We discuss the statistical properties of lifetimes of electromagnetic quasibound states in dielectric microresonators with fully chaotic ray dynamics. Using the example of a resonator of stadium geometry, we find that a recently proposed random-matrix model very well describes the lifetime statistics of long-lived resonances, provided that two effective parameters are appropriately renormalized. This renormalization is linked to the formation of short-lived resonances, a mechanism also known from the fractal Weyl law and the resonance-trapping phenomenon.

To search for the temporal variation in the fundamental constants, one needs to know dependence of atomic transition frequencies on these constants. We study the dependence of the hyperfine structure of atomic $s$ levels on nuclear radius and, via radius, on quark masses. An analytical formula has been derived and tested by the numerical relativistic Hartree-Fock calculations for Rb, ${\text{Cd}}^{+}$, Cs, ${\text{Yb}}^{+}$, and ${\text{Hg}}^{+}$. The results of this work allow the use of the results of past and future atomic clock experiments and quasar spectra measurements to put constraints on time variation in the quark masses.

We use delayed field ionization to observe the microwave resonance transitions of Sr from $5snf$ to $5sng$, $5snh$, and $5sni$. The energies of the $5sn\ell$, $\ell >3$ states are split by the indirect spin-orbit coupling of the Sr core to the Rydberg electron, producing the $K$ splittings. From the $K$ splittings we extract the ionic dipole and quadrupole matrix elements, $⟨5s|r|5p⟩=3.65\left(25\right)a_0$ and $⟨5s|r^2|4d⟩=12\left(14\right)a_0^2$. From the dipole matrix element we obtain the dipole polarizability of ${\text{Sr}}^{+}$. With the dipole polarizability and the quantum defect differences of adjacent $l$ states, we can determine the ${\text{Sr}}^{+}$ quadrupole polarizability. The dipole and quadrupole polarizabilities of ${\text{Sr}}^{+}$ are ${\alpha }_d=86\left(11\right)a_0^3$ and ${\alpha }_q=1.1\times {10}^3\left(10\right)a_0^5$, respectively.

We employ a straightforward relation between mutually unbiased and Bell bases to extend the latter in terms of a direct construction for the former. We analyze in detail the properties of these generalized Bell states, showing that they constitute an appropriate tool for testing entanglement in bipartite multiqudit systems.

We study cooling and squeezing the fluctuations of a nanomechanical beam using quantum feedback control. In our model, the nanomechanical beam is coupled to a transmission line resonator via a superconducting quantum interference device. The leakage of the electromagnetic field from the transmission line resonator is measured using homodyne detection. This measured signal is then used to design a quantum feedback control signal to drive the electromagnetic field in the transmission line resonator. Although the control is imposed on the transmission line resonator, this quantum feedback control signal indirectly affects the thermal motion of the nanomechanical beam via the inductive beam-resonator coupling, making it possible to cool and squeeze the fluctuations of the beam, allowing it to approach the standard quantum limit.

Different entropies which can characterize the inseparable quantum correlation in a two-electron entangled artificial atom proposed by Moshinsky are analyzed. The analysis is based on an exact representation for the trace of the $q$-order one-body reduced density matrix in terms of the interparticle coupling. The entanglement spectrum of the model system and the possible role of the entropy-maximum concept to practical applications of matrices are discussed as well. The ground-state energy, readily obtained from the Schrödinger Hamiltonian, is recalculated within a density-matrix-functional representation for its components.

We consider an atomic Fermi gas confined in a uniform optical lattice potential, where the atoms can pair into molecules via a magnetic-field-controlled narrow Feshbach resonance. The phase diagram of the resulting atom-molecule mixture in chemical and thermal equilibria is determined numerically in the absence of interactions under the constraint of particle conservation. In the limiting cases of vanishing or large lattice depth we derive simple analytical results for important thermodynamic quantities. One such quantity is the dissociation energy, defined as the detuning of the molecular energy spectrum with respect to the atomic one for which half of the atoms have been converted into dimers. Importantly we find that the dissociation energy has a nonmonotonic dependence on lattice depth.

