By direct comparison between experiment and theory with no adjustable parameters, we show how the classical fluctuations on a multistate atom laser beam increase with increasing flux. The fluctuations are inherent to state changing out coupling, rf, Raman, or otherwise and are likely to be present in all atom lasers, pulsed or continuous, that employ such out coupling. If not removed or avoided, these classical fluctuations will prevent shot noise limited measurement employing atom lasers of this kind.

Ultracold ${}^{87}\mathrm{Rb}\text{atoms}$ are delivered into a high-finesse optical microcavity using a translating optical lattice trap and detected via the cavity field. The atoms are loaded into an optical lattice from a magneto-optic trap and transported $1.5\mathrm{cm}$ into the cavity. Our cavity satisfies the strong-coupling requirements for a single intracavity atom, thus permitting real-time observation of single atoms transported into the cavity. This transport scheme enables us to vary the number of intracavity atoms from $1\text{to}>100$ corresponding to a maximum atomic cooperativity parameter of 5400, the highest value ever achieved in an atom-cavity system. When many atoms are loaded into the cavity, optical bistability is directly measured in real-time cavity transmission.

The Grover walk, which is related to Grover’s search algorithm on a quantum computer, is one of the typical discrete time quantum walks. However, a localization of the two-dimensional Grover walk starting from a fixed point is strikingly different from other types of quantum walks. The present paper explains the reason why the walker who moves according to the degree-four Grover operator can remain at the starting point with a high probability. It is shown that the key factor for the localization is due to the degeneration of eigenvalues of the time evolution operator. In fact, the global time evolution of the quantum walk on a large lattice is mainly determined by the degree of degeneration. The dependence of the localization on the initial state is also considered by calculating the wave function analytically.

We describe a scheme for quantum-error correction that employs feedback and weak measurement rather than the standard tools of projective measurement and fast controlled unitary gates. The advantage of this scheme over previous protocols [for example, Ahn et al. Phys. Rev. A 65, 042301 (2001)], is that it requires little side processing while remaining robust to measurement inefficiency, and is therefore considerably more practical. We evaluate the performance of our scheme by simulating the correction of bit flips. We also consider implementation in a solid-state quantum-computation architecture and estimate the maximal error rate that could be corrected with current technology.

We propose a model based on a generalized effective Hamiltonian for studying the effect of noise in quantum computations. The system-environment interactions are taken into account by including stochastic fluctuating terms in the system Hamiltonian. Treating these fluctuations as Gaussian Markov processes with zero mean and $\delta$-function correlation times, we derive an exact equation of motion describing the dissipative dynamics for a system of n qubits. We then apply this model to study the effect of noise on the quantum teleportation and a generic quantum controlled-NOT (CNOT) gate. For quantum teleportation, the effect of noise in the quantum channels is found to be additive, and the teleportation fidelity depends on the state of the teleported qubit. The effect of collective decoherence is also studied for the two-qubit entangled states. For the quantum CNOT gate, we study the effect of noise on a set of one- and two-qubit quantum gates, and show that the results can be assembled together to investigate the quality of a quantum CNOT gate operation. We compute the averaged gate fidelity and gate purity for the quantum CNOT gate and investigate phase, bit-flip, and flip-flop errors during the CNOT gate operation. The effects of direct interqubit coupling and fluctuations on the control fields are also studied. We find that the quality of the CNOT gate operation is sensitive to the strengths of the control fields and the strengths of the noise, and the effect of noise is additive regardless of its origin. We discuss the limitations and possible extensions of this model. In sum, we demonstrate a simple model that enables us to investigate the effect of noise in arbitrary quantum circuits under realistic device conditions.

Electron-impact ionization cross sections of Be-like ions are studied in the two-potential distorted-wave approximation. The relativistic and nonrelativistic total cross sections for incident energies from 1 to 10 units of ionization energy are calculated for ${\mathrm{B}}^{+}$, ${\mathrm{C}}^{2+}$, ${\mathrm{N}}^{3+}$, ${\mathrm{O}}^{4+}$, ${\mathrm{F}}^{5+}$, ${\text{Ne}}^{6+}$, ${\text{Al}}^{9+}$, ${\text{Ar}}^{14+}$, ${\text{Fe}}^{22+}$, ${\text{Ag}}^{43+}$, and ${\text{Hg}}^{76+}$. Systematic behaviors along the Be isoelectronic sequence are demonstrated.

We have used cold-target recoil-ion momentum spectroscopy to study electron capture from atomic and molecular hydrogen targets by slow $\left(0.3<\mathrm{v}<0.95\text{a.u.}\right)$ ${\mathrm{O}}^{8+}$ and ${\text{Ar}}^{8+}$ ions. For the atomic hydrogen target, we have performed coupled-channel calculations using an atomic orbital expansion to compare to the experimental results. The $Q$-value spectra show strong populations of both $n=5$ and $n=6$ states on the projectile, with a tendency for increasing the population of high-angular momentum states for higher projectile velocity. A strong population of $n=6$ is found, a result not previously reported but in good agreement with the present calculations.

