonator to a light-field quadrature that only contains cavity-filtered shot noise. Since this fact is independent of other degrees of freedom the resonator might be coupled to, our solution can be generalized, including to dissipatively or parametrically squeezed oscillators, as well as recent two-mode backaction-evading measurements.

We demonstrate the transfer of orbital angular momentum to an optically levitated microparticle in vacuum. The microparticle is placed within a Laguerre-Gaussian beam and orbits the annular beam profile with increasing angular velocity as the air drag coefficient is reduced. We explore the particle dynamics as a function of the topological charge of the levitating beam. Our results reveal that there is a fundamental limit to the orbital angular momentum that may be transferred to a trapped particle, dependent upon the beam parameters and inertial forces present.

We present an approach to study the interaction between matter and evanescent fields. The approach is based on the decomposition of evanescent plane waves into multipoles of well-defined angular-momentum transverse to both decay and propagation directions. We use the approach to identify the origin of the recently observed directional coupling of emitters into guided modes, and of the opposite Zeeman state excitation of atoms near a fiber. We explain how to rigorously quantify both effects and show that the directionality and the difference in excitation rates grow exponentially with the multipolar order of the light-matter interaction. We also use the approach to study and maximize the transverse torque exerted by an evanescent plane wave onto a given spherical absorbing particle. All the obtained physical insights can be traced back to the two main features of the decomposition of evanescent plane waves into transverse multipolar modes: A polarization independent exponential dominance of modes with large transverse angular momentum, and a polarization-controlled parity selection rule.

Simultaneous estimation of multiple parameters in quantum metrological models is complicated by factors relating to the (i) existence of a single probe state allowing for optimal sensitivity for all parameters of interest, (ii) existence of a single measurement optimally extracting information from the probe state on all the parameters, and (iii) statistical independence of the estimated parameters. We consider the situation when these concerns present no obstacle, and for every estimated parameter the variance obtained in the multiparameter scheme is equal to that of an optimal scheme for that parameter alone, assuming all other parameters are perfectly known. We call such models compatible. In establishing a rigorous theoretical framework for investigating compatibility, we clarify some ambiguities and inconsistencies present in the literature and discuss several examples to highlight interesting features of unitary and nonunitary parameter estimation, as well as deriving new bounds for physical problems of interest, such as the simultaneous estimation of phase and local dephasing.

We show that the closed-loop control obtained by feeding back the derivative of the signal from the homodyne measurement of one mode of the light exiting a two-mode optical cavity interacting with a mechanical resonator permits us to control and increase optical output entanglement. In particular, the proposed feedback-enhanced setup allows us to achieve a fidelity of coherent-state teleportation greater than the threshold value of 2/3 for secure teleportation and two-way steering between the two cavities' output modes down the line in the presence of loss, which otherwise would not be possible without feedback.

The dimension witness is an important concept in fundamental physics and quantum information processing which allows one to test the dimension of an unknown physical system in a device independent manner. Here, we report an experimental test of classical and quantum dimensions in a prepare and measure scenario through dimension witnesses based on quantum state discrimination. In our work, we have not only distinguished between quantum and classical systems of the same dimension (two, three, and four dimensions) but also distinguished between real and complex two-level quantum systems. We have also shown the strong link between dimension witnesses and quantum state discrimination which was introduced in N. Brunner, M. Navascués, and T. Vértesi [Phys. Rev. Lett. 110, 150501 (2013)].

The rigorous resource framework of quantum coherence has been set up recently and excited a wide variety of interests. Here we show that a quantum cavity optomechanical system, as an emerging platform, can behave with a certain value of quantum coherence at a macroscopic scale. We also find that the difference between the total optomechanical coherence and the sum of the optical and the mechanical coherence just equals their mutual information. Motivated by the detection of the optomechanical entanglement, an experimentally feasible scheme to probe the optomechanical coherence is proposed.