We propose a protocol for storage and retrieval of photon wave packets in a $\Lambda$-type atomic medium. This protocol derives from spectral hole burning and takes advantages of the specific properties of solid-state systems at low temperature, such as rare-earth ion-doped crystals. The signal pulse is tuned to the center of the hole that has been burnt previously within the inhomogeneously broadened absorption band. The group velocity is strongly reduced, being proportional to the hole width. This way the optically carried information and energy are carried over to the off-resonance optical dipoles. Storage and retrieval are performed by conversion to and from ground-state Raman coherence by using brief $\pi$ pulses. The protocol exhibits some resemblance with the well-known electromagnetically induced transparency process. It also presents distinctive features such as the absence of coupling beam. In this paper we detail the various steps of the protocol, summarize the critical parameters, and theoretically examine the recovery efficiency.

We present experimental evidence in support of the recent theoretical proposal that intrinsic $1/f$ frequency noise in short cavity erbium-doped fiber lasers is of thermal origin. We demonstrate that the power spectral density of frequency noise in distributed-feedback fiber lasers (DFB FL) exhibits predicted $T^2$ temperature dependence across all frequencies over a temperature range of almost 200 K. This temperature dependence is observed both in direct interferometric measurements of frequency noise in a single mode DFB FL and noninterferometric measurements of polarization-beat-frequency noise in a dual frequency DFB FL. It is also shown that frequency noise of orthogonal polarization modes in the dual frequency DFB FL is substantially correlated providing a strong indication of a common origin.

We formulate an iteration scheme for quantitative two-dimensional phase retrieval of complex scalar wave fields from input-output intensity profiles using a coherent rotationally symmetric shift-invariant linear optical imaging system. This method is a generalization of our previous method for quantitative single-image pure phase reconstruction using an imperfect shift-invariant linear imaging system. The method is somewhat analogous to the Gerchberg-Saxton iterative phase-retrieval algorithm, but typically converges much more rapidly. We have demonstrated the efficacy of the method using simulated data in the presence of noise.

In this paper we report an experiment on the observation of the recoil-induced resonances (RIR) and electromagnetically induced absorption (EIA) of cold ${}^{87}\text{R}\text{b}$ atoms in diffuse light. The pump light of the RIR and the EIA comes from the diffuse light in an integrating sphere, which also serves the cooling light. We measured the RIR and the EIA signal varying with the detuning of the diffuse laser light, and also measured the number and the temperature of the cold atoms at the different detunings. The mechanism of RIR and EIA in the configuration with diffuse-light pumping and laser probing are discussed, and the difference between the nonlinear spectra of cold atoms in a diffuse-light cooling system and in a magneto-optical trap is studied.

We consider a system of two spin-$\frac{1}{2}$ particles, initially in an entangled Bell state. If one of the particles is interacting with an environment (e.g., a collection of $N$ independent spins), the two-particle system undergoes decoherence. Using a simple model of decoherence, we show that this process has two consequences. First, the maximal amount by which the Clauser-Horne-Shimony-Holt inequality is violated decays to zero. Second, the set of directions of measurement for which the inequality is violated is reduced in the course of decoherence. The volume of that set is bounded above by $\text{const}\times {\left|r\right|}^2$, where $r$ is the decoherence factor. We obtain similar results for the case when each of the two particles is in interaction with a separate environment.

A scheme is proposed to include both cyclic and noncyclic geometric quantum computations in nuclear-magnetic-resonance system by the invariant theory. By controlling magnetic field and arbitrary parameters in the invariant operator, the phases accumulated in the entangling quantum gates for single- and two-qubit systems are pure geometric phases. Thus, fault tolerance may occur in some critical magnetic field parameters for either cyclic or noncyclic evolution by differently choosing for gate time.

We investigate the characteristics of complete tunneling of light through the impedance-matched dual singly negative media. In this special tunneling structure, only the normally incident light can tunnel the barrier out completely. This phenomenon occurs regardless of the refractive indices of the barrier-enclosing materials and the polarization states of incident light so that all kinds of polarized light can tunnel out completely without changing their initial polarization states. Its physical origin lies in the local surface mode of the barrier which has polarization degeneracy and whose propagation constant is zero.

We study the thermal Casimir effect between two thick slabs composed of plane-parallel layers of random dielectric materials interacting across an intervening homogeneous dielectric. It is found that the effective interaction at long distances is self-averaging and is given by a description in terms of effective dielectric functions. The behavior at short distances becomes random (sample dependent) and is dominated by the local values of the dielectric function proximal to each other across the dielectrically homogeneous slab.

