We consider a two-reservoir model of quantum error correction with a hot bath causing errors in the qubits and a cold bath cooling the ancilla qubits to a fiducial state. We consider error correction protocols both with and without measurement of the ancilla state. The error correction acts as a kind of refrigeration process to maintain the data qubits in a low entropy state by periodically moving the entropy to the ancilla qubits and then to the cold reservoir. We quantify the performance of the error correction as a function of the reservoir temperatures and cooling rate by means of the fidelity and the residual entropy of the data qubits. We also make a comparison with the continuous quantum error correction model of Sarovar and Milburn [Phys. Rev. A 72, 012306 (2005)].

We propose the schemes of quantum secure direct communication based on a secret transmitting order of particles. In these protocols, the secret transmitting order of particles ensures the security of communication, and no secret messages are leaked even if the communication is interrupted for security. This strategy of security for communication is also generalized to a quantum dialogue. It not only ensures the unconditional security but also improves the efficiency of communication.

The Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30, 825 (1997); R. Szmytkowski,30, 2747(E) (1997)] is used to derive an analytical formula for the static magnetic anapole (toroidal dipole) moment induced in the ground state of the relativistic hydrogenlike atom by a weak, spatially uniform, static electric field. An expression for the anapole polarizability for the system in question is found. This expression contains a single generalized hypergeometric series ${}_{3}F_2$ with the unit argument. In the nonrelativistic limit our result agrees with that of Lewis and Blinder [Phys. Rev. A 52, 4439 (1995)].

The $B$-spline $R$-matrix method is used to investigate the low-energy photodetachment of ${\mathrm{O}}^{-}\left(2p^5\right)$ for photon energies from threshold to $7\mathrm{eV}$. We report a detailed study regarding the dependence of the predicted partial and total photodetachment cross sections on the scattering model and the accuracy of the target description. A multiconfiguration Hartree-Fock method with nonorthogonal term-dependent orbitals is employed to generate accurate representations of the target wave functions. Four close-coupling scattering models with a different number of target states in the expansion are used to explore the dependence of the calculated photodetachment cross sections on the polarization of the target. Our largest model for the $e\text{−}\mathrm{O}$ collision problem in the final state includes 60 states, namely 25 bound and autoionizing states of neutral oxygen derived from the $1s^{2}2s^{2}2p^4$, $2s^{2}2p^{3}n\ell$, and $2s2p^5$ configurations, plus a set of pseudostates to partially account for the polarizability of the ground state $2p^4{}^{3}P$ and the metastable $2p^4{}^{1}D$ and ${}^{1}S$ states. We only find a small dependence of the calculated photodetachment cross section on the amount of target polarization accounted for, but a very strong dependence of the near-threshold results on the degree of short-range inner-core correlation incorporated in the target description.

The Rabi oscillations of a two-level atom illuminated by a laser on resonance with the atomic transition may be suppressed by the atomic motion through averaging or filtering mechanisms. The optical analogs of these velocity effects are described. The two atomic levels correspond in the optical analogy to orthogonal polarizations of light and the Rabi oscillations to polarization oscillations in a medium which is optically active, naturally or due to a magnetic field. In the latter case, the two orthogonal polarizations could be selected by choosing the orientation of the magnetic field, and one of them be filtered out. It is argued that the time-dependent optical polarization oscillations or their suppression are observable with current technology.

We consider a periodic vortex lattice in a rotating Bose-Einstein-condensed gas, where the centrifugal potential is exactly compensated by the external harmonic trap. By introducing a gauge transformation which makes the Hamiltonian periodic, we numerically solve the two-dimensional (2D) Gross-Pitaevskii equation finding the exact mean field ground state. In particular, we explore the crossover between the Thomas-Fermi regime, holding for large values of the coupling constant, and the lowest Landau level limit, corresponding to the weakly interacting case. Explicit results are given for the equation of state, the vortex core size, as well as the elastic shear modulus, which is crucial for the calculation of the Tkachenko frequencies.

