Corrections of order ${\alpha }^4\mathcal{R}$ are calculated for the singlet states $1{}^{1}S_0$ and $2{}^{1}S_0$ of the helium atom. The result for the $1{}^{1}S_0$ state is in slight disagreement with that of Korobov and Yelkhovsky [Phys. Rev. Lett. 87, 193003 (2001)]. The results obtained lead to a significant improvement of the transition frequencies between low-lying levels of the helium atom. In particular theoretical predictions for the $2{}^{1}S_0\text{−}1{}^{1}S_0$ transition are found to be in disagreement with experimental values.

The Floquet quasienergy spectrum of argon in a strong laser field of 800 nm wavelength is calculated for intensities up to $7\times {10}^{13}\mathrm{W}{\mathrm{cm}}^{-2}$, and beyond for some states, using a discrete complex basis set. Many of the dressed excited states of interest shift nonponderomotively in complicated ways but keep an ionization width narrow enough to produce sharp enhancements of above-threshold ionization (ATI) through Stark-shift-induced resonances. The quasienergy map is compared to high-resolution ATI spectra for $120\mathrm{fs}$ Ti:sapphire pulses [Nandor et al., Phys. Rev. A 60, R1771 (1999)]. The plateau enhancements happen at intensities where the dressed ground state is in resonance or in the wing of resonances with dressed excited states. The resonant dressed states are identified. In many cases, the same state is responsible for an enhancement of ATI in the low as well as the high orders. No evidence is found for enhancements that are not concomitant with any curve crossing and could thereby be interpreted as channel-closing enhancement.

We present oscillator strength spectra of the hydrogen Balmer $\alpha$ series in crossed strong magnetic and electric fields. Field strength regimes of interest ($\gamma \le 0.02\mathrm{a}.\mathrm{u}.$ and $F\le 1\times {10}^8\mathrm{V}∕\mathrm{m}$) are the characteristic strengths observed on the surface of white dwarf stars. Based on the pseudospectral discretization technique, two independent methods have been developed to achieve reliable oscillator strengths in crossed fields. The effect of relative orientation between the magnetic and electric fields is clarified. Compared to the parallel configuration, we have observed that for the field strength regimes of interest, the perpendicular component of electric fields only results in a weaker coupling between the states belonging to the different subspaces of magnetic quantum numbers. This observation explains why the spectrum of oscillator strengths in crossed electric and magnetic fields with arbitrary mutual orientation shows similar behavior compared to that in parallel fields. However, a careful analysis shows that the two stronger transition lines at $5546$ and $5620\mathrm{\AA }$ previously attributed to the Balmer $\alpha$ series are now identified to belong to the Balmer $\beta$ series. An effective scheme has also been suggested to calculate the bound-free opacities of hydrogen atoms in crossed fields.

We consider the effect of thermal fluctuations on rotating spinor $F=1$ condensates in axially symmetric vortex phases, when all the three hyperfine states are populated. We show that the relative phase among different components of the order parameter can fluctuate strongly due to the weakness of the interaction in the spin channel. These fluctuations can be significant even at low temperatures. Fluctuations of relative phase lead to significant fluctuations of the local transverse magnetization of the condensate. We demonstrate that these fluctuations are much more pronounced for the antiferromagnetic state than for the ferromagnetic one.

Using a nonperturbative quantum scattering theory, the photoelectron angular distributions (PADs) from the multiphoton detachment of ${\mathrm{H}}^{-}$ ions in strong, linearly polarized infrared laser fields are obtained to interpret recent experimental observations. In our theoretical treatment, the PADs in $n$-photon detachment are determined by the $n$th-order generalized phased Bessel (GPB) functions ${\mathcal{X}}_{-n}(Z_f,\eta )$. The advantage of using the GPB scenario to calculate PADs is its simplicity: a single special function (GPB) without any mixing coefficient can express PADs observed by recent experiments. Thus, the GPB scenario can be called a parameterless scenario.

We show that the derivation of the approximate solution for the motion of an unbound electron in the simultaneous presence of the Coulomb field and a circularly polarized plane wave given in Reiss and Krainov Phys. Rev. A 50, 910(R) (1994) contains an error caused by confusing the space coordinates before and after the Kramers-Henneberger transformation.

Blackbody radiation (BBR) shifts of the ${}^{3}P_0\text{−}{}^{1}S_0$ clock transition in the divalent atoms Mg, Ca, Sr, and Yb are evaluated. The dominant electric-dipole contributions are computed using accurate relativistic many-body techniques of atomic structure. At room temperatures, the resulting uncertainties in the $E1$ BBR shifts are large and substantially affect the projected ${10}^{-18}$ fractional accuracy of the optical-lattice-based clocks. A peculiarity of these clocks is that the characteristic BBR wavelength is comparable to the ${}^{3}P$ fine-structure intervals. To evaluate relevant $M1$ and $E2$ contributions, a theory of multipolar BBR shifts is developed. The resulting corrections, although presently masked by the uncertainties in the $E1$ contribution, are required at the ${10}^{-18}$ accuracy goal.

We propose a general method for introducing extensive characteristics of quantum entanglement. The method relies on polynomials of nilpotent raising operators that create entangled states acting on a reference vacuum state. By introducing the notion of tanglemeter, the logarithm of the state vector represented in a special canonical form and expressed via polynomials of nilpotent variables, we show how this description provides a simple criterion for entanglement as well as a universal method for constructing the invariants characterizing entanglement. We compare the existing measures and classes of entanglement with those emerging from our approach. We derive the equation of motion for the tanglemeter and, in representative examples of up to four-qubit systems, show how the known classes appear in a natural way within our framework. We extend our approach to qutrits and higher-dimensional systems, and make contact with the recently introduced idea of generalized entanglement. Possible future developments and applications of the method are discussed.

