Non-Abelian geometric phases are attracting increasing interest because of possible experimental application in quantum computation. We study the effects of the environment (modeled as an ensemble of harmonic oscillators) on a holonomic transformation and write the corresponding master equation. The solution is analytically and numerically investigated and the behavior of the fidelity analyzed: fidelity revivals are observed and an optimal finite operation time is determined at which the gate is most robust against noise.

We examine the problem of simulating lattice gauge theories on a universal quantum computer. The basic strategy of our approach is to transcribe lattice gauge theories in the Hamiltonian formulation into a Hamiltonian involving only Pauli spin operators such that the simulation can be performed on a quantum computer using only one- and two-qubit manipulations. We examine three models, the U(1), SU(2), and SU(3) lattice gauge theories, which are transcribed into a spin Hamiltonian up to a cutoff in the Hilbert space of the gauge fields on the lattice. The number of qubits required for storing a particular state is found to have a linear dependence on the total number of lattice sites. The number of qubit operations required for performing the time evolution corresponding to the Hamiltonian is found to be between a linear to quadratic function of the number of lattice sites, depending on the arrangement of qubits in the quantum computer. We remark that our results may also be easily generalized to higher $\mathrm{SU}\left(N\right)$ gauge theories.

We prove an analytical expression for the size of the gap between the ground and the first excited state of quantum adiabatic algorithm for the 3-satisfiability, where the initial Hamiltonian is a projector on the subspace complementary to the ground state. For large problem sizes the gap decreases exponentially and as a consequence the required running time is also exponential.

Cluster states serve as the central physical resource for one-way quantum computing. We here present an experimental demonstration of the efficient cluster-state construction scheme proposed by Browne and Rudolph. In our experiment, three-photon cluster states with high purity are created from two Bell states via a qubit “fusion” operation, showing a strong violation of a three-particle Mermin inequality of $\mid ⟨A⟩\mid =3.10\pm 0.03$. In addition, the entanglement properties of the cluster states are examined under ${\sigma }_z$ and ${\sigma }_x$ measurements on a qubit. This scheme could be extended to any desired number of qubits and represents an essential step for the optical one-way quantum computation.

A scheme for retrieving quantum information stored in collective atomic spin systems onto optical pulses is presented. Two off-resonant light pulses cross the atomic medium in two orthogonal directions and are interferometrically recombined in such a way that one of the outputs carries most of the information stored in the medium. In contrast to previous schemes our approach requires neither multiple passes through the medium nor feedback on the light after passing the sample, which makes the scheme very efficient. The price for that is some added noise which is, however, small enough for the method to beat the classical limits.

We address the problem of implementing high-fidelity one-qubit operations subject to time-dependent noise in the qubit energy splitting. We show with explicit numerical results that high-fidelity bit flip operations may be generated by imposing bounded control fields. For noise correlation times shorter than the time for a $\pi$ pulse, the time-optimal $\pi$ pulse itself yields the highest fidelity. For very long correlation times, fidelity loss is approximately due to systematic error, which is efficiently tackled by compensation for off resonance with a pulse sequence (CORPSE). For intermediate ranges of the noise correlation time, we find that short CORPSE, which is less accurate than CORPSE in correcting systematic errors, yields higher fidelities. Numerical optimization of the pulse sequences using gradient ascent pulse engineering results in noticeable improvement of the fidelity for a bit flip operation on the computational basis states and a small but still positive fidelity enhancement for the NOT gate.

For the metastable states of antiprotonic helium atoms, ${}^3\mathrm{He}^{+}\overline{p}$, the fine and hyperfine splittings of energy levels are calculated within the framework of the Breit-Pauli Hamiltonian. The latter represents the ${\alpha }^2$ order relativistic corrections to the nonrelativistic energy. Results include as well the leading ${\alpha }^3$ order contribution due to the anomalous magnetic moment of electron. The final relative accuracy of the hyperfine intervals is estimated to be about $5\times {10}^{-5}$.

