We present an experimental measurement of the ensemble averages of both the kinetic and interaction energies of the three-dimensional Bose-Hubbard model at finite temperature and various optical lattice depths across weakly to strongly interacting regimes, for an almost unit filling factor within single-band tight-binding approximation. The kinetic energy is obtained through Fourier transformation of a time-of-flight signal, and the interaction energy is measured using a newly developed atom-number-projection spectroscopy technique, by exploiting an ultranarrow optical transition of two-electron atoms. The obtained experimental results can be used as benchmarks for state-of-the-art numerical methods of quantum many-body theory. As an illustrative example, we compare the measured energies with numerical calculations involving the Gutzwiller and cluster-Gutzwiller approximations, assuming realistic trap potentials and particle numbers at nonzero entropy (finite temperature); we obtain good agreement without fitting parameters. We also discuss the possible application of this method to temperature estimations for atoms in optical lattices using the thermodynamic relation. This study offers a unique advantage of cold atom system for “quantum simulators.”

We show theoretically and demonstrate experimentally that collapsing elliptically polarized laser beams experience a nonlinear ellipse rotation that is highly sensitive to small fluctuations in the input power. For arbitrarily small fluctuations in the input power and after a sufficiently large propagation distance, the polarization angle becomes uniformly distributed in $[0,2\pi ]$ from shot to shot. We term this phenomenon loss of polarization. We perform experiments in fused-silica glass, nitrogen gas, and water and observe a significant increase in the fluctuations of the output polarization angle for elliptically polarized femtosecond pulses as the power is increased beyond the critical power for self-focusing. We also show numerically and confirm experimentally that this effect is more prominent in the anomalous group-velocity dispersion (GVD) regime compared to the normal-GVD regime due to the extended lengths of the filaments for the former. Such effects could play an important role in intense-field light-matter interactions in which elliptically polarized pulses are utilized.

The identification and separation of substances by chirality has always been an important problem in biomedical research and industry. Light beams carry optical momentum, and can exert optical force on any object they impinge due to the transfer of momentum. Different chiral objects will experience different optical forces when illuminated by the same light beam. We demonstrate here, based on the dipolar approximation, that a tightly focused vector beam can selectively trap and rotate small chiral particles in the transverse plane via the chirality-tailored optical forces. The radial optical force can transversely trap the chiral particles off axis or push them away depending on the real part of the chirality parameter, while the lateral optical force manifesting as the azimuthal optical force can drive the trapped particles to orbitally rotate with opposite chiral absorption in opposite directions. The study reported here may find applications in discriminating and separating chiral objects with specified chirality.

We report an experimental study of dynamics of the metastable ${}^3{P}_2$ state of bosonic ytterbium atoms in an optical lattice. The dissipative Bose-Hubbard system with on-site two-body atom loss is realized via its intrinsic strong inelastic collision of the metastable ${}^3{P}_2$ atoms. We investigate the atom loss behavior with the unit-filling Mott insulator as the initial state and find that the atom loss is suppressed by the strong correlation between atoms, which is attributed to both the on-site interaction and the inelastic loss. Also, as we decrease the potential depth of the lattice, we observe the growth of the phase coherence and find its suppression owing to the dissipation.

We discuss the spin, the angular momentum, and the magnetic moment of rotating chiral fermions using a kinetic theory. We find that, in addition to the chiral vortical contribution along the rotation axis, finite circular spin polarization is induced by the spin-momentum correlation of chiral fermions, which is canceled by a change in the orbital angular momentum. We point out that the eddy magnetic moment is nonvanishing due to the $g$ factors, exhibiting the chiral Barnett effect.