In this paper we investigate the absorptive and dispersive properties in the phase-sensitive optical parametric amplification inside a cavity. First, we study the single-resonant optical parametric amplifier theoretically and experimentally. In this case, the mode splitting in the transmission spectra and the M shape in the reflection spectra are observed. However, the shape of the phase shift of the reflected field is unchanged. Then, the double-resonant optical parametric amplifier is studied theoretically, in which electromagnetically induced transparency-like effect may be emulated when the cavity linewidth for the harmonic wave is narrower than for the subharmonic field. The narrow transparency window appears in the absorption spectrum and is accompanied by a very steep variation of the dispersive profile.

The phenomenon of dynamical, field-induced freezing of quantum evolution is discussed. It occurs when a time-dependent state is dynamically driven in such a way that the evolution of the corresponding wave function is effectively localized within a small region in the projective Hilbert space. As a consequence, the dynamics of the system is frozen and the expectation values of all physical observables hardly change with time. Necessary and sufficient conditions for inducing dynamical freezing are inferred from a general analysis of the geometry of quantum evolution. The relevance of the dynamical freezing for a sustainable in time, dynamical control is discussed and exemplified by a study of the coherent control of the kicked rotor motion.

We investigate the influence of environmental noise on polarization entangled light generated by parametric emission in a cavity. By adopting a recent separability criterion, we show that (i) self-stimulation may suppress the detrimental influence of noise on entanglement, but (ii) once it becomes effective, a noise-equipped classical model of parametric emission provides the same results of quantum theory with respect to the separability criterion. More generally we also show that, in the macroscopic limit, it is not possible to observe violations of local realism with measurements of finite order $n$-particle correlations only. These results provide a prototypical case of the emergence of macroscopic local realism in the presence of strong entanglement even in the absence of decoherence.

We present a clear observation of a resonant contribution to electron impact ionization of Li-like highly charged ions $\left({\mathrm{I}}^{50+}\right)$. Li-like ions are the simplest in which resonant-excitation double autoionization (REDA) can occur. REDA was observed by measuring the ratio of the numbers of trapped ions of two neighbring charge states as a function of electron energy under equilibrium conditions using an electron beam ion trap. The resonant strength was determined by normalizing the experimental data to theoretical ionization cross sections at the nonresonant interaction energies. Good agreement was found between the observed and calculated resonant strengths for this observation of REDA in Li-like highly charged ions.

Here we propose an implementation of all possible positive-operator-value measures (POVMs) of two-photon polarization states. POVMs are the most general class of quantum measurements. Our setup requires linear optics, Bell state measurements, and an entangled three-photon ancilla state, which can be prepared separately and in advance (or “off-line”). As an example we give the detailed settings for a simultaneous measurement of all four Bell states for an arbitrary two-photon polarization state, which is impossible with linear optics alone.

According to the Gottesman-Knill theorem, a class of quantum circuits—namely, the so-called stabilizer circuits—can be simulated efficiently on a classical computer. We introduce an algorithm for this task, which is based on the graph-state formalism. It shows significant improvement in comparison to an existing algorithm, given by Gottesman and Aaronson, in terms of speed and of the number of qubits the simulator can handle. We also present an implementation.

We show that the solution of a multistate system composed of $N$ degenerate lower (ground) states and one upper (excited) state can be reduced by using the Morris-Shore transformation to the solution of a two-state system involving only the excited state and a (bright) superposition of ground states. In addition, there are $N-1$ dark states composed of ground states. We use this decomposition to derive analytical solutions for degenerate extensions of the most popular exactly soluble models: the resonance solution, the Rabi, Landau-Zener, Rosen-Zener, Allen-Eberly, and Demkov-Kunike models. We suggest various applications of the multistate solutions, for example, as tools for creating multistate coherent superpositions by generalized resonant $\pi$ pulses. We show that such generalized $\pi$ pulses can occur even when the upper state is far off resonance, at specific detunings, which makes it possible to operate in the degenerate ground-state manifold without populating the (possibly lossy) upper state, even transiently.

