A semianalytical approach to the quantum dynamics of a plane pendulum is developed, based on Mathieu functions which appear as stationary wave functions. The time-dependent Schrödinger equation is solved for pendular analogs of coherent and squeezed states of a harmonic oscillator, induced by instantaneous changes of the periodic potential energy function. Coherent pendular states are discussed between the harmonic limit for small displacements and the inverted pendulum limit, while squeezed pendular states are shown to interpolate between vibrational and free rotational motion. In the latter case, full and fractional revivals as well as spatiotemporal structures in the time evolution of the probability densities (quantum carpets) are quantitatively analyzed. Corresponding expressions for the mean orientation are derived in terms of Mathieu functions in time. For periodic double well potentials, different revival schemes, and different quantum carpets are found for the even and odd initial states forming the ground tunneling doublet. Time evolution of the mean alignment allows the separation of states with different parity. Implications for external (rotational) and internal (torsional) motion of molecules induced by intense laser fields are discussed.

We demonstrate a practical possibility of loss compensation in measured photocounting statistics in the presence of dark counts and background radiation noise. It is shown that satisfactory results are obtained even in the case of low detection efficiency and large experimental errors.

In this paper, we investigate the localized surface modes in a defective multilayer structure. We show that the defective multilayer structure can support two different kinds of localized modes, depending on the position and the thickness of the defect layer. In one kind, the modes are localized at the interface between the multilayer structure and a homogeneous medium (the so-called surface modes). While, in the other one, the modes are localized at the defect layer (defect-localized modes). We reveal that in the presence of the defect layer, the dispersion curve of the surface modes are pushed to the lower (upper) edge of the photonic band gap when the homogeneous medium is a left-handed (right-handed) material. Therefore, the existence regions of the surface modes are restricted due to the defect layer. Moreover, the effect of defect on the energy flow velocity of the surface modes is discussed.

We study dissipative soliton pair solutions of the complex cubic-quintic Ginzburg-Landau equation with periodic phase modulation term. The external modulation changes the soliton-pair time separation as well as their phase difference, without destroying the existing two-soliton bound state. Transitions between different stable forms of the pair occur in the form of bifurcations. Quite remarkably, two types of bound states may coexist, which leads to hysteresis loops when the modulation depth is varied.

The light-induced atomic desorption effect, known as LIAD, has been explained so far by a debatable Atutov’s theory [S. N. Atutov et al., Phys. Rev. A 60, 4693 (1999)]. In this Brief Report, we propose an approach in which the difficulties of this theory are removed. The theory yields predictions for the atomic vapor density $n\left(t\right)$ in a fully illuminated resonance cell, the time $t_{max}$ that it takes the vapor density to arrive at a maximum value $n_{max}$ and the dependence of $n_{max}$ and $dn/d{t}_{t=+0}$ on the desorbing light intensity. Some of our results are at variance with outcomes of Atutov’s model (such as saturation effect for $n_{max}$ and the dependence of $t_{max}$ on the light intensity) but are in agreement with the experimental data. Additionally, the model presented in this Brief Report satisfactorily explains a reservoir effect recently investigated in experiments where cells equipped with a lockable stem were used.

The ground state of a spinor Bose liquid is ferromagnetic, while the softest excitation above the ground state is the magnon mode. The dispersion relation of the magnon in a one-dimensional liquid is periodic in the wave number $q$ with the period of $2\pi n$, determined by the density $n$ of the liquid. Dynamic correlation functions, such as, e.g., spin-spin correlation function, exhibit power-law singularities at the magnon spectrum, $\omega \to {\omega }_m\left(q,n\right)$. Without using any specific model of the interparticle interactions, we relate the corresponding exponents to independently measurable quantities $\partial {\omega }_m/\partial q$ and $\partial {\omega }_m/\partial n$.

We theoretically study the linear propagation of a stepwise pulse through a dilute dispersive medium when the frequency of the optical carrier coincides with the center of a natural or electromagnetically induced transparency window of the medium (slow-light systems). We obtain fully analytical expressions of the entirety of the step response and show that, for parameters representative of real experiments, Sommerfeld-Brillouin precursors, main field and second precursors (“postcursors”) can be distinctly observed, all with amplitudes comparable to that of the incident step. This behavior strongly contrasts with that of the systems generally considered up to now.

We investigate the Unruh effect on entanglement taking into account the spin degree of freedom of the Dirac field. We analyze spin Bell states in this setting, obtaining their entanglement dependence on the acceleration of one of the partners. Then, we consider simple analogs to the occupation number entangled state $|00⟩+|11⟩$ but with spin quantum numbers for $|11⟩$. We show that, despite their apparent similitude, while the spinless case is always $\text{qubit}\times \text{qubit}$, for the spin case acceleration produces a $\text{qubit}\times \text{four-level}$ quantum system state. We also introduce a procedure to consistently erase the spin information from our setting preserving occupation numbers. We show how the maximally entangled state for occupation number emerges from our setting. We as well analyze its entanglement dependence on acceleration, obtaining greater entanglement degradation than in the spinless case.