Atomic quadrupole moments and hyperfine constants of the metastable states of , , , , and are calculated by the multiconfiguration Dirac-Hartree-Fock and relativistic configuration-interaction methods. For , the configuration is . For the other ions, the configuration consists of a single -electron outside a set of closed shells. Current interest in the quadrupole moments of these states is due to the fact that optical transitions of these ions may be useful as references for frequency standards. Energy shifts of the metastable states due to the interactions of the quadrupole moments with external electric field gradients are among the largest sources of error in these frequency standards. For the quadrupole moments, agreement is obtained to within about 10% with the available measurements. For the hyperfine constants, good agreement is obtained with measurements and with other calculations, except for the factors of the states of , , and , where the correlation effects are so large that they reverse the sign of the constant relative to the Dirac-Hartree-Fock value. As a test of the calculational methods, quadrupole moments and hyperfine constants are calculated for the states in isoelectronic neutral Au. This yields a value of the nuclear quadrupole moment .

The exact quantum-mechanical solution of the two-state exponential model with one flat diabatic potential has been found for a specific energy below the higher threshold. The $N$ matrix has been derived in the adiabatic representation and the closed analytical expression for the transmission coefficient has been obtained. The results reveal the influence of the closed channel on the nonadiabatic transmission.

Absolute dissociation cross sections are reported for $\mathrm{H}_n{}^{+}$ clusters of varied mass $(n=3,5,\dots ,35)$ following collisions with He atoms at $60\mathrm{keV}∕\mathrm{amu}$. Initial results have been published previously for a smaller range of cluster sizes [Ouaskit et al., Phys. Rev. A 49, 1484 (1994)]. The present extended study includes further experimental results, reducing the statistical errors associated with the absolute cross sections. The previously suggested quasilinear dependence of the $\mathrm{H}_n{}^{+}$ dissociation cross sections upon $n$ is developed with reference to expected series of geometrical shells of ${\mathrm{H}}_2$ molecules surrounding a $\mathrm{H}_3{}^{+}$ core. Recent calculations identify $n=9$ as corresponding to the first closed ${\mathrm{H}}_2$ shell [e.g., Štich et al., J. Chem. Phys. 107, 9482 (1997)]. Recurrence of the distinct characteristics observed in the dissociation-cross-section dependence upon cluster size around $n=9$ provides the basis for the presently proposed subsequent closed shells at $n=15$, 21, 27, and 33, in agreement with the calculations of Nagashima et al. [J. Phys. Chem. 96, 4294 (1992)].

Using the $R$-matrix Floquet approach, we have investigated multiphoton single ionization of helium, neon, and argon subjected to laser light with a wavelength between 248.6 and $390\mathrm{nm}$. For a wavelength of $390\mathrm{nm}$, we have investigated ionization rates for Ne and Ar at intensities up to $2.5\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$. In this intensity regime, the ionization rates no longer follow the multiphoton $I^N$ power law. At an intensity of $2\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$, a tunneling model approximates the Ar ionization rates within a factor 3, but the differences are much larger for Ne. The ionization rates at $390\mathrm{nm}$ are affected by intermediate resonances, with these resonances both enhancing and inhibiting ionization. Multiphoton ionization cross sections for Ne and Ar at $248.6\mathrm{nm}$ have also been determined.

Using pump-probe spectroscopy with ultrashort laser pulses, we see an enhancement of the charge-asymmetric dissociation (CAD) channel, ${\left({{\mathrm{I}}_2}^{2+}\right)}^{*}\to {\mathrm{I}}^{2+}+\mathrm{I}$, over a narrow range of internuclear separation. The enhancement of the CAD channel appears to come from the excitation of the symmetric ground state dissociation channel $({\mathrm{I}}^{+}+{\mathrm{I}}^{+})$ for two reasons. First, there is a depletion in the symmetric channel at approximately the same pump-probe delay as the asymmetric enhancement. Second, for a fixed delay, the asymmetric channel increases as a function of probe intensity while the symmetric channel decreases. In addition, we find that the kinetic energy of the extra ${\mathrm{I}}^{2+}+\mathrm{I}$ ions decreases for increasing delay. To explain this dependence of the kinetic energy release on delay, we introduce model potential energy curves. Based on these curves, we conclude that the excitation is produced by a resonant three-photon transition within ${{\mathrm{I}}_2}^{2+}$ rather than by ionization of ${I_2}^{+}$.

Using techniques of complex analysis in an algebraic approach, we solve the wave equation for a two-level atom interacting with a monochromatic light field exactly. A closed-form expression for the quasienergies is obtained, which shows that the Bloch-Siegert shift is always finite, regardless of whether the original or the shifted level spacing is an integral multiple of the driving frequency $\omega$. We also find that the wave functions, though finite when the original level spacing is an integral multiple of $\omega$, become divergent when the intensity-dependent shifted energy spacing is an integral multiple of the photon energy. This result provides an ab initio theoretical explanation for the occurrence of the Freeman resonances observed in above-threshold ionization experiments.

