Regimes of antisynchronized quasiperiodic and synchronized and unsynchronized chaotic oscillations have been observed in a bidirectional solid-state ring laser with modulated pump and are chracterized in terms of the maximum Lyapunov exponent. The results can be understood in terms of the coupled dynamics of two counterpropagating modes of a ring laser coupled to atomic population inversion.

Recent experiments claiming the formation of quantum superposition states in near-macroscopic systems raise the question of how the sizes of general quantum superposition states in an interacting system are to be quantified. We propose here a measure of size for such superposition states that is based on what measurements can be performed to probe and distinguish the different branches of the state. The measure allows the comparison of the effective size for superposition states in very different physical systems. It can be applied to a very general class of superposition states and reproduces known results for near-ideal cases. Comparison with a prior measure based on analysis of coherence between branches indicates that significantly smaller effective superposition sizes result from our measurement-based measure. Application to a system of interacting bosons in a double-well trapping potential shows that the effective superposition size is strongly dependent on the relative magnitude of the barrier height and interparticle interaction.

Hamiltonian oracles are the continuum limit of the standard unitary quantum oracles. In this limit, the problem of finding the optimal query algorithm can be mapped into the problem of finding shortest paths on a manifold. The study of these shortest paths leads to lower bounds of the original unitary oracle problem. A number of example Hamiltonian oracles are studied in this paper, including oracle interrogation and the problem of computing the XOR of the hidden bits. Both of these problems are related to the study of geodesics on spheres with nonround metrics. For the case of two hidden bits a complete description of the geodesics is given. For $n$ hidden bits a simple lower bound is proven that shows the problems require a query time proportional to $n$, even in the continuum limit. Finally, the problem of continuous Grover search is reexamined leading to a modest improvement to the protocol of Farhi and Gutmann.

Minimizing the effect of decoherence on a quantum register must be a central part of any strategy to realize scalable quantum-information processing. Apart from the strength of the coupling to the environment, the decoherence rate is determined by the system level structure and by the spectral composition of the noise trace that the environment generates. Here, we discuss a relatively simple model that allows us to study these different effects quantitatively in detail. We evaluate the effect that the perturbation has on a nuclear magnetic resonance system while it performs a Grover search algorithm.

High resolution Fourier transform spectra (FTS) of laser induced fluorescence (LIF) of $C{}^1\Sigma ^{+};D{}^1\Pi \to A{}^1\Sigma ^{+}–b{}^3\Pi$ and $A{}^1\Sigma ^{+}–b{}^3\Pi \to X{}^1\Sigma ^{+}$ transitions in ${\mathrm{Na}}^{85}\mathrm{Rb}$ and ${\mathrm{Na}}^{87}\mathrm{Rb}$ were obtained. An analysis of the direct LIF spectra together with the rotational relaxation satellites provided highly accurate rovibronic term values for $(4⩽J⩽163)$ of the $A{}^1\Sigma ^{+}–b{}^3\Pi$ complex, covering about 1950 mostly singlet levels $0⩽v_A⩽49$ and a considerable number $(>360)$ of the predominantly triplet $b{}^3\Pi _{0,1}$ sublevels. The direct deperturbation analysis of the singlet-triplet $A–b$ complex was performed by means of the inverted channel-coupling approach with Hund’s coupling case $\mathbf{a}$ basis functions. The electronic matrix elements of the model $4\times 4$ Hamiltonian were defined as piecewise analytical functions of the internuclear distance. Besides the Born-Oppenheimer potential energy curves of the mutually perturbed states and the off-diagonal spin-orbit (SO) $A–b$ coupling function, the SO splitting of the $b{}^3\Pi$ state was determined due to the pronounced electronic-rotation interaction between the $b{}^3\Pi _0$ and $b{}^3\Pi _1$ components observed for high $J$ levels. Overall, 24 mass-invariant fitting parameters have been required to reproduce about 2300 experimental term values of both isotopomers with a standard deviation of $0.012{\mathrm{cm}}^{-1}$, which is consistent with the uncertainty of the FTS experiment. An analytical mapping procedure based on a reduced variable representation of the radial coordinate was used to diminish the computational effort for the uniform finite-difference grid solution of the coupled-channel equations. The derived nonadiabatic $A–b$ wave functions were used to evaluate the $A{}^1\Sigma ^{+}–b{}^3\Pi –D{}^1\Pi$, $a{}^3\Sigma ^{+}$, $X{}^1\Sigma ^{+}$ rovibronic transition probabilities. The relative intensity distributions predicted for the $D\to A–b$ and $A–b\to X$ LIF progressions agree with their experimental counterparts within the accuracy of the measurements. The calculated $A–b–a$, $X$ transition probabilities were applied for simulation of the stimulated Raman $a\to A–b\to X$ processes, which can lead to efficient formation of ultracold NaRb molecules in the ground level $v_X=0$; $J_X=0$.

