We study dark solitons near potential and nonlinearity steps and combinations thereof, forming rectangular barriers. This setting is relevant to the contexts of atomic Bose-Einstein condensates (where such steps can be realized by using proper external fields) and nonlinear optics (for beam propagation near interfaces separating optical media of different refractive indices). We use perturbation theory to develop an equivalent particle theory, describing the matter-wave or optical soliton dynamics as the motion of a particle in an effective potential. This Newtonian dynamical problem provides information for the soliton statics and dynamics, including scenarios of reflection, transmission, or quasitrapping at such steps. The case of multiple such steps and its connection to barrier potentials is additionally touched upon. The range of validity of the analytical approximation and radiation effects are also investigated. Our analytical predictions are found to be in very good agreement with the corresponding numerical results, where appropriate.

An optical frequency comb generated with an electro-optic phase modulator and a chirped radio-frequency waveform is used to perform pump-probe spectroscopy on the $D_1$ and $D_2$ transitions of atomic potassium at 770.1 and 766.7 nm, respectively. With a comb tooth spacing of 200 kHz and an optical bandwidth of 2 GHz the hyperfine transitions can be observed simultaneously. Interferograms are recorded in as little as 5 µs (a timescale corresponding to the inverse of the comb tooth spacing). Importantly, the sub-Doppler features can be measured as long as the laser carrier frequency lies within the Doppler profile, thus removing the need for slow scanning or a priori knowledge of the frequencies of the sub-Doppler features. Sub-Doppler optical frequency comb spectroscopy has the potential to dramatically reduce acquisition times and allow for rapid and accurate assignment of complex molecular and atomic spectra which are presently intractable.

Quantum state estimation aims at determining the quantum state from observed data. Estimating the full state can require considerable efforts, but one is often only interested in a few properties of the state, such as the fidelity with a target state, or the degree of correlation for a specified bipartite structure. Rather than first estimating the state, one can, and should, estimate those quantities of interest directly from the data. We propose the use of optimal error intervals as a meaningful way of stating the accuracy of the estimated property values. Optimal error intervals are analogs of the optimal error regions for state estimation [New J. Phys. 15, 123026 (2013)]. They are optimal in two ways: They have the largest likelihood for the observed data and the prechosen size, and they are the smallest for the prechosen probability of containing the true value. As in the state situation, such optimal error intervals admit a simple description in terms of the marginal likelihood for the data for the properties of interest. Here, we present the concept and construction of optimal error intervals, report on an iterative algorithm for reliable computation of the marginal likelihood (a quantity difficult to calculate reliably), explain how plausible intervals—a notion of evidence provided by the data—are related to our optimal error intervals, and illustrate our methods with single-qubit and two-qubit examples.

Fusion technique plays a key role in the preparation of large-scale $W$ states, but the currently existing fusion schemes are suffering from the qubit loss problem, i.e., the number of the output entangled qubits is smaller than the sum of numbers of the input entangled qubits, which will inevitably decrease the fusion efficiency and increase the number of fusion steps as well as the requirement of quantum memories. In this paper, we design a fusion mechanism to fuse two small-size $W$ states into a large-scale $W$ state without qubit loss, and thus we call it qubit-loss-free (QLF) fusion mechanism. This QLF fusion mechanism is based on a two-outcome positive-operator valued measurement on two qubits extracting from two small-size $W$ states, and works for both pure and mixed $W$ states. The QLF nature of this fusion mechanism clearly increases the final size of the obtained $W$ state, and greatly reduces the number of fusion steps as well as the requirement of quantum memories required to achieve a $W$ state of a target size, so it is more efficient and feasible than the currently existing fusion schemes. There is no complete failure output in our QLF fusion scheme, and all the garbage states are recyclable. Two example schemes are proposed to realize this QLF fusion mechanism in a cavity quantum electrodynamics system and three-qubit Heisenberg XYZ model, respectively, which demonstrates the possibility of the physical realization of this QLF fusion mechanism.

We investigate a system of dipolar bosons in an optical lattice with local two- and three-body interactions. Using the mean-field-theory approach, we obtain the ground-state phase diagram of the extended Bose-Hubbard model with both repulsive and attractive three-body interactions. We show that the additional three-body on-site interaction has strong effects on the phase diagram, especially on the supersolid phase. Positive values of the three-body interaction lead to the enhancement of the gapped phases at densities larger than unity by reducing the supersolid region. However, a small attractive three-body interaction enhances the supersolid phase.

Graphene and boron nitride are two-dimensional materials whose atoms are arranged in a honeycomb lattice. Their unique properties arise because their electrons behave like relativistic particles (without and with mass, respectively)—namely, they obey the Dirac equation. Here, we use a photonic analog of boron nitride to observe Dirac physics in a silicon integrated optical platform. This will allow for photonic applications of Dirac dispersions (gapped and ungapped) to be realized in an on-chip, integrated nanophotonic platform.

