We report the experimental observation and a theoretical description of the scattering of free falling dilute thermal clouds of ${}^{87}$Rb atoms by microscopically structured light beams with parabolic-cylindrical symmetry. These structured beams are known in the literature as Weber beams. High-fidelity Weber beams are generated by means of a spatial light modulator and an annular spatial filtering process, which yields a quasipropagation-invariant electromagnetic field in the region of interaction with the atom cloud. The dynamics of the atomic density profile and the phase space distribution of the scattered atoms is explored. A natural dynamical variable of Weber modes is the product of the angular momentum along the axis of propagation of the beam with a component of linear momentum perpendicular to that axis. To pave the way of the understanding about the transfer of this variable, we study the evolution of the analogous atomic variable.

We propose two atom lithography techniques with subwavelength resolution based on position-dependent Rabi oscillations. Our method either uses neutral or ionized atoms to write subwavelength patterns. We illustrate our proposal by numerical simulations of an experimental setup using rubidium Rydberg atoms. We show that, for a microwave wavelength of 1.4 cm, a spacing of a few hundred nanometers is possible.

We study the directional dissociative ionization of diatomic molecules (H${}_2$, N${}_2$, Ar${}_2$, and CO) by intense phase-controlled elliptically polarized two-color pulses. The phase between the two colors of our elliptically polarized two-color pulse is unambiguously and straightforwardly assigned by tracing the momentum of the released electron, streaked by the rotating laser field, which is imprinted in the momentum of the correlated ion. The laser-driven electron motion, electron-localization-assisted enhanced multielectron ionization, and role of the orbital shape for the asymmetric dissociative ionizations of various molecules are discussed.

We present an accurate and efficient nondipole computational approach in momentum space for the nonperturbative study of multiphoton above-threshold ionization (ATI) of atoms in superintense and ultrashort-wavelength laser fields. This approach has been successfully used to investigate the multiphoton processes of a hydrogen atom exposed to superintense free-electron x-ray laser fields. We find that, compared to results of the dipole approximation, the nondipole ATI spectra are enhanced substantially in the high-energy regime, and the photoelectron angular distributions are distorted significantly in higher-intensity and/or longer-pulse laser fields; in particular two lobes are induced, one along and one against the laser propagation direction. The origin of these phenomena has been explored in detail.

We extend the ideas of wave-packet interferometry [Remetter et al., Nat. Phys. 2, 323 (2006)] to implement the algorithm of spectral phase interferometry for direct electric-field reconstruction (SPIDER) for characterizing the amplitude and phase of electron wave packets. Single-photon ionization by an attosecond pulse launches an electron wave packet in the continuum. Ionization by a train of two attosecond pulses in the presence of a moderate infrared pulse creates an interferogram in the final photoelectron momentum distribution. From the interferogram, the complex electron wave function can be reconstructed. If the pulses are well characterized, the amplitude and phase of the bound-free dipole matrix element can be reconstructed over a wide energy range. This is demonstrated by application of the retrieval method to momentum distributions obtained by numerical solution of the time-dependent Schrödinger equation. The case of Coulombic potentials requires appropriate treatment of the laser-Coulomb coupled dynamics.

We study the mean-field dynamics of $p$-wave Feshbach-molecule production in an ultracold gas of Fermi atoms in the same internal state. We derive a separable potential to describe the low-energy scattering properties of such atoms, and use this potential to solve the mean-field dynamics during a magnetic-field sweep. Initially, on the negative scattering length side of a Feshbach resonance the gas is described by the BCS theory. We adapt the method by Szymańska et al. [Phys. Rev. Lett. 94, 170402 (2005)] to $p$-wave interacting Fermi gases and model the conversion dynamics of the gas into a Bose-Einstein condensate of molecules on the other side of the resonance under the influence of a linearly varying magnetic field. We have analyzed the dependence of the molecule production efficiency on the density of the gas, temperature, initial value of the magnetic field, and magnetic-field ramp speed. Our results show that in this approximation molecule production by a linear magnetic-field sweep is highly dependent on the initial state.

Recently spin-orbit (SO)-coupled superfluids in free space or harmonic traps have been extensively studied, motivated by the recent experimental realization of SO coupling for Bose-Einstein condensates (BEC). However, the rich physics of SO-coupled BEC in optical lattices has been largely unexplored. In this paper, we show that in a suitable parameter region the lowest Bloch state forms an isolated flat band in a one-dimensional SO-coupled optical lattice, which thus provides an experimentally feasible platform for exploring the recently celebrated topological flatband physics in lattice systems. We show that the flat band is preserved even with the mean-field interaction in BEC. We investigate the superfluidity of the BEC in SO-coupled lattices through dynamical and Landau stability analysis, and show that the BEC is stable on the whole flat band.

