Nuclear spin exchange occurs in ultracold collisions of fermionic alkaline-earth-metal-like atoms due to a difference between $s$- and $p$-wave phase shifts. We study the use of an optical Feshbach resonance, excited on the ${{}^{1}S}_0\to {{}^{3}P}_1$ intercombination line of ${}^{171}\text{Y}\text{b}$, to affect a large modification of the $s$-wave scattering phase shift and thereby optically mediate nuclear exchange forces. We perform a full multichannel calculation of the photoassociation resonances and wave functions and from these calculate the real and imaginary parts of the scattering length. As a figure of merit of this interaction, we estimate the fidelity to implement a $\sqrt{\text{SWAP}}$ entangling quantum logic gate for two atoms trapped in the same well of an optical lattice. For moderate parameters one can achieve a gate fidelity of $\sim 95\%$ in a time of $\sim 50\mu \text{s}$.

We investigate optical spatial solitons in a two-dimensional quasi-phase-matched geometry involving two concurrent noncollinear quadratic processes. The model, formally equivalent to that ruling second-harmonic generation in the presence of a one-dimensional transverse nonlinear grating, supports a class of simultons with a large domain of stability. We also identify a regime where the general equations predict walking solitary waves.

Noise poses a challenge for any real-world implementation in quantum information science. The theory of quantum error correction deals with this problem via methods to encode and recover quantum information in a way that is resilient against that noise. Unitarily correctable codes are an error correction technique wherein a single unitary recovery operation is applied without the need for an ancilla Hilbert space. Here, we present an optical implementation of a nontrivial unitarily correctable code for a noisy quantum channel with no decoherence-free subspaces or noiseless subsystems. We show that recovery of our initial states is achieved with high fidelity $\left(\ge 0.97\right)$, quantitatively proving the efficacy of this unitarily correctable code.

We report the long-overdue collision-induced Raman scattering spectrum by a pair of unlike rare gas atoms. Absolute-unit scattering intensities, both isotropic and anisotropic, are given for Ne-Ar, along with the depolarization ratio for this system, recorded by a gaseous room-temperature mixture over a wide range of frequency shift. We make a critical comparison with spectra computed quantum-mechanically on the basis of modern pair-polarizability representations for Ne-Ar, of either ab initio or density functional theory methods. We report a value for the Kerr second virial coefficient, deduced from our measurements. Our data are especially intended to add to the vital yet hitherto incomplete knowledge of the role of collision-induced processes in atmospheric environments.

Synchronously pumped parametric oscillators have been shown to have subthreshold giant amplification of such a magnitude that a macroscopic, entirely noise-driven, signal is present at output even when the device is below threshold. In this paper we quantify the magnitude of the amplification factor in terms of some key device parameters. We use non-normal operator theory to find the noise amplification factor (Kreiss constant) and show that the signal amplitude is proportional to it. We also determine that the noise sensitivity depends in a nontrivial way on the group velocity of the three fields.

We study how the nonadiabatic effect causes the observable fluctuation in the “geometric phase” for a two-level system, which is defined as the experimentally measurable quantity in the adiabatic limit. From the Rabi exact solution to this model, we give a reasonable explanation to the experimental discovery of phase fluctuation in the superconducting circuit system [P. J. Leek, J. M. Fink, A. Blais, R. Bianchetti, M. Göppl, J. M. Gambetta, D. I. Schuster, L. Frunzio, R. J. Schoelkopf, and A. Wallraf, Science 318, 1889 (2007)], which seemed to be regarded as the conventional experimental error.

We demonstrate sub-Doppler laser spectroscopy with a beam of ${{}^7\text{L}\text{i}}^{+}$ ions stored at 33.8% of the speed of light in the experimental storage ring at GSI. Using two lasers, the one copropagating and the other counterpropagating, with respect to the ion beam, a fluorescence line is observed via optical-optical double-resonance spectroscopy on a $\Lambda$-type level configuration. A linewidth of $\approx 114\text{MHz}$ is found, which is 12 times narrower than the Doppler broadening due to the momentum spread of the ion beam. Interpreted as a test of Lorentz invariance, we find $\left|{\widehat{\alpha }}_2\right|<1.2\times {10}^{-5}$, a $25\times$ tighter limit on $O\mathbf{\left(}{\left(v/c\right)}^4\mathbf{\right)}$ deviations from time dilation than any other experiment.

A one-step scheme is proposed to realize three-qubit controlled-PHASE (CPHASE) gate for electron spins in lateral quantum dots, and two different quantum-dot configurations (ring- and line-type) are considered. We investigate the effect of the acoustic phonon and spontaneous emission on the scheme. Numerical results show that the gate performance is primarily related to quantum-dot configuration and temperature, and can be significantly improved by selecting lower single-exciton resonance in line-type configuration.

I explore the entanglement dynamics of multiqubit systems suitable for use as quantum memories: decoherence free subspaces and noiseless subsystems. The aim of this exploration is to determine how a complete loss of entanglement affects the ability of these error-avoidance techniques to protect quantum information. I utilize negativity and concurrence as entanglement measures and find no correlation between complete system loss of entanglement and the fidelity of the stored quantum information. These results complement previous results in which quantum protocols not explicitly based on entanglement exhibit little correlation between entanglement sudden death and the accuracy of the given protocol.

