It has recently been proposed that quantum gravity might lead to the decoherence of superpositions in energy, corresponding to a discretization of time at the Planck scale. The proposal seems amenable to experimental verification with methods from quantum optics and atomic physics. However, we argue that the predicted decoherence is unobservable in such experiments if it acts globally on the whole experimental setup. This is related to the unobservability of the global phase in interference. We then show how local energy decoherence, which acts separately on system and phase reference, could be detected with remarkable sensitivity and over a wide range of length scales by long-distance Ramsey interferometry with metastable atomic states. The sensitivity of the experiments can be further enhanced using multiatom entanglement.

Above-threshold detachment of electrons from negative ions by an elliptically polarized laser field is analyzed within the strong-field approximation. The low-energy part of the spectrum, that is, its structure and its apparent cutoff, strongly depends on the orbital quantum number $l$ of the initial ground state. The high-energy part is characterized by the usual extended plateau caused by rescattering, which is essentially independent of the ground state. The potential that the returning electron experiences during rescattering is modeled by the sum of a polarization potential and a static potential. This rescattering potential does not have much effect on the shape of the plateau, but it does on its height. For ${\mathrm{H}}^{-}\left(l=0\right)$, the yield of rescattered electrons is five orders of magnitude below the direct electrons, while for ${\mathrm{I}}^{-}\left(l=1\right)$ the yields only differ by a factor of 40. We also analyze the dependence of the angle-resolved energy spectrum on the ellipticity of the laser field and confirm general symmetry properties. An angle-integrated elliptic dichroism parameter is introduced and analyzed.

We present a detailed theoretical analysis of micromotion in a time-averaged orbiting potential trap. Our treatment is based on the Gross-Pitaevskii equation, with the full time-dependent behavior of the trap systematically approximated to reduce the trapping potential to its dominant terms. We show that within some well specified approximations, the dynamic trap has solitary-wave solutions, and we identify a moving frame of reference which provides the most natural description of the system. In that frame eigenstates of the time-averaged orbiting potential trap can be found, all of which must be solitary-wave solutions with identical, circular center of mass motion in the laboratory frame. The validity regime for our treatment is carefully defined, and is shown to be satisfied by existing experimental systems.

A ${}^{87}\mathrm{Rb}$ Bose-Einstein condensate (BEC) is produced in a portable atom-chip system less than $30\times 30\times 15\mathrm{cm}$, where the ultrahigh vacuum is maintained by a small, $8\mathrm{L}∕\mathrm{s}$, ion pump and nonevaporable getter. An aluminum nitride chip with lithographically patterned copper is used to seal the vacuum system, provide the electrical feedthroughs, and create the magnetic trap potentials. All cooling and trapping processes occur $0.6–2.5\mathrm{mm}$ from ambient laboratory air. A condensate of about 2000 ${}^{87}\mathrm{Rb}$ atoms in $F=2,m_F=2$ is achieved after $4.21\mathrm{s}$ of rf forced evaporation. A magneto-optical trap lifetime of $30\mathrm{s}$ indicates the vacuum near the chip surface is about ${10}^{-10}\text{torr}$. This work suggests that a chip-based BEC-compatible vacuum system can occupy a volume of less than $0.5\mathrm{L}$.

The fragmentation of the ground state of a repulsive condensate immersed into a double-trap potential is found to be a general and critical phenomenon. It takes place for a given number of bosons if their scattering length is larger than some critical value or for a given value of the scattering length if the number of bosons is above some critical number. We demonstrate that the geometry of the inner trap determines these critical parameters while the number of the fragments and the fraction of bosons in the various fragments can be manipulated by the outer trap. There is also a maximal number of bosons for which the ground state is fragmented. If this number is exceeded, the fragmented state becomes a very low-lying excited state of the condensate. This maximal number of bosons can be substantially manipulated by varying the inner and outer traps. To study threefold fragmentation we have chosen a potential well with two barriers as the inner trap and embedded in two types of outer ones. A manifold fragmentation is also addressed.

For focused pulses of light in isotropic nonlinear media, third-harmonic generation can be strongly affected by group-velocity mismatch between the fundamental and third-harmonic. There is a characteristic time determined by the group-velocity mismatch and the Rayleigh range of the focused pulse. The dynamics depend on two dimensionless quantities, namely the ratio of the characteristic time to the pulse duration and the phase-velocity mismatch times the Rayleigh range. Pulses shorter than the characteristic time have physics described by simple analytic formulas. Pulses near the characteristic time have an intermediate behavior given by an explicit but more complicated formula. Pulses longer than the characteristic time tend to the continuous-wave case.