Since Bell's theorem we know that quantum mechanics is incompatible with local hidden-variable models, the phenomenon known as quantum nonlocality. However, despite steady progress over the years, a precise characterization of the set of quantum correlations has remained elusive. There are correlations compatible with the no-signaling principle and still beyond what can be achieved within quantum theory, which has motivated the search for physical principles and computational methods to decide the quantum or postquantum behavior of correlations. Here, we identify a feature of Bell correlations that we call quantum voids: faces of the no-signaling set where all nonlocal correlations are postquantum. Considering the simplest possible Bell scenario, we give a full characterization of quantum voids, also understanding its connections to known principles and its potential use as a dimension witness.

We investigate the measurement uncertainties of a triple of positive-operator-valued measures based on statistical distance and formulate state-independent tight uncertainty inequalities satisfied by the three measurements in terms of triplewise joint measurability. In particular, uncertainty inequalities for three unbiased qubit measurements are presented with analytical lower bounds which relates to the necessary and sufficient condition of the triplewise joint measurability of the given triple. We show that the measurement uncertainties for a triple measurement are essentially different from the ones obtained by pairwise measurement uncertainties by comparing the lower bounds of different measurement uncertainties.

Learning low-dimensional representation is a crucial issue for many machine-learning tasks, such as pattern recognition and image retrieval. In this article, we present a quantum algorithm and a quantum circuit to efficiently perform A-optimal projection for dimensionality reduction. Compared with the best-know classical algorithms, the quantum A-optimal projection (QAOP) algorithm shows an exponential speedup in both the original feature space dimension $n$ and the reduced feature space dimension $k$. We show that the space and time complexity of the QAOP circuit are $O\left[{log}_2(nk/\epsilon )\right]$ and $O\left[{log}_2\left(nk\right)\text{poly}\left({log}_2{\epsilon }^{-1}\right)\right],$ respectively, with fidelity at least $1-\epsilon$. First, a reformation of the original QAOP algorithm is proposed to help omit the quantum-classical interactions during the QAOP algorithm. Then the quantum algorithm and quantum circuit with performance guarantees are proposed. Specifically, the quantum circuit modules for preparing the initial quantum state and implementing the controlled rotation can be also used for other quantum machine-learning algorithms.

Symmetry plays an important role in the field of quantum mechanics. We consider a subclass of symmetric quantum states in the multipartite system $N^{\otimes d}$, namely, the completely symmetric states, which are invariant under any index permutation. It was hypothesized by L. Qian and D. Chu (arXiv:1810.03125 [quant-ph]) that the completely symmetric states are separable if and only if it is a convex combination of symmetric pure product states. We prove that this conjecture is true for the both bipartite and multipartite cases. Further, we prove that the completely symmetric state $\rho$ is separable if its rank is at most 5 or $N+1$. For the states of rank 6 or $N+2$, they are separable if and only if their range contains a product vector. We apply our results to a few widely useful states in quantum information, such as symmetric states, edge states, extreme states, and non-negative states. We also study the relation of completely symmetric states to Hankel and Toeplitz matrices.

We study the light-cone and front dynamics of a single-particle continuous time extended quantum walk on a one-dimensional lattice with finite range hopping. We show that, in general, for an initially localized state, propagating wave fronts can be characterized as ordinary or extremal fronts with the latter exhibiting an anomalous subdiffusive scaling behavior in the front region. We investigate the dynamical global and local scaling properties of the cumulative probability distribution function for the extended walk with nearest- and next-nearest-neighbor hopping using analytical and numerical methods. The global scaling shows the existence of a “causal light-cone” corresponding to excitations traveling with a velocity smaller than a maximal “light velocity.” Maximal fronts moving with fixed light velocity bound the causal cone. The front regions spread with time subdiffusively exhibiting a local Airy scaling which leads to an internal staircase structure. At a certain critical next-nearest-neighbor hopping strength, there is a transition from a phase with one ‘causal cone’ to a phase with two nested ‘causal cones’ and the existence of an internal staircase structure in the corresponding cumulative distribution profiles. We also connect the study to that in spin chain systems and indicate that a single-particle quantum walk on the one-dimensional lattice already captures the many-body physics of a spin chain system. In particular, we suggest that the time evolution of a single-particle quantum walk on the one-dimensional lattice with an initially localized state is equivalent to the time evolution of a domain-wall initial state in a corresponding spin chain system.