We present an experiment where two photonic systems of arbitrary dimensions can be entangled. The method is based on spontaneous parametric down-conversion with trains of $d$ pump pulses with a fixed phase relation, generated by a mode-locked laser. This leads to a photon pair created in a coherent superposition of $d$ discrete emission times, given by the successive laser pulses. Entanglement is shown by performing a two-photon interference experiment and by observing the visibility of the interference fringes increasing as a function of the dimension $d$. Factors limiting the visibility, such as the presence of multiple pairs in one train, are discussed.

We consider a single quantum particle in a spherical box interacting with a fixed scatterer at the center, to construct a model of a degenerate atomic Fermi gas close to a Feshbach resonance. One of the key predictions of the model is the existence of two branches for the macroscopic state of the gas, as a function of the magnetic field controlling the value of the scattering length. This model is able to draw a qualitative picture of all the different features recently observed in a degenerate atomic Fermi gas close to the resonance, even in the unitary limit.

We report on direct stabilization of a femtosecond laser by a high-finesse passive optical cavity. Detailed comparison of two distinct stabilization schemes leads to new understanding of the optimum conditions for cavity stabilization and limitations on the ability to transfer the frequency stability of the cavity to the microwave domain. The stability of the frequency comb is explored in both the optical and the radio frequency domain. With an independent, stable cw laser, we verify that the linewidth and stability of the optical comb components, respectively, reach below $300\text{Hz}$ and $5\times {10}^{-14}$ at 1 s averaging time, both limited by the reference cw laser.

A macroscopic electromagnetic field is quantized in a linear isotropic dielectric by the association of a damped quantum-mechanical harmonic oscillator with each mode of the radiation field. The macroscopic Langevin equation is used to describe the motion of a damped oscillator. We discuss a fully canonical approach for the quantization of a harmonic oscillator with damping subjected to a Langevin force operator. The conjugate momentum is defined in the usual way and the quantum-mechanical Hamiltonian is introduced. This provides us with a direct method for the quantization of the radiation field in a dielectric material. Special attention is paid to the decomposition of the radiation field into transverse and longitudinal parts and their difference is elucidated by this approach.

A characteristic action $\Delta S$ is defined whose magnitude determines some properties of the expectation value of a general quantum displacement operator. These properties are related to the capability of a given environmental “monitoring” system to induce decoherence in quantum systems coupled to it. We show that the scale for effective decoherence is given by $\Delta S\approx \hslash$. We relate this characteristic action with a complementary quantity, $\Delta Z$, and analyze their connection with the main features of the pattern of structures developed by the environmental state in different phase space representations. The relevance of the $\Delta S$-action scale is illustrated using both a model quantum system solved numerically and a set of model quantum systems for which analytical expressions for the time-averaged expectation value of the displacement operator are obtained explicitly.

An exterior complex rotated finite element method was applied on the diabatic multichannel Schrödinger equation in order to compute and compare rovibronic energy structures, predissociation widths, and nonradiative lifetimes for levels in the (1–4), (1–5), and $\left(1\text{–}6\right){}^1\Sigma _g^{+}$ manifolds of ${\mathrm{H}}_2$. The rotationless $\left(v,J=0\right)$ levels are found to be more or less shifted relative to each other when comparing the results for these three manifolds. The existence of homogeneous spectroscopic perturbations was investigated by studying the rovibronic $\left(v,J=0-10\right)$ sequences for energies and level widths. Known experimental and theoretical radiative lifetimes were used to estimate present levels that might be spectroscopically measurable. The computed level widths for the $EF$, $GK$, and $H$ electronic levels were generally found to be about two orders of magnitude larger than previously reported [P. Quadrelli, K. Pressler, and L. Woiniewicz, J. Chem. Phys. 93, 4958 (1990)], indicating a somewhat stronger predissociation.

We implement exchange-correlation functionals with correct asymptotic behavior in the framework of a real-space density-functional pseudopotential method. This formalism is applied to calculate excitation energies and absorption spectra for a number of test systems selected to represent a wide range of electronic and chemical properties. The energies and oscillator strengths of electronic transitions are computed using time-dependent linear-response theory. Compared to calculations based on the time-dependent local-density approximation, asymptotically correct functionals yield more accurate excitation and ionization energies for atoms, molecules, and small clusters. The most notable improvements are observed for transitions to the upper electronic levels and for systems where the local-density approximation predicts close to zero electron affinities. At the same time, asymptotic corrections appear to have almost no effect on the absorption spectra and optical gaps of large atomic clusters and quantum dots. It implies that the asymptotic behavior of the exchange-correlation potential is less important in the limit of large systems, and other, more complex functionals may be needed to further improve the quality of theoretical results for all cluster sizes.