A renormalized semiclassical quantization method for rescalable Hamiltonians is proposed. A classical Hamilton system having a potential function that consists of homogeneous polynomials like the Coulombic potential can have a scale invariance in its extended phase space (phase space plus time). Consequently, infinitely many copies of a single trajectory constitute a one-parameter family that is characterized in terms of a scaling factor. This scaling invariance in classical dynamics is lost in quantum mechanics due to the presence of the Planck constant. It is shown that in a system whose classical motions have a self-similarity in the above sense, classical trajectories adopted in the semiclassical scheme interact with infinitely many copies of their own that are reproduced by the relevant scaling procedure, thereby undergoing quantum interference among themselves to produce a quantized spectrum.

We calculate the entanglement between two spins in the ferromagnetic Heisenberg chain at low temperatures, and show that when only the ground state and the one-particle states are populated, the entanglement profile is a Gaussian with a characteristic length depending on the temperature and the coupling between spins. The magnetic field affects only the amplitude of the profile and not its characteristic length.

We propose two interesting methods of generating the four-photon $W$ state. These methods use parametric down-conversion processes, linear optical elements, and commercial photon detectors, which are readily feasible under current technology. They can also be used to generate the three-photon $W$ state, the three-photon Greenberger-Horne-Zeilinger state, and the three-photon maximally entangled photon-number state (a typical photon-number entanglement state) by simply changing some experimental components or their parameters. Moreover, assuming we have photon number-resolving detectors, these methods can develop into methods that generate a general $n$-photon $W$ state. They are expected to become powerful tools for experimental investigations of multipartite entanglement and its applications to quantum information processing.

We investigate the possibility of using dielectric microdisk resonators for the optical detection of single atoms trapped and cooled in magnetic microtraps near the surface of a substrate. The bound and evanescent fields of optical whispering-gallery modes are calculated and the coupling to straight waveguides is investigated using finite-difference time domain solutions of Maxwell’s equations. Results are compared with semianalytical solutions based on coupled mode theory. We discuss atom detection efficiencies and the feasibility of nondestructive measurements in such a system depending on key parameters such as disk size, disk-waveguide coupling, and scattering losses.

The scheme of high-intensity attosecond high-order harmonic generation driven by a synthesized laser field is proposed. The synthesized laser field is obtained by an appropriate superposition of a few-cycle laser pulse and a relatively long pulse of several tens of femtoseconds. Calculated results show that the intensity of the attosecond high-order harmonic pulse in helium driven by the synthesized laser field with a $8.8\times {10}^{13}\mathrm{W}∕{\mathrm{cm}}^2∕5\mathrm{fs}$ laser pulse and a $3.51\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2∕50\mathrm{fs}$ laser pulse is several orders of magnitude higher than that driven by a single $8.8\times {10}^{13}\mathrm{W}∕{\mathrm{cm}}^2∕5\mathrm{fs}$ laser pulse, and it is even stronger than that driven by a single $7.9\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2∕5\mathrm{fs}$ laser pulse, although the single and the synthesized pulses have the same peak electric-field strength.

We compare the predictions of the single-particle Dirac equation with quantum field theory for an electron subjected to a space and time dependent field. We demonstrate analytically and numerically that a transition into the negative-energy subspace predicted by the single-particle Dirac equation is directly associated with the degree of suppression of pair-production as described by quantum field theory. We show that the portion of the mathematical wave function that populates the negative-energy states corresponds to the difference between the positron spatial density for systems with and without an electron initially present.

We report on the coherent coupling of whispering gallery modes (WGM) in a photonic molecule formed from two melamine-formaldehyde spherical microcavities with a thin shell of CdTe nanocrystals. Utilizing a microporous polymer structure to orient the photonic molecule, we have excited the photonic molecule both on and off axis. This controllable geometry has allowed the observation of an off-axis fine structure that consists of very sharp peaks resulting from the removal of the WGM degeneracy with respect to the azimuthal quantum number $m$. The mode splittings are in very good agreement with theory.

We present a theory for the estimation of a classical magnetic field by an atomic sample with a Gaussian distribution of collective spin components. By incorporating the magnetic field and the probing laser field as quantum variables with Gaussian distributions on equal footing with the atoms, we obtain a very versatile description which is readily adapted to include probing with squeezed light, dissipation, and loss and additional measurement capabilities on the atomic system.

Optimal quantum machines can be implemented by linear projective operations. In the present work a general qubit symmetrization theory is presented by investigating the close links to the qubit purification process and to the programmable teleportation of any generic optimal antiunitary map. In addition, the contextual realization of the $N\to M$ cloning map and of the teleportation of the $N\to (M-N)$ universal-NOT (UNOT) gate is analyzed by a very general angular momentum theory. An extended set of experimental realizations by state symmetrization linear optical procedures is reported. These include the $1\to 2$ cloning process, the UNOT gate and the quantum tomographic characterization of the optimal partial transpose map of polarization encoded qubits.