Large-scale relativistic configuration-interaction method combined with many-body perturbation theory is consistently applied to calculations of the energy levels of the ground and inner-$L$-shell excited states of berylliumlike ions in the range $10\le Z\le 92$. The quantum electrodynamics, nuclear recoil, and frequency-dependent Breit corrections are taken into account. The obtained results are supplemented with the systematical estimation of the uncertainties.

Dissociative electron attachment to molecules in vibrationally excited states is associated with lower threshold energies and higher cross sections than for cold targets. To date, fewer studies have been performed for polyatomic molecules than for diatomic molecules, due to the experimental challenges and theoretical difficulties in describing the complicated dynamics. Here we report an observation of the dissociative electron attachment to $\mathrm{C}{\mathrm{O}}_2$ in the vibrationally excited states, where the vibrationally excited $\mathrm{C}{\mathrm{O}}_2$ targets are prepared by the electron-impact excitation at energies close to the ${}^2{\mathrm{\Pi }}_u$ resonant state of $\mathrm{C}{{\mathrm{O}}_2}^{-}$. The high-resolution anion momentum images of the ${\mathrm{O}}^{-}$ yield indicate that the rovibrational state distributions of the coproduct CO are dependent on the vibrationally excited states of symmetric bond stretching and bending modes of $\mathrm{C}{\mathrm{O}}_2$.

We investigate the time-optimal control of the purification of a qubit interacting with a structured environment, consisting of a strongly coupled two-level defect in interaction with a thermal bath. On the basis of a geometric analysis, we show for weak and strong interaction strengths that the optimal control strategy corresponds to a qubit in resonance with the reservoir mode. We investigate under which conditions qubit coherence and correlation between the qubit and the environment can speed up the control process.

Producing a substantial and stable resonant Bose-Einstein condensate (BEC) has proven to be a challenging experimental task due to heating and three-body losses that may occur even before the gas comes to thermal equilibrium. In this paper, by considering two-body correlations, we note that a sudden quench from small to large scattering lengths is not an efficient way to prepare a resonant BEC. As an alternative, we propose a two-step scheme that involves an intermediate scattering length, between 0 and $\infty$, which serves to maximize the transfer probability of $N$ bosons of mass $m$ in a harmonic trap with frequency $\omega$ to the resonant state. We find that the intermediate scattering length should be $a\approx 3.16N^{-2/3}\sqrt{\hslash /\left(m\omega \right)}$, and that it produces an optimum transition probability of $1.03N^{-1/6}$.

The dynamics of quantized vortices in two-dimensional two-component miscible Bose-Einstein condensates trapped by a box potential has been numerically studied using the Gross-Pitaevskii model. We have discovered a phenomenon where the vortices of the two components spatially separate from each other, which we call the phase separation of the distribution of vortices. This phase separation occurs when the intercomponent coupling is strong. Onsager vortices, on the other hand, are formed in both components when the intercomponent coupling is weak. We distinguish between Onsager vortices and phase-separated vortices by two types of effective distances between vortices. The dependence of the transition between the Onsager vortices and phase-separated vortices on the intercomponent interaction is also studied.

When seeking a numerical representation of a quantum-mechanical multiparticle problem it is tempting to replace a singular short-range interaction by a smooth finite-range pseudopotential. Finite basis set expansions, e.g., in Fock space, are then guaranteed to converge exponentially. The need to faithfully represent the artificial length scale of the pseudopotential, however, places a costly burden on the basis set. Here we discuss scaling relations for the required size of the basis set and demonstrate the basis set convergence on the example of a two-dimensional system of few fermions with short-range $s$-wave interactions in a harmonic trapping potential. In particular we show that the number of harmonic oscillator basis functions needed to reach a regime of exponential convergence for a Gaussian pseudopotential scales with the fourth power of the pseudopotential length scale, which can be improved to quadratic scaling when the basis functions are rescaled appropriately. Numerical examples for three fermions with up to a few hundred single-particle basis functions are presented and implications for the feasibility of accurate numerical multiparticle simulations of interacting ultracold-atom systems are discussed.

