Time-reversal symmetry is studied in the frame of quantum and classical mechanics in a space with noncommutativity of coordinates and noncommutativity of momenta of canonical type. The circular motion is examined as an apparent example of time-reversal symmetry breaking in the space. On the basis of an exact solution of the problem, we show that because of noncommutativity the period of the circular motion depends on its direction. We propose the way to recover the time-reversal and rotational symmetries in noncommutative phase space of canonical type. Namely, on the basis of the idea of generalization of parameters of noncommutativity to tensors, we construct noncommutative algebra which is rotationally invariant, invariant under time reversal, and equivalent to noncommutative algebra of canonical type.

We present a quantum algorithm for simulating the wave equation under Dirichlet and Neumann boundary conditions. The algorithm uses Hamiltonian simulation and quantum linear system algorithms as subroutines. It relies on factorizations of discretized Laplacian operators to allow for polynomially improved scaling in truncation errors and improved scaling for state preparation relative to general purpose quantum algorithms for solving linear differential equations. Relative to classical algorithms for simulating the $D$-dimensional wave equation, our quantum algorithm achieves exponential space savings and achieves a speedup which is polynomial for fixed $D$ and exponential in $D$. We also consider using Hamiltonian simulation for Klein-Gordon equations and Maxwell's equations.

We propose a scheme to enhance the fidelity of a symmetric quantum cloning machine via weak measurements. By adjusting the intensity of the weak measurement parameter $p$, we obtain copies of initial states with different values of fidelity. Choosing a proper value of $p$, we can obtain perfect copies. In this paper, we focus on $1-2$ quantum cloning for two nonorthogonal states. Sets containing more than two linear independent states are also briefly discussed. Due to the probabilistic nature of weak measurements, we obtain high-fidelity copies probabilistically. If the weak measurement is a success, we do subsequent operations to obtain high-fidelity copies; otherwise, the cloning process fails and we quit. From this perspective, the scheme we propose is economical for saving quantum resources and time. Our scheme may be very useful in quantum information processing.

We measure the differential polarizability of the ${}^{176}\mathrm{Lu}^{+} {}^1{S}_0\leftrightarrow {}^3{D}_1$ clock transition at multiple wavelengths. This experimentally characterizes the differential dynamic polarizability for frequencies up to 372 THz and allows an experimental determination of the dynamic correction to the blackbody radiation shift for the clock transition. In addition, measurements at the near resonant wavelengths of 598 and 646 nm determine the two dominant contributions to the differential dynamic polarizability below 372 THz. These additional measurements are carried out by two independent methods to verify the validity of our methodology. We also carry out a theoretical calculation of the polarizabilities using the hybrid method that combines the configuration interaction (CI) and the coupled-cluster approaches, incorporating for the first time quadratic nonlinear terms and partial triple excitations in the coupled-cluster calculations. The experimental measurements of the $|{\langle }^3{D}_1\parallel r{\parallel }^3{P}_J\rangle |$ matrix elements provide high-precision benchmarks for this theoretical approach.

We analytically investigate the recently proposed and implemented discrete-time quantum walk based on a kicked Bose-Einstein condensate. We extend previous work on the effective dynamics by taking into account spontaneous emission due to the kicking light. Spontaneous emission affects both the internal and external degrees of freedom arising from the entanglement between them during the walk dynamics. The result is a measurable degradation of the experimental walk signal that we characterize.

We study the motion of a self-attractive Bose-Einstein condensate with pseudospin $\frac{1}{2}$ driven by a synthetic Rabi (Zeeman-like) field. This field triggers the pseudospin dynamics resulting in a density redistribution between its components and, as a consequence, in changes of the overall density distribution. In the presence of an additional external potential, the latter produces a net force acting on the condensate and activates its displacement. As an example, here we consider the case of a one-dimensional condensate in a random potential.

We report an experimental demonstration of complementarity between path information and interference in second-order correlation with thermal light. The key apparatus is a Sagnac interferometer in which an off-axis slit is inserted. Two orthogonal thermal light beams travel through the slit clockwise and anticlockwise in the interferometer. The second-order interference fringes vanish when the path information is acquired. The interference fringes are revived when the path information is effaced.

We study the influence of mean-field cubic nonlinearity on Aharonov-Bohm caging in a diamond lattice with synthetic magnetic flux. For sufficiently weak nonlinearities, the Aharonov-Bohm caging persists as periodic nonlinear breathing dynamics. Above a critical nonlinearity, symmetry breaking induces a sharp transition in the dynamics and enables stronger wave-packet spreading. This transition is distinct from other flatband networks, where continuous spreading is induced by effective nonlinear hopping or resonances with delocalized modes and is in contrast to the quantum limit, where two-particle hopping enables arbitrarily large spreading. This nonlinear symmetry-breaking transition is readily observable in femtosecond laser-written waveguide arrays.

