We outline a kinetic theory of nonthermal fixed points for the example of a dilute Bose gas, partially reviewing results obtained earlier, thereby extending, complementing, generalizing, and straightening them out. We study universal dynamics after a cooling quench, focusing on situations where the time evolution represents a pure rescaling of spatial correlations, with time defining the scale parameter. The nonequilibrium initial condition set by the quench induces a redistribution of particles in momentum space. Depending on conservation laws, this can take the form of a wave-turbulent flux or of a more general self-similar evolution, signaling the critically slowed approach to a nonthermal fixed point. We identify such fixed points using a nonperturbative kinetic theory of collective scattering between highly occupied long-wavelength modes. In contrast, a wave-turbulent flux, possible in the perturbative Boltzmann regime, builds up in a critically accelerated self-similar manner. A key result is the simple analytical universal scaling form of the nonperturbative many-body scattering matrix, for which we lay out the concrete conditions under which it applies. We derive the scaling exponents for the time evolution as well as for the power-law tail of the momentum distribution function, for a general dynamical critical exponent $z$ and an anomalous scaling dimension $\eta$. The approach of the nonthermal fixed point is, in particular, found to involve a rescaling of momenta in time $t$ by $t^{\beta }$, with $\beta =1/z$, within our kinetic approach independent of $\eta$. We confirm our analytical predictions by numerically evaluating the kinetic scattering integral as well as the nonperturbative many-body coupling function. As a side result, we obtain a possible finite-size interpretation of wave-turbulent scaling recently measured by Navon et al.

In this paper, we report both numerically and experimentally an unexpected phenomenon of self-polarization occurring in the middle point of an isotropic optical fiber when two uncorrelated partially polarized waves are simultaneously injected at the ends of the fiber. More precisely, we demonstrate that two counterpropagating waves of equal intensity exhibit a spontaneous organization of their polarization states around two pools of attraction just in the middle point of propagation, and then both recover a partially polarized state at their respective fiber outputs. The self-polarization effect then remains hidden within the optical fiber in the sense that no apparent sign of this process is detected at the fiber outputs. A geometric definition of the degree of polarization is used to measure the efficiency of the polarization phenomenon.

Canonical variables for the Poisson algebra of quantum moments are introduced here, expressing semiclassical quantum mechanics as a canonical dynamical system that extends the classical phase space. New realizations for up to fourth order in moments for a single classical degree of freedom and to second order for a pair of classical degrees of freedom are derived and applied to several model systems. It is shown that these new canonical variables facilitate the derivation of quantum-statistical quantities and effective potentials. Moreover, by formulating quantum dynamics in classical language, these methods result in new heuristic pictures, for instance, of tunneling, that can guide further investigations.

We show that entanglement between two solitary qubits in quasi-one-dimensional Bose-Einstein condensates can be spontaneously generated due to quantum fluctuations. Recently we have shown that dark solitons are an appealing platform for qubits thanks to their appreciable long lifetime. We investigate the spontaneous generation of entanglement between dark-soliton qubits in the dissipative process of spontaneous emission. By driving the qubits with the help of oscillating magnetic field gradients, we observe the formation of long distance steady-state concurrence. Our results suggest that dark-soliton qubits are good candidates for quantum information protocols based purely on matter-wave phononics.

Robust and high-precision quantum control is extremely important but challenging for the functionalization of scalable quantum computation. In this paper, we show that this hard problem can be translated to a supervised machine learning task by thinking of the time-ordered quantum evolution as a layer-ordered neural network (NN). The seeking of robust quantum controls is then equivalent to training a highly generalizable NN, to which numerous tuning skills matured in machine learning can be transferred. This opens up a door through which a family of robust control algorithms can be developed. We exemplify such potential by introducing the commonly used trick of batch-based optimization, and the resulting batch-based gradient algorithm is numerically shown to be able to remarkably enhance the control robustness while maintaining high fidelity.

The transient Casimir-Polder force on a two-level atom introduced into a three-dimensional, inhomogeneous, generally nonreciprocal environment is evaluated using non-Markovian Weisskopf-Wigner theory in the strong- and weak-coupling regimes. Ground-state and excited atoms are shown to decouple into two separate initial-value problems, and both the short-time and long-time atomic population and force are evaluated. The results are compared with various Markov approximations of the Weisskopf-Wigner theory and with previous Markov results from the Heisenberg picture.

We use recently developed efficient versions of the configuration interaction method to perform ab initio calculations of the spectra of superheavy elements seaborgium (Sg, $Z=106$), bohrium (Bh, $Z=107$), hassium (Hs, $Z=108$), and meitnerium (Mt, $Z=109$). We calculate energy levels, ionization potentials, isotope shifts, and electric dipole transition amplitudes. Comparison with lighter analogs reveals significant differences caused by strong relativistic effects in superheavy elements. Very large spin-orbit interaction distinguishes subshells containing orbitals with a definite total electron angular momentum $j$. This effect replaces Hund's rule holding for lighter elements.

