A periodically driven multiple-parametric two-level model is introduced. Under certain special parameter conditions, an exact analytical solution to this model can be obtained in an explicit form. This gives an exact analytical demonstration of the well-known Landau-Zener-Stückelberg-Majorana resonances.

We investigate the quantum interference induced shifts between energetically close states in highly charged ions, with the energy structure being observed by laser spectroscopy. In this work, we focus on hyperfine states of lithiumlike heavy-$Z$ isotopes and quantify how much quantum interference changes the observed transition frequencies. The process of photon excitation and subsequent photon decay for the transition $2s\to 2p\to 2s$ is implemented with fully relativistic and full-multipole frameworks, which are relevant for such relativistic atomic systems. We consider the isotopes ${}^{207}\mathrm{Pb}^{79+}$ and ${}^{209}\mathrm{Bi}^{80+}$ due to experimental interest, as well as other examples of isotopes with lower $Z$, namely ${}^{141}\mathrm{Pr}^{56+}$ and ${}^{165}\mathrm{Ho}^{64+}$. We conclude that quantum interference can induce shifts up to 11% of the linewidth in the measurable resonances of the considered isotopes, if interference between resonances is neglected. The inclusion of relativity decreases the cross section by 35%, mainly due to the complete retardation form of the electric dipole multipole. However, the contribution of the next higher multipoles (e.g., magnetic quadrupole) to the cross section is negligible. This makes the contribution of relativity and higher-order multipoles to the quantum interference induced shifts a minor effect, even for heavy-$Z$ elements.

We present in this paper a theory of dynamic polarizability for an atomic state due to an external field of nonparaxial Laguerre-Gaussian (LG) beam using the sum-over-states technique. A highly correlated relativistic coupled-cluster theory is used to evaluate the most important and correlation-sensitive parts of the sum. The theory is applied on ${\mathrm{Sr}}^{+}$ to determine the magic wavelengths for $5s_{1/2}\to 4d_{3/2},4d_{5/2}$ transitions. Results show the variation of magic wavelengths with the choice of orbital and spin angular momenta of the incident LG beam. Also, the tunability of the magic wavelengths is studied by using the focusing angle of the LG beam and its efficiency in the near-infrared region is observed. Evaluations of the wide spectrum of magic wavelengths from infrared to ultraviolet have substantial importance to experimentalists for carrying out high-precision measurements in fundamental physics. These magic wavelengths can be used to confine the atom or ion at the dark central node or at the high-intensity ring of the LG beam.

Roles of electron correlation effects in the determination of attachment energies, magnetic-dipole hyperfine-structure constants, and electric-dipole $\left(E1\right)$ matrix elements of the low-lying states in the singly charged cadmium ion $\left({\mathrm{Cd}}^{+}\right)$ have been analyzed. We employ the singles and doubles approximated relativistic coupled-cluster (RCC) method to calculate these properties. Intermediate results from the Dirac-Hartree-Fock approximation,the second-order many-body perturbation theory, and considering only the linear terms of the RCC method are given to demonstrate propagation of electron correlation effects in this ion. Contributions from important RCC terms are also given to highlight the importance of various correlation effects in the evaluation of these properties. At the end, we also determine $E1$ polarizabilities $\left({\alpha }^{E1}\right)$ of the ground and $5p{}^2{P}_{1/2;3/2}$ states of ${\mathrm{Cd}}^{+}$ in the ab initio approach. We estimate them again by replacing some of the $E1$ matrix elements and energies from the measurements to reduce their uncertainties so that they can be used in the high-precision experiments of this ion.

We study the quadratic Zeeman effect (QZE) in a system of antiferromagnetic spin-1 bosons on a square lattice and derive the ground-state phase diagrams by means of quantum Monte Carlo simulations and mean-field treatment. The QZE imbalances the populations of the magnetic sublevels $\sigma =\pm 1$ and $\sigma =0$, and therefore affects the magnetic and mobility properties of the phases. Both methods show that the tip of the even Mott lobes, stabilized by singlet state, is destroyed when turning on the QZE, thus leaving the space to the superfluid phase. Contrariwise, the tips of odd Mott lobes remain unaffected. Therefore, the Mott-superfluid transition with even filling strongly depends on the strength of the QZE, and we show that the QZE can act as a control parameter for this transition at fixed hopping. Using quantum Monte Carlo simulations, we elucidate the nature of the phase transitions and examine in detail the nematic order: the first-order Mott-superfluid transition with even filling observed in the absence of QZE becomes second order for weak QZE, in contradistinction to our mean-field results which predict a first-order transition in a larger range of QZE. Furthermore, a spin nematic order with director along the $z$ axis is found in the odd Mott lobes and in the superfluid phase for energetically favored $\sigma =\pm 1$ states. In the superfluid phase with even filling, the $xy$ components of the nematic director remain finite only for moderate QZE.