Multiphoton absorption processes have a nonlinear dependence on the amplitude of the incident optical field, i.e., the number of photons. However, multiphoton absorption is generally weak and multiphoton events occur with extremely low probability. Consequently, it is extremely challenging to engineer quantum nonlinear devices that operate at the single photon level and the majority of quantum technologies have to rely on single photon interactions. Here we demonstrate experimentally and theoretically that exploiting coherent absorption of $N=2$ NOON states makes it possible to enhance the number of two-photon states that are absorbed by at most a factor of 2 with respect to a linear absorption process. An absorbing metasurface placed inside a Sagnac-style interferometer into which we inject an $N=2$ NOON state, exhibits two-photon absorption with $40.5\%$ efficiency, close to the theoretical maximum. This high probability of simultaneous absorption of two photons holds the promise for applications in fields that require multiphoton upconversion but are hindered by high peak intensities.

A closed form of the disentangling theorem is used to derive an exact expression for the quantum mechanical intermediate scattering function describing long-range coherent quantum tunneling. The result applies to a single particle in a large periodic nearest-neighbor tight-binding system in one spatial dimension, with one localized site per unit cell. The result is exact up to the assumption of orthogonal localized states and the substitution of the coordinate operator with a discrete representation diagonal in the on-site basis. The intermediate scattering function is expressed in terms of modified Bessel functions, and consists of a symmetric real part and antisymmetric imaginary part. The real and imaginary parts both exhibit decaying oscillations reflecting the oscillatory dynamics among neighboring sites combined with the long-term spreading of the wave function from any initial site. The imaginary part is significant only when the thermal energy is comparable to or smaller than the width of the tight-binding energy band, and represents quantum recoil or the asymmetry of energy exchange probability in quasielastic scattering from the coherent system. The one-dimensional result is extended, in the form of $\mathbf{k}$-space integrals, to describe the coherent tunneling dynamics in hexagonal and honeycomb systems. The prospects for observing the phenomenology of the analytical line shapes are discussed with respect to the practical implementation of helium-3 surface spin echo spectroscopy.

We examine a simple scheme to generate genuine multipartite entangled states across disjoint qubit registers. We employ a shuttle qubit that is sequentially coupled, in an energy preserving manner, to the constituents within each register through rounds of interactions. We establish that stable $W$-type entanglement can be generated among all qubits within the registers. Furthermore, we find that the entanglement is sensitive to how the shuttle is treated, showing that a significantly larger degree is achieved by performing projective measurements on it. Finally, we assess the resilience of this entanglement generation protocol to several types of noise and imperfections, showing that it is remarkably robust.

Adiabatic quantum computation is of fundamental importance in the field of quantum computation as it offers an alternative approach to the gate-based model for the manipulation of quantum systems. Recently, an interesting work [arXiv:1805.10549] indicated that we can solve a linear equation system via an algorithm inspired by adiabatic quantum computing. Here we demonstrate the algorithm in a four-qubit nuclear magnetic resonance system by determining the solution of an eight-dimensional linear equation $A\mathbf{x}=\mathbf{b}$. The result is by far the maximum-dimensional linear equation solution with a limited number of qubits in experiments, which include some ingenious simplifications. Our experiment provides the possibility of solving so many practical problems related to linear equations systems and has the potential applications in designing the future quantum algorithms.

We present an optimal probabilistic protocol to distill quantum coherence. Inspired by a specific entanglement distillation protocol, our main result yields a strictly incoherent operation that produces one of a family of maximally coherent states of variable dimension from any pure quantum state. We also expand this protocol to the case where it is possible, for some initial states, to avert any waste of resources as far as the output states are concerned, by exploiting an additional transformation into a suitable intermediate state. These results provide practical schemes for efficient quantum resource manipulation.

Negativity is an entanglement monotone frequently used to quantify entanglement in bipartite states. Because negativity is a nonanalytic function of a density matrix, existing methods used in the physics literature are insufficient to compute its derivatives. To this end we develop techniques in the calculus of complex, patterned matrices and use them to conduct a perturbative analysis of negativity in terms of arbitrary variations of the density operator. The result is an easy-to-implement expansion that can be carried out to all orders. On the way we provide convenient representations of the partial transposition map appearing in the definition of negativity. Our methods are well suited to study the growth and decay of entanglement in a wide range of physical systems, including the generic linear growth of entanglement in many-body systems, and have broad relevance to many functions of quantum states and observables.

