In open quantum systems, phenomenological master equations with unknown parameters are often introduced. Here we propose a time-independent procedure based on quantum tomography to reconstruct the potentially unknown parameters of a wide class of Markovian master equations. According to our scheme, the system under investigation is initially prepared in a Gaussian state. At an arbitrary time $t$, in order to retrieve the unknown coefficients one needs to measure only a finite number (ten at maximum) of points along three time-independent tomograms. Due to the limited amount of measurements required, we expect our proposal to be especially suitable for experimental implementations.

We present a scheme to drive a finite-dimensional quantum system into the decoherence-free subspaces (DFS) by Lyapunov control. Control fields are established by Lyapunov function. This proposal works well for both closed and open quantum systems, with replacing the DFS by desired subspaces for closed systems. An example which consists of a four-level system with three degenerate states driven by three lasers is presented to gain further insight on the scheme. Numerical simulations for the dynamics of the system are performed and the results are good.

In this paper, the degenerate ground states of $Z_2$ topological order on a plane with holes (the so-called planar codes) are used as the protected code subspace to build a topological quantum computer by tuning their quantum tunneling effect. Using a designer Hamiltonian—the Kitaev toric-code model as an example, we study quantum tunneling effects of the planar codes and obtain its effective theory. Finally, we show how to do topological quantum computation including the initialization, the unitary transformation and the measurement.

We present a scheme to perform universal quantum computation using global control with an arbitrary subsystem dimension (not necessarily finite). The scheme is developed over a one spatial dimension $N$-element array, using only mirror-symmetric logical encoding, global pulses for single subsystem operations, uniform Ising-type interaction, and an all zero initial pure state. A mechanism using ancillary degrees of freedom for subsystem specific measurement is also presented.

We investigate the propagation of information through one-dimensional nearest-neighbor interacting quantum spin chains in the presence of external fields which fluctuate independently on each site. We study two fundamentally different models: (i) a model with general nearest-neighbor interactions in a field which fluctuates in both strength and direction and (ii) the $XX$ chain placed in a fluctuating field aligned in the $z$ direction. In both cases we find that information propagation is suppressed in a way which is quite different from the suppression observed when the $XX$ model is placed in a statically disordered field.

Given $n$ linearly independent pure states and their prior probabilities, we study the optimum unambiguous state discrimination problem. We derive the conditions for the optimum measurement strategy to achieve the maximum average success probability and establish two sets of equations that must be satisfied by the optimum solution in different situations. We also provide the detailed steps to find the optimum measurement strategy. The method and results we obtain are given a geometrical illustration with a numerical example. Furthermore, using these equations, we derive a formula which shows a clear analytical relation between the optimum solution and the $n$ states to be discriminated. We also solve a generalized equal-probability measurement problem analytically. Finally, as another application of our result, the unambiguous discrimination problem of three pure states is studied in detail and analytical solutions are obtained for some interesting cases.

We present even-parity autoionizing resonances in barium using two-step laser excitation via $5d6p$ ${{}^{1}P}_1$ intermediate level covering the energy region from the first ionization threshold to the $5d$ ${{}^{2}D}_{5/2}$ limit. The data are achieved using an atomic beam apparatus in conjunction with a time-of-flight mass spectrometer and a Nd:YAG pumped dye laser system. True line shape of the $6p^2$ ${{}^{1}S}_0$ autoionizing resonance at $44850\pm 50{\text{cm}}^{-1}$, its width $\left(980\pm 50{\text{cm}}^{-1}\right)$, and the absolute value of photoionization cross section $\left(185\pm 35\text{Mb}\right)$ are reported. A combination of parallel and perpendicular polarization vectors of the exciting and the ionizing dye lasers reveals unambiguous $J$-value assignments of the excited states. The interactions between the $6p^2$ ${{}^{1}S}_0$ broad feature with the $5d_{5/2}nd$ $J=0$ Rydberg series have been simulated using the phase-shifted multichannel quantum defect theory.