The generalization of quasi-phase-matching using polarization beating and of multimode quasi-phase-matching (MMQPM) for the generation of high-order harmonics is explored, and a method for achieving polarization beating is proposed. If two (and in principle more) modes of a waveguide are excited, modulation of the intensity, phase, and/or polarization of the guided radiation will be achieved. By appropriately matching the period of this modulation to the coherence length, quasi-phase-matching of high-order-harmonic radiation generated by the guided wave can occur. We show that it is possible to achieve efficiencies with multimode quasi-phase-matching greater than the ideal square wave modulation. We present a Fourier treatment of QPM and use this to show that phase modulation, rather than amplitude modulation, plays the dominant role in the case of MMQPM. The experimental parameters and optimal conditions for this scheme are explored.

In this work we present an extensive study of the scaling symmetry typical of a paraxial wave theory. In particular, by means of a Lagrangian approach we derive the conservation law and the corresponding generalized charge associated with the scale invariance symmetry. In general, such a conserved charge, $q_s$ say, can take any value that remains constant during propagation. However, it is explicitly proven that for the whole class of physically realizable shape-invariant fields, that is, fields whose intensity distribution maintains its shape on propagation, $q_s$ must necessarily vanish. Finally, an interesting relation between such charge $q_s$ and the effective radius of a beam, as introduced by Siegman some years ago, is derived.

Coherent interconversion between an optical and a mechanical excitation in an optomechanical resonator can be used for the storage of an optical pulse as an excitation in a mechanical oscillator. This optomechanical light storage is enabled by external writing and readout pulses at one mechanical frequency below the optical resonance. In this paper, we expand an earlier experimental study [Phys. Rev. Lett. 107, 133601 (2011)] on storing an optical pulse as a radial breathing mode in a silica microsphere. We show that the heterodyne beating between a readout pulse and the corresponding retrieved pulse features a periodic oscillation with a well-defined phase and with the beating period given by the mechanical frequency, demonstrating directly the coherent nature of the light storage process. The coherent interconversion accelerates with increasing optomechanical coupling rates, providing an effective mechanism for tailoring the temporal profile of the retrieved pulse. Experimental studies on both light storage and optomechanically induced transparency under nearly the same conditions also illustrate the connections between these two closely related processes.

We determine the phase diagram of $N$ identical three-level systems interacting with a single photonic mode in the thermodynamical limit ($N\to \infty$) by accounting for the so-called diamagnetic term and the inequalities imposed by the Thomas-Reich-Kuhn (TRK) oscillator strength sum rule. The key role of transitions between excited levels and the occurrence of first-order phase transitions is discussed. We show that, in contrast to two-level systems, in the three-level case the TRK inequalities do not always prevent a superradiant phase transition in the presence of a diamagnetic term.

We present an exact analytical method of engineering the localization of classical waves in a fractal waveguide network. It is shown that a countable infinity of localized eigenmodes with a multitude of localization lengths can exist in a Vicsek fractal geometry built with diamond-shaped monomode waveguides as the “unit cells.” The family of localized modes forms clusters of increasing size. The length scale at which the onset of localization for each mode takes place can be engineered at will, following a well-defined prescription developed within the framework of a real space renormalization group. The scheme leads to an exact evaluation of the wave vector for every such localized state, a task that is nontrivial, if not impossible for any random or deterministically disordered waveguide network.

We show that all $2\otimes 4$ states with strong positive partial transposes (SPPTs) are separable. We also construct a family of $2\otimes 5$ entangled SPPT states, so the conjecture on the separability of SPPT states is completely settled. In addition, we clarify the relation between the set of all $2\otimes d$ separable states and the set of all $2\otimes d$ SPPT states for the case of $d=3,4$.

We propose a fast ground-state optomechanical cooling scheme through the use of a two-mode optical cavity with a quarter-wave plate inside. Two cavity modes are orthogonally polarized; one cavity mode dissipates to the external environment at a fast rate while the other dissipates at a slow rate. The quarter-wave plate provides linear mixing interaction between these two cavity modes. The cooling process is dominated by scattering process via the fast-decay channel, which is significantly enhanced as compared with that obtained in the resolved-sideband optomechanical cooling scheme. Meanwhile, the heating process is significantly suppressed by exploiting the destructive quantum interference between the two cavity modes with the help of the quarter-wave plate.

