We introduce the notion of adiabatic state flip of a Floquet Hamiltonian associated with a non-Hermitian system that it is subjected to two driving schemes with clear separation of time scales. The fast (Floquet) modulation scheme is utilized to reallocate the exceptional points in the parameter space of the system and redefine the topological features of an adiabatic cyclic modulation associated with the slow driving scheme. Such topological reorganization can be used in order to control the adiabatic transport between two eigenmodes of the Floquet Hamiltonian. The proposed scheme provides a degree of reconfigurability of adiabatic state transfer which can find applications in system control in photonics and microwave domains.

The problem of measuring a time-varying phase, even when the statistics of the variation is known, is considerably harder than that of measuring a constant phase. In particular, the usual bounds on accuracy, such as the $1/\left(4\overline{n}\right)$ standard quantum limit with coherent states, do not apply. Here, by restricting to coherent states, we are able to analytically obtain the achievable accuracy, the equivalent of the standard quantum limit, for a wide class of phase variation. In particular, we consider the case where the phase has Gaussian statistics and a power-law spectrum equal to ${\kappa }^{p-1}/{\left|\omega \right|}^p$ for large $\omega$, for some $p>1$. For coherent states with mean photon flux $\mathcal{N}$, we give the quantum Cramér-Rao bound on the mean-square phase error as ${[psin(\pi /p)]}^{-1}{(4\mathcal{N}/\kappa )}^{-(p-1)/p}$. Next, we consider whether the bound can be achieved by an adaptive homodyne measurement in the limit $\mathcal{N}/\kappa \gg 1$, which allows the photocurrent to be linearized. Applying the optimal filtering for the resultant linear Gaussian system, we find the same scaling with $\mathcal{N}$, but with a prefactor larger by a factor of $p$. By contrast, if we employ optimal smoothing we can exactly obtain the quantum Cramér-Rao bound. That is, contrary to previously considered ($p=2$) cases of phase estimation, here the improvement offered by smoothing over filtering is not limited to a factor of 2 but rather can be unbounded by a factor of $p$. We also study numerically the performance of these estimators for an adaptive measurement in the limit where $\mathcal{N}/\kappa$ is not large and find a more complicated picture.

The discrete-variable quantum key distribution protocols based on the 1984 protocol of Bennett and Brassard (BB84) are known to be secure against an eavesdropper, Eve, intercepting the flying qubits and performing any quantum operation on them. However, these protocols may still be vulnerable to side-channel attacks. We investigate the Trojan-horse side-channel attack where Eve sends her own state into Alice's apparatus and measures the reflected state to estimate the key. We prove that the separable coherent state is optimal for Eve among the class of multimode Gaussian attack states, even in the presence of thermal noise. We then provide a bound on the secret key rate in the case where Eve may use any separable state.

In this paper, we propose a scheme for realizing nonadiabatic holonomic computation assisted by two atoms and the shortcuts to adiabaticity (STA). The blockade effect induced by strong Rydberg-mediated interaction between two Rydberg atoms provides us the possibility to simplify the dynamics of the system, and the STA helps us design pulses for implementing the holonomic computation with high fidelity. Numerical simulations show the scheme is noise immune and decoherence resistant. Therefore, the current scheme may provide some useful perspectives for realizing nonadiabatic holonomic computation.

Studies of quantum metrology have shown that the use of many-body entangled states can lead to an enhancement in sensitivity when compared with unentangled states. In this paper, we quantify the metrological advantage of entanglement in a setting where the measured quantity is a linear function of parameters individually coupled to each qubit. We first generalize the Heisenberg limit to the measurement of nonlocal observables in a quantum network, deriving a bound based on the multiparameter quantum Fisher information. We then propose measurement protocols that can make use of Greenberger–Horne–Zeilinger (GHZ) states or spin-squeezed states and show that in the case of GHZ states the protocol is optimal, i.e., it saturates our bound. We also identify nanoscale magnetic resonance imaging as a promising setting for this technology.

