We provide a twofold extension of Landau-Pollak uncertainty relations for mixed quantum states and for positive operator-valued measures, by recourse to geometric considerations. The generalization is based on metrics between pure states, having the form of a function of the square of the inner product between the states. The triangle inequality satisfied by such metrics plays a crucial role in our derivation. The usual Landau-Pollak inequality is thus a particular case (derived from Wootters metric) of the family of inequalities obtained, and, moreover, we show that it is the most restrictive relation within the family.

When a pair of photons that are entangled in terms of their transverse modes, such as an orbital angular momentum (OAM) basis, propagates through atmospheric turbulence, the scintillation causes a decay of the entanglement. Here, we use numerical simulations to study how this decoherence process depends on the various dimension parameters of the system. The relevant dimension parameters are the propagation distance, the wavelength, the beam radius, and the refractive index structure constant, indicating the strength of the turbulence. We show that beyond the weak scintillation regime, the entanglement evolution cannot be accurately modeled by a single phase screen that is specified by a single dimensionless parameter. Two dimensionless parameters are necessary to describe the OAM entanglement evolution. Furthermore, it is found that higher OAM modes are not more robust in turbulence beyond the weak scintillation regime.

In this paper, we report on a laser spectroscopy measurement of ${}^{84-87}\mathrm{Rb}$ isotopes in superfluid helium (He ii) at 1.8 K using laser–radio-frequency double-resonance spectroscopy. Rb ion beams $(>60$ MeV/u) provided by the RIKEN projectile fragment separator (RIPS) were injected and trapped into He ii. The stopping position of atoms in He ii was precisely confirmed by laser spectroscopy. By optically pumping the trapped Rb isotopes, large atomic spin polarization (up to 40%) of each observed isotope in the ground state was achieved. The laser–radio-frequency double-resonance spectra were observed for stable ${}^{85,87}\mathrm{Rb}$ isotopes as well as for unstable isotopes ${}^{84,84m,86}\mathrm{Rb}$ by scanning a weak magnetic field with a fixed-frequency RF field. From the measured Zeeman splitting, nuclear spin values for ${}^{84m,84-87}\mathrm{Rb}$ isotopes were determined with reasonable accuracy. The number of ions injected into He ii for the resonance spectra measurement was on the order of $10{}^4$ particles per second. This work may open new opportunities for the study of various particles trapped in condensed helium in several fields.

By only using electric-dipole forbidden emission lines, in what we label forbidden-line spectroscopy, we identified several energy levels in cadmium-like tungsten, ${\mathrm{W}}^{26+}$. The spectrum was recorded at the Shanghai permanent-magnet electron beam ion trap in the visible region. The identifications were supported by large-scale multiconfiguration Dirac–Hartree–Fock calculations which involved careful investigations of core-valence and core-core correlation effects, and by relativistic many-body perturbation theory calculations. With this novel method we identified in all seven lines and measured their wavelengths. From this we can determine the relative position of seven energy levels. Due to the close degeneracy of two levels, we give alternative energies for three of the levels.

We discuss a possible one-dimensional trapping and cooling of atoms and molecules due to their nonresonant interaction with counterpropagating light pulse trains. The counterpropagating pulses form a one-dimensional trap for atoms and molecules and a properly chosen carrier frequency detuning from the transition frequency of the atoms or molecules keeps the temperature of the atomic or molecular ensemble close to the Doppler cooling limit. The calculation by the Monte Carlo wave-function method is carried out for the two-level and three-level schemes of the atom's and the molecule's interaction with the field, respectively. The models discussed are applicable to atoms and molecules with almost diagonal Frank-Condon factor arrays. Illustrative calculations are carried out for ensemble-averaged characteristics for sodium atoms and SrF molecules in the trap. The potential for the nanoparticle light pulses's trap formed by counterpropagating light pulse trains is also discussed.

A resonantly driven bosonic Josephson junction supports stable collective excitations, or quasiparticles, which constitute analogs of the Trojan wave packets previously explored with Rydberg atoms in strong microwave fields. We predict a quantum beating effect between such symmetry-related many-body Trojan states taking place on time scales which are long in comparison with the driving period. Within a mean-field approximation, this quantum beating can be regarded as a manifestation of dynamical tunneling. On the full $N$-particle level, the beating phenomenon leads to an experimentally feasible, robust strategy for probing highly entangled mesoscopic states.

Topological states of interacting many-body systems are at the focus of current research due to the exotic properties of their elementary excitations. In this paper we suggest a realistic experimental setup for the realization of a simple version of such a phase. We show how $\delta$-interacting bosons hopping on the links of a one-dimensional ladder can be used to simulate the thin-torus limit of the two-dimensional (2D) Hofstadter-Hubbard model at one-quarter magnetic flux per plaquette. Bosons can be confined to ladders by optical superlattices, and synthetic magnetic fields can be realized by laser-assisted tunneling. We show that twisted boundary conditions can be implemented, enabling the realization of a fractionally quantized Thouless pump. Using numerical density-matrix-renormalization-group calculations, we show that the ground state of our model is an incompressible symmetry-protected topological charge density wave phase at average filling $\rho =1/8$ per lattice site, related to the $1/2$ Laughlin-type state of the corresponding 2D model.

