It is known that measurement-device-independent quantum key distribution (MDI-QKD) provides ultimate security from all types of side-channel attack on detectors at the expense of low key rate. In the present study, we propose MDI-QKD using three-dimensional quantum states and show that the protocol improves the secret key rate under the analysis of mismatched-basis statistics. Specifically, we analyze security of the $3d$-MDI-QKD protocol with askew aligned sources, meaning that the original sources contain unwanted states instead of the expected one. We evaluate the secret key rate of the protocol and identify the regime in which the key rate is higher than the protocol with the qubit MDI-QKD.

Given an arbitrary $2^w\times 2^w$ unitary matrix $U$, a powerful matrix decomposition can be applied, leading to four different syntheses of a $w$-qubit quantum circuit performing the unitary transformation. The demonstration is based on a recent theorem by H. Führ and Z. Rzeszotnik [Linear Algebra Its Appl. 484, 86 (2015)] generalizing the scaling of single-bit unitary gates ($w=1$) to gates with arbitrary value of $w$. The synthesized circuit consists of controlled one-qubit gates, such as negator gates and phasor gates. Interestingly, the approach reduces to a known synthesis method for classical logic circuits consisting of controlled not gates in the case that $U$ is a permutation matrix.

We show that a bipartite quantum state of rank four is distillable if its partial transpose has at least one negative eigenvalue; that is, the state is a non-positive-partial transpose (NPT). For this purpose we prove that if the partial transpose of a two-qutrit NPT state has at least two non-positive eigenvalues, then the state is distillable. We further construct a parametrized two-qutrit NPT state of rank five which is not 1-distillable and show that it is not $n$-distillable for any given $n$ when the parameter is sufficiently small. This state has the smallest rank among all 1-undistillable NPT states. We conjecture that the state is not distillable.

We develop a technique to prove simultaneous subspace controllability on multiple invariant subspaces, which specifically enables us study the controllability properties of spin systems that are not amenable to standard controllability arguments based on energy level connectivity graphs or simple induction arguments on the length of the chain. The technique is applied to establish simultaneous subspace controllability for Heisenberg spin chains subject to limited local controls. This model is theoretically important and the controllability result shows that a single control can be sufficient for complete controllability of an exponentially large subspace and universal quantum computation in the exponentially large subspace. The controllability results are extended to prove subspace controllability in the presence of control field leakage and discuss minimal control resources required to achieve controllability over the entire spin chain space.

Absolute double differential cross sections (DDCS) of electron emission were measured for ionization of ${\mathrm{N}}_2$ by fast electrons with energy 7 keV. Measurements were performed for different electron emission angles and energies. Evidence of oscillation due to Young-type interference was observed in the DDCS ratios for all angles. The frequency for large backward angle is found to be larger compared to that for small forward angle. Consequently, the forward-backward asymmetry parameter reveals the oscillatory structure even more clearly. The oscillations observed for both experimental-to-theoretical DDCS ratios and forward-backward asymmetry were well explained by the Cohen-Fano model of interference in a molecular double slit. A periodic deviation of the Cohen-Fano model from the asymmetry parameter data reveals the presence of a higher-frequency component. The first Born model was employed to explain the results of molecular nitrogen for which a complete-neglect-of-differential-overlap approximation was used along with an effective atomic number.

The ionization behavior of the two diatomic molecules nitrogen and oxygen in strong laser fields has been investigated. For this purpose, the time-dependent Schrödinger equation is solved numerically within the many-electron single-determinant approximation. Three different orientations of the molecular axis with respect to the laser field have been considered: $0^{\circ },{45}^{\circ }$, and ${90}^{\circ }$. The photon wavelength has been varied from 25 to 800 nm, covering a range from XUV to infrared radiation. Nitrogen and oxygen were chosen as they possess the same molecular symmetry but different orbital structures. The ionization from different orbitals is discussed.

We experimentally investigate the recoil-ion momentum distribution along the laser polarization direction for nonsequential double ionization of Xe by 50 fs, 2400 nm laser pulses at intensities of $(22-68) \mathrm{TW}/{\mathrm{cm}}^2$. The observed doubly charged ion momentum distribution exhibits a distinct transition from a flat-top structure near zero longitudinal momentum at $22\mathrm{TW}/{\mathrm{cm}}^2$ to the one with two maxima at nonzero longitudinal momentum at $37\mathrm{TW}/{\mathrm{cm}}^2,52\mathrm{TW}/{\mathrm{cm}}^2$, and $68\mathrm{TW}/{\mathrm{cm}}^2$, which is remarkably different from the case of 800 nm. Simulation based on a semiclassical model is used to obtain the ratios of contributions from the recollision-impact ionization (RII) and the recollision-induced excitation with subsequent field ionization (RESI) in nonsequential double ionization. Our calculation reveals that the increasing contribution of the RII channel is responsible for the more prominent double-hump structure at longer wavelength or higher laser intensity. Moreover, a simple fitting based on the calculated ratios allows one to reproduce the experimental ion momentum distributions well and obtain contributions from these two channels.