The relation between unstable periodic orbits and resonator modes in a fully chaotic open-sided two-dimensional laser resonator is theoretically investigated in the short wavelength limit. We derive a periodic-orbit-sum formula for eigenvalues of the resonator modes by applying the semiclassical approximation to the extended Fox-Li mode calculation method. With this formula, we show that the complicated wavelength dependence of the power-coupling coefficients of the fully chaotic quasi-stadium laser resonator can be explained by a few kinds of unstable periodic orbits.

Specific types of atomic coherences between Zeeman sublevels can be generated and detected using a method based on nonlinear magneto-optical rotation with frequency-modulated light. Linearly polarized, frequency-modulated light is employed to selectively generate ground-state coherences between Zeeman sublevels for which $\mathrm{\Delta }m=2$ and $\mathrm{\Delta }m=4$ in ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb}$ atoms, and additionally $\mathrm{\Delta }m=6$ in ${}^{85}\mathrm{Rb}$. The atomic coherences are detected with a separate, unmodulated probe light beam. Separation of the pump and probe beams enables independent investigation of the processes of creation and detection of the atomic coherences. With the present technique the transfer of the Zeeman coherences, including high-order coherences, from excited to ground state by spontaneous emission has been observed.

The evaluation of a tunneling tail by the Herman-Kluk method, which is a quasiclassical way to compute quantum dynamics, is examined by asymptotic analysis. In the shallower part of the tail, as well as in the classically allowed region, it is shown that the leading terms of semiclassical evaluations of quantum theory and the Herman-Kluk formula agree, which is known as an asymptotic equivalence. In the deeper part, it is shown that the asymptotic equivalence breaks down, due to the emergence of unusual “tunneling trajectory,” which is an artifact of the Herman-Kluk method.

We describe a scanning optical microscope based on polarization Sagnac interferometry for measuring ultrasmall phase shifts, and use this method to detect small numbers of absorbing molecules in a solid without the use of fluorescence. The absorption and concomitant optical phase shift of terrylene dopant molecules in a $p$-terphenyl host crystal are made time dependent by periodic optical saturation of the sample. A detection sensitivity of $8.75\times {10}^{-8}\mathrm{rad}$ is achieved with a $0.078\mathrm{Hz}$ bandwidth, and detection of signals from as few as $19\pm 3$ terrylene molecules is demonstrated at room temperature.

We present accurate ab initio nonperturbative calculations of the Breit correction to the parity nonconserving (PNC) amplitudes of the $6s\text{−}7s$ and $6s\text{−}5d_{3∕2}$ transitions in Cs, $7s\text{−}8s$ and $7s\text{−}6d_{3∕2}$ transitions in Fr, $6s\text{−}5d_{3∕2}$ transition in ${\mathrm{Ba}}^{+}$, $7s\text{−}6d_{3∕2}$ transition in ${\mathrm{Ra}}^{+}$, and $6p_{1∕2}\text{−}6p_{3∕2}$ transition in Tl. The results for the $6s\text{−}7s$ transition in Cs and $7s\text{−}8s$ transition in Fr are in good agreement with other calculations. We demonstrate that higher-orders many-body corrections to the Breit interaction are especially important for the $s\text{−}d$ PNC amplitudes. We confirm good agreement of the PNC measurements for cesium and thallium with the standard model.

It is shown that for two open quantum dots connected by a wire, “bound states in the continuum” of a single electron are formed at nearly periodic distances between the dots. This is due to Fabry-Pérot interference between quasibound states in each dot. The bound states are nonlocal, describing the electron trapped in both dots at the same time. Theoretical and numerical results show that trapped states exist even if the wire connecting the dots is relatively long.