A general separability condition on the second moment (covariance matrix) for continuous-variable two-party systems is derived by an analysis analogous to the derivation of Kennard’s uncertainty relation without referring to the non-negativity of the partially transposed density matrix. This separability criterion is generally more stringent than that used by Simon which is based on the non-negativity of partially transposed density matrix, and thus this criterion may be useful in the analysis of general continuous two-party systems. Another separability criterion used by Duan et al. is shown to be generally weaker than that of Simon. We thus have a hierarchy of separability criterions, but all these criterions when combined with suitable squeezing become equivalent at the boundary of the $P$-representation condition and thus turned out to be sufficient to analyze the separability of two-party Gaussian systems.

We implement an iterative quantum state transfer exploiting the natural dipolar couplings in a spin chain of a liquid-crystal NMR system. During each iteration, a finite part of the amplitude of the state is transferred and, by applying an external operation on only the last two spins, the transferred state is made to accumulate on the spin at the end point. The transfer fidelity reaches one asymptotically through increasing the number of iterations. We also implement the inverted version of the scheme which can transfer an arbitrary state from the end point to any other position of the chain and entangle any pair of spins in the chain, acting as a full quantum data bus.

The effects of high optical depth phenomena, such as superradiance, are investigated in potential quantum memory materials. The results may have relevance for several schemes, including controlled reversible inhomogeneous broadening, atomic frequency combs, and quantum memories based on electromagnetically induced transparency, which are based on using ensembles as storage media. It is shown that strong superradiant effects manifested as decay rates larger than $1/T_2^{\ast }$ are present even for moderate values of $\alpha L\le 5$ and increases as a function of $\alpha L$. For even higher $\alpha L$, effects such as off-resonant slow light is demonstrated and discussed and, finally, the efficiency of time-reversed optimized input pulses is tested. A maximum retrieval efficiency of $\sim 20\%$ is reached and agreement with the theoretically expected result is discussed.

A time-dependent density-functional (TDDFT) response equation for the effective Kohn-Sham potential instead of the electron densities is presented that enables the use of orbital-dependent exchange-correlation kernels. In combination with the frequency-dependent exact-exchange kernel the present approach describes long-range charge-transfer excitations qualitatively correct in contrast to standard TDDFT methods, as shown by formal analysis and applications to molecular systems. Even charge-transfer excitations obtained with the adiabatic frequency-independent exact-exchange kernel exhibit a long-range dependence with the distance of the charge transfer, which, however, is too weak by a factor of 2. This indicates that it is not the frequency dependence of the kernel alone that leads to a correct description of charge-transfer excitations.

Time-independent density-functional theoretic approaches to pure excited states are considered, with special emphasis on the extensions of the constrained search to excited states. Links between the Levy-Nagy and Görling formulations are revealed. The excited-state analog of the Legendre-transform functional for ground states is constructed. Powerful results for Coulombic systems may facilitate the construction of an excited-state density functional with a simple and universal form.

We develop a method that can constrain any local exchange-correlation potential to preserve basic exact conditions. Using the method of Lagrange multipliers, we calculate for each set of given Kohn-Sham orbitals a constraint-preserving potential which is closest to the given exchange-correlation potential. The method is applicable to both the time-dependent (TD) and independent cases. The exact conditions that are enforced for the time-independent case are Galilean covariance, zero net force and torque, and Levy-Perdew virial theorem. For the time-dependent case we enforce translational covariance, zero net force, Levy-Perdew virial theorem, and energy balance. We test our method on the exchange (only) Krieger-Li-Iafrate (xKLI) approximate-optimized effective potential for both cases. For the time-independent case, we calculated the ground state properties of some hydrogen chains and small sodium clusters for some constrained xKLI potentials and Hartree-Fock (HF) exchange. The results (total energy, Kohn-Sham eigenvalues, polarizability, and hyperpolarizability) indicate that enforcing the exact conditions is not important for these cases. On the other hand, in the time-dependent case, constraining both energy balance and zero net force yields improved results relative to TDHF calculations. We explored the electron dynamics in small sodium clusters driven by cw laser pulses. For each laser pulse we compared calculations from TD constrained xKLI, TD partially constrained xKLI, and TDHF. We found that electron dynamics such as electron ionization and moment of inertia dynamics for the constrained xKLI are most similar to the TDHF results. Also, energy conservation is better by at least one order of magnitude with respect to the unconstrained xKLI. We also discuss the problems that arise in satisfying constraints in the TD case with a non-cw driving force.

