The spectrum of the cavity-QED microlaser or micromaser is expected to show distinctive features of the coherent light-matter interaction, which are obscured in the conventional Schawlow-Townes linewidth theory. However, the spectral studies have been limited to resonant atom-cavity interaction so far. Here we consider the dispersive interaction in the off-resonance case, from which we uncover a quantum frequency pulling effect in the microlaser or micromaser spectrum. We present a quantum theory of the spectrum which introduces the notion of a frequency-pulling distribution associated with the photon number. In contrast to the conventional laser, periodic variation of the mean frequency pulling is observed with increasing pump parameter and it is attributed to the strong atom-cavity coupling. The pulling distribution gives rise to a spectral broadening, which can be dominant over the nondispersive broadening addressed in the previous works. We also developed a corresponding semiclassical theory and discuss how the introduction of the frequency shift fits in with the extended quantum theory.

I theoretically demonstrate the collective population evolution of two-level atoms, based on the mean-field theory. Optical materials with abrupt changes of electromagnetic local densities of states enable steady-state population inversion of two-level atoms which is generally considered impossible. In previous studies, details of the population evolution of a single two-level atom were discussed. However, behaviors of the population evolution of collective two-level atoms are very different from those of a single two-level atom. In this paper, temporal behaviors of the collective population evolution for input electric fields with constant and time-dependent amplitudes are discussed in detail. Moreover, I develop the effective method to calculate the collective spontaneous emission for non-Markovian dynamics. Finally, I discuss the validity of the mean-field theory for a large number of two-level atoms in spontaneous emission using the Markovian approximation.

We investigate the phase diagrams of two-dimensional lattice dipole systems with variable geometry. For bipartite square and triangular lattices with tunable vertical sublattice separation, we find rich phase diagrams featuring a sequence of easy-plane magnetically ordered phases separated by incommensurate spin-wave states.

We present an analytic solution describing the quantum state of a single photon after interacting with a moving mirror in a cavity. This includes situations when the photon is initially stored in a cavity mode as well as when the photon is injected into the cavity. In addition, we obtain the spectrum of the output photon in the resolved-sideband limit, which reveals spectral features of the single-photon strong-coupling regime in this system. We also clarify the conditions under which the phonon sidebands are visible and the photon-state frequency shift can be resolved.

Information theory has its particles, bits and qubits, just as physics has electrons and photons. However, in physics we have a special category of objects with no clear counterparts in information theory: quasiparticles. They are introduced to simplify complex emergent phenomena making otherwise very difficult calculations possible and providing additional insight into the inner workings of the system. We show that we can adopt a similar approach in information theory. We introduce the hyperbits, information quasiparticles which we prove to be a resource equivalent to entanglement and classical communication, and we give examples of how they can be used to simplify calculations and get more insight into communication protocols.

Linear optics quantum computing is a promising approach to implementing scalable quantum computation. However, this approach has very demanding physical resource requirements. Recently, Aaronson and Arkhipov (e-print arXiv:1011.3245) showed that a simplified model, which avoids the requirement for fast feed-forward and postselection, while likely not capable of solving BQP-complete problems efficiently, can solve an interesting sampling problem believed to be classically hard. Loss and mode mismatch are the dominant sources of error in such systems. We provide evidence that even lossy systems or systems with mode mismatch are likely to be classically hard to solve. This is of practical interest to experimentalists wishing to demonstrate such systems since it suggests that, even with errors in their implementation, they are likely implementing an algorithm that is classically hard to solve. Our results also equivalently apply to the multiwalker quantum walk model.

We study the behavior of a quantum gyroscope, that is, a quantum system which singles out a direction in space in order to measure certain properties of incoming particles such as the orientation of their spins. We show that repeated Heisenberg interactions of the gyroscope with several incoming spin-$\frac{1}{2}$ particles provides a simple model of decoherence which exhibits both relaxation and dephasing. Focusing on the semiclassical limit, we derive equations of motion for the evolution of a coherent state and investigate the evolution of a superposition of such states. While a coherent state evolves on a time scale given by the classical ratio of the angular momentum of the gyroscope to that of the incoming particles, dephasing acts on a much shorter time scale that depends only on the angular difference of the states in the superposition.