It is well known that in quantum mechanics a weak scatterer can act as a perfect reflector provided it oscillates at a specific frequency, which is close to that of the incident particles. This is a Fano resonance, in which case the propagating wave mode destructively interferes with the bound state. Due to the high frequencies of the optical domain, it is not possible to design an optical device, which is based on this effect. However, if the beam propagates in a narrow waveguide with conducting boundaries, then even a weak dielectric scatterer, which oscillates at the frequency difference between the optical frequency and the threshold frequency of the waveguide, can block the optical beam. This frequency difference can be arbitrarily small. A model for such a system is presented and solved exactly numerically without approximations. For a weak scatterer an approximate analytical expression is suggested for the point of perfect reflection. Finally, a physical realization is suggested. This effect can be used for controlling optical beams by submicron devices.

We propose how topologically nontrivial states can dynamically organize in a fermionic quantum gas that is confined to a two-dimensional optical lattice potential and coupled to the field of an optical cavity. The spontaneously emerging cavity field induces, together with coherent pump laser fields, a dynamical gauge field for the atoms. Upon adiabatic elimination of the cavity degree of freedom, the system is described by an effective Hofstadter model with a self-consistency condition that determines the tunneling amplitude along the cavity direction. The fermions are found to self-organize into topologically nontrivial states that carry an extended edge state for a finite system size. Due to the dissipative nature of the cavity field, the topological steady states are protected from external perturbations.

In bipartite quantum systems, entanglement correlations between the parties exerts direct influence in the phenomenon of wave-particle duality. This effect has been quantitatively analyzed in the context of two qubits by Jakob and Bergou [Opt. Commun. 283, 827 (2010)]. Employing a description of the $K$-meson propagation in free space where its weak decay states are included as a second party, we study here this effect in the kaon-antikaon oscillations. We show that a new quantitative “triality” relation holds, similar to the one considered by Jakob and Bergou. In our case, it relates the distinguishability between the decay-product states corresponding to the distinct kaon propagation modes $K_S, K_L$, the amount of wave-like path interference between these states, and the amount of entanglement given by the reduced von Neumann entropy. The inequality can account for the complementarity between strangeness oscillations and lifetime information previously considered in the literature, therefore allowing one to see how it is affected by entanglement correlations. As we will discuss, it allows one to visualize clearly through the $K^0-\overline{K}{}^0$ oscillations the fundamental role of entanglement in quantum complementarity.

The Bloch-Messiah (BM) reduction allows the decomposition of an arbitrarily complicated Gaussian unitary into a very simple scheme in which linear optical components are separated from nonlinear ones. The nonlinear part is due to the squeezing possibly present in the Gaussian unitary. The reduction is usually obtained by exploiting the singular value decomposition (SVD) of the matrices appearing in the Bogoliubov transformation of the given Gaussian unitary. This paper discusses a different approach, where the BM reduction is obtained in a straightforward way. It is based on the Takagi factorization of the (complex and symmetric) squeeze matrix and has the advantage of avoiding several matrix operations of the previous approach (polar decomposition, eigendecomposition, SVD, and Takagi factorization). The theory is illustrated with an application example in which the previous and present approaches are compared.

Information-theoretic definitions for the noise associated with a quantum measurement and the corresponding disturbance to the state of the system have recently been introduced [F. Buscemi et al., Phys. Rev. Lett. 112, 050401 (2014)]. These definitions are invariant under relabeling of measurement outcomes, and lend themselves readily to the formulation of state-independent uncertainty relations both for the joint estimate of observables (noise-noise relations) and the noise-disturbance tradeoff. Here we derive such relations for incompatible qubit observables, which we prove to be tight in the case of joint estimates, and present progress towards fully characterizing the noise-disturbance tradeoff. In doing so, we show that the set of obtainable noise-noise values for such observables is convex, whereas the conjectured form for the set of obtainable noise-disturbance values is not. Furthermore, projective measurements are not optimal with respect to the joint-measurement noise or noise-disturbance tradeoffs. Interestingly, it seems that four-outcome measurements are needed in the former case, whereas three-outcome measurements are optimal in the latter.

Hypothetical models have been proposed in which explicit collapse mechanisms prevent the superposition principle from holding at large scales. In particular, the model introduced by Ellis et al. [J. Ellis et al., Phys. Lett. B 221, 113 (1989)] suggests that quantum gravity might be responsible for the collapse of the wave function of massive objects in spatial superpositions. We consider here a recent experiment reporting on interferometry with atoms delocalized over half a meter for a time scale of 1 s [T. Kovachy et al., Nature (London) 528, 530 (2015)] and show that the corresponding data strongly bound quantum-gravity-induced decoherence and rule it out in the parameter regime considered originally.

