Noise is often regarded as anathema to quantum computation, but in some settings it can be an unlikely ally. We consider the problem of learning the class of $n$-bit parity functions by making queries to a quantum example oracle. In the absence of noise, quantum and classical parity learning are easy and almost equally powerful, both information-theoretically and computationally. We show that in the presence of noise this story changes dramatically. Indeed, the classical learning problem is believed to be intractable, while the quantum version remains efficient. Depolarizing the qubits at the oracle's output at any constant nonzero rate does not increase the computational (or query) complexity of quantum learning more than logarithmically. However, the problem of learning from corresponding classical examples is the learning parity with noise problem, for which the best known algorithms have superpolynomial complexity. This creates the possibility of observing a quantum advantage with a few hundred noisy qubits. The presence of noise is essential for creating this quantum-classical separation.

Quantum theory imposes fundamental limitations on the amount of information that can be carried by any quantum system. On the one hand, the Holevo bound rules out the possibility of encoding more information in a quantum system than in its classical counterpart, comprised of perfectly distinguishable states. On the other hand, when states are uniformly distributed in the state space, the so-called subentropy lower bound is saturated. How uniform quantum systems are can be naturally quantified by characterizing them as $t$-designs, with $t=\infty$ corresponding to the uniform distribution. Here we show the existence of a trade-off between the uniformity of a quantum system and the amount of information it can carry. To this aim, we derive a hierarchy of informational bounds as a function of $t$ and prove their tightness for qubits and qutrits. By deriving asymptotic formulas for large dimensions, we also show that the statistics generated by any $t$-design with $t>1$ contains no more than a single bit of information, and this amount decreases with $t$. Holevo and subentropy bounds are recovered as particular cases for $t=1$ and $t=\infty$, respectively.

We report entanglement swapping with time-bin entangled photon pairs, each constituted of a 795-nm photon and a 1533-nm photon, that are created via spontaneous parametric down conversion in a nonlinear crystal. After projecting the two 1533-nm photons onto a Bell state, entanglement between the two 795-nm photons is verified by means of quantum state tomography. As an important feature, the wavelength and bandwidth of the 795-nm photons is compatible with ${\mathrm{Tm}:\mathrm{LiNbO}}_3$-based quantum memories, making our experiment an important step towards the realization of a quantum repeater.

Analog quantum simulators can be used to study quantum correlation in novel many-body systems by emulating the Hamiltonian of these systems. One essential question in quantum simulation is to probe the properties of an emulated many-body system. Here we present a circuit QED scheme for probing such properties by measuring the spectrum of a superconducting resonator coupled to a quantum simulator. We first study a general framework of this approach and show that the spectrum of the resonator is directly related to the correlation function of the coupling operator between the resonator and the simulator. We then apply this scheme to a simulator of the transverse field Ising model implemented with superconducting qubits, where the resonance peaks in the resonator spectrum correspond to the frequencies of the elementary excitations. The effects of resonator damping, qubit decoherence, and resonator backaction are also discussed. This setup can be used to probe a broad range of many-body models.

There are different predictions regarding the position of the isomeric state of ${}^{229m}\mathrm{Th}$. There is some question as to whether it even exists. We propose simple experiments to provide the evidence of the existence of this isomeric state. If the metastable isomeric state exists, we should be able to observe the effects of mixing of the nuclear wave functions of the ground state $I=5/2$ and the isomeric $I=3/2$ state via electronic shells. It will be shown as the differences between the hyperfine $A$ and $B$ constants, which will be measured by means of the laser-induced fluorescence methods and those predicted by semiempirical calculations. The wave function for the atomic state $|\mathrm{conf}.SLJIF\rangle$ contains contributions from both nuclear states $I=5/2$ and $3/2$, thus its effects on the hyperfine-structure patterns of spectral lines should be observed, confirming the existence of this isomeric state.

By explicit construction of counterexamples having the same eigenvalue spectrum of one-matrix, but different two-matrix, we show that density-matrix functionals for the electronic energy that are based solely on the eigenvalues of the one-matrix cannot be unique in functional representation of the two-matrix. The one-to-many mapping may be understood either through the number of independent parameters or the contraction relation.

It is demonstrated that the TaN molecule is the best candidate to search for a T,P-violating nuclear magnetic quadrupole moment (MQM), and it looks promising for the search for other T,P-odd effects. We report results of coupled-cluster calculations of T,P-odd effects in TaN produced by the Ta nucleus MQM, electron electric dipole moment (EDM), and scalar-pseudoscalar nucleus-electron interactions, as well as of the molecule-axis hyperfine structure constant and dipole moment. Nuclear calculations of ${}^{181}\mathrm{Ta}$ MQM are performed to express the T,P-odd effect in terms of the strength constants of T,P-odd nuclear forces, proton and neutron EDM, QCD parameter $\theta$, and quark chromo-EDM.