We provide accurate expressions for the $s$-wave scattering length for a Gaussian potential well in one, two, and three spatial dimensions. The Gaussian potential is widely used as a pseudopotential in the theoretical description of ultracold-atomic gases, where the $s$-wave scattering length is a physically relevant parameter. We first describe a numerical procedure to compute the value of the $s$-wave scattering length from the parameters of the Gaussian, but find that its accuracy is limited in the vicinity of singularities that result from the formation of new bound states. We then derive simple analytical expressions that capture the correct asymptotic behavior of the $s$-wave scattering length near the bound states. Expressions that are increasingly accurate in wide parameter regimes are found by a hierarchy of approximations that capture an increasing number of bound states. The small number of numerical coefficients that enter these expressions is determined from accurate numerical calculations. The approximate formulas combine the advantages of the numerical and approximate expressions, yielding an accurate and simple description from the weakly to the strongly interacting limit.

A theoretical study of the low-energy scattering properties of two aligned identical bosonic and fermionic dipoles in the presence of isotropic spin-orbit coupling is presented. A general treatment of particles with arbitrary (pseudo)spin is given in the framework of multichannel scattering. At ultracold temperatures and away from shape resonances or closed-channel dominated resonances, the cross section can be well described within the Born approximation to within corrections due to the $s$-wave scattering. We compare our findings with numerical calculations and find excellent agreement.

We theoretically investigate long-range interactions between an excited $L$-state He atom and two identical $S$-state He atoms for the cases of the three atoms all in spin-singlet states or all in spin-triplet states, denoted by He($n_0^{\lambda }S$)-He($n_0^{\lambda }S$)-He($n_0^{\prime \lambda }L$), with $n_0$ and $n_0^{\prime }$ principal quantum numbers, $\lambda =1$ or 3 the spin multiplicity, and $L$ the orbital angular momentum of a He atom. Using degenerate perturbation theory for the energies up to second-order, we evaluate the coefficients $C_3$ of the first-order dipolar interactions and the coefficients $C_6$ and $C_8$ of the second-order additive and nonadditive interactions. Both the dipolar and dispersion interaction coefficients, for these three-body degenerate systems, show dependences on the geometrical configurations of the three atoms. The nonadditive interactions start to appear in second-order. To demonstrate the results and for applications, the obtained coefficients $C_n$ are evaluated with highly accurate variationally generated nonrelativistic wave functions in Hylleraas coordinates for $\text{He}\left(1{}^{1}S\right)\text{−}\text{He}\left(1{}^{1}S\right)\text{−}\text{He}\left(2{}^{1}S\right)$, $\text{He}\left(1{}^{1}S\right)\text{−}\text{He}\left(1{}^{1}S\right)\text{−}\text{He}\left(2{}^{1}P\right)$, $\text{He}\left(2{}^{1}S\right)\text{−}\text{He}\left(2{}^{1}S\right)\text{−}\text{He}\left(2{}^{1}P\right)$, and $\text{He}\left(2{}^{3}S\right)\text{−}\text{He}\left(2{}^{3}S\right)\text{−}\text{He}\left(2{}^{3}P\right)$. The calculations are given for three like nuclei for the cases of hypothetical infinite mass He nuclei, and of real finite mass ${}^4\mathrm{He}$ or ${}^3\mathrm{He}$ nuclei. The special cases of the three atoms in equilateral triangle configurations are explored in detail, and for the cases in which one of the atoms is in a $P$ state, we also present results for the atoms in an isosceles right triangle configuration or in an equally spaced collinear configuration. The results can be applied to construct potential energy surfaces for three helium atom systems.

We investigate the fine and spin structure of ultralong-range Rydberg molecules exposed to a homogeneous magnetic field. Each molecule consists of a ${}^{87}\mathrm{Rb}$ Rydberg atom the outer electron of which interacts via spin-dependent $s$- and $p$-wave scattering with a polarizable ${}^{87}\mathrm{Rb}$ ground-state atom. Our model includes also the hyperfine structure of the ground-state atom as well as spin-orbit couplings of the Rydberg and ground-state atom. We focus on $d$-Rydberg states and principal quantum numbers $n$ in the vicinity of 40. The electronic structure and vibrational states are determined in the framework of the Born-Oppenheimer approximation for varying field strengths ranging from a few up to hundred Gauss. The results show that the interplay between the scattering interactions and the spin couplings gives rise to a large variety of molecular states in different spin configurations as well as in different spatial arrangements that can be tuned by the magnetic field. This includes relatively regularly shaped energy surfaces in a regime where the Zeeman splitting is large compared to the scattering interaction but small compared to the Rydberg fine structure, as well as more complex structures for both weaker and stronger fields. We quantify the impact of spin couplings by comparing the extended theory to a spin-independent model.