We present a necessary condition for two sets of maximally entangled states to be locally equivalent in terms of local invariants. With the help of these invariants, first, we are able to completely classify all the distinguishable and indistinguishable sets of four generalized Bell states in the $4\otimes 4$ quantum system: there are ten inequivalent classes including three locally indistinguishable and seven locally distinguishable quadruples. All distinguishable quadruples in this case can be distinguished by using only one-way classical communication, implying that the two-way classical communication has no advantage over one-way classical communication, similar to the case of qubit lattice states. Second, we are able to completely classify all the triplets of generalized Bell states in the quantum systems of all prime dimensions as well as in some composite dimensions.

Using a simplified one-dimensional model of a diatomic molecule, the associated interacting density and corresponding Kohn-Sham (KS) potential have been obtained analytically for all fractional molecule occupancies $N$ between 0 and 2. For the homonuclear case, and in the dissociation limit, the exact Kohn-Sham potential builds a barrier at the midpoint between the two atoms, whose strength increases linearly with $N$, with $1<N\le 2$. In the heteronuclear case, the dissociating KS potential besides the barrier also exhibits a plateau around the atom with the higher ionization potential, whose size (but not its strength) depends on $N$. An anomalous zero-order scaling of the Kohn-Sham potential with regards to the strength of the electron-electron repulsion is clearly displayed by our model; without this property both the unusual barrier and the plateau features will be absent.

In the intramolecular scattering process, the interference between the rescattered electron waves emanating from each atomic center gives rise to additional oscillations superimposed on the Young-type oscillatory structure in the observed electron intensity. Here we explore numerically this behavior for coherent electron emission from the dimer ${{\mathrm{Rb}}_2}^{+}$ by fast-moving highly charged ions, which is achieved by solving the two-dimensional time-dependent Schrödinger equation. Well-defined modulations with higher frequency are observed in the momentum distribution of the ejected electron, which are well reproduced by additional quantitative calculations based on the third-order Born series. This demonstrates without ambiguity the dynamic interference induced by multiple scattering paths of the electron prior to emission. Furthermore, the dependence of the phenomenon on the emission direction of the electron and the orientation of the molecular axis also is investigated. The phenomenon is not specific to ${{\mathrm{Rb}}_2}^{+}$ as investigated in the present study, but is broadly applicable to other systems with sufficiently large internuclear distances, thus opening new prospects for the investigation of electron emission process from large systems.

We present a comprehensive theoretical and computational study on harmonic generation (HG) of Li atoms in one- and two-photon Rabi-flopping regimes where the population transfer from the ground $2s$ state to the excited $2p$, $3s$, and $3d$ states is substantial. Our all-electron approach is based on the time-dependent density-functional theory and takes into account the polarization of the core and the dynamic response of the electrons to the laser field. We show that the population oscillations in the time domain with the Rabi frequency $\mathrm{\Omega }$ are reflected in the fine structure of the HG spectra in the frequency domain on the scale of $2\mathrm{\Omega }$. Our results also manifest that even finer structures of the harmonic peaks on the smaller frequency scale originate from the pulse-shape-related interference effects. These features are clearly seen in one-photon Rabi-flopping regime between the $2s$ and $2p$ states. The pattern in the HG spectra becomes more complex in the two-photon Rabi-flopping regime involving $3s$ and $3d$ states. Our findings can be used for developing coherent control methods for HG in the Rabi-flopping regime.

We investigate the equilibrium phase-coherence properties of Bose-condensed particle systems, focusing on their shape dependence and finite-size scaling (FSS). We consider three-dimensional (3D) homogeneous systems confined to anisotropic $L\times L\times L_a$ boxes, below the Bose-Einstein-condensate (BEC) transition temperature $T_c$. We show that the phase correlations develop peculiar anisotropic FSS for any $T<T_c$, in the large-$L$ limit keeping the ratio $\lambda \equiv L_a/L^2$ and the particle density fixed. This phenomenon is effectively described by the 3D spin-wave theory. Its universality is confirmed by quantum Monte Carlo simulations of the 3D Bose-Hubbard model in the BEC phase. The phase-coherence correlations of very elongated BEC systems, $\lambda \to \infty$, are characterized by the coherence length ${\xi }_a\sim A_t{\rho }_s/T$, where $A_t$ is the transverse area and ${\rho }_s$ is the superfluid density.