We consider a rapidly rotating two-component Bose-Einstein condensate (BEC) containing a vortex lattice. We calculate the dispersion relation for small oscillations of vortex positions (Tkachenko modes) in the mean-field quantum Hall regime, taking into account the coupling of these modes with density excitations. Using an analytic form for the density of the vortex lattice, we numerically calculate the elastic constants for different lattice geometries. We also apply this method to calculate the elastic constant for the single-component triangular lattice. For a two-component BEC, there are two kinds of Tkachenko modes, which we call acoustic and optical in analogy with phonons. For all lattice types, acoustic Tkachenko mode frequencies have quadratic wave-number dependence at long wavelengths, while the optical Tkachenko modes have linear dependence. For triangular lattices the dispersion of the Tkachenko modes are isotropic, while for other lattice types the dispersion relations show directional dependence consistent with the symmetry of the lattice. Depending on the intercomponent interaction there are five distinct lattice types, and four structural phase transitions between them. Two of these transitions are second order and are accompanied by the softening of an acoustic Tkachenko mode. The remaining two transitions are first order and while one of them is accompanied by the softening of an optical mode, the other does not have any dramatic effect on the Tkachenko spectrum. We also find an instability of the vortex lattice when the intercomponent repulsion becomes stronger than the repulsion within components.

Correlation functions related to the dynamic density response of the one-dimensional Bose gas in the model of Lieb and Liniger are calculated. An exact Bose-Fermi mapping is used to work in a fermionic representation with a pseudopotential Hamiltonian. The Hartree-Fock and generalized random phase approximations are derived and the dynamic polarizability is calculated. The results are valid to first order in $1∕\gamma$, where $\gamma$ is Lieb-Liniger coupling parameter. Approximations for the dynamic and static structure factor at finite temperature are presented. The results preclude superfluidity at any finite temperature in the large-$\gamma$ regime due to the Landau criterion. Due to the exact Bose-Fermi duality, the results apply for spinless fermions with weak $p$-wave interactions as well as for strongly interacting bosons.

We study theoretically the coherent and correlated motion of many fermions inside an infinite square well potential. We will look at electrons and ${}^3\mathrm{He}$ atoms, which behave very differently not only because of their masses, but also because of their different interaction potential. Also, the level of theory and the role of approximations in the solution of the time-dependent Schrödinger equation will be discussed.

The role of anyonic excitations in fast rotating harmonically trapped Bose gases in a fractional quantum Hall state is examined. Standard Chern-Simons anyons as well as “nonstandard” anyons obtained from a statistical interaction having Maxwell-Chern-Simons dynamics and suitable nonminimal coupling to matter are considered. Their respective ability to stabilize attractive Bose gases under fast rotation in the thermodynamical limit is studied. Stability can be obtained for standard anyons while for nonstandard anyons, stability requires that the range of the corresponding statistical interaction does not exceed the typical wavelength of the atoms.

We present a realization of weak measurement for the arrival time of a single photon in virtue of the simultaneous characteristic of biphotons. Our experimental setup is based on a Hong-Ou-Mandel interferometer. A birefringent crystal is used to perform weak measurement between a preselected and a postselected measurement by two polarizers. The extreme weak values lie well outside of the eigenvalues of the observable.

The nonlinearity exhibited by the kinetic inductance of a superconducting stripline couples stripline resonator modes together in a manner suitable for quantum nondemolition measurement of the number of photons in a given resonator mode. Quantum nondemolition measurement is accomplished by coherently driving another resonator mode, referred to as the detector mode, and measuring its response. We show that the sensitivity of such a detection scheme is directly related to the dephasing rate induced by such an intermode coupling. We show that high sensitivity is expected when the detector mode is driven into the nonlinear regime and operated close to a point where critical slowing down occurs.

We report the best figure-of-merit achieved for an internal nuclear polarized hydrogen gas target and a Monte Carlo simulation of spin-exchange optical pumping. The dimensions of the apparatus were optimized using the simulation, and the experimental results were in good agreement with the simulation. The best result achieved for this target was 50.5% polarization with 58.2% degree of dissociation of the sample beam exiting the storage cell at a hydrogen flow rate of $1.1\times {10}^{18}\mathrm{atoms}∕\mathrm{s}$.