In this paper, the problem of achieving an arbitrary $\text{SU}\left(1,1\right)$ coherent state is considered via switching the control field back and forth between admissible values with minimal number of switching times. When the controlled system Hamiltonian is hyperbolical or parabolical, the results show that the minimal switching number is one or two, which lies on whether the argument of the involved control is adjustable or not, and is independent of the target $\text{SU}\left(1,1\right)$ coherent state. While for the elliptical case, the results indicate that the minimal number of switches needed depends on the target $\text{SU}\left(1,1\right)$ coherent state and is provided as a function of it. In this case, one switch can also be saved if the argument of the involved control is adjustable. The theory developed here can also be extended to solve the optimal bang-bang control problem for a general $\text{SU}\left(1,1\right)$ time evolution.

We present an analytically exactly soluble two-state model, in which a hyperbolic-secant-shaped pulsed interaction has a phase jump of $\varphi$ at the time of its maximum. The detuning has a constant part and a hyperbolic-tangent chirp term. For $\varphi =0$, this model reduces to the Demkov-Kunike model, which in turn contains as particular cases three other well-known models: the Rosen-Zener, Allen-Eberly, and Bambini-Berman models. A nonzero $\varphi$ induces dramatic changes in the transition probability, ranging from complete population inversion to complete population return. The analytic results are particularly instructive in the adiabatic limit and demonstrate that complete population inversion can always occur for a suitable choice of $\varphi$. The jump phase $\varphi$ can therefore be used as a control parameter for the two-state transition probability.

Amplifying on a proposal by O’Dell et al. for the realization of Bose-Einstein condensates of neutral atoms with attractive $1∕r$ interaction, we point out that the instance of self-trapping of the condensate, without an external trap potential, is physically best understood by introducing appropriate “atomic” units. This reveals a remarkable scaling property: the physics of the condensate depends only on the two parameters $N^{2}a∕a_u$ and $\gamma ∕N^2$, where $N$ is the particle number, $a$ the scattering length, $a_u$ the “Bohr” radius, and $\gamma$ the trap frequency in atomic units. We calculate accurate numerical results for self-trapping wave functions and potentials, and for energies, sizes, and peak densities, and compare with previous variational results. We point out the existence of a second solution of the extended Gross-Pitaevskii equation for negative scattering lengths, with and without trapping potential, which is born together with the ground state in a tangent bifurcation. This indicates the existence of an unstable collectively excited state of the condensate for negative scattering lengths.

The optical response of high quality three dimensionally (3D) ordered photonic crystals is analyzed in the high energy region. By tuning the reflectance with the angle of incidence of light, the peaks in the reflection spectrum that correspond to the first, second, and third order photonic stop bands and the van Hove singular point in the photon density of states are clearly distinguished. The high energy features have been observed for photonic crystals made from colloids of different diameters, having different index contrast and fabricated by two different self-assembly routes. The observation of van Hove singularity at near-normal incidence of light and its presence even in low index-contrast photonic crystals provide conclusive evidence that these high energy features are due to the perfect periodic ordering present in the photonic crystals with less defects and disorder.

Bethe’s theory is applied to the optical transmission through an array of apertures in an infinitely thin perfect electric conductor. This method shows that, in the small-aperture limit, the lowest-order TM evanescent mode governs the transmission process, allowing for both 100% transmission at the passband wavelength and zero transmission at the Wood’s anomaly. The applicability of this theory to total transmission in other systems is discussed, and a specific example of a single aperture in a transverse screen of a rectangular waveguide is given.

Quantum state transfer and teleportation, with qubits encoded in internal states of atoms in cavities, among spatially separated nodes of a quantum network in a decoherence-free subspace are proposed, based on a cavity-assisted interaction with single-photon pulses. We show in detail the implementation of a logic-qubit Hadamard gate and a two-logic-qubit conditional gate, and discuss the experimental feasibility of our scheme.