The fine-structure mixing and quenching cross sections of the cesium 7${}^{2}P$ state in mixtures of helium, methane, and ethane were measured using laser-induced fluorescence techniques. This research was performed to study the kinetics associated with an optically pumped blue cesium laser operating on the 7${}^2{P}_{1/2}$-$6S_{1/2}$ transition. Fluorescence decay curves from pulsed-laser experiments were analyzed as a function of buffer gas density at cell temperatures near 393 K. The fine-structure mixing cross sections for He, CH${}_4$, and C${}_2$H${}_6$ are $14\pm 3$, $35\pm 6$, and $73\pm 10$ Å${}^2$, respectively. The ${}^2$$P_{3/2}$ state is quenched more rapidly than the ${}^2{P}_{1/2}$ state. A model that includes the effects of radiation trapping and independent quenching cross sections for each fine-structure sublevel is compared to the experimental data. The rapid quenching negatively impacts the performance of a recently demonstrated optically pumped blue laser. We compare the cross sections for alkali-metal and noble gases and extend the adiabaticity analysis to the higher-lying excited states.

In this work we consider the theoretical treatment of the interaction of a laser pulse with an atom and focus on the methodology used to extract the quantity that is observed experimentally, i.e., the electron probability density. We solve the time-dependent Schrödinger equation (TDSE) using two techniques: the spectral method, which makes use of an expansion of the wave function onto the field-free atomic eigenstates, and the wave-function method, where the TDSE is numerically solved on a grid. In this work we show that the electron probability density can be extracted from the final wave function, obtained by the wave-function method, by using the resolvent technique with a proper choice of the energy resolution. The advantage of this approach is that it does not require the calculation of the field-free atomic eigenstates. As an illustration of this method we compare the spectral and wave-function methods in the case of atomic hydrogen interacting with a linearly polarized mid-IR laser pulse. The comparison shows excellent agreement.

We perform a detailed analysis of the importance of causality within the strong-field approximation and the steepest-descent framework for the recollision-excitation with subsequent tunneling ionization (RESI) pathway in laser-induced nonsequential double ionization (NSDI). In this time-delayed pathway, an electron returns to its parent ion and, by recolliding with the core, gives part of its kinetic energy to excite a second electron at a time $t^{\prime }$. The second electron then reaches the continuum at a later time $t$ by tunneling ionization. We show that, if $t^{\prime }$ and $t$ are complex, the condition that recollision of the first electron occurs before tunnel ionization of the second electron translates into boundary conditions for the steepest-descent contours and thus puts constraints on the saddles to be taken when computing the RESI transition amplitudes. We also show that this generalized causality condition has a dramatic effect on the shapes of the RESI electron momentum distributions for few-cycle laser pulses. Physically, causality determines how the dominant sets of orbits of an electron returning to its parent ion can be combined with the dominant orbits of a second electron tunneling from an excited state. All features encountered are analyzed in terms of such orbits and their quantum interference.

We explore the stability of the interface between two phase-separated Bose gases in relative motion on a lattice. Gross-Pitaevskii-Bogoliubov theory and the Gutzwiller ansatz are employed to study the short- and long-time stability properties. The underlying lattice introduces effects of discreteness, broken spatial symmetry, and strong correlations, all three of which are seen to have considerable qualitative effects on the Kelvin-Helmholtz instability. Discreteness is found to stabilize low flow velocities because of the finite energy associated with displacing the interface. Broken spatial symmetry introduces a dependence not only on the relative flow velocity but also on the absolute velocities. Strong correlations close to a Mott transition will stop the Kelvin-Helmholtz instability from affecting the bulk density and creating turbulence; instead, the instability will excite vortices with Mott-insulator-filled cores.

We study the formation of stable homonuclear and heteronuclear pentamers from ultracold atoms via a generalized stimulated Raman adiabatic passage scheme. The atom-molecule dark-state solutions for the system are obtained, and the linear instability and the adiabatic fidelity of the dark state are investigated. We also discuss the effects of external field parameters on the conversion efficiency.

We present a scheme for subwavelength single-atom localization that is based on the photon statistics measurement of the resonance fluorescence from the two-level atomic system. The photon number distribution of the resonance fluorescence depends on the position of the atom inside the standing-wave driving field via the position-dependent Rabi frequency. We show that this position-dependent Rabi frequency can be used to localize the atom within the subwavelength region.

