Previous work developed a $K$-matrix formalism applicable to positive energies for the scattering between two $s$-wave interacting particles with two internal states, isotropic spin-orbit coupling and vanishing center-of-mass momentum [H. Duan, L. You, and B. Gao, Phys. Rev. A 87, 052708 (2013).]. This work extends the formalism to the entire energy regime. Explicit solutions are obtained for the total angular momentum $J=0$ and 1 channels. The behavior of the partial cross sections in the negative energy regime is analyzed in detail. We find that the leading contributions to the partial cross sections at the negative energy thresholds are governed by the spin-orbit coupling strength $k_{\text{so}}$ and the mass ratio. The fact that these contributions are independent of the two-body scattering length $a_s$ is a direct consequence of the effective reduction of the dimensionality, and hence of the density of states, near the scattering thresholds due to the single-particle spin-orbit coupling terms. The results are analytically continued to the energy regime where bound states exist. It is shown that our results are consistent with results obtained by alternative approaches. Our formulation, which can be regarded as an extension of the standard textbook partial wave decomposition, can be generalized to two-body systems with other types of spin-orbit coupling, including cases where the center-of-mass momentum does not vanish.

We classify the ground states and topological defects of two-component Bose-Einstein condensates under the effect of internal coherent Rabi coupling. We present numerical phase diagrams which show the boundaries between symmetry-breaking components and various vortex patterns (triangular, square, bound state between vortices). We estimate the Rabi energy in the Thomas-Fermi limit which allows us to have an analytical description of the point energy leading to the formation of the various vortex patterns.

We show numerically that a harmonically trapped and coherently Rabi-coupled three-component Bose-Einstein condensate can host unconventional vortex lattices in its rotating ground state. The discovered lattices incorporate square and zig-zag patterns, vortex dimers and chains, and doubly quantized vortices, and they can be quantitatively classified in terms of a skyrmionic topological index, which takes into account the multicomponent nature of the system. The exotic ground-state lattices arise due to the intricate interplay of the repulsive density-density interactions and the Rabi couplings as well as the ubiquitous phase frustration between the components. In the frustrated state, domain walls in the relative phases can persist between some components even at strong Rabi coupling, while vanishing between others. Consequently, in this limit the three-component condensate effectively approaches a two-component condensate with only density-density interactions. At intermediate Rabi coupling strengths, however, we face unique vortex physics that occurs neither in the two-component counterpart nor in the purely density-density-coupled three-component system.

A number of techniques have been developed to characterize the attosecond emission from high-order-harmonic sources. These techniques are broadly classified as ex situ, where the attosecond pulse train photoionizes a target gas in the presence of an infrared field, and in situ, where the measurement takes place in the medium in which the attosecond pulses are generated. It is accepted that ex situ techniques measure the characteristics of the electromagnetic field, including the phase of the recombination transition moment of the emitting atom or molecule, when the phase of the second medium is known. However, there is debate about whether in situ techniques measure the electromagnetic field, or only the characteristics of the recolliding electron before recombination occurs. We show numerically that in situ measurements are not sensitive to the recombination phase, when implemented in the perturbative regime as originally envisioned, and that they do not measure the electromagnetic phase of the emission.

We explore the question of using an entangled state as a universal resource for implementing quantum measurements by local operations and classical communication (LOCC). We show that for most systems consisting of three or more subsystems, there is no entangled state from the same space that can enable all measurements by LOCC. This is in direct contrast to the bipartite case, where a maximally entangled state is a universal resource. Our results are obtained showing an equivalence between the problem of local state transformation and that of entanglement-assisted local unambiguous state discrimination.

A system of two or more quantum dots interacting with a dissipative plasmonic nanostructure is investigated in detail by using a cavity quantum electrodynamics approach with a model Hamiltonian. We focus on determining and understanding system configurations that generate multiple bipartite quantum entanglements between the occupation states of the quantum dots. These configurations include allowing for the quantum dots to be asymmetrically coupled to the plasmonic system. Analytical solution of a simplified limit for an arbitrary number of quantum dots and numerical simulations and optimization for the two- and three-dot cases are used to develop guidelines for maximizing the bipartite entanglements. For any number of quantum dots, we show that through simple starting states and parameter guidelines, one quantum dot can be made to share a strong amount of bipartite entanglement with all other quantum dots in the system, while entangling all other pairs to a lesser degree.

