We report our study of the magneto-optical effect in a strictly linear regime on spin-polarized cold cesium atoms. Due to the low intensity and the short illumination period of the probe beam, less than 7.5% of the sample atoms change their states by absorbing probe photons. We produce a medium of atoms at rest in either the $6S_{1∕2},F=3,m_F=0$ or $6S_{1∕2},F=3,m_F=3$ state by optically pumping atoms trapped in a magneto-optical trap. We use the $D1$ resonance with large lower and upper state hyperfine splittings as a probe transition to avoid hyperfine mixing from the Zeeman interaction. Under this idealized situation we measure the Stokes parameters in order to find the polarization rotation and circular dichroism experienced by the probe light. We find that there are qualitative differences between the results for the $m_F=0$ and $m_F=3$ cases. While dispersion and consequent Faraday rotation play a dominant role when the atoms are in the $m_F=0$ state, it is dissipation and circular dichroism that are important when they are in the $m_F=3$ state. Similarly, while the size of the Faraday rotation and the circular dichroism for the $m_F=0$ case scales linearly with the applied magnetic field, for the $m_F=3$ case it is the shift of the probe polarization change versus frequency that is linearly proportional to the magnetic field strength.

A five-level tripod scheme is proposed for obtaining a high efficiency four-wave-mixing (FWM) process. The existence of double-dark resonances leads to a strong modification of the absorption and dispersion properties against a pump wave at two transparency windows. We show that both of them can be used to open the four-wave mixing channel and produce efficient mixing waves. In particular, higher FWM efficiency is always produced at the transparent window corresponding to the relatively weak-coupling field. By manipulating the intensity of the two coupling fields, the conversion efficiency of FWM can be controlled.

Beyond the quantum Markov approximation, we calculate the geometric phase of a two-level system driven by a quantized magnetic field subject to phase dephasing. The phase reduces to the standard geometric phase in the weak-coupling limit, and it involves the phase information of the environment in general. In contrast with the geometric phase in dissipative systems, the geometric phase acquired by the system can be observed on a long time scale. We also show that with the system decohering to its pointer states, the geometric phase factor tends to a weighted sum over the phase factors pertaining to the pointer states.

We report the energy-dependent fragmentation cross sections for several of the more likely fragmentation channels for protons with up to $10\mathrm{keV}$ impact energy colliding with acetylene and ethane. We find that the predominant channels are those which involve the dissociation of a carbon-hydrogen bond, and we find that the cross sections for these channels are maximum in the low-projectile-energy region. The cross sections for fragmentation involving dissociation of a C-C bond are an order of magnitude smaller and peak at somewhat higher projectile energy. Although there are no experimental values with which to compare, it appears that selection of projectile energy can be used to influence branching ratios in proton-hydrocarbon collisions and, by implication, in other ion-molecule and atom-molecule collisions.

We investigate the problem of copying pure two-qubit states of a given degree of entanglement in an optimal way. Completely positive covariant quantum operations are constructed which maximize the fidelity of the output states with respect to two separable copies. These optimal copying processes hint at the intricate relationship between fundamental laws of quantum theory and entanglement.

By using the measure of concurrence, mode entanglement of an electron moving in four kinds of one-dimensional determined and random potentials is studied numerically. The extended and localized states can be distinguished by mode entanglement. There are sharp transitions in concurrence at mobility edges. It provides that the mode entanglement may be a new index for a metal-insulator transition.

A scheme is proposed to implement a conditional quantum phase gate between atoms trapped in spatially separated cavities. Instead of direct interaction between atoms, quantum interference of polarized photons decayed from the optical cavities is used to realize the desired quantum operation between two distant atoms. The scheme requires a twofold coincidence detection, and is insensitive to the imperfection of the photon detectors.

Wave functions of complex lanthanide atoms $\mathrm{Nd}\mathrm{I}$, $\mathrm{Pm}\mathrm{I}$, and $\mathrm{Sm}\mathrm{I}$, obtained via multiconfiguration Dirac-Fock method, are analyzed for density of states in terms of partial densities, strength functions $\left[F_k\left(E\right)\right]$, number of principal components $\left[{\xi }_2\left(E\right)\right]$, and occupancies $\left({⟨n_{\alpha }⟩}^E\right)$ of single-particle orbits using embedded Gaussian orthogonal ensemble of one plus two-body random matrix ensembles $\left[\mathrm{EGOE}(1+2)\right]$. It is seen that density of states are in general multi-modal, $F_k\left(E\right)$’s exhibit variations as function of the basis states energy and ${\xi }_2\left(E\right)$’s show structures arising from localized states. The sources of these departures from $\mathrm{EGOE}(1+2)$ are investigated by examining the partial densities, correlations between $F_k\left(E\right)$, ${\xi }_2\left(E\right)$, and ${⟨n_{\alpha }⟩}^E$ and also by studying the structure of the Hamiltonian matrices. These studies point out the operation of $\mathrm{EGOE}(1+2)$ but at the same time suggest that weak admixing between well separated configurations should be incorporated into $\mathrm{EGOE}(1+2)$ for more quantitative description of chaos and localization in $\mathrm{Nd}\mathrm{I}$, $\mathrm{Pm}\mathrm{I}$, and $\mathrm{Sm}\mathrm{I}$.

Spectrum calculations have been performed in the Breit-Pauli approximation for all levels in $\mathrm{Si}\mathrm{I}$ up to $3s^{2}3p3d$${}^{3}D^o$. Included are energy levels and transition probabilities for E1 and some E2 and M1 transitions between these levels from which lifetimes were determined. All lifetimes are within experimental error bars except for the high-lying $3s^{2}3p3d$${}^{1}P^o$ and ${}^{3}D^o$ levels. The lifetime for $3s3p^3$${}^{3}D^o$, however, does not agree with the most accurate experimental value. Detailed correlation studies are performed for the $3s^{2}3p^2\text{to}3s^{2}3p3d$ allowed transitions. The resulting length and velocity forms of the weighted oscillator strength are in excellent agreement. For $3s3p^3$ the effect of core polarization was investigated. The final results are compared with experiment and other theory.

