In this paper, traveling-wave (TW) equations of stimulated Raman scattering (SRS) process are deduced in detail with the phonon lifetime and backward Raman scattering considered. The numerical methods of second-order accuracy are deduced for TW equations of the SRS process. Spontaneous Raman scattering is simulated by including the stochastic shot-noise sources in phonon wave equations. The TW method is adopted to simulate the evolution of the fundamental laser inside actively $Q$-switched lasers, and the numerical results show periodical self-modulation of actively $Q$-switched pulses, which were also studied experimentally. The theoretical results were in good agreement with the experimental ones. The self-mode locking of intracavity Raman lasers are investigated numerically by adopting the TW method. It is found that the mode locking of the Stokes laser is due to the resonator net gain. The dependences of the mode-locking effect on the resonator length, transverse relaxation time of laser medium, and phonon lifetime of the Raman medium are studied numerically.

We evaluate the Uhlmann fidelity between two one-mode displaced thermal states as the maximal probability transition between appropriate purifications of the given states. The optimal purifications defining the fidelity are proved to be two-mode displaced Gaussian states.

Optical trapping of selected species of radioactive atoms has great potential in precision measurements for testing fundamental physics such as the electric dipole moment, atomic parity nonconservation, and parity-violating $\beta$-decay correlation coefficients. We report on the trapping of ${10}^4$ radioactive ${}^{82}\mathrm{Rb}$ atoms $(t_{1∕2}=75\mathrm{s})$ with a trap lifetime of $\sim 55\mathrm{s}$ in an optical dipole trap. Transfer efficiency from the magneto-optical trap is $\sim 14\%$. We further report evidence of spontaneous spin polarization of the atoms in optical dipole trap loading. These advancements are an important step toward a new generation of precision nuclear-spin–$\beta$-emission direction correlation measurements with polarized ${}^{82}\mathrm{Rb}$ atoms.

We introduce an operational framework to analyze nonadiabatic Abelian and non-Abelian, cyclic and noncyclic, geometric phases in open quantum systems. In order to remove the adiabaticity condition, we generalize the theory of dynamical invariants to the context of open systems evolving under arbitrary convolutionless master equations. Geometric phases are then defined through the Jordan canonical form of the dynamical invariant associated with the superoperator that governs the master equation. As a by-product, we provide a sufficient condition for the robustness of the phase against a given decohering process. We illustrate our results by considering a two-level system in a Markovian interaction with the environment, where we show that the nonadiabatic geometric phase acquired by the system can be constructed in such a way that it is robust against both dephasing and spontaneous emission.

Fast and accurate measurement is a highly desirable, if not vital, feature of quantum computing architectures. In this work we investigate the usefulness of adaptive measurements in improving the speed and accuracy of qubit measurement. We examine a particular class of quantum computing architectures, ones based on qubits coupled to well-controlled harmonic oscillator modes (reminiscent of cavity QED), where adaptive schemes for measurement are particularly appropriate. In such architectures, qubit measurement is equivalent to phase discrimination for a mode of the electromagnetic field, and we examine adaptive techniques for doing this. In the final section we present a concrete example of applying adaptive measurement to the particularly well-developed circuit-QED architecture.

The generation of entanglement between two identical, interacting quantum dots—initially in ground states—by a coherent field and the subsequent time evolution of the entanglement are studied by calculating the concurrence between the two dots. The results predict that while it is possible to generate entanglement (or entanglement of formation, as defined for a mixed state) between the two dots, at no time do the dots become fully entangled to each other or is a maximally entangled Bell state ever achieved. We also observe that the degree of entanglement increases with an increase in the photon number inside the cavity and a decrease in the dot-photon coupling. The behavior of the two-dot system, initially prepared in an entangled state and interacting with thermal light, is also studied.

We present two continuous-time quantum search algorithms similar to the adiabatic search algorithm, but now without the requirement of adiabatic evolution. Both algorithms can find the marked state in a time proportional to $\sqrt{N}$. The behavior of the first algorithm is, essentially, similar to Grover’s algorithm, but the second model possesses the important property that one does not need to single out a given time in order to find the searched state. After a well-defined transition time, this second algorithm will converge towards the marked state with a high probability, provided the parameters of the Hamiltonian are chosen appropriately. This convergence shows a resemblance to quantum search algorithms with a fixed point [L. K. Grover, Phys. Rev. Lett. 95, 150501 (2005)].