We propose to create superposition states of over 100 strontium atoms in a ground state or metastable optical clock state using the Kerr-type interaction due to Rydberg state dressing in an optical lattice. The two components of the superposition can differ by an order of 300 eV in energy, allowing tests of energy decoherence models with greatly improved sensitivity. We take into account the effects of higher-order nonlinearities, spatial inhomogeneity of the interaction, decay from the Rydberg state, collective many-body decoherence, atomic motion, molecular formation, and diminishing Rydberg level separation for increasing principal number.

Work on classical closed orbits in the diamagnetic Kepler problem is predominately focused on the chaos observed in the polar launch angle as opposed to the azimuthal launch angle. This is due to atomic systems, along with widely studied external-field geometries (parallel magnetic and electric fields or pure magnetic field), being uniform in azimuthal angle, rendering the azimuthal angle unimportant. In the case of crossed magnetic and electric fields, this is no longer the case, and closed orbits do present an azimuthal launch angle dependence. In atomic systems, due to their spherical symmetry, the electric-field orientation in the plane perpendicular to the magnetic field does not affect the spectrum of orbits. However, in shallow $n$-type donors in anisotropic semiconductors such as silicon, the orientation of the external fields with respect to conduction-band valleys will be important. In this work we examine the Garton-Tomkins orbit in crossed magnetic and electric fields, and analyze how it and its harmonics' azimuthal dependencies behave through variation of the scaled field or scaled energy. At low scaled fields, harmonics have either twofold or fourfold azimuthal dependencies determined by the rotational symmetry of the individual harmonics. As the scaled field or scaled energy is increased, several harmonics undergo significant bifurcations, resulting in large azimuthal angular regions of essentially closed orbits, which will lead to strong resonances in experimental work.

In this paper, we study phase diagrams of dipolar hard-core boson gases on a honeycomb lattice. The system is described by the Haldane-Bose-Hubbard model with complex hopping amplitudes and nearest-neighbor repulsion. By using the slave-particle representation of the hard-core bosons and also the path-integral quantum Monte Carlo simulations, we investigate the system and show that the systems have a rich phase diagram. There are Mott, superfluid, chiral superfluid, and sublattice chiral superfluid phases as well as the density-wave phase. We also found a coexisting phase of superfluid and chiral superfluid. Critical behaviors of the phase transitions are also clarified.

We develop a generalized gradient expansion of the inhomogeneous dynamical mean-field theory method for determining properties of ultracold atoms in a trap. This approach goes beyond the well-known local density approximation and at higher temperatures, in the normal phase, it shows why the local density approximation works so well, since the local density and generalized gradient approximations are essentially indistinguishable from each other (and from the exact solution within full inhomogeneous dynamical mean-field theory). But because the generalized gradient expansion only involves nearest-neighbor corrections, it does not work as well at low temperatures, when the systems enter into ordered phases. This is primarily due to the problem that ordered phases often satisfy some global constraints, which determine the spatial ordering pattern, and the local density and generalized gradient approximations are not able to impose those kinds of constraints; they also overestimate the tendency to order. The theory is applied to phase separation of different mass fermionic mixtures represented by the Falicov-Kimball model and to determining the entropy per particle of a fermionic system represented by the Hubbard model. The generalized gradient approximation is a useful diagnostic for the accuracy of the local density approximation—when both methods agree, they are likely accurate, when they disagree, neither is likely to be correct.

We show that a multicolor modulation of the depth of an optical lattice allows for a flexible independent control of correlated hopping, occupation-dependent gauge fields, effective on-site interactions without Feshbach resonances, and nearest-neighbor interactions. As a result, the lattice-depth modulation opens the possibility of engineering with minimal experimental complexity a broad class of lattice models in current experiments with ultracold atoms, including Hubbard models with correlated hopping, peculiar extended models, and two-component anyon-Hubbard models.

In the optomechanical cooling of a dispersively coupled oscillator, it is only possible to reach the oscillator ground state in the resolved sideband regime, where the cavity-mode linewidth is smaller than the resonant frequency of the mechanical oscillator being cooled. In this paper, we show that the dispersively coupled system can be cooled to the ground state in the unresolved sideband regime using an ancillary oscillator, which has a high quality factor and is coupled to the same optical mode via dissipative interaction. The ancillary oscillator has a resonant frequency close to that of the target oscillator; thus, the ancillary oscillator is also in the unresolved sideband regime. We require only a single blue-detuned laser mode to drive the cavity.