In this paper it is demonstrated that electron vibrational absorption of molecules driven by strong IR field provides rich physical interpretations of dynamical processes on a short time scale. The phase of an infrared field influences strongly the trajectory of the nuclear wave packet and the probing spectrum. It is shown that the probe spectrum keeps memory of the infrared phase even after that the pump field left the system. The phase effect takes maximum value when the duration of the probe pulse is of the order of the infrared field period, and can be enhanced by a proper control of the duration and intensity of the pump pulse. The phase effect is different for oriented and disordered molecules and depends strongly on the intensity of pump radiation. It can be an effective tool to study charge transfer processes like proton transfer in hydrogen bonded networks.

We consider the equilibration rate for fermions in Bose-Fermi mixtures undergoing cross-dimensional rethermalization. Classical Monte Carlo simulations of the relaxation process are performed over a wide range of parameters, focusing on the effects of the mass difference between species and the degree of initial departure from equilibrium. A simple analysis based on Enskog’s equation is developed and shown to be accurate over a variety of different parameter regimes. This allows predictions for mixtures of commonly used alkali-metal atoms.

It is shown that in an anisotropic harmonic trap that rotates with the properly chosen rotation rate, the force of gravity leads to a resonant behavior. Full analysis of the dynamics in an anisotropic, rotating trap in three dimensions is presented and several regions of stability are identified. On resonance, the oscillation amplitude of a single particle, or of the center of mass of a many-particle system (for example, BEC), grows linearly with time and all particles are expelled from the trap. The resonances can only occur when the rotation axis is tilted away from the vertical position. The positions of the resonances (there are always two of them) do not depend on the mass but only on the characteristic frequencies of the trap and on the direction of the angular velocity of rotation.

We study experimentally nonlinear optical processes in which Stokes and anti-Stokes fields build up under strong, resonant, counterpropagating pump laser excitation in atomic sodium vapor. We find that, at some pump frequency, two off-axis anti-Stokes emissions propagating along reflection-symmetric directions are strongly temporally correlated, with a correlation time of $0.5\mu \mathrm{s}$ and a correlation range of $1\mathrm{mrad}$. It is shown by the numerical analysis based on six-wave mixing process involving pump, Stokes, and anti-Stokes waves in the forward and the backward directions that such correlated anti-Stokes emissions are possible when the medium is opaque for the Stokes field and transparent for the anti-Stokes field. Possibilities of quantum correlation for entangled photon generation using this system are discussed.

We observed Moiré fringes in spatial quantum correlations between twin photons generated by parametric down-conversion. Spatially periodic structures were nonlocally superposed giving rise to beat frequencies typical of Moiré patterns. This result brings interesting perspectives regarding metrological applications of such a quantum optical setup.

We consider the situation in which an observer internal to an isolated system wants to measure the total energy of the isolated system (this includes his own energy, that of the measuring device and clocks used, etc.). We show that he can do this in an arbitrarily short time, as measured by his own clock. This measurement is not subjected to a time-energy uncertainty relation. The properties of such measurements are discussed in detail with particular emphasis on the relation between the duration of the measurement as measured by internal clocks versus external clocks.

We study the effect of thermal fluctuations in a recently proposed protocol for transmission of unknown quantum states through quantum spin chains. We develop a low-temperature expansion for general spin chains. We then apply this formalism to study exactly thermal effects on short spin chains of four spins. We show that optimal times for extraction of output states are almost independent of the temperature, which lowers only the fidelity of the channel. Moreover we show that thermal effects are smaller in the antiferromagnetic chains than the ferromagnetic ones.

In this paper, we generalize the residual entanglement to the case of multipartite states in arbitrary dimensions by making use of a different method. Through the introduction of a special entanglement measure, the residual entanglement of mixed states takes on a form that is more elegant than that in Ref. [7] used by Coffman et al. [Phys. Rev. A 61, 052306 (2000)]. The result obtained in this paper is different from the previous one given in Ref. [8] by Wong and Christensen [Phys. Rev. A 63, 044301 (2000)]. Several examples demonstrate that our present result is a good measurement of the multipartite entanglement. Furthermore, the original residual entanglement is a special case of our result.

We show that potentials for exchange-correlation functionals within the Kohn-Sham density-functional-theory framework may be written as potentials for simpler functionals multiplied by a factor close to unity, and in a self-consistent field calculation, these effective potentials find the correct self-consistent solutions. This simple theory is demonstrated with self-consistent exchange-only calculations of the atomization energies of some small molecules using the Perdew-Kurth-Zupan-Blaha (PKZB) meta–generalized-gradient-approximation (meta-GGA) exchange functional. The atomization energies obtained with our method agree with or surpass previous meta-GGA calculations performed in a non-self-consistent manner. The results of this work suggest the utility of this simple theory to approximate exchange-correlation potentials corresponding to energy functionals too complicated to generate closed forms for their potentials. We hope that this method will encourage the development of complex functionals which have correct boundary conditions and are free of self-interaction errors without the worry that the functionals are too complex to differentiate to obtain potentials.

We derive the optimal $N\to M$ phase-covariant quantum cloning for equatorial states in dimension $d$ with $M=kd+N$, $k$ integer. The cloning maps are optimal for both global and single-qudit fidelity. The map is achieved by an “economical” cloning machine, which works without ancilla.