A quantum state of an electron influences its electromagnetic field. If a spatial profile of the electron wave packet is not Gaussian, the particle may acquire additional intrinsic multipole moments, which alter its field, especially at small distances. Here the fields of a vortex electron with orbital angular momentum $\ell$ are obtained in a form of a multipole expansion with an electric quadrupole term kept by using the generalized (nonparaxial) Laguerre-Gaussian beams. The quadrupole contribution arises beyond a paraxial approximation, is linearly enhanced for highly twisted packets with $\left|\ell \right|\gg 1$, and can be important for the interactions of twisted beams with bulk matter and artificial structures. Moreover, this term results in an azimuthal asymmetry of the magnetic field in a rest frame of the electron, which appears thanks to the spreading of the packet with time. Thus, somewhat contrary to physical intuition, the spreading may enhance nonparaxial phenomena. For the available electron beams, this asymmetry can in principle be reliably detected, which would be experimental evidence of a nonparaxial effect with the vortex electrons.

We study in detail the scattering of light on a soliton propagating in a waveguide which has been proposed as an experimental system in which one could observe the analog Hawking effect. When not applying the rotating-wave approximation, we show that the linearized wave equation governing perturbations has the same structure as that governing phonon propagation in an atomic Bose condensate. By taking into account the full dispersion relation, we then show that the scattering coefficients encoding the production of photon pairs are amplified by a resonance effect related to the modulation instability occurring in the presence of a continuous wave. When using a realistic example of a silicon nitride waveguide on a silica substrate, we find that a soliton of duration $10\mathrm{fs}$ would spontaneously emit about one photon pair for every cm it travels, which makes the effect readily observable. This result is confirmed by numerically solving the equation encoding the Kerr nonlinearity and governing the evolution of the full field (soliton plus perturbations). We discuss the link with previous works devoted to the analog Hawking effect where the pair creation rates were about six orders of magnitude smaller.

The quantum Fisher information (QFI) of certain multipartite entangled quantum states is larger than what is reachable by separable states, providing a metrological advantage. Are these nonclassical correlations strong enough to potentially violate a Bell inequality? Here, we present evidence from two examples. First, we discuss a Bell inequality designed for spin-squeezed states which is violated only by quantum states with a large QFI. Second, we relax a well-known lower bound on the QFI to find the Mermin Bell inequality as a special case. However, a fully general link between QFI and Bell correlations is still open.

The weak equivalence principle (WEP) in the quantum regime has been the subject of many studies with a broad range of approaches to the problem. Here, we tackle the problem anew through the time of arrival (TOA) operator approach. This is done by constructing the TOA operator for a nonrelativistic and structureless particle that is projected upward in a uniform gravitational field with an intended arrival point below the classical turning point. The TOA operator is constructed under the constraint that the inertial and gravitational masses are equivalent and that Galilean invariance is preserved. These constraints are implemented by Weyl quantization of the corresponding classical TOA function for the projectile. The expectation value of the TOA operator is explicitly shown to be equal to the classical time of arrival plus mass-dependent quantum correction terms, implying incompatibility of the WEP with quantum mechanics. The full extent of the violation of the WEP is shown through the mass dependence of TOA distribution for the projectile.

Variational hybrid quantum classical algorithms to optimizations are important applications for near-term quantum computing. This paper proposes two quantum algorithms (the second one is variational) for training neural networks. Both of them obtain exponential speedup at the number of samples and polynomial speedup at the dimension of the samples over classical training algorithms. Moreover, the proposed quantum algorithms return the classical information of the training weight so that the outputs can be used directly to solve other problems. For practicality, we draw the quantum circuits to implement the two algorithms. Finally, as an inspiration, we show how to apply the variational algorithm to achieve speedup at the number of constraints in solving convex optimization problems.

In a recent experimental work [Z. Wu et al., Science 354, 83 (2016)], the PKU-USTC group realized a two-dimensional two-band quantum anomalous Hall model on a square Raman lattice. By quenching the atom-laser detuning of such a Raman lattice, the time-dependent Bloch vectors for each quasimomentum points define a Hopf mapping from quasimomentum-time space $(k_x,k_y,t)\in T^3$ to the Bloch sphere $S^2$. The Hopf links between the preimages of any two Bloch vectors on $S^2$ can be measured experimentally through Bloch-state tomography using spin-resolved time-of-flight measurement together with suitable radio-frequency manipulations. The dynamical Hopf invariants, which are quasimomentum-time integrations of Chern-Simons densities, can also be extracted experimentally through certain quench processes. As the Hopf invariant equals the Chern number of the postquench Hamiltonian, the measurements of Hopf links and Hopf invariants provide an alternative way of understanding the topological phase diagram of the equilibrium system.