We construct a practical method for finding optimal Gaussian probe states for the estimation of parameters encoded by Gaussian unitary channels. This method can be used for finding all optimal probe states, rather than focusing on the performance of specific states as shown in previous studies. As an example, we apply this method to find optimal probes for the channel that combines the phase-change and squeezing channels, and for generalized two-mode squeezing and mode-mixing channels. The method enables a comprehensive study of temperature effects in Gaussian parameter estimation. It has been shown that the precision in parameter estimation using single-mode states can be enhanced by increasing the temperature of the probe. We show that not only higher temperature, but also larger temperature differences between modes of a Gaussian probe state can enhance the estimation precision.

Relativistic cryptography exploits the fact that no information can travel faster than the speed of light in order to obtain security guarantees that cannot be achieved from the laws of quantum mechanics alone. Recently, Lunghi et al. [Phys. Rev. Lett. 115, 030502 (2015)] presented a bit-commitment scheme where each party uses two agents that exchange classical information in a synchronized fashion, and that is both hiding and binding. A caveat is that the commitment time is intrinsically limited by the spatial configuration of the players, and increasing this time requires the agents to exchange messages during the whole duration of the protocol. While such a solution remains computationally attractive, its practicality is severely limited in realistic settings since all communication must remain perfectly synchronized at all times. In this work, we introduce a robust protocol for relativistic bit commitment that tolerates failures of the classical communication network. This is done by adding a third agent to both parties. Our scheme provides a quadratic improvement in terms of expected sustain time compared with the original protocol, while retaining the same level of security.

The nonresonant, two-photon, one-electron ionization of neutral atoms is studied theoretically in the framework of relativistic second-order perturbation theory and independent particle approximation. In particular, the importance of relativistic and screening effects in the total two-photon ionization cross section is investigated. Detailed computations have been carried out for the $K$-shell ionization of neutral Ne, Ge, Xe, and U atoms. The relativistic effects significantly decrease the total cross section; for the case of U, for example, they reduce the total cross section by a factor of two. Moreover, we have found that the account for the screening effects of the remaining electrons leads to occurrence of an unexpected minimum in the total cross section at the total photon energies equal to the ionization threshold; for the case of Ne, for example, the cross section drops there by a factor of three.

In the present paper we propose nonlinear femtosecond x-ray pump-probe spectroscopy to study the vibrational dynamics of a core-excited molecular state and discuss numerical results in CO. A femtosecond pump resonantly excites the carbon core-excited $1s\text{−}1{\pi }^{*}$ state of the CO molecule. A second strong probe (control) pulse is applied at variable delay and is resonantly coupled to a valence excited state of the molecule. The strong nonlinear coupling of the control pulse induces Rabi flopping between the two electronic states. During this process, a vibrational wave packet in the core-excited state is created, which can be effectively manipulated by changing the time delay between pump and control pulses. We present an analysis of the resonant Auger electron spectrum and the transient absorption or emission spectrum on the pump transition and discuss their information content for reconstruction of the vibrational wave packet.

Recently there have been experimental results on Poisson spot matter-wave interferometry followed by theoretical models describing the relative importance of the wave and particle behaviors for the phenomenon. We propose an analytical theoretical model for Poisson's spot with matter waves based on the Babinet principle, in which we use the results for free propagation and single-slit diffraction. We take into account effects of loss of coherence and finite detection area using the propagator for a quantum particle interacting with an environment. We observe that the matter-wave Gouy phase plays a role in the existence of the central peak and thus corroborates the predominantly wavelike character of the Poisson's spot. Our model shows remarkable agreement with the experimental data for deuterium (${\text{D}}_2$) molecules.

Optical Fano resonances are an increasingly important line-shape engineering tool with applications ranging from high-sensitivity sensing and ultrasmall lasers to low-power optical switching or modulating. Here we demonstrate a fully on-chip resonant nanostructure on a photonic crystal molecule platform exhibiting typical double- and Ramsey-Fano resonances, which can be actively controlled by the modification of the blockade transmittance in the waveguide. First, we investigate the transmission spectrum of a coupled double-cavity setting, showing a kind of double-Fano resonance line shape which consists of an asymmetric low-frequency Fano (LF) resonance and a high-frequency Fano (HF) resonance. At the same time, we elucidate the influences of various physical quantities on the generated LF and HF resonances. Second, and more interestingly, we reveal the occurrence of the Ramsey-Fano resonance profile by extending a double-cavity arrangement to a coupled-cavity-array arrangement. This Ramsey-Fano resonance can be attributed to the multiple quantum interference among a variety of light pathways. Finally, as an application, we discuss how to use an asymmetric double-Fano resonance line shape, which features the steep spectral slope, to improve the sensing performance. Our obtained results may stimulate future experimental efforts in controlling the double- and Ramsey-Fano resonance line shapes of this system more accurately.