A complete physical approach to quantum information requires a robust interface among flying qubits, long-lifetime memory, and computational qubits. Here we present a unified interface for microwave and optical photons, potentially connecting engineerable quantum devices such as superconducting qubits at long distances through optical photons. Our approach uses an ultracold ensemble of atoms for two purposes: quantum memory and to transduce excitations between the two frequency domains. Using coherent control techniques, we examine an approach for converting and storing quantum information between microwave photons in superconducting resonators, ensembles of ultracold atoms, and optical photons, as well as a method for transferring information between two resonators.

We present experimental and theoretical evidence on the breakdown of the simple man's model in the high-energy recollision region by examining both the energy-resolved angular distribution of photoelectrons in above-threshold ionization and the spectrum of high-order harmonics generated in elliptically polarized driver fields. With the help of a semiclassical model calculation, we show that, surprisingly, even for the high-energy recollision electrons, their wave-packet dynamics can be influenced strongly by the Coulomb field.

It is shown that the dissonance, a quantum correlation which is equal to quantum discord for separable state, is required for assisted optimal state discrimination. We find that only one side discord is required in the optimal process of assisted state discrimination, while another side discord and entanglement is not necessary. We confirm that the quantum discord, which is asymmetric depending on local measurements, is a resource for assisted state discrimination. With the absence of entanglement, we give the necessary and sufficient condition for vanishing one side discord in assisted state discrimination for a class of $d$ nonorthogonal states. As a by-product, we find that the positive-partial-transposition condition is the necessary and sufficient condition for the separability of a class of $2\times d$ states.

A nondestructive approach to determine an unknown two-qubit Werner state of an ensemble is proposed. The approach is feasible for all four types of Werner states which contain different kinds of Bell states. Our scheme can detect the magnitude of the real parameter of an initial Werner state. An easy two-step method is also presented to determine which type of Bell state is included in the Werner state. The initial state can be preserved during the measurements. Our nondemolition determinations are demonstrated experimentally in a nuclear-magnetic-resonance quantum-information processor.

We introduce the study of quantum protocols that probabilistically simulate quantum channels from a sender in the future to a receiver in the past. The maximum probability of simulation is determined by causality and depends on the amount and type (classical or quantum) of information that the channel can transmit. We illustrate this dependence in several examples, including ideal classical and quantum channels, measure-and-prepare channels, partial trace channels, and universal cloning channels. For the simulation of partial trace channels, we consider generalized teleportation protocols that take $N$ input copies of a pure state in the future and produce $M\le N$ output copies of the same state in the past. In this case, we show that the maximum probability of successful teleportation increases with the number of input copies, a feature that was impossible in classical physics. In the limit of asymptotically large $N$, the probability converges to the probability of simulation for an ideal classical channel. Similar results are found for universal cloning channels from $N$ copies to $M>N$ approximate copies, exploiting a time-reversal duality between universal cloning and a partial trace.

We present a theoretical framework for the calculation of photon-yield spectra from radiative-cascade decays of photoexcited helium atoms in a static electric field for incident photon energies below the first ($N=1$) ionization threshold. The present theory takes full account of the singlet-triplet mixing among the singly excited states with principal quantum numbers $n\lesssim 10$. The model predicts the enhancement of transition probabilities to triplet final states due to the field-induced mixing. In particular, for a field strength of 9.17 kV/cm, polarization of incident photons perpendicular to the field, and a 4 meV broad excitation function tuned to the $1s6p{}^{1}P$ states, the $1s6\ell \to 1s2p{}^{3}P$ and $1s5\ell \to 1s2p{}^{3}P$ emitted photon yields are predicted to be about 70 times and 20 times lower, respectively, than the photon yields for transitions to the corresponding singlet final states.

We propose a simple yet efficient method for generating abruptly autofocusing optical beams with arbitrary caustics. In addition, we introduce a family of abruptly autodefocusing beams whose maximum intensity suddenly decreases by orders of magnitude right after the target. The method relies on appropriately modulating the phase of a circularly symmetric optical wavefront, such as that of a Gaussian, and subsequently on Fourier-transforming it by means of a lens. If two such beams are superimposed in a Bessel-like standing wave pattern, then a complete mirror-symmetric, with respect to the focal plane, caustic surface of revolution is formed that can be used as an optical bottle. We also show how the same method can be used to produce accelerating 1D or 2D optical beams with arbitrary convex caustics.