Variational solutions of the Boltzmann equation usually rely on the concept of linear response. We extend the variational approach for tight-binding models at high entropies to a regime far beyond linear response. We analyze both weakly interacting fermions and incoherent bosons on a lattice. We consider a case where the particles are driven by a constant force, leading to the well-known Bloch oscillations, and we consider interactions that are weak enough not to overdamp these oscillations. This regime is computationally demanding and relevant for ultracold atoms in optical lattices. We derive a simple theory in terms of coupled dynamic equations for the particle density, energy density, current, and heat current, allowing for analytic solutions. As an application, we identify damping coefficients for Bloch oscillations in the Hubbard model at weak interactions and compute them for a one-dimensional toy model. We also approximately solve the long-time dynamics of a weakly interacting, strongly Bloch-oscillating cloud of fermionic particles in a tilted lattice, leading to a subdiffusive scaling exponent.

A theory of dispersive soliton of the self-induced transparency in a medium consisting of atoms or semiconductor quantum dots of two types is considered. A two-component medium is modeled by a set of two-level atoms of two types embedded into a conductive host material. These types of atoms correspond to passive atoms (attenuator atoms) and active atoms (amplifier atoms) with inverse population of the energetic levels. The complete solution is given of the Maxwell–Bloch equations for ensembles of two-type atoms with different parameters and different initial conditions by inverse scattering transform. The solutions of the Maxwell–Bloch equations for many-component atomic systems by inverse scattering transform are also discussed. The influence of the difference between dipole moments of atoms, the longitudinal and transverse relaxation times, pumping, and conductivity on the soliton is taken into account by means of perturbation theory. The memory effects are described in terms of generalized non-Markovian optical Bloch equations. The condition of a balance between the energy supplied and lost is obtained.

We study the manipulation of Goos-Hänchen (GH) shifts for the reflected and transmitted probe light pulses injected into a cavity containing four-level configuration mercury atoms where the probe transition is in the ultraviolet (UV) region with a wavelength of $253.7\mathrm{nm}$. Different behaviors of the GH shifts can be observed in the absence, or presence, of two driving fields as well as an incoherent pump field. When neither coherent driving fields nor incoherent pumping is turned on, we realize negative reflected GH shifts for anomalous dispersion. Including only one driving field leads to subluminal-based light propagation with positive lateral shifts at certain incident angles. Taking into account the impact of both driving fields, negative GH shifts reappear in the reflected part of the incident light. The origin of this defect is attributed to interacting double dark resonances due to a high-resolution absorption peaks with a very steep negative slope of dispersion in the susceptibility profile. We then show that one can surpass this defect by applying a weak incoherent pumping field to obtain positive GH shifts for both reflected and transmitted light beams. Finally, using the $6{}^1{P}_1\leftrightarrow 6{}^1{S}_0$ transition of Hg, we generalize our study to the case where the wavelength of the probe transition is $185\mathrm{nm}$ which is in the vacuum-ultraviolet domain. Although the number of oscillations is now increased, however, similar results are reported with respect to the case of UV transition.

We present a two-waveguide coupler which realizes complete achromatic all-optical switching. The coupling of the waveguides has a hyperbolic-secant shape, while the phase mismatch has a sign flip at the maximum of the coupling. We derive an analytic solution for the electric field propagation using coupled-mode theory and show that the light switching is robust against small to moderate variations in the coupling strength and phase mismatch. Thus, we realize an achromatic light switching between the two waveguides. We further consider the extended case of three coupled waveguides in an array and pay special attention to the case of equal bidirectional achromatic light beam splitting.

The unextendible product basis is generalized to the unextendible entangled basis with any arbitrarily given Schmidt number $k$ (UEBk) for any bipartite system ${\mathbb{C}}^d\otimes {\mathbb{C}}^{d^{\prime }}$ $\left(2\le k<d\le d^{\prime }\right)$, which can also be regarded as a generalization of the unextendible maximally entangled basis. A general way of constructing such a basis with arbitrary $d$ and $d^{\prime }$ is proposed. Consequently, it is shown that there are at least $k-r$ (here $r=d\text{mod}k$ or $r=d^{\prime }\text{mod}k)$ sets of UEBks when $d$ or $d^{\prime }$ is not a multiple of $k$, while there are at least $2(k-1)$ sets of UEBks when both $d$ and $d^{\prime }$ are multiples of $k$.

The robustness of the three-level transitionless quantum driving proposed by Giannelli and Arimondo [L. Giannelli and E. Arimondo, Phys. Rev. A 89, 033419 (2014)] is investigated. In the case when the excited state is barely populated during the evolution, its decay rate has little effect on the adiabatic population transfer. However, the dephasing which is due to collisions or phase fluctuations of the driving fields will produce a significant effect on the evolution. We found that the dephasing reduces the performance of the population transfer and the fidelity can be far below the quantum computation target even for small dephasing rates.