Nanomaterials, which show large reflectivity for external radiation, are of general interest in science and technology. We report a result from our ongoing research on the reflection of low-energy neutrons from powders of detonation diamond nanoparticles. Our previous work showed a large probability for quasispecular reflection of neutrons from this medium. The model of neutron scattering from nanoparticles, which we have developed, suggests two ways to increase the quasispecular reflection probability: (1) the reduction of incoherent scattering by substitution of hydrogen with fluorine inside the nanoparticles, and (2) the sharpening of the neutron optical potential step by removal of amorphous $s{p}^2$ carbon from the nanoparticle shells. We present experimental results on scattering of slow neutrons from both raw and fluorinated diamond nanoparticles with amorphous $s{p}^2$ carbon removed by gas-solid fluorination. These results show a clear increase in quasispecular reflection probability.

I present a semiclassical analysis of a spatial-mode demultiplexing (SPADE) measurement scheme for far-field incoherent optical imaging under the effects of diffraction and photon shot noise. Building on previous results that assume two point sources or the Gaussian point-spread function, I generalize SPADE for a larger class of point-spread functions and evaluate its errors in estimating the moments of an arbitrary subdiffraction object. Compared with the limits to direct imaging set by the Cramér-Rao bounds, the results show that SPADE can offer far superior accuracy in estimating second- and higher-order moments.

We report nonclassical aspects of the collective behavior of two atoms in a cavity by investigating the photon statistics and photon distribution over a very broad domain of parameters. Starting with the dynamics of two atoms radiating in phase into the cavity, we study the photon statistics for arbitrary interatomic phases as revealed by the second-order intensity correlation function at zero time, $g^{\left(2\right)}\left(0\right)$, and the Mandel $Q$ parameter. We find that the light field can be tuned from antibunched to (super-)bunched as well as nonclassical to classical behavior by merely modifying the atomic position. The highest nonclassicality in the sense of the smallest $Q$ parameter is found when spontaneous emission, cavity decay, coherent pumping, and atom-cavity coupling are of comparable magnitude. We introduce a quantum version of the negative binomial distribution with its parameters directly related to $Q$ and $g^{\left(2\right)}\left(0\right)$ and discuss its range of applicability. We also examine the Klyshko parameter, which highlights the nonclassicality of the photon distribution.

There is a common understanding in quantum optics that nonclassical states of light are states that do not have a positive semidefinite and sufficiently regular Glauber-Sudarshan $P$ function. Almost all known nonclassical states have $P$ functions that are highly irregular, which makes working with them difficult and direct experimental reconstruction impossible. Here we introduce classes of nonclassical states with regular, non-positive-definite $P$ functions. They are constructed by “puncturing” regular smooth positive $P$ functions with negative Dirac-$\delta$ peaks or other sufficiently narrow smooth negative functions. We determine the parameter ranges for which such punctures are possible without losing the positivity of the state, the regimes yielding antibunching of light, and the expressions of the Wigner functions for all investigated punctured states. Finally, we propose some possible experimental realizations of such states.

We study the quantum Zeno effect (QZE) and quantum anti-Zeno effect (QAZE) in a two-level system (TLS) interacting with an environment that has $1/f$ noise. Using a numerically exact method based on the thermofield dynamics theory and the matrix product states, we obtain exact evolutions of the TLS and bath (environment) under repetitive measurements at both zero and finite temperatures. At zero temperature, we observe a transition from a pure QZE in the short time scale to a QZE-QAZE crossover in the long time scale by considering the measurement-induced non-Markovian effect. At finite temperature, we exploit that the thermal fluctuation suppresses the decay of the survival probability in the short time scale, whereas it enhances the decay in the long time scale.

We analyze families of measures for the quantum statistical speed which include as special cases the quantum Fisher information, the trace speed, i.e., the quantum statistical speed obtained from the trace distance, and more general quantifiers obtained from the family of Schatten norms. These measures quantify the statistical speed under generic quantum evolutions and are obtained by maximizing classical measures over all possible quantum measurements. We discuss general properties, optimal measurements, and upper bounds on the speed of separable states. We further provide a physical interpretation for the trace speed by linking it to an analog of the quantum Cramér-Rao bound for median-unbiased quantum phase estimation.