We have developed a model of Feshbach resonances in gases of ultracold alkali-metal atoms using the ideas of multichannel quantum-defect theory. Our model requires just three parameters describing the interactions—the singlet and triplet scattering lengths, and the long-range van der Waals coefficient—in addition to known atomic properties. Without using any further details of the interactions, our approach can accurately predict the locations of resonances. It can also be used to find the singlet and triplet scattering lengths from measured resonance data. We apply our technique to ${}^6\text{L}\text{i-}{}^{40}\text{K}$ and ${}^{40}\text{K}\text{−}{}^{87}\text{R}\text{b}$ scattering, obtaining good agreement with experimental results, and with the more computationally intensive coupled channels technique.

We explore the effect of two-dimensional position-space noncommutativity on the bipartite entanglement of continuous-variable systems. We first extend the standard symplectic framework for studying entanglement of Gaussian states of commutative systems to the case of noncommutative systems residing in two dimensions. Using the positive partial transpose criterion for separability of bipartite states, we derive a condition on the separability of a noncommutative system that is dependent on the noncommutative parameter $\theta$. We then consider the specific example of a bipartite Gaussian state and show the quantitative reduction in entanglement originating from noncommutative dynamics. We show that such a reduction in entanglement for a noncommutative system arising from the modification of the variances of the phase-space variables (uncertainty relations) is clearly manifested between two particles that are separated by small distances.

Via explicit examples we show that the pre-existing entanglement can really enhance (not only behave as an assistance for) the efficiency of the quantum error-correcting codes (QECCs) in a single block of encoding or decoding as well as help in beating the quantum Hamming bound. A systematic approach to constructing entanglement-assisted (or enhanced) quantum error-correcting codes (EAQECCs) via graph states is also presented, and an infinite family of entanglement-enhanced codes has been constructed. Furthermore we generalize the EAQECCs to the case of not-so-perfectly protected qubit and introduce the quantity infidelity as a figure of merit and show that the EAQECCs also outperform the ordinary QECCs.

Charge state specific euv spectra from a range of tin ions have been recorded at Tokyo Metropolitan University. The spectra were produced from charge-exchange collisions between tin ions and helium atoms using an electron cyclotron resonance source. At low target gas pressures, the spectra were dominated by single capture events. The spectra were, unexpectedly, found to be dominated by an intense unresolved transition array near 13 nm while the resonance lines, including the previously identified $4p-4d$ ${{}^{1}S}_0\to {{}^{1}P}_1$ resonance line of Sn XV, were relatively weak. From atomic structure calculations, it was found that the unresolved transition array arises from $4s^{2}4p^{m-1}4d-4s^{2}4p^{m-1}4f+4s^{2}4p^{m-2}4d^2$ transitions. In addition it proved necessary to include interaction with core excited $4s4p^{m}4d$ configurations to fully explain the observed spectra.

One of the major deficiencies of the standard density functionals is their inability to describe dispersion interactions. Becke and Johnson recently proposed a conceptually simple yet accurate dispersion model called the exchange-dipole moment (XDM) model, which allows the calculation of both intermolecular and intramolecular dispersion interactions with density functional theory (DFT). In this paper, we present an efficient self-consistent-field (SCF) solution of the XDM model. We also give detailed analysis of the post-SCF approach in which the dispersion term is added to the Hamiltonian as a perturbation, and show that it has an error on the order of ${10}^{-5}$ in density matrix due to the addition of dispersion to the Hamiltonian. In addition, for gradient calculations with respect to the atomic movement, we introduce a further approximation in which the electronic part of the XDM gradient formula is omitted, and show that it yields an error smaller than ${10}^{-3}\text{a}\text{.u}\text{.}$ These approximations offer a simple and efficient route with good precision for the implementation of XDM model and other dispersion models into existing DFT codes. The effectiveness of our implementation is demonstrated through several examples. The first example shows that inclusion of the XDM model leads to much more accurate prediction of enthalpies of formation of straight-chain alkanes than does the Becke three-parameter Lee-Yang-Parr (B3LYP) functional. The inclusion of the dispersion is also shown to improve the accuracy in the calculation of isomerization energies and bond-dissociation energies of alkanes. The last example shows that the qualitative difference in optimal geometries of a tyrosine-glycine peptide, calculated using the B3LYP functional and the second-order Møller-Plesset method, essentially disappears when XDM is added to the DFT calculation.