Experimentally obtained Stark-recurrence spectra taken at low principal quantum numbers show unusual degrees of orbit profile asymmetry. To clearly illustrate the semiclassical mechanisms behind this behavior a numerical experiment is performed where orbit profiles (recurrence strength as a function of scaled energy) are found from computed Stark spectra. These spectra are generated for a wide range of quantum defects assuming a highly simplified excitation and core structure which represents a semiclassical system restricted to $s$-wave scattering. It is noted that at low quantum numbers, the expected dominant nonhydrogenic feature of recurrence spectra is scattered orbits whose scaled actions are unresolved from existing hydrogenic orbits. The semiclassical orbit profiles obtained from absorption spectra are compared with semiclassical closed-orbit theory. Closed-orbit theory successfully predicts the systematic shifting of recurrence strength as a function of quantum defect. In the limited parameter space investigated it is found that the distribution of recurrence strength is influenced primarily by interference with scattered combinations containing a primitive orbit repetition. The systematic shifting of recurrence strength as a function of quantum defect is attributed to a relative phase shift between the contributing orbits.

Relativistic effects on the nuclear magnetic shielding $\mathit{\sigma }\left(M\right)$ of the series of diatomics $M\text{F}$ ($M=\text{Cu}$, Ag, Au) are calculated and analyzed using the Dirac-Hartree-Fock (DHF) method in the random phase approximation (RPA). Significant differences due to relativistic effects on the shielding constant $\mathit{\sigma }\left(M\right)$ are found in this series of atoms. The high electronegativity of the fluorine atom works in conjunction with the spin-orbit coupling to increase the calculated value for $\mathit{\sigma }\left(\text{Au}\right)$. An unusually large diamagnetic contribution to the shielding constant is observed. Nonrelativistic nuclear magnetic shielding $\left[{\mathit{\sigma }}^{\text{NR}}\left(M\right)\right]$ shows very good linear correlation with the nuclear charge ($Z$) of the metal, while the relativistic shielding $\left[{\mathit{\sigma }}^{\text{rel}}\left(M\right)\right]$ varies as $Z^{2.26}$.

The differential cross sections for low-energy muonic hydrogen atom scattering in solid molecular ${\mathrm{H}}_2$, ${\mathrm{D}}_2$, and ${\mathrm{T}}_2$ targets under low pressure have been calculated for various temperatures. The polycrystalline fcc and hcp structure of the solid hydrogenic targets are considered. The Bragg and phonon scattering processes are described using the Debye model of a solid. The calculated cross sections are used for Monte Carlo simulations of the muonic atom slowing down in these targets. They have been successfully applied for a description of the production of the muonic atom beams in the multilayer hydrogenic crystals.

We describe the properties of a pair of ultracold bosonic atoms in a one-dimensional harmonic trapping potential with a tunable zero-ranged barrier at the trap center. The full characterization of the ground state is done by calculating the reduced single-particle density, the momentum distribution, and the two-particle entanglement. We derive several analytical expressions in the limit of infinite repulsion (Tonks-Girardeau limit) and extend the treatment to finite interparticle interactions by numerical solution. As pair interactions in double wells form a fundamental building block for many-body systems in periodic potentials, our results have implications for a wide range of problems.

We propose a method to perform precision measurements of the interaction parameters in systems of $N$ ultracold spin $1∕2$ atoms. The spectroscopy is realized by first creating a coherent spin superposition of the two relevant internal states of each atom and then letting the atoms evolve under a squeezing Hamiltonian. The nonlinear nature of the Hamiltonian decreases the fundamental limit imposed by the Heisenberg uncertainty principle to $N^{-2}$, a factor of $N$ smaller than the fundamental limit achievable with noninteracting atoms. We study the effect of decoherence and show that, even with decoherence, entangled states can outperform the signal to noise limit of nonentangled states. We present two possible experimental implementations of the method using Bose-Einstein spinor condensates and fermionic atoms loaded in optical lattices and discuss their advantages and disadvantages.

The entanglement properties of two mode fields generated from four-wave mixing are discussed in the system of an ensemble of $V$-type three-level atoms embedded in a two-mode cavity, in which the atomic transitions from the two excited states to the ground state are driven by one strong and one relative weak laser field, respectively. The nondegenerate four-wave mixing process occurs in the strong laser-driven transition, which is also coupled by the two cavity modes. With the help of the auxiliary atomic transition driven by the weak laser field and adjusting the frequency difference of the two modes, highly squeezed and entangled light with high intensity can be generated.