We present a method to identify the coupled, normal modes of a superconducting transmission line with an embedded lumped element circuit. We evaluate the effective transmission-line nonlinearities in the case of Kerr-like Josephson interactions in the circuit and in the case where the embedded circuit constitutes a qubit degree of freedom, which is Rabi coupled to the field in the transmission line. Our theory quantitatively accounts for the very high and positive Kerr nonlinearities observed in a recent experiment [M. Rehák, P. Neilinger, M. Grajcar, G. Oelsner, U. Hübner, E. Il'ichev, and H.-G. Meyer, Appl. Phys. Lett. 104, 162604 (2014)], and we can evaluate the accomplishments of modified versions of the experimental circuit.

Molecular vibrational transitions are prime candidates for model-independent searches for variation of the proton-to-electron mass ratio. Searches for present-day variation achieve the highest sensitivity with deep molecular potentials. We identify several high-sensitivity transitions in the deeply bound ${\mathrm{O}}_2{}^{+}$ molecular ion. These transitions are electric-dipole forbidden and have narrow linewidths. The most sensitive transitions take advantage of an accidental degeneracy between vibrational states in different electronic potentials. We suggest experimentally feasible routes to a measurement with uncertainty below current limits on present-day variation in $m_p/m_e$.

In the year 2013, Danan et al. published a paper [Phys. Rev. Lett. 111, 240402 (2013)] demonstrating a counterintuitive behavior of photons in nested Mach–Zehnder interferometers. The authors then proposed an explanation based on the two-state vector formalism. This experiment and the authors' explanation raised a vivid debate within the scientific community. In this paper, we contribute to the ongoing debate by presenting an alternative experimental implementation of the Danan et al. scheme. We show that no counterintuitive behavior is observed when performing direct spectrally resolved detection.

Due to the axioms of quantum mechanics, perfect cloning of an unknown quantum state is impossible. But since imperfect cloning is still possible, a question arises: “Is there an optimal quantum cloning machine?” Buzek and Hillery answered this question and constructed their famous B-H quantum cloning machine. The B-H machine clones the state of an arbitrary single qubit in an optimal manner and hence it is universal. Generalizing this machine for a two-qubit system is straightforward, but during this procedure, except for product states, this machine loses its universality and becomes a state-dependent cloning machine. In this paper, we propose some classes of optimal universal local quantum state cloners for a particular class of two-qubit systems, more precisely, for a class of states with known Schmidt basis. We then extend our machine to the case that the Schmidt basis of the input state is deviated from the local computational basis of the machine. We show that more local quantum coherence existing in the input state corresponds to less fidelity between the input and output states. Also we present two classes of a state-dependent local quantum copying machine. Furthermore, we investigate local broadcasting of two aspects of quantum correlations, i.e., quantum entanglement and quantum discord, defined, respectively, within the entanglement-separability paradigm and from an information-theoretic perspective. The results show that although quantum correlation is, in general, very fragile during the broadcasting procedure, quantum discord is broadcasted more robustly than quantum entanglement.

Nonadiabatic holonomic quantum computation provides the means to perform fast and robust quantum gates by utilizing the resilience of non-Abelian geometric phases to fluctuations of the path in state space. While the original scheme [E. Sjöqvist et al., New J. Phys. 14, 103035 (2012)] needs two loops in the Grassmann manifold (i.e., the space of computational subspaces of the full state space) to generate an arbitrary holonomic one-qubit gate, we propose single-loop one-qubit gates that constitute an efficient universal set of holonomic gates when combined with an entangling holonomic two-qubit gate. Our one-qubit gate is realized by dividing the loop into path segments, each of which is generated by a $\mathrm{\Lambda }$-type Hamiltonian. We demonstrate that two path segments are sufficient to realize arbitrary single-loop holonomic one-qubit gates. We describe how our scheme can be implemented experimentally in a generic atomic system exhibiting a three-level $\mathrm{\Lambda }$-coupling structure by utilizing carefully chosen laser pulses.