An exterior complex scaling technique is applied to compute Stark resonance parameters for two molecular orbitals ($1b_1$ and $1b_2$) represented in the field-free limit in a single-center expansion. For electric dc field configurations that guarantee azimuthal symmetry of the solution the calculation is carried out by solving a two-dimensional partial differential equation in spherical polar coordinates using a finite-element method. The resonance positions and widths as a function of electric field strengths are shown for field strengths starting in the tunneling ionization regime and extending well into the over-barrier ionization region.

Simultaneous two-electron emission processes of Ar induced by high-order harmonics of near-infrared femtosecond laser pulses were investigated by coincidence photoelectron spectroscopy. Two-photon double ionization processes via the $3s3p^{6}np(n\sim 25)$ intermediate resonances of Ar were observed, which selectively created the $3s3p^5{}^{1}P$ state of $\mathrm{A}{\mathrm{r}}^{2+}$. The similar double ionization processes were also observed in Kr. The selective creation indicates that the core electron configuration of the doubly ionized state tends to be the same as that of the intermediate state and that the emitted two electrons tend to form the singlet state.

Stable self-trapped vortex annuli (VA) with large values of topological charge $S$ (giant VA) not only are a subject of fundamental interest, but are also sought for various applications, such as quantum information processing and storage. However, in conventional atomic Bose-Einstein condensates (BECs) VA with $S>1$ are unstable. Here we demonstrate that robust self-trapped fundamental solitons (with $S=0$) and bright VA (with the stability checked up to $S=5$) can be created in the free space by means of the local-field effect (the feedback of the BEC on the propagation of electromagnetic waves) in a condensate of two-level atoms coupled by a microwave (MW) field, as well as in a gas of MW-coupled fermions with spin $1/2$. The fundamental solitons and VA remain stable in the presence of an arbitrarily strong repulsive contact interaction (in that case, the solitons are constructed analytically by means of the Thomas-Fermi approximation). Under the action of the attractive contact interaction with strength $\beta$, which, by itself, would lead to collapse, the fundamental solitons and VA exist and are stable, respectively, at $\beta <{\beta }_{max}\left(S\right)$ and $\beta <{\beta }_{\mathrm{st}}\left(S\right)$, with ${\beta }_{\mathrm{st}}(S=0)={\beta }_{max}(S=0)$ and ${\beta }_{\mathrm{st}}(S\ge 1)<{\beta }_{max}(S\ge 1)$. Accurate analytical approximations are found for both ${\beta }_{\mathrm{st}}$ and ${\beta }_{max}$, with ${\beta }_{\mathrm{st}}\left(S\right)$ growing linearly with $S$. Thus, higher-order VA are more robust than their lower-order counterparts, in contrast to what is known in other systems that may support stable self-trapped vortices. Conditions for the experimental realizations of the VA are discussed.

We investigate a variant of the Aubry-André-Harper (AAH) model corresponding to a bosonic optical lattice of ultracold atoms under an effective oscillatory magnetic field. In the limit of high-frequency oscillation, the system maybe approximated by an effective time-independent Hamiltonian. We have studied localization-delocalization transition exhibited by the effective Hamiltonian. The effective Hamiltonian is found to retain the tight-binding tridiagonal form in position space. In a striking contrast to the usual AAH model, this non-dual system shows an energy-dependent mobility edge—a feature which is usually reminiscent of Hamiltonians with beyond-nearest-neighbor hoppings in real space. Finally, we discuss possibilities of experimentally realizing this system in optical lattices.

We study interactions of extremely short three-dimensional bipolar electromagnetic pulses propagating towards each other in an array of semiconductor carbon nanotubes, along any direction perpendicular to their axes. The analysis provides a full account of the effects of the nonuniformity of the pulses' fields along the axes. The evolution of the electromagnetic field and charge density in the sample is derived from the Maxwell's equations and the continuity equation, respectively. In particular, we focus on indirect interaction of the pulses via the action of their fields on the electronic subsystem of the nanotube array. Changes in the shape of pulses in the course of their propagation and interaction are analyzed by calculating and visualizing the distribution of the electric field in the system. The numerical analysis reveals a possibility of stable post-collision propagation of pulses over distances much greater than their sizes.