Single- and double-electron capture cross sections have been measured for ${\mathrm{He}}^{2+}$ impact on ${\mathrm{O}}_2$, ${\mathrm{H}}_2$, and ${\mathrm{D}}_2$ at impact energies smaller than $2\mathrm{keV}∕\mathrm{amu}$. The method applied combines the collection of slow product ions and electrons with primary ion-beam attenuation and stopping in a differentially pumped target gas chamber. Comparison with previous experimental and theoretical results is made. For ${\mathrm{He}}^{2+}$ collisions with ${\mathrm{H}}_2$ we find that double-electron capture is more important than single-electron capture below $0.2\mathrm{keV}∕\mathrm{amu}$. This result is also confirmed by cross-section measurements for ${\mathrm{He}}^{2+}$ on ${\mathrm{D}}_2$.

We report an experimental study of atomic coherence and interference in a three-level $\Lambda$ system of cold Rb atoms driven by multicolor coupling and probe fields. The multicolor coupling and probe fields open multiple channels for a two-photon Raman process. Interference between the open channels leads to rich spectral features in the $\Lambda$ system and can be controlled by the phase of the probe field. The constructive-interference-induced transparency or the destructive-interference-induced absorption with a subnatural linewidth can be selectively created near the atomic resonance.

Spin noise sets fundamental limits to the attainable precision of measurements using spin-polarized atomic vapors and therefore merits a careful study. On the other hand, it has been recently shown that spin noise contains useful physical information about the atomic system, otherwise accessible via magnetic-resonance-type experiments. We here show in yet another manifestation of the fluctuation-dissipation theorem, that spin noise reveals information on the spin-coherence dissipation properties of the atomic system, described by $1∕T_2$, the transverse spin-relaxation rate. We present the high-resolution measurements of spin noise at a low magnetic field, leading to an accurate comparison of the extracted relaxation rates with the ones inferred from traditional magnetic-resonance-type measurements in optical pumping experiments.

We investigate Bose-Einstein condensates (BEC) containing a large number of bosonic atoms interacting via a finite-range semirealistic interatomic interaction. Ground state properties for an increasing number of atoms in the condensate have been calculated using a modification of the potential harmonic expansion method (including a short range correlation function in the expansion basis) to solve the many-body Schrödinger equation. An improved numerical algorithm for the calculation of the potential matrix elements permits us to have up to 14 000 atoms in the condensate. Although our approach is approximate and justified for dilute condensates, our results agree well with available diffusion Monte Carlo results for the same case. The ground state energies also agree well with those by the Gross-Pitaevskii equation method for up to 100 particles in the trap and become gradually larger than the latter (up to 5% for 14 000 atoms). The difference is attributed to the effects of finite range interatomic interaction and two-body correlations. Our approach presents a clear physical picture of the condensate, being computationally economical at the same time.

We theoretically study the Coulomb effects on the photoionization processes of the H atom irradiated by the intense laser fields with circular and linear polarizations. For this purpose we represent the final continuum state by the Coulomb-Volkov state. Total ionization rates, photoelectron energy spectra, and angular distribution of photoelectrons are calculated and compared with those obtained using the Volkov state. We find that how much the Coulomb field influences the ionization dynamics depends on the momentum of photoelectrons, among which the photoelectron angular distributions in the linearly polarized laser field represent the most striking difference.

The interaction between two species of atoms in the condensate has been deduced and the trial wave functions that conserve the total spin have been constructed for the states of the ground band. A couple of generalized Gross-Pitaevskii equations have been derived for the spatial wave functions and the energies. The mixture of ${}^{23}\mathrm{Na}$ and ${}^{87}\mathrm{Rb}$ has been calculated as an example. The density of states is found to exhibit a ladder shape.

In this paper the influence of the prepulse current on a capillary-discharge $46.9\mathrm{nm}$ Ne-like Ar extreme-ultraviolet laser is reported. A current pulse with a typical $RC$ shape (decay time of $\sim 30\mu \mathrm{s}$) was used as a prepulse. Measurements indicate that when the filling pressure is low, the output can be improved by reducing the time delay between the application of the prepulse current and the onset of the main discharge current. For high pressure the reverse is true. This change is most significant for time delays between 2 and $4\mu \mathrm{s}$, and beyond these time delays, the effect is less significant. This effect is attributed to the changes in the capillary channel pressure and also to the absorption of the laser emission by the plasma plume ejected during the prepulse. Thus, apart from ensuring a minimal amount of prepulse current to prevent nonuniformity effects, the timing of the application of the prepulse current is also important.

A theory of linear susceptibility has been developed in the presence of dipole-dipole interaction for photonic-band-gap (PBG) materials doped with an ensemble of five-level nanoparticles. An external probe laser induces dipole moments in nanoparticles. When the concentration of the particles is high, the induced dipoles interact with one another through dipole-dipole interaction. Mean-field theory is used to include the effect of dipole-dipole interaction in the calculation of susceptibility. Numerical simulations are performed for the real and imaginary susceptibilities and it is found that the system switches between inversionless and noninversionless states. In addition the system switches between absorptionless and nonabsorptionless states. These occur when the resonance energy lies near the valence-band edge of the photonic-band-gap material. The theory also predicts a polarization catastrophe in PBG materials doped with nanoparticles.