Atom-surface forces using excited states have a host of compelling applications, including repulsive and lateral forces. However, such states can be fragile and difficult to prepare. Here we report an explicit normal-mode based calculation of the Casimir-Polder potential between a ground-state atom and a nondispersive surface in the presence of an external quantized field. The potential we derive shares some features with that of excited-state Casimir-Polder forces even though we consider a ground-state atom. Our work provides a physically transparent and intuitive picture of driven Casimir-Polder potentials, as well as expanding on previous investigations by providing analytic results that fully include retardation, as well as being applicable for any choice of mutual alignment of the atom's dipole moment, the external field, and the surface normal.

We propose the difference of reaction rates of the weak interaction between enantiomers produces the small imbalance of the number density between pairs of enantiomers, which may be the origin of the homochirality in nature. Since left-handed particles have larger reaction rate of the weak interaction than right-handed particles, the nonzero total electron chirality in a chiral molecule, which is the integrated chirality density over the whole molecule, induces different reaction rate of the weak interaction between an enantiomeric pair. Due to this difference of reaction rates, one of the enantiomeric pair is more destroyed than the other by interactions with astronomical particles in space, such as cosmic rays and neutrinos emitted by nuclear fusion in star cores. It is numerically shown that chiral molecules generally have nonzero total electron chirality in addition to parity-violating energy shift, for ${\mathrm{H}}_2{X}_2$ ($X=\text{O}$, S, Se, Te) molecules as a typical sample of chiral molecules. This total chirality is shown to be related to the dihedral angle of ${\mathrm{H}}_2{X}_2$ molecules and is the result of the cancellation between large contributions from some highest occupied molecular orbitals. It is shown that the value of total chirality in a chiral molecule is drastically enhanced if the molecule is ionized or excited, since this cancellation is broken. The parity-violating energy shift has this property also though the enhancement is smaller for ${\mathrm{H}}_2{X}_2$ molecules.

Electronic-current dynamics play an important role in photoinduced processes and magnetooptics. We theoretically demonstrate ultrafast oscillating-magnetic-field generation based on the electronic dynamics from current carrying states irradiated by a nonhelical, linearly polarized laser field. In this driving field, the electronic currents oscillate periodically, which is attributed to the laser-induced energy shift of orbitals. These electronic currents can induce a strong spatial-localized oscillating magnetic field $\mathbf{B}(\mathbf{r},t)$ of several tens of Teslas (${10}^4$ G) at the center of targets. The frequency of the induced magnetic field ranges from terahertz to petahertz and can be continuously adjusted by varying the driving laser intensity. The optically induced oscillating magnetic fields we demonstrated will serve as a potential tool for investigations of the ultrafast dynamics in magnetic materials and chiral media.

While conventional lasers are based on gain media with three or four real levels, unconventional lasers including virtual levels and two-photon processes offer new opportunities. We study lasing that involves a two-photon process through a virtual lower level, which we realize in a cloud of cold ytterbium atoms that are magneto-optically trapped inside a cavity. We pump the atoms on the narrow ${}^{1}S_0\leftrightarrow {}^{3}P_1$ line and generate laser emission on the same transition. Lasing is verified by a threshold behavior of output power vs pump power and atom number, a flat $g^{\left(2\right)}$-correlation function above threshold, and the polarization properties of the output. In the proposed lasing mechanism the trapping beams create the virtual lower level of the lasing transition. The laser process runs continuously, needs no further repumping, and might be adapted to other atoms or transitions such as the ultranarrow ${}^{1}S_0\leftrightarrow {}^{3}P_0$ clock transition in ytterbium.

We uncover dramatic variations of the Wigner photoemission time delay with energy and angle in the vicinity of a Fano resonance with the time delay taking opposite signs at different angles at the same energy as well as at the opposite sides of the resonance at the same angle. These variations are illustrated by choosing the Ne $2s\to 3p$ autoionizing state as a case study. Moreover, we demonstrate the existence of strikingly significant changes in time delay due to relativistic effects despite Ne being a low-$Z$ atom. This finding shows the possibility for utilizing time delay chronoscopy as a route towards experimental probing of relativistic interactions and the phases of individual transition matrix elements upon atomic photoionization of low-$Z$ atoms. Finally, we develop a practical parametrization to model and explain the angle and energy variation of the autoionizing resonance time delay in the nonrelativistic limit.