We theoretically investigate the quantum properties of $nS$, $nP$, and $nD$ Rydberg atoms in a magnetic Ioffe-Pritchard trap. In particular, it is demonstrated that the two-body character of Rydberg atoms significantly alters the trapping properties opposed to pointlike particles with identical magnetic moment. Approximate analytical expressions describing the resulting Rydberg trapping potentials are derived and their validity is confirmed for experimentally relevant field strengths by comparisons to numerical solutions of the underlying Schrödinger equation. In addition to the electronic properties, the center-of-mass dynamics of trapped Rydberg atoms is studied. In particular, we analyze the influence of a short-time Rydberg excitation, as required by certain quantum-information protocols, on the center-of-mass dynamics of trapped ground-state atoms. A corresponding heating rate is derived and the implications for the purity of the density matrix of an encoded qubit are investigated.

We study numerically the behavior of rotational revivals in a molecular gas when subject to the fluctuating electric field of a background plasma. We model a molecule using a rigid rotor Hamiltonian and couple it to an electric field using permanent and induced multipole interaction terms. The evolution of the density matrix for the molecule is calculated for a short intense laser pulse, followed by a fluctuating background electric field. A broad superposition of angular momentum eigenstates of a molecule is created by the laser field, and the result of an ensemble average over initial molecular orientation is a set of recurring peaks in the probability density for observing a particular orientation—the so-called “rotational revivals.” The fluctuating background field is created using the dressed particle technique, and the result is a loss of coherence between the phases of the various basis states of the molecule, which causes a decreasing amplitude for subsequent alignment peaks. Modern short-pulse lasers operate with sufficient intensity to make this effect relevant to experiments in molecular alignment.

We present a quantitative investigation of strong-field short-pulse nondipole dynamics in laser-matter interactions. We find excellent agreement between ab initio numerical and analytic results obtained using the Magnus expansion. We show that in the short-pulse limit, ultrafast transfer and control of population can be achieved using nondipole effects. The relative importance of nondipole to dipole effects depends on the displacement imparted to a free classical electron.

We theoretically investigate the effect of a zero-area pulse on the excitations of interacting Rydberg atoms. The unexpected breakdown of dipole blockade occurs in the strong Rydberg blockade regime, which results from the nonadiabatic character of a phase-jump pulse interacting with the atoms. We also check the effect of the modulation on the final probability of double excitations and find that the switching time should be short enough to observe the breakdown of dipole blockade.

Two-photon laser spectroscopy of the $6{{}^{1}S}_0-7{{}^{1}S}_0$ transition in mercury has been performed using two copropagating continuous-wave laser beams. One laser beam is at 254 nm wavelength and can be tuned to the $6{{}^{1}S}_0-6{{}^{3}P}_1$ resonance. The other laser beam is at 408 nm. Two very different regimes can be distinguished, one far off resonance and one near resonance with the one-photon resonance. A resonance which is not Doppler broadened has been observed for low Rabi frequencies. This velocity-selective double resonance in a three-level ladder system is analogous to the dark resonance in three-level $\Lambda$ systems.

Considering ultracold atoms traversing a high-$Q$ Fabry-Pérot cavity, we theoretically demonstrate a quantum nondemolition measurement of the photon number. This fully quantum mechanical approach may be understood utilizing concepts as effective mass and group velocity of the atom. The various photon numbers induce a splitting of the atomic wave packet, and a time-of-flight measurement of the atom thereby reveals the photon number. While repeated atomic measurements increase the efficiency of the protocol, it is shown that by considering long interaction times only a few atoms are needed to resolve the photon number with almost perfect accuracy.

We systematically study ground-state properties of fermionic dipolar gases in a planar array of one-dimensional potential tubes for arbitrary orientation of dipole moments. Using the Luttinger liquid theory with the generalized Bogoliubov transformation, we calculate the elementary excitations and the Luttinger scaling exponents for various relevant quantum orders. The complete quantum phase diagrams for arbitrary polar angle of the dipole moment are obtained including charge-density wave, $p$-wave superfluid, intertube gauge-phase density wave, and intertube $s$-wave superfluid, where the last two break the U(1) gauge symmetry of the system (conservation of particle number in each tube) and occur only when the intertube interaction is larger than the intratube interaction. We then discuss the physical properties and experimental features of these many-body phases.

