We theoretically investigate molecular photoelectron momentum distributions (MPMDs) by bichromatic [frequencies $({\omega }_1,{\omega }_2)]$ circularly polarized attosecond UV laser pulses. Simulations performed on aligned single-electron ${\mathrm{H}}_2{}^{+}$ by numerically solving the corresponding three-dimensional time-dependent Schrödinger equation within a static nucleus frame show that MPMDs exhibit a spiral structure for both co-rotating and counter-rotating schemes. Results are analyzed by attosecond perturbation ionization models. Coherent electron wave packets created, respectively, by the two color pulses in the continuum interfere with each other. Photoionization distributions are functions of the photoelectron momentum $p$ and the ejection angle $\theta$, thus leading to spiral MPMDs. The dependence of spiral MPMDs on the time delay between the bicircular pulses and their relative phases is also presented. The spiral interference patterns are determined by the helicities and frequencies $\left({\omega }_1,{\omega }_2\right)$ of the bicircular fields. It is also found that the spiral patterns are sensitive to the molecular alignment and suppressed by two-center ionization interference, thus offering new tools for imaging molecular geometry.

Exploiting the correspondence between the Wigner distribution function and the frequency-resolved optical gating (FROG) measurement, we experimentally demonstrate the existence of chessboardlike interference patterns with a time-bandwidth product smaller than that of a transform-limited pulse in the phase-space representation of compass states. Using superpositions of four electric pulses as the realization of compass states, we have shown via direct measurements that displacements leading to orthogonal states can be smaller than limits set by uncertainty relations. In the experiment we observe an exactly chronocyclic correspondence to the sub-Planck structure in the interference pattern appearing for the superposition of two Schrödinger-cat-like states in a position-momentum phase space.

We use weak-value amplification to enhance the polarization-sensitive fast-light effect from induced Raman absorption in hot rubidium vapor. We experimentally demonstrate that projecting the output signal into an appropriate polarization state enables a pulse advancement of $4.2\mu \mathrm{s}$, which is more than 15 times larger than that naturally caused by dispersion. More significantly, we show that combining weak-value amplification with the dispersive response of an atomic system provides a clear advantage in terms of the maximum pulse advance achievable for a given value of loss. This technique has potential applications for designing novel quantum-information-processing gates and optical buffers for telecommunication systems.

Although there is a broad consensus on the fact that critical behavior in stacked triangular Heisenberg antiferromagnets—an example of frustrated magnets with competing interactions—is described by a Landau-Ginzburg-Wilson Hamiltonian with $\text{O}\left(3\right)\times \text{O}\left(2\right)$ symmetry, the nature of the phase transition in three dimensions is still debated. We show that spin-one Bose gases provide us with a simulator of the $\text{O}\left(3\right)\times \text{O}\left(2\right)$ model. Using a renormalization-group approach, we argue that the transition is weakly first order and shows pseudoscaling behavior, and give estimates of the pseudocritical exponent $\nu$ in ${}^{87}\mathrm{Rb}$, ${}^{41}\mathrm{K}$, and ${}^7\mathrm{Li}$ atom gases which can be tested experimentally.

Topologically ordered phase has emerged as one of most exciting concepts that not only broadens our understanding of phases of matter, but also has been found to have potential application in fault-tolerant quantum computation. The direct measurement of topological properties, however, is still a challenge, especially in interacting quantum system. Here we realize two to four spin one-dimensional Heisenberg chains using nuclear magnetic resonance simulators and observe interaction-induced topological transitions, where Berry curvature in the parameter space of Hamiltonian is probed by means of dynamical response and then the first Chern number is extracted by integrating the curvature over the closed surface. The utilized experimental method provides a powerful means to explore topological phenomena in quantum systems with many-body interactions.

We consider physical situations where the resource theories of coherence and thermodynamics play competing roles. In particular, we study the creation of quantum coherence using unitary operations with limited thermodynamic resources. We find the maximal coherence that can be created under unitary operations starting from a thermal state and find explicitly the unitary transformation that creates the maximal coherence. Since coherence is created by unitary operations starting from a thermal state, it requires some amount of energy. This motivates us to explore the trade-off between the amount of coherence that can be created and the energy cost of the unitary process. We also find the maximal achievable coherence under the constraint on the available energy. Additionally, we compare the maximal coherence and the maximal total correlation that can be created under unitary transformations with the same available energy at our disposal. We find that when maximal coherence is created with limited energy, the total correlation created in the process is upper bounded by the maximal coherence, and vice versa. For two-qubit systems we show that no unitary transformation exists that creates the maximal coherence and maximal total correlation simultaneously with a limited energy cost.