We report sensitive detection of parametric resonances in a high-density sample of ultracold ${}^{87}\text{R}\text{b}$ atoms confined to a far-off-resonance optical dipole trap. Fluorescence imaging of the expanded ultracold atom cloud after a period of parametric excitation shows significant modification of the atomic spatial distribution and has high sensitivity compared with traditional measurements of parametrically driven trap loss. Using this approach, a significant shift of the parametric resonance frequency is observed and attributed to the anharmonic shape of the dipole trap potential.

We consider the manipulation of Bose-Einstein condensate vortices by optical potentials generated by focused laser beams. It is shown that for appropriate choices of the laser strength and width it is possible to successfully transport vortices to various positions inside the trap confining the condensate atoms. Furthermore, the full bifurcation structure of possible stationary single-charge vortex solutions in a harmonic potential with this type of impurity is elucidated. The case when a moving vortex is captured by a stationary laser beam is also studied, as well as the possibility of dragging the vortex by means of periodic optical lattices.

As a contribution to a current controversial discussion we show that the smoothness properties of the quantum-mechanical and the WKB phase shifts for elastic scattering by a smooth repulsive radially symmetric potential in two spatial dimensions are different.

Landau states, i.e., quantum states of a charged particle in a uniform magnetic field, are considered in cylindrical gauge. The asymptotic behavior $\left|m\right|\to \infty$ ($m$ eigenvalue of $\mathbf{r}\wedge \mathbf{p}$) of the wave functions relevant to the three variables $r$, $p_r$, and modulus of momentum $p$, all can be expressed in terms of one-dimensional oscillator wave functions. Before taking the limit $\left|m\right|\to \infty$, wave functions relevant to the conjugate momentum $p_r$ of the radial coordinate $r$ are first determined as a finite sum involving confluent hypergeometric functions.

I use the recently proposed framework of ontological models (N. Harrigan, T. Rudolph, and S. Aaronson, e-print arXiv:0709.1149) to obtain economical models for the results of tomographically complete sets of measurements on finite-dimensional quantum systems. I describe a procedure that simplifies the models by decreasing the number of necessary ontic states and present an explicit model with just 33 ontic states for a qutrit.

We consider using a secret key and a noisy quantum channel to generate noiseless public communication and noiseless private communication. The optimal protocol for this setting is the publicly enhanced private father protocol. This protocol exploits random coding techniques and “piggybacking” of public information along with secret-key-assisted private codes. The publicly enhanced private father protocol is a generalization of the secret-key-assisted protocol of Hsieh, Luo, and Brun and a generalization of a protocol for simultaneous communication of public and private information suggested by Devetak and Shor.

We introduce and experimentally demonstrate a method to measure the Schmidt number of pure two-photon states entangled in transverse-mode structure. Our method is based on the connection between the Schmidt decomposition in quantum theory and the coherent-mode decomposition in classical coherence theory. We apply the method to two-photon states generated by spontaneous parametric down conversion and show that our results are in excellent agreement with numerical calculations based on the Schmidt decomposition.

We investigate the change in entanglement of photons due to propagation and postselection. We find that postselected entanglement varies by propagation and that states with maximum bipartite and tripartite entanglement can be generated from propagation of unentangled photons. We generalize the results to $n$ photons and show that entangled states with permutation symmetry can be generated from propagation of unentangled states. We discuss the creation of $n$-photon Greenberger-Horne-Zeilinger states as an example of a class of states with the desired symmetry.

We consider collision between a dipole-bound molecular anion and a neutral polar molecule and show that the excess electron can bind two neutral molecules into a dimer. Using a variational approach similar to the Heitler-London model of $\text{H}_2{}^{+}$ ion, we obtain the energy terms of such a dimer. Their difference determines the cross section of electron transfer from the anion to the neutral molecule in quasiclassical near-resonant Born-Oppenheimer approximation. We obtain for the cross section an analytical expression containing the weak (logarithmic) factor depending on the molecular dipole moment and the collision velocity. With the prelogarithmic factor proportional to inverse binding energy of the electron in the molecular anion, such weak dependence on the collision velocity is somewhat similar to the expressions appearing in the hard-sphere collision model. However the large logarithmic factor connected with long-range dipole-dipole interaction between the colliding molecules contradict to the hard-sphere approximation even for qualitative description of the charge transfer. Our analytical calculations are in a good accordance with the results of a recent experiment [Y. Liu, M. Cannon, L. Suess, F. B. Dunning, V. E. Chernov, and B. A. Zon, Chem. Phys. Lett. 433, 1 (2006)].

We report the measurements of depolarization probabilities of polarized ${}^3\text{H}\text{e}$ in a rectangular acrylic cell with a deuterated tetraphenyl butadiene-doped deuterated polystyrene coating filled with superfluid ${}^4\text{H}\text{e}$ at $\sim 330\text{mK}$ with a magnetic holding field of $\sim 7.3\text{G}$. We achieve a wall depolarization probability of $\sim 1.0\times {10}^{-7}$. Such a surface will find application in a new experiment searching for the neutron electric dipole moment and other applications.

We analyze the structure of spin-one Bose-Einstein condensates in the presence of a homogeneous magnetic field. We classify the homogeneous stationary states and study their existence, bifurcations, and energy spectra. We reveal that phase separation can occur in the ground state of antiferromagnetic (polar) condensates while the spin components of the ferromagnetic condensates are always miscible and no phase separation occurs. Our theoretical model, confirmed by numerical simulations, explains that this phenomenon takes place when the energy of the lowest homogeneous state is a concave function of the magnetization. In particular, we predict that phase separation can be observed in a ${}^{23}\text{N}\text{a}$ condensate confined in a highly elongated harmonic trap. Finally, we discuss the phenomena of dynamical instability and spin domain formation.