Quantum synchronization and its connection with other quantum correlations have attracted considerable attention. Here we present a theoretical scheme to simultaneously represent and significantly enhance the level of quantum synchronization and entanglement between two indirectly coupled mechanical membranes, which are coupled to a common optical field within a cavity. By applying a two-tone driving laser with weighted amplitudes and specific frequencies, both synchronization gauged by Mari's criterion and entanglement estimated by logarithmic negativity can be greatly enhanced. We then clarify the relationship between quantum synchronization and entanglement in detail. Numerical simulation results show that the influence of the coupling asymmetry $G_2/G_1$ on quantum complete synchronization behaves similarly to that on the purity while the influence of the coupling asymmetry $G_2/G_1$ on quantum phase synchronization is more similar to that on quantum entanglement. Besides, we demonstrate that although quantum synchronization and quantum entanglement are not directly related, both of them are sensitive to the squeezing parameter and the cooling effect. Furthermore, it is also shown that detuning the frequencies of two mechanical oscillators can actually help quantum synchronization and entanglement, which is somewhat similar to the case of quantum synchronization blockade.

Frequency-resolved quantum correlation of resonance fluorescence is investigated in a two-atom radiating system. In this quantum radiating system, only one atom is driven by a laser field, and the spontaneous transition of the undriven atom resonates with one of the Rabi sidebands of the driven atom. A single-mode empty cavity is applied to serve as a Lorentzian filter to output the superbunched fluorescent photon pairs when its frequency is tuned to halfway between the central peak and one of the side peaks. In the case of large filter width, two-photon correlation signal and its physical correspondence can be bridged analytically in our approach. It reveals that this superbunching effect turns out to be the constructive quantum interference between a pair of coupled two-photon cascaded transitions. Ulteriorly, it is the consequence of the modulations of the unfiltered dressed-state transition amplitudes by the filter. Our analytical formalism also shows that, although the dipole-dipole interaction is usually weak, the interatomic coherence caused by this weak perturbation can also play a crucial role in breaking through the superbunching limit obtained from a single two-level atom in the same parameter regime. In addition to being a treasurable quantum pump to probe into the target quantum system, it is also found in our investigation that this superbunched fluorescence can serve as a promising quantum response in detecting this weak perturbation in the interior of the quantum source. A general case is also considered when the two-atom radiating system is monitored by two filter-detector monitoring systems. It is found that this filtered strong quantum correlation can be maintained even though the two photons are spatially separated.

We demonstrate a magnetically controllable nonreciprocal Goos-Hänchen (GH) shift enabled by the magnetic plasmonic gradient metasurfaces (GMSs) consisting of an array of ferrite rods with a rotation gradient introduced to the rod dimers in the unit cell. The incident Gaussian beam is observed to exhibit an evident GH shift about $5\lambda$ when it is incident from one side, whereas for the Gaussian beam incident from the geometrically symmetric direction with respect to surface normal only a very small GH shift comes into appearance. The phenomenon arises from the unidirectional coupling of the incident beam with the magnetic plasmonic GMSs due to the time-reversal-symmetry-breaking nature of the magnetic system as evidenced from the photonic band diagrams of the edge states. The unidirectional GH shift can also be implemented at different incident angles by either engineering the gradient of the GMSs or tuning the bias magnetic field. By designing the magnetic plasmonic GMSs with more exquisite configurations we can expect a lot more nonreciprocal properties, adding additional freedom in manipulating electromagnetic waves.