We identify a physical scenario whereby optical-field waveforms with peak powers several decades above the critical power of self-focusing can self-compress to subcycle pulse widths. With beam breakup, intense hot spots, and optical damage of the material avoided within the pulse compression length by keeping this length shorter than the modulation-instability buildup length, the beam is shown to preserve its continuity at the point of subcycle pulse generation.

We study a variant of the quantum approximate optimization algorithm [E. Farhi, J. Goldstone, and S. Gutmann, arXiv:1411.4028] with a slightly different parametrization and a different objective: rather than looking for a state which approximately solves an optimization problem, our goal is to find a quantum algorithm that, given an instance of the maximum 2-satisfiability problem (MAX-2-SAT), will produce a state with high overlap with the optimal state. Using a machine learning approach, we chose a “training set” of instances and optimized the parameters to produce a large overlap for the training set. We then tested these optimized parameters on a larger instance set. As a training set, we used a subset of the hard instances studied by Crosson, Farhi, C. Y.-Y. Lin, H.-H. Lin, and P. Shor (CFLLS) (arXiv:1401.7320). When tested, on the full set, the parameters that we find produce a significantly larger overlap than the optimized annealing times of CFLLS. Testing on other random instances from 20 to 28 bits continues to show improvement over annealing, with the improvement being most notable on the hardest instances. Further tests on instances of MAX-3-SAT also showed improvement on the hardest instances. This algorithm may be a possible application for near-term quantum computers with limited coherence times.

Several information measures have recently been defined that capture the notion of recoverability. In particular, the fidelity of recovery quantifies how well one can recover a system $A$ of a tripartite quantum state, defined on systems $ABC$, by acting on system $C$ alone. The relative entropy of recovery is an associated measure in which the fidelity is replaced by relative entropy. In this paper we provide concrete operational interpretations of the aforementioned recovery measures in terms of a computational decision problem and a hypothesis testing scenario. Specifically, we show that the fidelity of recovery is equal to the maximum probability with which a computationally unbounded quantum prover can convince a computationally bounded quantum verifier that a given quantum state is recoverable. The quantum interactive proof system giving this operational meaning requires four messages exchanged between the prover and verifier, but by forcing the prover to perform actions in superposition, we construct a different proof system that requires only two messages. The result is that the associated decision problem is in QIP(2) and another argument establishes it as hard for QSZK (both classes contain problems believed to be difficult to solve for a quantum computer). We finally prove that the regularized relative entropy of recovery is equal to the optimal type II error exponent when trying to distinguish many copies of a tripartite state from a recovered version of this state, such that the type I error is constrained to be no larger than a constant.

We present an experimental technique that allows us to determine the zero-field intervals between high-$\ell$ states of Rb in a magneto-optical trap, in spite of the fact that we can only control the stray electric field in one direction. The technique is based on measuring a property of the atom that depends on the field, as opposed to its square. This approach allows the determination of the zero-field intervals and the magnitude of the stray field in the uncontrolled perpendicular direction. We use this technique to observe the microwave transitions of rubidium from the $(n+1)d_{5/2}$ states to the $ng$ and $nh$ states of $27\le n\le 30$. From the observed microwave transitions, we determine the quantum defects of the $ng$ and $nh$ states. Using the quantum defects of the $ng$ and $nh$ states and the adiabatic core polarization theory, we determine the ${\mathrm{Rb}}^{+}$ ionic dipole and quadrupole polarizabilities to be ${\alpha }_d=9.12\left(2\right)a_0^3$ and ${\alpha }_q=14\left(3\right)a_0^5$, respectively.

We analyze the imprint of nodal planes in high-order-harmonic spectra from aligned diatomic molecules in intense laser fields whose components exhibit orthogonal polarizations. We show that the typical suppression in the spectra associated to nodal planes is distorted, and that this distortion can be employed to map the electron's angle of return to its parent ion. This investigation is performed semianalytically at the single-molecule response and single-active orbital level, using the strong-field approximation and the steepest descent method. We show that the velocity form of the dipole operator is superior to the length form in providing information about this distortion. However, both forms introduce artifacts that are absent in the actual momentum-space wave function. Furthermore, elliptically polarized fields lead to larger distortions in comparison to two-color orthogonally polarized fields. These features are investigated in detail for ${\mathrm{O}}_2$, whose highest occupied molecular orbital provides two orthogonal nodal planes.