Open quantum systems are studied from the thermodynamical point of view unifying the principle of maximum informational entropy and the hypothesis of relaxation times hierarchy. The result of the unification is a non-Markovian and local-in-time master equation that provides a direct connection for dynamical and thermodynamical properties of open quantum systems. The power of the approach is illustrated by the application to the damped harmonic oscillator and the damped driven two-level system, resulting in analytical expressions for the non-Markovian and nonequilibrium entropy and inverse temperature.

We propose an implementation of a twin-paradox scenario in superconducting circuits, with velocities as large as a few percent of the speed of light. Ultrafast modulation of the boundary conditions for the electromagnetic field in a microwave cavity simulates a clock moving at relativistic speeds. Since our cavity has a finite length, the setup allows us to investigate the role of clock size as well as interesting quantum effects on time dilation. In particular, our theoretical results show that the time dilation increases for larger cavity lengths and is shifted due to quantum particle creation.

A continuous-variable measurement-device-independent quantum key distribution (CV-MDI QKD) protocol using squeezed states is proposed where the two legitimate partners send Gaussian-modulated squeezed states to an untrusted third party to realize the measurement. Security analysis shows that the protocol can not only defend all detector side channels, but also attain higher secret key rates than the coherent-state-based protocol. We also present a method to improve the squeezed-state CV-MDI QKD protocol by adding proper Gaussian noise to the reconciliation side. It is found that there is an optimal added noise to optimize the performance of the protocol in terms of both key rates and maximal transmission distances. The resulting protocol shows the potential of long-distance secure communication using the CV-MDI QKD protocol.

We calculated, using seven realistic ${}^4\mathrm{He}\text{−}{}^4\mathrm{He}$ potentials in the literature, the Efimov spectra of the ${}^4\mathrm{He}$ trimer and tetramer and analyzed the universality of the systems. The three-(four-)body Schrödinger equations were solved fully nonadiabatically with the high-precision calculation method employed in our previous work on the ${}^4\mathrm{He}$ trimer and tetramer [Phys. Rev. A 85, 022502 (2012); Phys. Rev. A 85, 062505 (2012)]. We found the following universality in the four-boson system: (i) The critical scattering lengths at which the tetramer ground and excited states couple to the four-body threshold are independent of the choice of the two-body realistic potentials in spite of the difference in the short-range details and do not contradict the corresponding values observed in the experiments in ultracold alkali-metal atoms when scaled with the van der Waals length $r_{\mathrm{vdW}}$, and (ii) the four-body hyperradial potential has a repulsive barrier at the four-body hyperradius $R_4\approx 3r_{\mathrm{vdW}}$, which prevents the four particles from getting close together to explore nonuniversal features of the interactions at short distances. This result is an extension of the universality in Efimov trimers that the appearance of the repulsive barrier at the three-body hyperradius $R_3\approx 2r_{\mathrm{vdW}}$ makes the critical scattering lengths independent of the short-range details of the interactions as reported in the literature and also in the present work for the ${}^4\mathrm{He}$ trimer with the realistic potentials.

The electric-dipole and quadrupole polarizabilities of the $5s5p{}^3{P}_1^o$ state and the $C_6$ and $C_8$ coefficients for the ${}^1{S}_0+{}^1{S}_0$ and ${}^1{S}_0+{}^3{P}_1^o$ dimers of strontium are calculated using a high-precision relativistic approach that combines configuration interaction and linearized coupled-cluster methods. Our recommended values of the long-range dispersion coefficients for the $0_u$ and $1_u$ energy levels are $C_6\left(0_u\right)=3771\left(32\right)$ a.u. and $C_6\left(1_u\right)=4001\left(33\right)$ a.u., respectively. They are in good agreement with recent results from experimental photoassociation data. We also calculate $C_8$ coefficients for Sr dimers, which are needed for precise determination of long-range interaction potential. We confirm the experimental value for the magic wavelength, where the Stark shift on the ${}^1{S}_0\text{−}{}^3{P}_1^o$ transition vanishes. The accuracy of calculations is analyzed and uncertainties are assigned to all quantities reported in this work.

The main limitation of most ultracold chemistry studies to date is the lack of an analysis of reaction products. Here, we discuss a generally tractable, rigorous theoretical framework for computing statistical product-state distributions for ultracold reactions in external fields. We show that fields have two main effects on the products of a statistical reaction, by (1) modifying the product energy levels and thus potentially reshaping the product distributions and/or (2) adding or removing product states by changing the reaction exothermicity. By analyzing these effects and the strength of the formalism to distinguish between different reaction mechanisms in benchmark reactions involving ${}^{40}\mathrm{K}$ and ${}^{87}\mathrm{Rb}$ species, we argue that statistical predictions will help understanding product formation and control, and lead developments to realize the full potential of ultracold chemistry.