We show that magnetic-field-induced circular differential deflection of light can be observed in reflection or refraction at a single interface. The difference in the reflection or refraction angles between the two circular polarization components is a function of the magnetic-field strength and the Verdet constant, and permits the observation of the Faraday effect not via polarization rotation in transmission, but via changes in the propagation direction. Deflection measurements do not suffer from $n\text{−}\pi$ ambiguities and are shown to be another means to map magnetic fields with high axial resolution, or to determine the sign and magnitude of magnetic-field pulses in a single measurement.

We construct a linear optics measurement process to determine the entanglement measure, named $I$ concurrence, of a set of $4\times 4$-dimensional two-photon entangled pure states produced in the optical parametric down conversion process. In our experiment, an equivalent symmetric projection for the twofold copy of a single subsystem [presented by L. Aolita and F. Mintert, Phys. Rev. Lett. 97, 050501 (2006)] can be realized by observing the one-side two-photon coincidence without any triggering detection on the other subsystem. Here, for the first time, we realize the measurement for entanglement contained in biphoton pure states by taking advantage of the indistinguishability and the bunching effect of photons. Our method can determine the $I$ concurrence of generic high-dimensional bipartite pure states produced in the parametric down conversion process.

The Zeeman line components of the magnetic-dipole $\left(M1\right)$ $1s^{2}2s^{2}2p$ ${}^{2}P_{1∕2}–{}^{2}P_{3∕2}$ transition in boronlike ${\mathrm{Ar}}^{13+}$ were experimentally resolved by high-precision emission spectroscopy using the Heidelberg electron beam ion trap. We determined the gyromagnetic $\left(g\right)$ factors of the ground and first-excited levels to be $g_{1∕2}=0.663\left(7\right)$ and $g_{3∕2}=1.333\left(2\right)$, respectively. This corresponds to a measurement of the $g$ factor of a relativistic electron in a bound non-$S$ state of a multielectron ion with a 1.5 parts-per-thousand accuracy. The results are compared to theoretical calculations by means of the configuration interaction Dirac-Fock-Sturmian method including electron correlation effects and additional quantum electrodynamic corrections. Our measurements show that the classical Landé $g$ factor formula is sufficiently accurate to the present level of accuracy in few-electron ions of medium nuclear charge number $Z$.

We have observed the phase lag in the sinusoidal variation of the asymmetric photoelectron angular distributions into two ionization channels of atomic barium using an $\omega \text{−}2\omega$ excitation scheme. We excite atomic barium from the $6s6p{{}^{1}P}_1$ intermediate state electron to an energy between the $5d_{3∕2}ϵ$ and the $5d_{5∕2}ϵ$ thresholds with concurrent one-photon and two-photon interactions. The left-right asymmetry of the photoelectron angular distributions for the two energy-resolved product states, $6s_{1∕2}ϵ$ and $5d_{3∕2}ϵ$, show sinusoidal modulation as a function of the relative phase of the $\omega \text{−}2\omega$ fields. The phase difference between these signals, or phase lag, varies rapidly with the laser frequency when the interaction is nearly resonant with autoionizing resonances in the continuum. An exceptionally large phase lag variation of over $2\pi$ was measured.

Tunnel ionization of room-temperature ${\mathrm{D}}_2$ in an ultrashort (12 femtosecond) near infrared $\left(800\mathrm{nm}\right)$ pump laser pulse excites a vibrational wavepacket in the ${{\mathrm{D}}_2}^{+}$ ions; a rotational wavepacket is also excited in residual ${\mathrm{D}}_2$ molecules. Both wavepacket types are collapsed a variable time later by an ultrashort probe pulse. We isolate the vibrational wavepacket and quantify its evolution dynamics through theoretical comparison. Requirements for quantum computation (initial coherence and quantum state retrieval) are studied using this well-defined (small number of initial states at room temperature, initial wavepacket spatially localized) single-electron molecular prototype by temporally stretching the pump and probe pulses.

We propose a simple experiment to create a sonic horizon in isotropically trapped cold atoms within currently available experimental techniques. Numerical simulation of the Gross-Pitaevskii equation shows that the sonic horizon should appear by making the condensate expand. The expansion is triggered by changing the interaction which can be controlled by the Feshbach resonance in real experiments. The sonic horizon is shown to be quasistatic for sufficiently strong interaction or large number of atoms. The characteristic temperature that is associated with particle emission from the horizon, which corresponds to the Hawking temperature in an ideal situation, is estimated to be a few nK.