We present a theoretical study on the energy loss of protons in wolframium by calculating target fully relativistic wave functions and binding energies. The HULLAC code is employed to obtain numerical solutions of the Dirac equation. We use the shellwise local plasma approximation (SLPA) to evaluate the different moments of the energy loss. The partial contribution of each subshell of target electrons is calculated separately, including the screening among the electrons of the same binding energy. We pay special attention to the role of the outer $4f$ shell and the screening between electrons of near subshells (i.e., the $5p$ and $4f$ electrons). Results for stopping and straggling cross sections are compared to the experimental data available. Our calculations describe rather well the stopping measurements around the maximum and for very high energies, but overestimate the data for impact energies around 1MeV. We find that the SLPA results tend clearly to Bethe limit, but show a systematic overestimation in the energy region of 1–2 MeV. This overestimation may indicate the presence of other mechanisms included neither in the SLPA nor in Bethe formulations. We also present results for the stopping number of W, Au, Pb, and Bi which follow quite well the Lindhard scaling. A theoretical mean excitation energy $I\left(W\right)=710\text{eV}$ is obtained, in good agreement with the suggested value of $727\pm 30\text{eV}$. Theoretical mean excitation energies for Au, Pb, and Bi are also presented, which are in good agreement with the experimental ones.

Unconstrained searches over quantum control landscapes are theoretically predicted to generally exhibit trap-free monotonic behavior. This paper makes an explicit experimental demonstration of this intrinsic monotonicity for two controlled quantum systems: frequency unfiltered and filtered second-harmonic generation (SHG). For unfiltered SHG, the landscape is randomly sampled and interpolation of the data is found to be devoid of landscape traps up to the level of data noise. In the case of narrow-band-filtered SHG, trajectories are taken on the landscape to reveal a lack of traps. Although the filtered SHG landscape is trap free, it exhibits a rich local structure. A perturbation analysis around the top of these landscapes provides a basis to understand their topology. Despite the inherent trap-free nature of the landscapes, practical constraints placed on the controls can lead to the appearance of artificial structure arising from the resultant forced sampling of the landscape. This circumstance and the likely lack of knowledge about the detailed local landscape structure in most quantum control applications suggests that the a priori identification of globally successful (un)constrained curvilinear control variables may be a challenging task.

We model the behavior of $N$ classical impurity fields immersed in a larger Bose-Einstein condensate by $N+1$ coupled nonlinear Schrödinger equations in one, two, and three space dimensions. We discuss the stability of the uniform miscible system and show the importance of surface tension for self-localization of the impurity fields. We derive analytically the attractive tail of the impurity-impurity interaction due to mediation by the underlying condensate. Assuming all impurity fields interact with the same strength, we explore numerically the resulting phase diagram, which contains four phases: (I) all fields are miscible; (II) the impurity fields are miscible with each other but phase separate from the condensate as a single bubble; (III) the localized impurity fields stay miscible with the condensate, but not with each other; and (IV) the impurity fields phase separate from the condensate and each other, forming a crystalline structure within a bubble. Thus, we show that a crystal can be constructed solely from superfluid components. Finally, we argue that the crystalline phases maintain their superfluid behavior, i.e., they possess a nonclassical rotational inertia, which—combined with lattice order—is a characteristic of supersolidity.

The generalized purity is employed for investigating the process of coherence loss and delocalization of the $Q$ function in the Bloch sphere of a two-mode Bose-Einstein condensate in a symmetrical double well with cross collision. Quantum phase transition of the model is signaled by the generalized purity as a function of an appropriate parameter of the Hamiltonian and the number of particles $\left(N\right)$. A power-law dependence of the critical parameter with $N$ is derived.

We study the optical control for birefringence of a polarized light by an atomic ensemble with a tripod configuration, which is mediated by the electromagnetically induced transparency with a spatially inhomogeneous laser. The atomic ensemble splits the linearly polarized light ray into two orthogonally polarized components, whose polarizations depend on quantum superposition of the initial states of the atomic ensemble. Accompanied with this splitting, the atomic ensemble behaves as a birefringent lens, which allows one polarized light ray passing through straightly while focuses the other light of vertical polarization with finite aberration of focus.

Adiabaticity occurs when, during its evolution, a physical system remains in the instantaneous eigenstate of the Hamiltonian. Unfortunately, existing results, such as the quantum adiabatic theorem based on a slow down evolution $\left[H\left(ϵt\right),ϵ\to 0\right]$, are insufficient to describe an evolution driven by the Hamiltonian $H\left(t\right)$ itself. Here we derive general criteria and exact bounds, for the state and its phase, ensuring an adiabatic evolution for any Hamiltonian $H\left(t\right)$. As a corollary, we demonstrate that the commonly used condition of a slow Hamiltonian variation rate, compared to the spectral gap, is indeed sufficient to ensure adiabaticity but only when the Hamiltonian is real and nonoscillating (for instance, containing exponential or polynomial but no sinusoidal functions).