An initial unknown quantum state can be determined with a single measurement apparatus by letting it interact with an auxiliary, ancilla, system as proposed by Allahverdyan, Balian, and Nieuwenhuizen [Phys. Rev. Lett. 92, 120402 (2004)]. In the case of two qubits, this procedure allows one to reconstruct the initial state of the qubit of interest, $S$, by measuring three commuting observables and therefore by means of a single apparatus, for the total system $S+A$ at a later time. The determinant of the matrix of the linear transformation connecting the measurements of three commuting observables at time $t>0$ to the components of the polarization vector of $S$ at time $t=0$ is used as an indicator of the reconstructability of the initial state of the system $S$. We show that a connection between the entanglement entropy of the total system $S+A$ and such a determinant exists, and that for a pure state a vanishing entanglement individuates, without a need for any measurement, those intervals of time for which the reconstruction procedure is least efficient. This property remains valid for a generic dimension of $S$. In the case of a mixed state, this connection is lost.

We discuss how the bath’s memory affects the dynamics of a SWAP gate. We present an exactly solvable model that shows various dynamical transitions when treated beyond the Fermi golden rule. By moving continuously a single parameter, the unperturbed Rabi frequency, we sweep through different analytic properties of the density of states: (I) collapsed resonances that split at an exceptional point in (II) two resolved resonances; (III) out-of-band resonances; (IV) virtual states; and (V) pure point spectrum. We associate them with distinctive dynamical regimes: overdamped, damped oscillations, environment controlled quantum diffusion, anomalous diffusion, and localized dynamics, respectively. The frequency of the SWAP gate depends differently on the unperturbed Rabi frequency. In region I there is no oscillation at all, while in the regions III and IV the oscillation frequency is particularly stable because it is determined by the environment’s band width. The anomalous diffusion could be used as a signature for the presence of the elusive virtual states.

We show that we can achieve global density-operator controllability for most $N$-dimensional bilinear Hamiltonian control systems with general fixed couplings using a single, locally acting actuator that modulates one energy-level transition. Controllability depends upon the position of the actuator and relies on the absence of either decompositions into noninteracting subgroups or symmetries restricting the dynamics to a subgroup of $\mathrm{SU}\left(N\right)$. These results are applied to spin-chain systems and used to explicitly construct control sequences for a single binary-valued switch actuator.

We study the Braunstein-Kimble protocol for the continuous variable teleportation of a coherent state. We determine lower and upper bounds for the optimal fidelity of teleportation, maximized over all local Gaussian operations for a given entanglement of the two-mode Gaussian state shared by the sender (Alice) and the receiver (Bob). We also determine the optimal local transformations at Alice and Bob sites and the corresponding maximum fidelity when one restricts to local trace-preserving Gaussian completely positive maps.

Twenty-one fine-structure intervals between $n=10$ argon Rydberg levels with $L⩾5$ were measured using microwave spectroscopy, determining the relative positions of all twenty levels with sub-MHz precision. Analysis of the measured pattern using the effective potential model yields determinations of the quadrupole moment, scalar and tensor dipole polarizability, and $g$ factor for the ${}^{2}P_{3∕2}$ ground state of ${\mathrm{Ar}}^{+}$: $Q=-0.52083\left(2\right)e{a}_0^2$, ${\alpha }_{d,0}=6.807\left(2\right)a_0^3$, ${\alpha }_{d,2}=0.077\left(2\right)a_0^3$, $g_J=1.335\left(17\right)$.

Plasma screening effects on the properties of bound-bound transitions of hydrogenlike ions imbedded in Debye plasmas are investigated. The electron eigenenergies and wave functions are determined by numerically solving the scaled Schrödinger equation with a Debye potential by the fourth-order symplectic integration scheme. The scaled spectral properties of hydrogenlike ions in the plasma, including the transition frequencies, absorption oscillator strengths, radiative transition probabilities, as well as the line intensities of the Lyman and Balmer series, are presented for a wide range of plasma screening parameters. While for the $\Delta n\ne 0$ transitions the oscillator strengths and spectral line intensities decrease with increasing the plasma screening, those for the $\Delta n=0$ transitions rapidly increase. The lines associated with the $\Delta n\ne 0$ transitions are redshifted, whereas those for $\Delta n=0$ transitions are blueshifted. Comparison of present results with those of other authors, when available, is made. The results reported here should be useful in the interpretation of spectral properties of hydrogenlike ions in laboratory and astrophysical Debye plasmas.