Whispering-gallery-mode (WGM) microresonator optomechanical systems that can attain high quality factors, exhibit small optical mode volume, and can be excited through their evanescent field are versatile platforms for both theoretical and experimental studies in quantum and nonlinear optics. Investigating photon statistical properties in WGM microresonator optomechanical systems is an important avenue to understand their inner interaction mechanism. Here, the interference-modulated photon statistics in a three-mode coupling, i.e., a pair of counterpropagating optical cavity modes and a mechanical mode, in WGM microresonator optomechanical systems is studied. In the case that one optical mode is driven by an external field, strong antibunching photon statistics can be observed in the presence of mode coupling. When the two cavity modes are driven simultaneously, it is found that the photon statistical properties can be well steered by modulating the interference between different transition paths with the help of the amplitudes of the two input fields and their relative phase. Especially, we show in detail that the antibunching photon statistics can be optimized within the weak optomechanical coupling regime by properly adjusting the relative phase. We also find that it is necessary to prepare the mechanical resonator near to the ground state to eliminate the detrimental effect of thermal phonon number on the photon statistical properties. This investigation can deepen our understanding of the interaction between clockwise or counterclockwise light and mechanical motion as well as be useful for the construction of integrated on-chip single-photon sources.

Blind quantum computation is a scheme that adds unconditional security to cloud quantum computation. In the protocol proposed by Broadbent, Fitzsimons, and Kashefi, the ability to prepare and transmit a single qubit is required for a user (client) who uses a quantum computer remotely. In case a weak coherent pulse is used as a pseudo-single-photon source, however, we must introduce decoy states, owing to the inherent risk of transmitting multiple photons. In this paper, we demonstrate that by using a heralded single-photon source and a probabilistic photon number resolving detector we can gain a higher blind state generation efficiency and longer access distance, owing to noise reduction on account of the heralding signal.

Using a laser intensity modulated synchronously with a 15.9 GHz microwave field we have examined laser excitation of Li atoms to the vicinity of the ionization limit in the presence of the microwave field and a parallel static field. The static field breaks the symmetry of ionization in the two microwave half cycles, and as the intensity modulated laser beam is delayed relative to the microwave field, maxima in the ionization are observed every microwave field cycle, not every half cycle, as in the absence of the static field. When the laser is tuned below the ionization limit there is an unexpected phase reversal of the modulation in the ionization, the origin of which is clarified by a classical model.

Photoelectron circular dichroism results from one-photon ionization of chiral molecules by circularly polarized light and manifests itself in forward-backward asymmetry of electron emission in the direction orthogonal to the light polarization plane. What is the physical mechanism underlying asymmetric electron ejection? How “which way” information builds up in a chiral molecule and maps into forward-backward asymmetry? We introduce instances of bound chiral wave functions resulting from stationary superpositions of states in a hydrogen atom and use them to show that the chiral response in one-photon ionization of aligned molecular ensembles originates from two propensity rules: (i) sensitivity of ionization to the sense of electron rotation in the polarization plane and (ii) sensitivity of ionization to the direction of charge displacement or stationary current orthogonal to the polarization plane. In the companion paper [Phys. Rev. A 99, 043417 (2019)], we show how the ideas presented here are part of a broader picture valid for all chiral molecules and arbitrary degrees of molecular alignment.

Photoelectron circular dichroism results from one-photon ionization of chiral molecules by circularly polarized light and manifests itself in forward-backward asymmetry of electron emission in the direction orthogonal to the light polarization plane. To expose the physical mechanism responsible for asymmetric electron ejection, we first establish a rigorous relation between the responses of unaligned and partially or perfectly aligned molecules. Next, we identify a propensity field, which is responsible for the chiral response in the electric-dipole approximation, i.e., a chiral response without magnetic interactions. We find that this propensity field, up to notations, is equivalent to the Berry curvature in a two-band solid. The propensity field directly encodes optical propensity rules, extending our conclusions regarding the role of propensity rules in defining the sign of forward-backward asymmetry from the specific case of chiral hydrogen [Ordonez and Smirnova, Phys. Rev. A 99, 043416 (2019)] to generic chiral systems. Optical propensity rules underlie the chiral response in photoelectron circular dichroism. The enantiosensitive flux of the propensity field through the sphere in momentum space determines the forward-backward asymmetry in unaligned molecules and suggests a geometrical origin of the chiral response. This flux has opposite sign for opposite enantiomers and vanishes for achiral molecules.

We propose to track the position and velocity of mobile Rydberg excited impurity atoms through the elastic interactions of the Rydberg electron with a host condensate. Tracks first occur in the condensate phase, but are then naturally converted to features in the condensate density or momentum distribution. The condensate thus acts analogously to the cloud or bubble chambers in the early days of elementary particle physics. The technique will be useful for exploring Rydberg-Rydberg scattering, rare inelastic processes involving the Rydberg impurities, coherence in Rydberg motion, and forces exerted by the condensate on the impurities. Our simulations show that resolvable tracks can be generated within the immersed Rydberg lifetime and condensate heating is under control. Finally, we demonstrate the utility of this Rydberg tracking technique to study ionizing Rydberg collisions or angular momentum changing interactions with the condensate.

We report on a discrete-time quantum walk that uses the momentum of ultra-cold rubidium-87 atoms as the walk space and two internal atomic states as the coin degree of freedom. Each step of the walk consists of a coin toss (a microwave pulse) followed by a unitary shift operator (a resonant ratchet pulse). We carry out a comprehensive experimental study on the effects of various parameters, including the strength of the shift operation, coin parameters, noise, and initialization of the system on the behavior of the walk. The walk dynamics can be well controlled in our experiment; potential applications include atom interferometry and engineering asymmetric walks.