In a recent paper Yu and Eberly [Phys. Rev. Lett. 93, 140404 (2004)] have shown that two initially entangled and afterward not interacting qubits can become completely disentangled in a finite time. We study transient entanglement between two qubits coupled collectively to a multimode vacuum field, assuming that the two-qubit system is initially prepared in an entangled state produced by the two-photon coherences, and find the unusual feature that the irreversible spontaneous decay can lead to a revival of the entanglement that has already been destroyed. The results show that this feature is independent of the coherent dipole-dipole interaction between the atoms but it depends critically on whether or not collective damping is present.

We investigate the entanglement properties of a finite size $1+1$ dimensional Ising spin chain, and show how these properties scale and can be utilized to reconstruct the ground state wave function. Even at the critical point, few terms in a Schmidt decomposition contribute to the exact ground state, and to physical properties such as the entropy. Nevertheless the entanglement here is prominent due to the lower-lying states in the Schmidt decomposition.

An open ended spin chain can serve as a quantum data bus for the coherent transfer of quantum state information. In this paper, we investigate the efficiency of such quantum spin channels which work in a decoherence environment. Our results show that the decoherence will significantly reduce the fidelity of quantum communication through the spin channels. Generally speaking, as the distance increases, the decoherence effects become more serious, which will put some constraints on the spin chains for long distance quantum state transfer.

We relate the reduced density matrices of quadratic fermionic and bosonic models to their Green’s function matrices in a unified way and calculate the scaling of the entanglement entropy of finite systems in an infinite universe exactly. For critical fermionic two-dimensional (2D) systems at $T=0$, two regimes of scaling are identified: generically, we find a logarithmic correction to the area law with a prefactor dependence on the chemical potential that confirms earlier predictions based on the Widom conjecture. If, however, the Fermi surface of the critical system is zero-dimensional, then we find an area law with a sublogarithmic correction. For a critical bosonic 2D array of coupled oscillators at $T=0$, our results show that the entanglement entropy follows the area law without corrections.

We investigate the feasibility of combining Raman optical lattices with a quantum computing architecture based on lattice-confined magnetically interacting neutral atoms. A particular advantage of the standing Raman field lattices comes from reduced interatomic separations leading to increased interatomic interactions and improved multiqubit gate performance. Specifically, we analyze a $J=3∕2$ Zeeman system placed in ${\sigma }_{+}\text{−}{\sigma }_{-}$ Raman fields which exhibit $\lambda ∕4$ periodicity. We find that the resulting controlled-NOT (CNOT) gate operations times are in the order of millisecond. We also investigate motional and magnetic-field induced decoherences specific to the proposed architecture.

A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock-wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, e.g., traveling fronts with steep gradients. However, the governing Gross-Pitaevskii (GP) equation that describes the mean field of a BEC admits no dissipation, hence classical dissipative shock solutions do not explain the phenomena. Instead, wave dynamics with small dispersion is considered and it is shown that this provides a mechanism for the generation of a dispersive shock wave (DSW). Computations with the GP equation are compared to experiment with excellent agreement. A comparison between a canonical one-dimensional (1D) dissipative and dispersive shock problem shows significant differences in shock structure and shock-front speed. Numerical results associated with the three-dimensional experiment show that three- and two-dimensional approximations are in excellent agreement and 1D approximations are in good qualitative agreement. Using 1D DSW theory, it is argued that the experimentally observed blast waves may be viewed as dispersive shock waves.

We study the self-organizing properties of an optically driven semiconductor microresonator especially designed and optimized for optical pumping wherein patterns and cavity solitons are observed for the first time with all-optical excitations. We demonstrate both coherent and incoherent writing and erasure of cavity solitons achievable on the same sample, enriching the spectrum of the system functionalities. Finally, we show how the system lends itself to the multiplication of the number of cavity solitons and how they possibly coexist.

We have shown that a coherently driven solid state medium can potentially produce strong controllable short pulses of THz radiation. The high efficiency of the technique is based on excitation of maximal THz coherence by applying resonant optical pulses to the medium. The excited coherence in the medium is connected to macroscopic polarization coupled to THz radiation. We have performed detailed simulations by solving the coupled density matrix and Maxwell equations. By using a simple V-type energy scheme for ruby, we have demonstrated that the energy of generated THz pulses ranges from hundreds of pico-Joules to nano-Joules at room temperature and micro-Joules at liquid helium temperature, with pulse durations from picoseconds to tens of nanoseconds. We have also suggested a coherent ruby source that lases on two optical wavelengths and simultaneously generates THz radiation. We discussed also possibilities of extension of the technique to different solid-state materials.

The stability of entanglement of two atoms in a cavity is analyzed in this work. By studying the general Werner states, we clarify the role of Bell singlet state in the problem of suppression of disentanglement due to spontaneous emission. It is also shown explicitly that the final amount of entanglement depends on the initial ingredients of the Bell singlet state.

We propose schemes to create cluster states and $W$ states by many superconducting quantum-interference-device qubits in cavities under the influence of the cavity decay. Our schemes do not require auxiliary qubits, and the excited levels are only virtually coupled throughout the scheme, which could much reduce the experimental challenge. We consider the cavity decay in our model and analytically demonstrate its detrimental influence on the prepared entangled states.

We analyze the quantum phase transition for a set of $N$ two-level systems interacting with a bosonic mode in the adiabatic regime. Through the Born-Oppenheimer approximation, we obtain the finite-size scaling expansion for many physical observables and, in particular, for the entanglement content of the system.