By analyzing measured infrared absorption of pure $\mathrm{C}{\mathrm{H}}_4$ gas under both “free” (large sample cell) and “confined” (inside the pores of a silica xerogel sample) conditions we give a demonstration that molecule-molecule and molecule-surface collisions lead to very different propensity rules for rotational-state changes. Whereas the efficiency of collisions to change the rotational state (observed through the broadening of the absorption lines) decreases with increasing rotational quantum number $J$ for $\mathrm{C}{\mathrm{H}}_4\text{-C}{\mathrm{H}}_4$ interactions, $\mathrm{C}{\mathrm{H}}_4$-surface collisions lead to $J$-independent linewidths. In the former case, some (weak) collisions are inefficient whereas, in the latter case, a single collision is sufficient to remove the molecule from its initial rotational level. Furthermore, although some gas-phase collisions leave $J$ unchanged and only modify the angular momentum orientation and/or symmetry of the level (as observed through the spectral effects of line mixing), this is not the case for the molecule-surface collisions since they always change $J$ (in the studied $J=0–14$ range).

Using the reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) technique, a nonzero phase difference is observed in the two-photon ionization transition of krypton atoms into the ionization channels ${}^{2}P_{1/2}$ and ${}^{2}P_{3/2}$ when an electron is removed from the $4p$ shell. The phase difference is studied for excitation energies ranging from $\approx 18\mathrm{eV}$ up to $\approx 28\mathrm{eV}$. The phase differences are found to depend on the relative directions of linear polarization of the photoionization laser pulses and the pulses inducing the subsequent continuum-continuum transition. The experimental results are compared to phase differences calculated on the basis of dipole matrix elements for photoionization and scattering phases known for krypton from earlier experiments. The results indicate that the RABBITT phase differences do not give an obvious direct access to time-delay differences in the primary photoionization step of the atom.

Spin-exchange interaction between atoms in a spin-1 Bose-Einstein condensate causes atomic spin evolving periodically under the single-spatial-mode approximation in the mean-field theory. By applying fast magnetic pulses according to a two-step or a four-step control protocol, we find analytically that the spin dynamics is significantly suppressed for an arbitrary initial state. Numerical calculations under single-mode approximation are carried out to confirm the validity and robustness of these protocols. This localization method can be readily utilized to improve the sensitivity of a magnetometer based on spin-1 Bose-Einstein condensates.

Using the lattice Monte Carlo method, we compute the energy and Tan's contact in the ground state as well as the first excited state of few- to many-fermion systems in a one-dimensional periodic box. We focus on unpolarized systems of $N=4,6,...,12$ particles, with a zero-range interaction, and a wide range of attractive couplings. In addition, we provide extrapolations to the infinite-volume and thermodynamic limits.

We propose a scheme to simulate and explore Weyl semimetal physics with ultracold fermionic atoms in a two-dimensional square optical lattice subjected to experimentally realizable spin-orbit coupling and an artificial dimension from an external parameter space, which may increase experimental feasibility compared with the cases in three-dimensional optical lattices. It is shown that this system with a tight-binding model is able to describe essentially three-dimensional Weyl semimetals with tunable Weyl points. The relevant topological properties are also addressed by means of the Chern number and the gapless edge states. Furthermore, we illustrate that the mimicked Weyl points can be experimentally detected by measuring the atomic transfer fractions in a Bloch-Zener oscillation, and the characteristic topological invariant can be measured with the particle pumping approach.

We study a two-dimensional spin-orbit-coupled dipolar Bose-Einstein condensate with repulsive contact interactions by both the variational method and the imaginary-time evolution of the Gross-Pitaevskii equation. The dipoles are completely polarized along one direction in the two-dimensional plane to provide an effective attractive dipole-dipole interaction. We find two types of solitons as the ground states arising from such attractive dipole-dipole interactions: a plane-wave soliton with a spatially varying phase and a stripe soliton with a spatially oscillating density for each component. Both types of solitons possess smaller size and higher anisotropy than the soliton without spin-orbit coupling. Finally, we discuss the properties of moving solitons, which are nontrivial because of the violation of Galilean invariance.

We study the resonant properties of photonic crystal slabs theoretically. An $\omega -k_x$ Fano line shape that approximates the transmission (reflection) spectrum is obtained. This approximation, being a function of light's frequency and in-plane wave vector, generalizes the conventional Fano line shape. Two particular approximations, parabolic and hyperbolic, are obtained and investigated in detail, taking into account the symmetry of the structure, the reciprocity, and the energy conservation. The parabolic approximation considers a single resonance at normal incidence, while the hyperbolic one takes into account two modes, the symmetric and the antisymmetric. Using rigorous simulations based on the Fourier modal method we show that the hyperbolic line shape provides a better approximation of the transmission spectrum. By deriving the causality conditions for both approximations, we show that only the hyperbolic one provides causality in a relativistic sense.