We demonstrate a method for the deterministic production of single ions by exploiting the correlation between an electron and associated ion following ionization. Coincident detection and feedback in combination with Coulomb-driven particle selection allows for high-fidelity heralding of ions at a high repetition rate. Extension of the scheme beyond time-correlated feedback to position- and momentum-correlated feedback will provide a general and powerful means to optimize the ion beam brightness for the development of next-generation focused ion beam technologies.

Using time-dependent density-functional theory, high-harmonic generation (HHG) is studied in one-dimensional structures of sizes from a single nucleus up to hundreds of nuclei. The HHG cutoff is observed to extend linearly with the system size from the well-known atomic HHG cutoff and is found to converge into the previously observed cutoffs for bulk solids only for large systems. A change in the response from that of single atoms or small molecules is observed from system sizes of $N\approx 6$ nuclei and becomes independent of system size at $N\gtrsim 60$. The system-size dependence of the observed HHG cutoffs is found to follow the limitations, set by the finite-size solid, on the classical motion of electron-hole pairs. Because of the relation between recombination energy and electron-hole propagation length in the system, high-energy recombination events are not possible in small systems but become accessible for larger systems, resulting in the change of the cutoff energies with system size. When varying the field intensity we observe that the cutoffs move linearly with the intensity, even for small systems of $N\gtrsim 6$ that are far from the limit of a bulk solid.

We propose a method of producing high-purity angular-momentum-state Rydberg atoms by a pair of unipolar laser pulses. The first positive-polarity optical half-cycle pulse is used to prepare an excited-state wave packet while the second one is less intense, but with opposite polarity and time delayed, and is employed to drag back the escaping free electron and clip the shape of the bound Rydberg wave packet, selectively increasing or decreasing a fraction of the angular-momentum components. An intelligent choice of laser parameters such as phase and amplitude helps us to control the orbital-angular-momentum composition of an electron wave packet with more facility; thus, a specified angular-momentum state with high purity can be achieved. This scheme of producing high-purity angular-momentum-state Rydberg atoms has significant application in quantum-information processing.

We present an extension of the framework introduced in previous work [L. Mingarelli, E. E. Keaveny, and R. Barnett, J. Phys.: Condens. Matter 28, 285201 (2016)] to treat multicomponent systems, showing that new degrees of freedom are necessary in order to obtain the desired boundary conditions. We then apply this extended framework to the coupled Gross-Pitaevskii equations to investigate the ground states of two-component systems with equal masses, thereby extending previous work in the lowest Landau limit [E. J. Mueller and T.-L. Ho, Phys. Rev. Lett. 88, 180403 (2002)] to arbitrary interactions within Gross-Pitaevskii theory. We show that away from the lowest Landau level limit, the predominant vortex lattice consists of two interlaced triangular lattices. Finally, we derive a linear relation which accurately describes the phase boundaries in the strong interacting regimes.

The statics, stability, and dynamical properties of dark-bright soliton pairs are investigated here, motivated by applications in a homogeneous two-component repulsively interacting Bose-Einstein condensate. One of the intraspecies interaction coefficients is used as the relevant parameter controlling the deviation from the integrable Manakov limit. Two different families of stationary states are identified consisting of dark-bright solitons that are either antisymmetric (out-of-phase) or asymmetric (mass imbalanced) with respect to their bright soliton. Both of the above dark-bright configurations coexist at the integrable limit of equal intra and interspecies repulsions and are degenerate in that limit. However, they are found to bifurcate from it in a transcritical bifurcation. This bifurcation interchanges the stability properties of the bound dark-bright pairs rendering the antisymmetric states unstable and the asymmetric ones stable past the associated critical point (and vice versa before it). Finally, on the dynamical side, it is found that large kinetic energies and thus rapid soliton collisions are essentially unaffected by the intraspecies variation, while cases involving near equilibrium states or breathing dynamics are significantly modified under such a variation.

We propose a self-consistent vectorial method, based on a Green's function technique, to describe the resonances that appear in guided-mode resonance gratings. The model provides intuitive expressions of the reflectivity and transmittivity matrices of the structure, involving coupling integrals between the modes of a planar reference structure and radiative modes. When one mode is excited, the diffracted field for a suitable polarization can be written as the sum of a resonant and a nonresonant term, thus extending the intuitive approach used to explain the Fano shape of the resonance in scalar configurations. When two modes are excited, we derive a physical analysis in a configuration which requires a vectorial approach. We provide numerical validations of our model. From a technical point of view, we show how the Green's tensor of our planar reference structure can be expressed as two scalar Green's functions, and how to deal with the singularity of the Green's tensor.