We present quantum fidelity benchmarks for continuous-variable (CV) quantum devices to outperform quantum channels which can transmit at most $k$-dimensional coherences for positive integers $k$. We determine an upper bound of an average fidelity over Gaussian distributed coherent states for quantum channels whose Schmidt class is $k$. This settles fundamental fidelity steps where the known classical limit and quantum limit correspond to the two end points of $k=1$ and $k=\infty$, respectively. It turns out that the average fidelity is useful to verify to what extent an experimental CV gate can transmit a high-dimensional coherence. The result is further extended to be applicable to general quantum operations or stochastic quantum channels. Although the fidelity is often associated with heterodyne measurements in quantum optics, we can also obtain similar criteria based on quadrature deviations determined via homodyne measurements.

The tune-out wavelength at 413 nm for the $2{}^3{S}_1$ state of helium is expected to be sensitive to finite nuclear mass, relativistic, and quantum electrodynamic (QED) corrections, which provides a scheme for testing atomic structure theory [J. Mitroy and L.-Y. Tang, Phys. Rev. A 88, 052515 (2013)]. In the present work, a large-scale full-configuration-interaction calculation based on both the Dirac-Coulomb-Breit Hamiltonian and the nonrelativistic Hamiltonian is performed for the dynamic dipole polarizabilities of helium in the $2{}^3{S}_1$ state. The tune-out wavelengths for the magnetic sublevels $M_J=0$ and $M_J=\pm 1$ are determined to be 413.0801(4) nm and 413.0859(4) nm, respectively, at sub-ppm accuracy, including finite nuclear mass and relativistic corrections. Our value for the $M_J=1$ sublevel agrees with the measured value of 413.0938(20)(9) nm [B. M. Henson et al., Phys. Rev. Lett. 115, 043004 (2015)] at the level of 19 ppm. The discrepancy between these two values is mainly due to the uncalculated QED contribution. Our current value confirms quantitatively the prediction of Mitroy and Tang. Also, for the state of $2{}^3{S}_1$ we find that the corrections due to finite nuclear mass and relativistic effects to the static dipole polarizability of 315.7227(4)$a_0^3$ are about 600 ppm and 310 ppm, respectively, which are about 1.4 and 5.4 times larger than those for the ground state. A measurement at the level of 10 ppm for the static dipole polarizability of helium in $2{}^3{S}_1$ can be used to determine the transition matrix element between $2{}^{3}S$ and $2{}^{3}P$ at the level of ${10}^{-5}$.

Hyperfine-induced electric dipole contributions may significantly increase probabilities of otherwise very weak electric octupole and magnetic quadrupole atomic clock transitions (e.g., transitions between $s$ and $f$ electron orbitals). These transitions can be used for exceptionally accurate atomic clocks, quantum information processing, and the search for dark matter. They are very sensitive to new physics beyond the standard model, such as temporal variation of the fine-structure constant, the Lorentz invariance, and Einstein equivalence principle violation. We formulate conditions under which the hyperfine-induced electric dipole contribution dominates and perform calculations of the hyperfine structure and E3, M2 and the hyperfine-induced E1 transition rates for a large number of atoms and ions of experimental interest. Due to the hyperfine quenching the electric octupole clock transition in ${}^{173}\mathrm{Yb}^{+}$ is 2 orders of magnitude stronger than that in currently used ${}^{171}\mathrm{Yb}^{+}$. Some enhancement is found in ${}^{143}\mathrm{Nd}^{13+}$, ${}^{149}\mathrm{Pm}^{14+}$, ${}^{147}\mathrm{Sm}^{14+}$, and ${}^{147}\mathrm{Sm}^{15+}$ ions.

We report on an efficient production scheme for a large quantum degenerate sample of fermionic lithium. The approach is based on our previous work on narrow-line $2S_{1/2}\to 3P_{3/2}$ laser cooling resulting in a high phase-space density of up to $3\times {10}^{-4}$. This allows utilizing a large-volume crossed optical dipole trap with a total power of $45\mathrm{W}$, leading to high loading efficiency and $8\times {10}^6$ trapped atoms. The same optical trapping configuration is used for rapid adiabatic transport over a distance of $25\mathrm{cm}$ in $0.9\mathrm{s}$, and subsequent evaporative cooling. With optimized evaporation we achieve a degenerate Fermi gas with $1.7\times {10}^6$ atoms at a temperature of $60\mathrm{nK}$, corresponding to $T/T_{\text{F}}=0.16\left(2\right)$. Furthermore, the performance is demonstrated by evaporation near a broad Feshbach resonance creating a molecular Bose-Einstein condensate of $3\times {10}^5$ lithium dimers.

We demonstrate the relativistic electromagnetic force and power distributions of the field-kinetic and canonical electromagnetic subsystems with respect to light normally incident upon a moving, lossless magnetodielectric slab of material. Time-averaged and time-varying studies are preformed to demonstrate the continuum mathematical approach and discern between the physical characteristics of both field-kinetic and canonical subsystems. It is shown that when considering time-averaged fields, both subsystems are equivalent and thereby yield equivalent electromagnetic force and power results. The time-varying case demonstrates the differences between the field-kinetic and canonical subsystems, where the field-kinetic subsystem attempts to distort the media and the canonical subsystem satisfies global conservation principles.