We have studied collisions between slow highly charged ions and pure ${\mathrm{C}}_{70}$ and ${\mathrm{C}}_{60}$ molecular targets, and report on measurements of target ionization and fragmentation in electron transfer processes. The intensity distributions in the fragmentation spectra for ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{70}$ are rather similar, indicating that similar roles are played by evaporation (neutral ${\mathrm{C}}_2$ emission) and fission processes (charged particle emission) in the two systems. For ${\mathrm{C}}_{70}$, intact molecular ions are formed in charge states up to $10+$, while the maximum charge state for ${\mathrm{C}}_{60}$ molecules is $9+$ following collisions with ${\mathrm{Xe}}^{23+}$ at $69\text{keV}$. The kinetic-energy releases measured for asymmetric fission of ${\mathrm{C}}_{70}$ ions $\left(\mathrm{C}_{70}{}^{r+}\to \mathrm{C}_{68}{}^{(r-1)}+\mathrm{C}_2{}^{+}\right)$ are mostly close to the corresponding ones for ${\mathrm{C}}_{60}$, while both sets of results are significantly lower than those reported for electron-impact ionization studies of ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{70}$. Kinetic-energy releases and fission barrier heights are estimated for ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{70}$ ions using an electrostatic model. An increased intensity of the higher charge states of ${\mathrm{C}}_{70}$ ions is observed compared to the ${\mathrm{C}}_{60}$ case, which most likely is due to a larger number of degrees of freedom on which the internal excitation energy may be distributed.

We study the quantum dynamics of a number of model systems as their coupling constants are changed rapidly across a quantum critical point. The primary motivation is provided by the recent experiments of Greiner et al. [Nature (London) 415, 39 (2002)] who studied the response of a Mott insulator of ultracold atoms in an optical lattice to a strong potential gradient. In a previous work, it had been argued that the resonant response observed at a critical potential gradient could be understood by proximity to an Ising quantum critical point describing the onset of density wave order. Here we obtain numerical results on the evolution of the density wave order as the potential gradient is scanned across the quantum critical point. This is supplemented by studies of the integrable quantum Ising spin chain in a transverse field, where we obtain exact results for the evolution of the Ising order correlations under a time-dependent transverse field. We also study the evolution of transverse superfluid order in the three-dimensional case. In all cases, the order parameter is best enhanced in the vicinity of the quantum critical point.

We investigate the quantum theory of a vortex line in a stack of weakly coupled two-dimensional Bose-Einstein condensates, that is created by a one-dimensional optical lattice. We derive the dispersion relation of the Kelvin modes of the vortex line and also study the coupling between the Kelvin and quadrupole modes. We solve the coupled dynamics of the vortex line and the quadrupole modes, both classically as well as quantum mechanically. The quantum mechanical solution reveals the possibility of generating nonequilibrium squeezed vortex states by strongly driving the quadrupole modes.

Quantum theory of interference phenomena does not take the diameter of the particle into account, since particles were much smaller than the width of the slits before the rise of molecular interferometry. In the experiments with large molecules, the diameter of the particle has approached the width of the slits. Therefore, an analytical description of these cases should include a finite particle size. An asymmetric double-slit grating seems to be very suitable for the study of the influence of a particle’s size on the interference pattern. We identify three characteristic cases for the ratio of slit widths ${\delta }_1$ and ${\delta }_2$ and the particle diameter $D$: $D⪡{\delta }_1$ and $D⪡{\delta }_2$, ${\delta }_1>D>{\delta }_2$, and $D>{\delta }_1>{\delta }_2$. Taking into account the influence of both slits on the particle wave function, regardless of through which slit the particle passed, we treat the particle-wall interaction in a simple fashion, such that if the particle size is greater than the slit opening there is no transmission. The transverse momentum distribution is independent of the distance from the slits and the particle size, while the space distribution strongly depends on this distance and the particle size. We found that the interference is absent only when the particle’s diameter is larger than both slit widths, $D>{\delta }_1>{\delta }_2$.

We examine the phase diagram of an effectively repulsive Bose-Einstein condensate of atoms that rotates in a quadratic-plus-quartic potential. With use of a variational method we identify the three possible phases of the system as a function of the rotational frequency of the trap and of the coupling constant. The derived phase diagram is shown to be universal and partly exact in the limit of weak interactions and small anharmonicity. The variational results are found to be consistent with numerical solutions of the Gross-Pitaevskii equation.

The properties of low-density, low-energy matter wave packets propagating through waveguide bends are investigated. Time-dependent quantum-mechanical calculations using simple harmonic oscillator confining potentials are performed for a range of parameters close to those accessible by recent “atom chip”-based experiments. We compare classical calculations based on Ehrenfest’s theorem to these results to determine whether classical mechanics can predict the amount of transverse excitation as measured by the transverse heating. The present results thus elucidate some of the limits for which matter wave propagation through microstructures can be reliably considered using classical particle motion.