We demonstrate the initialization, readout, and high-speed manipulation of a qubit stored in a single ${}^{87}\mathrm{Rb}$ atom trapped in a submicrometer-sized optical tweezer. Single-qubit rotations are performed on a time scale below $100\mathrm{ns}$ using two-photon Raman transitions. Using the spin-echo technique, we measure an irreversible dephasing time of $34\mathrm{ms}$. The readout of the single atom qubit is at the quantum projection noise limit when averaging up to 1000 individual events.

The problem that the strong-field approximation (SFA) in the length gauge (LG) cannot give the correct molecular harmonic generation spectrum when the internuclear distance is large is studied. By introducing the first excited state in addition to the ground state in the SFA and a procedure to resum translation invariance, the problem is resolved and the superiority of the LG to the velocity gauge in this case is discussed.

We demonstrate the efficient generation of high-order sum and difference frequencies in the extreme-ultraviolet (xuv) wavelength region both experimentally and theoretically. Experimentally, we combine a weak Nd:yttrium aluminum garnet (YAG) laser field $\left(1064\mathrm{nm}\right)$ with an intense Ti:sapphire laser field $(\sim 805\mathrm{nm})$. Besides the “pure” harmonics of the Ti:sapphire field, sum and difference frequencies of Ti:sapphire photons and up to two YAG photons are observed. Surprisingly, intensities of the sum and difference frequencies are comparable to or even higher than those of the pure harmonics even though the intensity of the YAG field is lower than that of the Ti:sapphire field by more than two orders of magnitude. Theoretically, we use the extended Lewenstein model to investigate high-order harmonic generation, sum-frequency generation, and difference-frequency generation using two-color laser fields. Theoretical calculations support our experimental observations and point out that choosing appropriate wavelengths for the weak combined field is crucial for the efficient generation of sum and difference frequencies. Furthermore, we discuss the effect of molecular alignment when ${\mathrm{N}}_2$ molecules are employed as a medium.

We consider the pooling of quantum states when Alice and Bob both have one part of a tripartite system and, on the basis of measurements on their respective parts, each infers a quantum state for the third part $S$. We denote the conditioned states which Alice and Bob assign to $S$ by $\alpha$ and $\beta$, respectively, while the unconditioned state of $S$ is $\rho$. The state assigned by an overseer, who has all the data available to Alice and Bob, is $\omega$. The pooler is told only $\alpha$, $\beta$, and $\rho$. We show that for certain classes of tripartite states, this information is enough for her to reconstruct $\omega$ by the formula $\omega \propto \alpha {\rho }^{-1}\beta$. Specifically, we identify two classes of states for which this pooling formula works: (i) all pure states for which the rank of $\rho$ is equal to the product of the ranks of the states of Alice’s and Bob’s subsystems; (ii) all mixtures of tripartite product states that are mutually orthogonal on $S$.

Though both theoretical and experimental investigations have revealed the superluminal behavior of evanescent electromagnetic waves, there are many disputes about the physical meaning and validity of such superluminal phenomenon, which is due to the fact that the traditional investigations are based on the theory of tunneling time and concerned with the problem of what the group velocity of evanescent waves means. In this paper, by studying the quantum probability amplitude for photons to propagate over a spacelike interval along an undersized waveguide, we present theoretical evidence for such superluminality.

In a quantum computation with pure states, the generation of large amounts of entanglement is known to be necessary for a speedup with respect to classical computations. However, examples of quantum computations with mixed states are known, such as the deterministic computation with one quantum qubit (DQC1) model [Knill and Laflamme, Phys. Rev. Lett. 81, 5672 (1998)], in which entanglement is at most marginally present, and yet a computational speedup is believed to occur. Correlations, and not entanglement, have been identified as a necessary ingredient for mixed-state quantum computation speedups. Here we show that correlations, as measured through the operator Schmidt rank, are indeed present in large amounts in the DQC1 circuit. This provides evidence for the preclusion of efficient classical simulation of DQC1 by means of a whole class of classical simulation algorithms, thereby reinforcing the conjecture that DQC1 leads to a genuine quantum computational speedup.

We present an efficient algorithm for twirling a multiqudit quantum state. The algorithm can be used for approximating the twirling operation in an ensemble of physical systems in which the systems cannot be individually accessed. It can also be used for computing the twirled density matrix on a classical computer. The method is based on a simple nonunitary operation involving a random unitary. When applying this basic building block iteratively, the mean squared error of the approximation decays exponentially. In contrast, when averaging over random unitary matrices the error decreases only algebraically. We present evidence that the unitaries in our algorithm can come from a very imperfect random source or can even be chosen deterministically from a set of cyclically alternating matrices. Based on these ideas we present a quantum circuit realizing twirling efficiently.