We demonstrate that a lateral optical force (LOF) can be induced on chiral nanoparticles immersed in the two interfering plane waves. The LOF can push the chiral nanoparticle sideways, in the direction relying on the helicity of the particle as well as the phase difference between two waves. Analytical theory reveals that the LOF comes mostly from the direct coupling of the optical vorticity with the particle chirality. In particular, the LOF has a magnitude comparable to the gradient force and radiation pressure when the particle chirality is sufficiently large. The LOF may serve for chirality sorting due to its unusual properties and also provide an opportunity for passive chiral spectroscopy.

We analyze theoretically and investigate experimentally the transfer of phase to intensity power spectra of spatial frequencies through free-space Fresnel diffraction. Depending on $\lambda z$ (where $\lambda$ is the wavelength and $z$ is the free-space propagation distance) and the phase-modulation strength $S$, we demonstrate that for multiscale and broad phase spectra critical behavior transmutes a quasilinear to a nonlinear diffractogram except for low frequencies. On the contrary, a single-scale and broad phase spectrum induces a critical transition in the diffractogram at low frequencies. In both cases, identifying critical behavior encoded in the intensity power spectra is of fundamental interest because it exhibits the limits of perturbative power counting but also guides resolution and contrast optimization in propagation-based, single-distance, phase-contrast imaging, given certain dose and coherence constraints.

We present a family of quantum error-correcting codes that support a universal set of transversal logic gates using only local operations on a two-dimensional array of physical qubits. The construction is a subsystem version of color codes where gauge fixing through local measurements dynamically determines which gates are transversal. Although the operations are local, the underlying code is not topological in structure, which is how the construction circumvents no-go constraints imposed by the Bravyi-König and Pastawski-Yoshida theorems. We provide strong evidence that the encoding has no error threshold in the conventional sense, though it is still possible to have logical gates with error probability much lower than that of physical gates.

We generalize the efficient decomposition method for phase-sparse diagonal operators of J. Welch et al. [Quantum Info. Comput. 16, 87 (2016)] to qudit systems. The phase-context-aware method focuses on cascaded entanglers, whose decomposition into multicontrolled inc gates can be optimized by the choice of a proper signed base-$d$ representation for the natural numbers. While the gate count of the best-known decomposition method for general diagonal operators on qubit systems scales with $O\left(2^n\right)$, the circuits synthesized by the Welch algorithm for diagonal operators with $k$ distinct phases are upper-bounded by $O\left(n^{2}k\right)$, which is generalized to $O\left(d{n}^{2}k\right)$ for the qudit case in this paper.

We propose a quantum algorithm for solving the following problem: given the Hamiltonian of a physical system and one of its eigenvalues, how do we obtain the corresponding eigenstate? The algorithm is based on the resonance phenomenon. For a probe qubit coupled to a quantum system, the system exhibits resonance dynamics when the frequency of the probe qubit matches a transition frequency in the system. Therefore the system can be guided to evolve to the eigenstate with a known eigenvalue by inducing the resonance between the probe qubit and a designed transition in the system. This algorithm can also be used to obtain the energy spectrum of a physical system and can achieve even quadratic speedup over the phase estimation algorithm.

By using a well-established “ab initio” theoretical approach developed in the past to quantitatively study the superconductivity of condensed matter systems, based on the Kohn-Sham density functional theory, I study the superfluid properties and the BCS-BEC crossover of two parallel bi-dimensional layers of fermionic dipolar molecules, where the pairing mechanism leading to superfluidity is provided by the interlayer coupling between dipoles. The finite temperature superfluid properties of both the homogeneous system and one where the fermions in each layer are confined by a square optical lattice are studied at half filling conditions, and for different values of the strength of the confining optical potential. The T = 0 results for the homogeneous system are found to be in excellent agreement with diffusion Monte Carlo results. The superfluid transition temperature in the BCS region is found to increase, for a given interlayer coupling, with the strength of the confining optical potential. A transition occurs at sufficiently small interlayer distances, where the fermions becomes localized within the optical lattice sites in a square geometry with an increased effective lattice constant, forming a system of localized composite bosons. This transition should be signaled by a sudden drop in the superfluid fraction of the system.

The rovibrational eigenenergy set of molecular systems is a key feature needed to understand and model elementary chemical reactions. A unique class of molecular systems, represented by an ${}^4{A}^{\prime \prime }$ excited electronic state of the ${\left[\mathrm{H},\mathrm{S},\mathrm{N}\right]}^{-}$ system comprising several distinct dipole-bound isomers, is found to contain both bent and linear minima separated by relatively small barriers. Full-dimensional nuclear-motion computations performed in Jacobi coordinates using three-dimensional potential energy surfaces describing the stable isomers and the related transition states yield rovibrational eigenstates located both below and above the barriers. The rovibrational wave functions are well localized, regardless of whether the state's energy is below or above the barriers. We also show that the states preserve the memory of the isomeric forms they “originate from,” which is signature of a strong vibrational memory effect above isomerization barriers.