Einstein-Podolsky-Rosen steering is a form of quantum nonlocality, which is weaker than Bell nonlocality, but stronger than entanglement. Here we present a method to check Einstein-Podolsky-Rosen steering in the scenario where the steering party performs two black-box measurements and the trusted party performs projective qubit measurements corresponding to two arbitrary mutually unbiased bases. This method is based on decomposing the measurement correlations in terms of extremal boxes of the steering scenario. In this context, we propose a measure of steerability called steering cost. We show that our steering cost is a convex steering monotone. We illustrate our method to check steerability with two families of measurement correlations and find out their steering cost.

Covert communication allows the transmission of messages in such a way that it is not possible for adversaries to detect that the communication is occurring. This provides protection in situations where knowledge that two parties are talking to each other may be incriminating to them. In this work, we study how covert communication can be used for a different purpose: secret key expansion. First, we show that any message transmitted in a secure covert protocol is also secret and therefore unknown to an adversary. We then propose a covert communication protocol where the amount of key consumed in the protocol is smaller than the transmitted key, thus leading to secure secret key expansion. We derive precise conditions for secret key expansion to occur, showing that it is possible when there are sufficiently low levels of noise for a given security level. We conclude by examining how secret key expansion from covert communication can be performed in a computational security model.

We consider the bipartite state of a two-photon polarization system and obtain the exact analytical expression for the von Neumann entropy in the particular case of a five-parameter polarization density matrix. We investigate and graphically illustrate the dependence of the entropy on these five parameters, in particular, the existence of exotic, transition from exotic to nonexotic, and nonexotic states, where the quantum conditional entropy is negative, both positive and negative, and positive, respectively. We study the “cooling” or “heating” effect that follows from the reduced density of photon 2 when a measurement is performed on photon 1.

We investigate how to manipulate the tripartite frequency correlation of triplets which are generated from cascaded spontaneous parametric down-conversions. A monolithic quadratic nonlinear crystal is designed to contain two segments of periodically poled lithium niobate waveguide as nonlinear mediums to produce cascaded photon pairs both under phase-matching and group-velocity-matching conditions. By choosing proper pump bandwidth and crystal length, the tripartite frequency will show a full correlation, partial correlation, or no correlation, corresponding an inseparable triplet, separable one photon and biphoton, or three separable photons, respectively. This opens up a way to manipulate the tripartite correlation, which is important for understanding quantum fundamentals and also can supply key elements for developing new quantum technologies.

We demonstrate a method for general linear optical networks that allows one to factorize any $\mathrm{SU}(n$) matrix in terms of two $\mathrm{SU}(n-1)$ blocks coupled by an SU(2) entangling beam splitter. The process can be recursively continued in a straightforward way, ending in a tidy arrangement of SU(2) transformations. The method hinges only on a linear relationship between input and output states, and can thus be applied to a variety of scenarios, such as microwaves, acoustics, and quantum fields.

We propose general methodology of deterministic single-mode quantum interaction nonlinearly modifying single quadrature variable of a continuous-variable system. The methodology is based on linear coupling of the system to ancillary systems subsequently measured by quadrature detectors. The nonlinear interaction is obtained by using the data from the quadrature detection for dynamical manipulation of the coupling parameters. This measurement-induced methodology enables direct realization of arbitrary nonlinear quadrature interactions without the need to construct them from the lowest-order gates. Such nonlinear interactions are crucial for more practical and efficient manipulation of continuous quadrature variables as well as qubits encoded in continuous-variable systems.

We theoretically study the Casimir-Polder force on an atom in an arbitrary initial state in a rather general electromagnetic environment wherein the materials may have a nonreciprocal bianisotropic dispersive response. It is shown that under the Markov approximation the force has resonant and nonresonant contributions. We obtain explicit expressions for the optical force both in terms of the system Green function and of the electromagnetic modes. We apply the theory to the particular case wherein a two-level system interacts with a topological gyrotropic material, showing that the nonreciprocity enables exotic light-matter interactions and the opportunity to sculpt and tune the Casimir-Polder forces on the nanoscale. With a quasistatic approximation, we obtain a simple analytical expression for the optical force and unveil the crucial role of surface plasmons in fluctuation-induced forces. Finally, we derive the Green function for a gyrotropic material half-space in terms of a Sommerfeld integral.