We introduce a primitive for quantum cryptography that we term “state targeting.” We show that increasing one’s probability of success in this task above a minimum amount implies an unavoidable increase in the probability of a particular kind of failure. This is analogous to the unavoidable disturbance to a quantum state that results from gaining information about its identity, and can be shown to be a purely quantum effect. We solve various optimization problems for state targeting that are useful for the security analysis of two-party cryptographic tasks implemented between remote antagonistic parties. Although we focus on weak coin flipping, the results are significant for other two-party protocols, such as strong coin flipping, partially binding and concealing bit commitment, and bit escrow. Furthermore, the results have significance not only for the traditional notion of security in cryptography, that of restricting a cheater’s ability to bias the outcome of the protocol, but also for a different notion of security that arises only in the quantum context, that of cheat sensitivity. Finally, our analysis leads to some interesting secondary results, namely, a generalization of Uhlmann’s theorem and an operational interpretation of the fidelity between two mixed states.

The collective oscillations of one-dimensional (1D) repulsive Bose gas with external harmonic confinement in two different regimes are studied. The first regime is the mean-field regime when the density is high. The second regime is the Tonks-Girardeau regime when the density is low. We investigate the resonances under periodic modulations of the trap potential and the effective nonlinearity. Modulations of the effective nonlinear coefficient result from modulations of the atomic scattering length by the Feshbach resonance method or variations of the transverse trap frequency. In the mean-field regime we predict bistability in the nonlinear oscillations of the condensate. In the Tonks-Girardeau regime the resonance has the character of a linear parametric resonance. In the case of rapid strong modulations of the nonlinear coefficient we find analytical expressions for the nonlinearity managed soliton width and the frequency of the slow secondary oscillations near the fixed point. We confirm the analytical predictions by direct numerical simulations of the 1D Gross-Pitaevskii equation and the effective nonlinear Schrödinger equation with quintic nonlinearity and trap potential.

Excitation of Rydberg states in isolated ${\mathrm{C}}_{60}$ is studied by time-resolved photoelectron spectroscopy in a femtosecond two-color pump-probe experiment. The relaxation time for electron-electron interaction is determined to be approximately $100\mathrm{fs}$ with the $t_{1g}(\mathrm{LUMO}+1)$ orbital being considered to define the doorway state in a nonadiabatic multielectron excitation process. The internal energy stored in vibrational modes of the ${\mathrm{C}}_{60}$ at $770\mathrm{K}$ is found to support the excitation process very efficiently while in “cold” ${\mathrm{C}}_{60}$ $\left(80\mathrm{K}\right)$, no significant Rydberg population is detected.

We measure the magnetic-field dependence of the frequency and damping time for the radial breathing mode of an optically trapped Fermi gas of ${}^6\mathrm{Li}$ atoms near a Feshbach resonance. The measurements address the apparent discrepancy between the results of Kinast et al. [Phys. Rev. Lett. 92, 150402 (2004)] and those of Bartenstein et al. [Phys. Rev. Lett. 92, 203201 (2004)]. Over the range of magnetic field from $770\text{to}910\mathrm{G}$, the measurements confirm the results of Kinast et al. Close to resonance, the measured frequencies are in excellent agreement with predictions for a unitary hydrodynamic gas. At a field of $925\mathrm{G}$, the measured frequency begins to decrease below predictions. For fields near $1080\mathrm{G}$, we observe a breakdown of hydrodynamic behavior, which is manifested by a sharp increase in frequency and damping rate. The observed breakdown is in qualitative agreement with the sharp transition observed by Bartenstein et al. at $910\mathrm{G}$.

We consider the nonrelativistic four-boson system with short-range forces and large scattering length in an effective quantum mechanics approach. We construct the effective interaction potential at leading order in the large scattering length and compute the four-body binding energies using the Yakubovsky equations. Cutoff independence of the four-body binding energies does not require the introduction of a four-body force. This suggests that two- and three-body interactions are sufficient to renormalize the four-body system. We apply the equations to ${}^4\mathrm{H}\mathrm{e}$ atoms and calculate the binding energy of the ${}^4\mathrm{H}\mathrm{e}$ tetramer. We observe a correlation between the trimer and tetramer binding energies similar to the Tjon line in nuclear physics. Over the range of binding energies relevant to ${}^4\mathrm{H}\mathrm{e}$ atoms, the correlation is approximately linear.