We describe a technique for the preparation of quantum spin correlations in a lattice gas of ultracold atoms using an atom-light interaction of the kind routinely employed in quantum spin polarization spectroscopy. Our method is based on entropic cooling via quantum nondemolition measurement and feedback, and allows the creation and detection of quantum spin correlations, as well as a certain degree of multipartite entanglement which we verify using a generalization of the entanglement witness described previously M. Cramer et al., Phys. Rev. Lett. 106, 020401 (2011). We illustrate the procedure with examples drawn from the bilinear-biquadratic Hamiltonian, which can be modeled by a one-dimensional chain of spin-1 atoms.

We analyze the performance of continuous-variable quantum key distribution protocols where the entangled source originates not from one of the trusted parties, Alice or Bob, but from the malicious eavesdropper in the middle. This is in contrast to the typical simulations where Alice creates the entangled source and sends it over an insecure quantum channel to Bob. By using previous techniques and identifying certain error-correction-protocol equivalences, we show that Alice and Bob do not need to trust their source and can still generate a positive key rate. Such a situation can occur in a quantum network where the untrusted source originated in between the two users.

A possible building block for a scalable quantum computer has recently been demonstrated [Mariantoni et al., Science 334, 61 (2011)]. This architecture consists of superconducting qubits capacitively coupled both to individual memory resonators as well as a common bus. In this work we study a natural primitive entangling gate for this and related resonator-based architectures, which consists of a controlled-${\sigma }^z$ (cz) operation between a qubit and the bus. The cz gate is implemented with the aid of the noncomputational qubit $|2\rangle$ state [Strauch et al., Phys. Rev. Lett. 91, 167005 (2003)]. Assuming phase or transmon qubits with 300 MHz anharmonicity, we show that by using only low frequency qubit-bias control it is possible to implement the qubit-bus cz gate with 99.9$\%$ (99.99$\%$) fidelity in about $17\mathrm{ns}$ ($23\mathrm{ns}$) with a realistic two-parameter pulse profile, plus two auxiliary $z$ rotations. The fidelity measure we refer to here is a state-averaged intrinsic process fidelity, which does not include any effects of noise or decoherence. These results apply to a multiqubit device that includes strongly coupled memory resonators. We investigate the performance of the qubit-bus cz gate as a function of qubit anharmonicity, identify the dominant intrinsic error mechanism and derive an associated fidelity estimator, quantify the pulse shape sensitivity and precision requirements, simulate qubit-qubit cz gates that are mediated by the bus resonator, and also attempt a global optimization of system parameters including resonator frequencies and couplings. Our results are relevant for a wide range of superconducting hardware designs that incorporate resonators and suggest that it should be possible to demonstrate a $99.9\%$ cz gate with existing transmon qubits, which would constitute an important step towards the development of an error-corrected superconducting quantum computer.

Analytically exact solutions of a driven two-level system are extremely important in many areas of physics [E. Barnes and S. Das Sarma, Phys. Rev. Lett. 109, 060401 (2012)]. Here we present a simple method of synchronous and asynchronous combined modulations to generate such exact solutions, and apply several of the simplest solutions to perform the coherent control of quantum states. The interesting physical phenomena, such as the arbitrary population transfers between the different and/or asymptotic stationary states and the controlled coherent population oscillation, are achieved analytically and numerically. Simplification of the exact solutions and the modulated fields renders the control strategies more transparent and the qubit manipulation more convenient in experiments.

We show that magnetic dipolar interactions can stabilize superfluidity in atomic gases, but the dipole alignment direction required to achieve this varies depending on whether the flow is oscillatory or continuous. If a condensate is made to oscillate through a lattice, damping of the oscillations can be reduced by aligning the dipoles perpendicular to the direction of motion. However, if a lattice is driven continuously through the condensate, superfluid behavior is best preserved when the dipoles are aligned parallel to the direction of motion. We explain these results in terms of the formation of topological excitations and tunnel barrier heights between lattice sites.

We show that the recently developed optical lattices with Peierls substitution—which can be modeled as a lattice with a complex tunneling coefficient—may be used to induce controllable quantum transport of ultracold atoms. In particular, we show that by ramping up the phase of the complex tunneling coefficient in a spatially uniform fashion, a finite quasi-steady-state current (QSSC) ensues from the exact dynamics of noninteracting fermions. The direction and magnitude of the current can be controlled by the overall phase difference but not the details of the ramp. The entanglement entropy does not increase when the QSSC lasts. Due to different spin statistics, condensed noninteracting bosons do not support a finite QSSC under the same setup. We also find that an approximate form of the QSSC survives when perturbative effects from interactions, weak harmonic background traps, and finite temperature are present, which suggests that our findings should be observable with available experimental capabilities.