We propose a method for detecting paired states in either bosonic or fermionic systems using interference experiments with independent or weakly coupled low-dimensional systems. We demonstrate that our method can be used to detect both the Fulde, Ferrel, Larkin, Ovchinnikov, and the $d$-wave paired states of fermions, as well as quasicondensates of singlet pairs for polar $F=1$ atoms in two-dimensional systems. We discuss how this method can be used to perform phase-sensitive determination of the symmetry of the pairing amplitude.

We consider the propagation of a light pulse in a medium with a single resonance. If the frequency of the pulse is tuned far from resonance and the pulse duration is much shorter than the lifetime of the excited state of the resonant particles in the medium (atoms in a gas, impurity ions in a solid, etc.), the group velocity of the pulse is appreciably reduced. It is shown that the slowing down of the group velocity of the pulse is accompanied with a pulse chirp, which produces a pulse broadening in time. It is proposed to use two samples in sequence with opposite chirps (up chirp and down chirp or vice versa) compensating the pulse broadening. Then the pulse can be delayed with almost no losses, distortion, and broadening. However, there is a maximum distance, beyond which the pulse experiences corruption. Pumping with an auxiliary laser beam can control the delay time of the light pulse in the medium. Conditions to eliminate the contribution of the dephasing processes in the pulse propagation are considered.

We calculate the Casimir interaction between two short-range scatterers embedded in a background of one-dimensional massless Dirac fermions using a force-operator approach. We obtain the force between two finite-width square barriers and take the limit of zero width and infinite potential strength to study the Casimir force mediated by the fermions. For the case of identical scatterers, we recover the conventional attractive one-dimensional Casimir force. For the general problem with inequivalent scatterers, we find that the magnitude and sign of this force depend on the relative spinor polarizations of the two scattering potentials, which can be tuned to give an attractive, a repulsive, or a compensated null Casimir interaction.

By using the effective Hamiltonian approach, we present a self-consistent framework for the analysis of geometric phases and dynamically stable decoherence-free subspaces in open systems. Comparisons to the earlier works are made. This effective Hamiltonian approach is then extended to a non-Markovian case with the generalized Lindblad master equation. Based on this extended effective Hamiltonian approach, the non-Markovian master equation describing a dissipative two-level system is solved, an adiabatic evolution is defined, and the corresponding adiabatic condition is given.

The photoionization of Ar, Kr, and Xe rare-gas clusters was investigated using angle-resolved time-of-flight photoelectron spectroscopy. Fine-structure-resolved photoelectron angular distributions were determined for the Ar $2p$, Kr $3d$, and Xe $4d$ core levels and the Ar $3s$ inner-valence level as a function of photon energy for two average cluster sizes. Overall, the angular distributions of inner-shell photoelectrons from the cluster and the free atom are found to be very similar, except for the first $10–15\mathrm{eV}$ above the respective photoionization thresholds, where the angular anisotropy of the atomic photoelectrons is high, while our measurements demonstrate considerably less anisotropy in the cluster photoelectron emission. The angular distribution of Ar $3s$ inner-valence photoelectrons from the cluster is substantially less anisotropic than for the atomic photoelectrons throughout the covered photon energy range, but the difference decreases for increasing photon energy.

We theoretically demonstrate that the strong field dynamics such as above-threshold ionization and high-order harmonic generation can be significantly altered by the introduction of the time-delayed two-color laser field consisting of the near-infrared and mid-infrared frequencies. Specifically we apply the idea to the one-dimensional hydrogen atom, and show that the strong field dynamics significantly depend on the time delay between the two fields, as represented, for instance, by the change of the cutoff energies of above-threshold ionization and high-order harmonic generation. It turns out, however, that the delay dependence is different for those processes. In particular, if the duration of the near-infrared pulse is as short as a few cycles, its carrier-envelope phase also plays a very important role. Our classical results for the two processes are consistent with the numerical results.

We demonstrate that the soliton-effect compression to few- and single-cycle pulse widths in a highly nonlinear fiber can be optimized by properly choosing the input soliton number. Soliton compression to a $2\text{−}\mathrm{fs}$ pulse width with a compression ratio up to 50 is demonstrated for light pulses with an initial central wavelength of $1070\mathrm{nm}$ by solving the generalized nonlinear Schrödinger equation for a dispersion profile typical of a small-core photonic-crystal fiber.