We demonstrate a type of chiral effect of an atomic medium. Polarization rotation of a probe beam is observed only when both a magnetic field and a linearly polarized coupling beam are present. We compare it with other chiral effects like optical activity, the Faraday effect, and the optically induced Faraday effect from the viewpoint of spatial inversion and time reversal transformations. As a theoretical model we consider a five-level configuration involving the cesium $D2$ transition. We use spin-polarized cold cesium atoms trapped in a magneto-optical trap to measure the polarization rotation versus probe detuning. The result shows reasonable agreement with a calculation from the master equation of the five-level configuration.

We present a theory describing trapping of the normally dispersive radiation by the Raman solitons in optical fibers. Frequency of the radiation component is continuously blueshifting, while the soliton is redshifting. Underlying physics of the trapping effect is in the existence of the inertial gravitylike force acting on light in the accelerating frame of reference. We present analytical calculations of the rate of the opposing frequency shifts of the soliton and trapped radiation and find it to be greater than the rate of the redshift of the bare Raman soliton. Our findings are essential for understanding of the continuous shift of the high-frequency edge of the supercontinuum spectra generated in photonic crystal fibers toward higher frequencies.

The dynamics of pulse propagation accompanied by harmonic generation, stimulated Raman scattering, amplified spontaneous emission, and superfluorescence is studied near the two-photon resonance. We explore the optical limiting of intense and short laser pulses. The numerical solutions of the coupled Bloch and Maxwell’s equations for the $4,4^{\prime }$-bis(dimethylamino) stilbene molecule are compared with the two-photon area theorem. It is shown that the area theorem explains qualitatively the major dynamical properties of pulse propagation even if the propagation is accompanied by the generation of new fields. In agreement with the area theorem, we see that the conventional dependence of the transmittance on the propagation depth is not valid for intense pulses.

A recent work on two-photon fluorescence is extended by considering the pump field to be a coherent state, which represents a laser field operating well above threshold. The dynamical conditions are investigated under which the two-photon spectrum gives rise, in addition to a Lorentzian line shape at the pump frequency, to two Voigt spectral sideband profiles. Additional conditions are found under which the Voigt profile behaves like either a Gaussian or a Lorentzian line shape.

The Gaussian continuous-variable quantum key distribution protocol based on coherent states and heterodyne detection [Phys. Rev. Lett. 93, 170504 (2004)] has the advantage that no active random basis switching is needed on the receiver’s side. Its security is, however, not very satisfyingly understood today because the bounds on the secret key rate that have been derived from Heisenberg relations are not attained by any known scheme. Here, we address the problem of the optimal Gaussian individual attack against this protocol, and derive tight upper bounds on the information accessible to an eavesdropper. Interestingly, this protocol is proven to be even more resistant to individual attacks than originally thought. Optical schemes achieving these bounds are also exhibited, which concludes the security analysis of Gaussian protocols against individual attacks.

We propose a scheme for long-distance $\left(10\mathrm{km}\right)$ distribution of quantum entanglement between two stationary qubits in cavities via a flying qubit in a network. This entanglement is performed by properly choosing the form of driving pulses such as Gaussian pulse, Hermite pulse, and damped pulse according to the need to suppress the experimental artifacts, then adjusting the parameters of the chosen pulses according to the motion equation of the real system. This scheme can even work well in the situation where the imperfect factors are very large, e.g., the spontaneous emission rate and the cavity mode leakage rate are 100 times and 1000 times as large as those considered in the proposal of Yao et al., respectively.

We demonstrate that rotary motion of a two-dimensional soliton trapped in a Bessel lattice can be precisely controlled by application of a finite-time push to the lattice, due to the transfer of the lattice’s linear momentum to the orbital momentum of the soliton. A simple analytical consideration treating the soliton as a particle provides for an accurate explanation of numerical findings. Some effects beyond the quasi-particle approximation are explored too, such as destruction of the soliton by a hard push.