Analytical solutions are presented for the electromagnetic radiation by an arbitrary pulsed source into a homogeneous time-varying background medium. In the constant-impedance case an explicit radiation formula is obtained for the synchronous permittivity and permeability described by any positive function of time. As might be expected, such a medium introduces significant spectral shifts and spatiotemporal modulation, which are analyzed here for the linear and exponential time variations of the medium parameters. In the varying-impedance case the solution is obtained for the fourth-order polynomial time dependence of the permittivity. In addition to the spectral shifts and modulation this spatially homogeneous medium scatters the field introducing causal echoes at the receiver location.

When beams are interacting with each other in strongly nonlocal nonlinear media, they together induce a graded refractive index profile whose axis is located at the center of mass of the combined field. The center of mass undergoes a straight trajectory whose slope can be steered by the amplitude and/or the phase distribution of the interacting beams. In the comoving reference frame, the propagation of each interacting beam can be regarded as the cross-induced fractional Fourier transform. The intensity patterns of the interacting beams evolve periodically with a period that is inversely proportional to the square root of the total power of the interacting beams. If a beam is shape-invariant in free space, it presents as a breather or a soliton in the interaction case. Every interacting beam undergoes a trajectory that oscillates about the straight line of the center of mass in the one-dimensional case; and in the two-dimensional case the projection of the trajectory on the transverse plane is an ellipse. During propagation, every interacting beam experiences cross-induced phase shift, which is induced not only by the initial transverse spatial momentum and the total power of the combined field, but also by the trajectory and the transverse structure of the interacting beam.

We present, experimentally and theoretically, nonlinear magneto-optical rotation (NMOR) using two spatially separated laser beams, the pump laser beam for creation and the probe laser beam for detection of the coherence between ground Zeeman sublevels. Both pump and probe lasers are tuned to $F_g=2\to F_e=1$ transition in ${}^{87}\text{R}\text{b}$. With the specially designed spatial configuration of the pump and the probe beams we were able to obtain dispersively shaped probe laser NMOR resonances in the Rb vacuum gas cell. The theory indicates that the obtained line shapes are due to the interference between prepared atomic states and the probe laser field. The interference nature of the resonances is supported by narrowing of NMOR resonances with increased separation between laser beams, and by the shift of the central fringe from the zero magnetic field with increased angle between initial orientation of electric vectors of linearly polarized pump and probe beams.

We have computed from first principles the dependence of the formation of the resonance profile of the $\text{He}2s2p$ ${{}^{1}P}^o$ state at 60.1 eV on the duration of the interaction of $\text{He}1s^2$ ${}^{1}S$ with ultrashort Gaussian electromagnetic pulses for field strengths smaller than 0.04 a.u. The calculations took into account the self-consistent field, the state-specific electron correlations and the mixing of bound with scattering components. Apart from the new physical information that they reveal, such results, and similar ones for other resonance states, can be of use to current developments toward the accurate characterization of ultrashort pulses from free-electron lasers in the regimes of a few femtoseconds to a few hundreds of attoseconds.

We demonstrate selective vibrational population transfer in cold cesium dimers using a simple approach based on the use of a shaped incoherent broadband diode laser near threshold. Optical pumping into a single vibrational level is accomplished with an incoherent light source by eliminating transitions from the targeted vibrational level. The broadband spectrum of the laser is wide enough to electronically excite several vibrational states of the molecule simultaneously. This method is relatively inexpensive, simple, and flexible to allow for development of new applications, in particular, the preparation of optically closed molecular system, opening the way to direct laser cooling of molecules.

Ternary flavor mixtures of ultracold fermionic atoms in an optical lattice are studied in the case of equal repulsive on-site interactions $U>0$. The corresponding SU(3) invariant Hubbard model is solved numerically exactly within dynamical mean-field theory using multigrid Hirsch-Fye quantum Monte Carlo simulations. We establish Mott transitions close to integer filling at low temperatures and show that the associated signatures in the compressibility and pair occupancy persist to high temperatures, i.e., they should be accessible to experiments. In addition, we present spectral functions and discuss the properties of a “semicompressible” state observed for large $U$ near half filling.