The spatiotemporal evolutions of ultrashort pulses in two dimensions are investigated numerically by solving the coupled Maxwell-Bloch equations without invoking the slowly varying envelope approximation and rotating-wave approximation. For an on-axis $2n\pi$ sech pulse, local delay makes the temporal split $2\pi$ sech pulses crescent-shaped in the transverse distribution. Due to the transverse effect, the temporal split $2\pi$ sech pulses become unstable and experience reshaping during the propagation process. Then, interference occurs between the successive crescent-shaped pulses and multiple self-focusing can form.

The spectrum of non-Hermitian Hamiltonians is studied using the point-group symmetries of the Hermitian and non-Hermitian parts of the Hamiltonian. We show that, in principle, the symmetry properties of the Hamiltonian are responsible for the appearance of real eigenvalues in the spectrum of the non-Hermitian Hamiltonian. In practice, however, one must take into account the “strength” of the non-Hermitian part of the Hamiltonian. An effective energy-dependent Hermitian Hamiltonian is constructed that has the same real spectrum as the non-Hermitian Hamiltonian. Several properties, including the self-orthogonality of the states at branch points of the spectrum, are proven using this effective representation. An interesting possibility of complex eigenvalues returning to the real axis is exemplified along with several examples of non-Hermitian Hamiltonians with real eigenvalues.

We propose a scheme to realize the Heisenberg model of any spin in an arbitrary array of coupled cavities. Our scheme is based on a fixed number of atoms confined in each cavity and collectively applied constant laser fields, and is in a regime where both atomic and cavity excitations are suppressed. It is shown that as well as optically controlling the effective spin Hamiltonian, it is also possible to engineer the magnitude of the spin. Our scheme would open up a way to simulate otherwise intractable high-spin problems in many-body physics.

Using the wave-packet propagation method of Rodberg and Thaler and the density matrix method of Fano and Blum, we have defined by completely quantum-mechanical methods the cross sections for the creation, destruction, and transfer of atomic multipole moments by both elastic and inelastic scattering of electrons by atomic targets. All cross sections obtained quantum mechanically, except for the coherence transfer cross sections, agree in form with those obtained semiclassically by Fujimoto and co-workers. We also used the converged close-coupling (CCC) method to calculate numerically some of the above cross sections for selected transitions in electron scattering from hydrogen and barium atoms.

We demonstrate the implications of Efimov physics in the recently measured recombination rate of ${}^{133}\mathrm{Cs}$ atoms. By employing previously calculated results for the energy dependence of the recombination rate of ${}^4\mathrm{He}$ atoms, we obtain three independent scaling functions that are capable of describing the recombination rates over a large energy range for identical bosons with large scattering length. We benchmark these and previously obtained scaling functions by successfully comparing their predictions with full atom-dimer phase shift calculations with artificial ${}^4\mathrm{He}$ potentials yielding large scattering lengths. Exploiting universality, we finally use these functions to determine the three-body recombination rate of ${}^{133}\mathrm{Cs}$ atoms with large positive scattering length, compare our results to experimental data obtained by Kraemer et al. at Innsbruck and find excellent agreement.

The $L$-shell ionization processes of a Ne gas target associated with single-electron capture by bombardment of ${\mathrm{C}}^{q+}$ and ${\mathrm{O}}^{q+}$ $(q=2,3)$ are investigated using the projectile-recoil-ion coincidence method in the energy range from $80\text{to}400\mathrm{keV}∕\mathrm{u}$ $(v_p=1.8–4\mathrm{a.u.})$. The cross-section ratios $\left(R_{k1}\right)$ of $k$-fold ionization to single capture are compared with the results for ${\mathrm{He}}^{2+}\text{−}\mathrm{Ne}$ collisions by Dubois [Phys. Rev. A 36, 2585 (1987)]. All the velocity dependences are quite similar. The ratios increase as the projectile energy increases in the lower-energy region, reach the maxima for projectile energies around $E_{\max }=160q^{1∕2}\mathrm{keV}∕\mathrm{u}$, and then decrease at higher energies. These results qualitatively agree with our calculations in terms of the Bohr-Lindhard model within the independent-electron approximation.