Typically the use of the Rayleigh-Sommerfeld diffraction formula as a photon propagator is widely accepted due to the abundant experimental evidence that suggests that it works. However, a direct link between the propagation of the electromagnetic field in classical optics and the propagation of photons where the square of the probability amplitude describes the transverse probability of the photon detection is still an issue to be clarified. We develop a mathematical formulation for the photon propagation using the formalism of electromagnetic field quantization and the path-integral method, whose main feature is its similarity with a fractional Fourier transform (FRFT). Here we show that because of the close relation existing between the FRFT and the Fresnel diffraction integral, this propagator can be written as a Fresnel diffraction, which brings forward a discussion of the fundamental character of it at the photon level compared to the Huygens-Fresnel principle. Finally, we carry out an experiment of photon counting by a rectangular slit supporting the result that the diffraction phenomenon in the Fresnel approximation behaves as the actual classical limit.

The phenomenon of quantum phase transition is considered in the special case in which the evolution laws remain unitary and in which the bound-state energies remain observable. The conventional Hermiticity of observables is lost at the interface, replaced by the so-called quasi-Hermiticity. Several features of the passage of the system through the interface are discussed and illustrated by elementary illustrative $\mathcal{PT}$-symmetric examples.

The generation of electron vortex states in ionization by intense and short laser pulses is analyzed under the scope of the lowest-order Born approximation. For near-infrared laser fields and nonrelativistic intensities of the order of ${10}^{16} \mathrm{W}/{\mathrm{cm}}^2$, we show that one has to modify the nonrelativistic treatment of ionization by accounting for recoil and relativistic mass corrections. By using the corrected quasirelativistic theory, the requirements for the observation of electron vortex states with non-negligible probability and large topological charge are determined.

During a collision of Bose-Einstein condensates correlated pairs of atoms are emitted. The scattered massive particles, in analogy to photon pairs in quantum optics, might be used in the violation of Bell's inequalities, demonstration of Einstein-Podolsky-Rosen correlations, or sub-shot-noise atomic interferometry. Usually, a theoretical description of the collision relies either on stochastic numerical methods or on analytical treatments involving various approximations. Here, we investigate elastic scattering of atoms from colliding elongated Bose-Einstein condensates within the Bogoliubov method, carefully controlling performed approximations at every stage of the analysis. We derive expressions for the one- and two-particle correlation functions. The obtained formulas, which relate the correlation functions to the condensate wave function, are convenient for numerical calculations. We employ the variational approach for condensate wave functions to obtain analytical expressions for the correlation functions, whose properties we analyze in detail. We also present a useful semiclassical model of the process and compare its results with the quantum one. The results are relevant for recent experiments with excited helium atoms, as well as for planned experiments aimed at investigating the nonclassicality of the system.

We study the one-dimensional dynamics of dark-dark solitons in the miscible regime of two density-coupled Bose-Einstein condensates having repulsive interparticle interactions within each condensate ($g>0$). By using an adiabatic perturbation theory in the parameter $g_{12}/g$, we show that, contrary to the case of two solitons in scalar condensates, the interactions between solitons are attractive when the interparticle interactions between condensates are repulsive $g_{12}>0$. As a result, the relative motion of dark solitons with equal chemical potential $\mu$ is well approximated by harmonic oscillations of angular frequency $w_r=(\mu /\hslash )\sqrt{(8/15)g_{12}/g}$. We also show that, in finite systems, the resonance of this anomalous excitation mode with the spin-density mode of lowest energy gives rise to alternating dynamical instability and stability fringes as a function of the perturbative parameter. In the presence of harmonic trapping (with angular frequency $\mathrm{\Omega }$) the solitons are driven by the superposition of two harmonic motions at a frequency given by $w^2={(\mathrm{\Omega }/\sqrt{2})}^2+w_r^2$. When $g_{12}<0$, these two oscillators compete to give rise to an overall effective potential that can be either single well or double well through a pitchfork bifurcation. All our theoretical results are compared with numerical solutions of the Gross-Pitaevskii equation for the dynamics and the Bogoliubov equations for the linear stability. A good agreement is found between them.