Second-harmonic (SH) generation is tremendously important for nonlinear sensing, microscopy, and communication systems. One of the great challenges of current designs is to enhance the SH signal and simultaneously tune its radiation direction with a high directivity. In contrast to the linear plasmonic scattering dominated by a bulk dipolar mode, a complex surface-induced multipolar source at the doubled frequency sets a fundamental limit to control the SH radiation from metallic nanostructures. In this work, we harness a plasmonic hybridization mechanism together with a special selection rule governing the SH radiation to achieve the high-intensity and tunable-direction emission by a metallic particle-in-cavity nanoantenna (PIC-NA). The nanoantenna is modelled with a first-principle, self-consistent boundary element method, which considers the depletion of pump waves. The giant SH enhancement arises from a hybridized gap plasmon resonance between the small particle and the large cavity that functions as a concentrator and reflector. Centrosymmetry breaking of the PIC-NA not only modifies the gap plasmon mode boosting the SH signal, but also redirects the SH wave with a unidirectional emission. The PIC-NA has a significantly larger SH conversion efficiency compared to existing literature. The main beam of the radiation pattern can be steered over a wide angle by tuning the particle's position.

We develop a dual description of quantum optics adapted to dielectric systems without magnetic property. Our formalism, which is shown to be equivalent to the standard one within some dipolar approximations discussed in the article, is applied to the description of polaritons in dielectric media. We show that the dual formalism leads to the Huttner-Barnett equations [B. Huttner and S. M. Barnett, Phys. Rev. A 46, 4306 (1992)] for QED in dielectric systems. More generally, we discuss the role of electromagnetic duality in the quantization procedure for optical systems and derive the structure of the dynamical laws in the various representations.

We investigate the quantum melting of one-dimensional crystals that are realized in an atomic lattice in which ground state atoms are laser excited to two Rydberg states. We focus on a regime where both, intra- and interstate density-density interactions as well as coherent exchange interactions contribute. We determine stable crystalline phases in the classical limit and explore their melting under quantum fluctuations introduced by the excitation laser as well as two-body exchange. We find that within a specific parameter range quantum fluctuations introduced by the laser can give rise to a devil's staircase structure which one might associate with transitions in the classical limit. The melting through exchange interactions is shown to also proceed in a steplike fashion, in the case of small crystals, due to the proliferation of Rydberg spin waves.

The mechanism of decoherence for a mesoscopic quantum system with rotational degrees of freedom is studied. From a simple model of elastic scattering, we show that the nondiagonal density-matrix elements of the system exponentially decay. The decay rate depends on the difference of scattering amplitudes for different rotational configurations, leading to the gradual loss of quantum coherence between the pointer states in the orientational space. For a dielectric ellipsoid immersed in a photon-gas environment (assuming no absorption), the decay rate is found to be proportional to the seventh power of the temperature. For an ellipsoidal object interacting with massive particles, the decay rate is proportional to the 5/2 power of the temperature. Both are different from the case of translational decoherence induced by the same environment scattering. For photon scattering, the coherence time in the rotational degrees of freedom is shown to be much shorter than that in the translational degrees of freedom.

In the weak measurement (WM) scenario involving weak interaction and postselection by projective measurement, the empirical significance of weak values is manifested in terms of shifts in the measurement pointer's mean position and mean momentum. In this context, a general quantitative treatment is presented in this paper by taking into account the hitherto unexplored effect of correlations among the pointer degrees of freedom which pertain to an arbitrary multidimensional preselected pointer state. This leads to an extension of the earlier results, showing that, for complex weak values, the correlations among different pointer degrees of freedom can crucially affect the way the imaginary parts of the weak values are related to the observed shifts of the mean pointer position and momentum. The particular relevance of this analysis is discussed in the case of sequential weak interactions followed by a projective measurement enabling postselection (called sequential WM) which, in the special case, reduces to the usual WM scheme (involving a single weak interaction and postseletion) modified by the effect of pointer-state correlations.

We study the ergodic properties of excited states in a model of interacting fermions in quasi-one-dimensional chains subjected to a random vector potential. In the noninteracting limit, we show that arbitrarily small values of this complex off-diagonal disorder trigger localization for the whole spectrum; the divergence of the localization length in the single-particle basis is characterized by a critical exponent $\nu$ which depends on the energy density being investigated. When short-range interactions are included, the localization is lost, and the system is ergodic regardless of the magnitude of disorder in finite chains. Our numerical results suggest a delocalization scheme for arbitrary small values of interactions. This finding indicates that the standard scenario of the many-body localization cannot be obtained in a model with random gauge fields.

The dynamics of light pulses with amplitude and phase modulations is investigated for a medium of resonant two-level atoms. It is shown that the pulse-like variations of the phase can be also described in terms of group velocity. It is found that in the nonlinear regime of atom-field interaction, the group velocities of amplitude and phase pulses can have a large imbalance. Namely, amplitude pulses travel at a velocity less than $c$, whereas the group velocity of phase pulses is greater than the velocity of light in free space or it is even negative. The predicted imbalance of the group velocities can be important in the case of chirped pulses propagating in a resonant medium.