Bare-state population inversion is demonstrated in a two-level system with all dipole matrix elements nonzero. A laser field is resonantly driving the sample, whereas a second weaker and lower frequency coherent field additionally pumps it near resonance with the dynamically Stark-splitted states. Due to the existence of differing permanent dipole moments in the excited and ground bare states, quantum coherences among the involved dressed states are induced, leading to inversion in the steady state. Furthermore, large refractive indices are feasible, as well as the determination of the diagonal matrix elements via the absorption or emission spectra. The results apply to available biomolecular, spin, or asymmetric quantum dot systems.

We investigate the range of validity of the recently developed steady-state ab initio laser theory (SALT). While very efficient in describing various microlasers, SALT is conventionally believed not to be applicable to lasers featuring fully or nearly degenerate pairs of resonator modes above the lasing threshold. Here we demonstrate how SALT can indeed be extended to describe such cases as well, with the effect that we significantly broaden the theory's scope. In particular, we show how to use SALT in conjunction with a linear stability analysis to obtain stable single-mode lasing solutions that involve a degenerate mode pair. Our flexible and efficient approach is tested on one-dimensional ring lasers as well as on two-dimensional microdisk lasers with broken symmetry.

Synchronous-asynchronous mode-locking transition in a hybrid active and passive mode-locked laser is investigated theoretically. Three distinct mode-locking states are found and their transition diagram under varying detuning frequency and modulation strength is determined. By examining the steady-state lasing gain as a function of the detuning modulation frequency, we also clarify why the laser will become unstable near the transition points and why the nonlinear saturable absorption effect is crucial for the stable asynchronous mode-locking operation.

A lot of experimental and theoretical studies of a system in cavity quantum electrodynamics (cavity QED), which consists of two spatially separated quantum emitters strongly coupled to a single optical cavity mode, have recently attracted much interest in the quantum optics community for various quantum information applications. Here, we propose a method for high-order harmonic generation in a photonic crystal microcavity coupled to single semiconductor quantum dots (QDs). The system is coherently driven by a bichromatic laser consisting of the control and signal fields at low input power (a few nanowatts) and the cavity output power via the cavity loss channel is monitored. Via numerical simulations, we thoroughly explore the difference of the generated high-order harmonic spectra between two QDs, one QD, and zero QDs in microcavity. The results clearly indicate that harmonic generation can be significantly enhanced via collective coherent coupling in the case of two spatially separated QDs coupled to the same photonic crystal microcavity mode. In addition, we present a study of the carrier-envelope phase (CEP) effect on high-order harmonic spectra, which may provide the insight of CEP effect in a new regime. Beyond this, our obtained results also apply to other classes of single-mode cavity-QED setup incorporating two-level atoms or comparable solid-state emitters.

The dynamic dipole polarizabilities for the four lowest triplet states ($2{}^{3}S, 3{}^{3}S, 2{}^{3}P$, and $3{}^{3}P$) of helium are calculated using the $B$-spline configuration interaction method. Present values of the static dipole polarizabilities in the length, velocity, and acceleration gauges are in good agreement with the best Hylleraas results. Also the tune-out wavelengths in the range 400 nm–4.2 $\mu \mathrm{m}$ for the four lowest triplet states are identified, and the magic wavelengths in the range 460 nm–3.5 $\mu \mathrm{m}$ for the $2{}^{3}S\to 3{}^{3}S, 2{}^{3}S\to 2{}^{3}P$, and $2{}^{3}S\to 3{}^{3}P$ transitions are determined. We show that the tune-out wavelength of $2{}^{3}S$ state is $413.03828\left(3\right)$ nm, which corroborates the value of Mitroy and Tang [Phys. Rev. A 88, 052515 (2013)], and the magic wavelength around 1066 nm for the $2{}^{3}S\to 3{}^{3}P$ transition can be expected for precision measurement to determine the ratio of transition matrix elements $(2{}^{3}S\to 2{}^{3}P)/(3{}^{3}P\to 6{}^{3}S)$.

In this paper, we propose an in-depth review of the vector and tensor polarizabilities of the two energy levels of the ${}^{87}\mathrm{Sr}$ clock transition whose measurement was reported in P. G. Westergaard et al. [Phys. Rev. Lett. 106, 210801 (2011)]. We conduct a theoretical calculation that reproduces the measured coefficients. In addition, we detail the experimental conditions used for their measurement in two Sr optical lattice clocks and exhibit the quadratic behavior of the vector and tensor shifts with the depth of the trapping potential and evaluate their impact on the accuracy of the clock.