We study electromagnetically induced transparency in a vacuum rubidium atomic cell and show that reflected drive radiation results in the reshaping and shift of dark resonance. We show that those effects are connected with (i) Bragg reflection of the probe radiation in optically thick atomic coherent medium modulated by the standing-wave drive field, as well as with (ii) quantum interference enhanced absorption of the probe radiation in four-level N-configuration formed due to the reflected drive field.

We show theoretically that two atomic dipoles in a resonator constitute a nonlinear medium, whose properties can be controlled through the relative position of the atoms inside the cavity and the detuning and intensity of the driving laser. We identify the parameter regime where the system operates as a parametric amplifier, based on the cascade emission of the collective dipole of the atoms, and determine the corresponding spectrum of squeezing of the field at the cavity output. This dynamics might be observed as a result of self-organization of laser-cooled atoms in resonators.

Ultrafast and narrow linewidth lasers are combined to study multiphoton photoassociative ionization (PAI) in a Rb magneto-optical trap. Through the use of time of flight spectroscopy and by varying the parameters of the ultrafast laser, the excitation pathway for PAI was determined. It was found that ${{\mathrm{Rb}}_2}^{+}$ is formed, not by direct photoionization, but by sequential excitation of ${\mathrm{Rb}}_2$ to an autoionizing state. Determining the excitation and ionization pathway was a necessary first step for future efforts in trying to establish coherent control techniques, first for the efficient production of translationally cold ${\mathrm{Rb}}_2$, and then for transferring population to a desired vibrationally cold molecular state.

The correspondence principle is investigated in the framework of deterministic predictions for individual systems. Exact analytical results are obtained for the quantum and Liouvillian dynamics of a nonlinear oscillator coupled to a phase-damping reservoir at a finite temperature. In this context, the time of critical wave function spreading—the Ehrenfest time—emerges as the characteristic time scale within which the concept of deterministic behavior is admissible in physics. A scenario of quasideterminism may then be defined, within which the motion is experimentally indistinguishable from the truly deterministic motion of Newtonian mechanics. Beyond this time scale, predictions for individual systems can be given only statistically and, in this case, it is shown that diffusive decoherence is indeed a necessary ingredient to establish the quantum-classical correspondence. Moreover, the high-temperature regime is shown to be an additional condition for the quantum-classical transition and, accordingly, a lower bound for the reservoir temperature is derived for our model.

We demonstrate the use of trapped ytterbium ions as quantum bits for quantum information processing. We implement fast, efficient state preparation and state detection of the first-order magnetic field-insensitive hyperfine levels of ${}^{171}\mathrm{Yb}^{+}$, with a measured coherence time of $2.5\mathrm{s}$. The high efficiency and high fidelity of these operations is accomplished through the stabilization and frequency modulation of relevant laser sources.

We introduce schemes for quantum computing based on local measurements on entangled resource states. This work elaborates on the framework established in Gross and Eisert [Phys. Rev. Lett. 98, 220503 (2007); quant-ph/0609149]. Our method makes use of tools from many-body physics—matrix product states, finitely correlated states, or projected entangled pairs states—to show how measurements on entangled states can be viewed as processing quantum information. This work hence constitutes an instance where a quantum information problem—how to realize quantum computation—was approached using tools from many-body theory and not vice versa. We give a more detailed description of the setting and present a large number of examples. We find computational schemes, which differ from the original one-way computer, for example, in the way the randomness of measurement outcomes is handled. Also, schemes are presented where the logical qubits are no longer strictly localized on the resource state. Notably, we find a great flexibility in the properties of the universal resource states: They may, for example, exhibit nonvanishing long-range correlation functions or be locally arbitrarily close to a pure state. We discuss variants of Kitaev’s toric code states as universal resources, and contrast this with situations where they can be efficiently classically simulated. This framework opens up a way of thinking of tailoring resource states to specific physical systems, such as cold atoms in optical lattices or linear optical systems.

Total electron-${\mathrm{H}}_2\mathrm{O}$ scattering cross sections have been measured from 50 to $5000\mathrm{eV}$ with experimental errors of about 5%. Integral elastic and inelastic cross sections have been calculated over a broad energy range $(1–10000\mathrm{eV})$ with an optical potential method assuming an independent atom representation. Dipole rotational excitations have also been included in the framework of the first Born approximation. From a detailed evaluation of the present results and their comparison with previous theoretical and experimental data, a set of recommended integral cross sectional data is provided. By combining these data with an average excitation energy derived from the experimental energy loss spectra, the stopping power of electrons in ${\mathrm{H}}_2\mathrm{O}$ has been obtained from 5 to $5000\mathrm{eV}$.