We revisit here the Kibble-Zurek mechanism for superfluid bosons slowly driven across the transition toward the Mott-insulating phase. By means of a combination of the time-dependent variational principle and a tree-tensor network, we characterize the current flowing during annealing in a ring-shaped one-dimensional Bose-Hubbard model with artificial classical gauge field on up to 32 lattice sites. We find that the superfluid current shows, after an initial decrease, persistent oscillations which survive even when the system is well inside the Mott insulating phase. We demonstrate that the amplitude of such oscillations is connected to the residual energy, characterizing the creation of defects while crossing the quantum critical point, while their frequency matches the spectral gap in the Mott insulating phase. Our predictions can be verified in future atomtronics experiments with neutral atoms in ring-shaped traps. We believe that the proposed setup provides an interesting but simple platform to study the nonequilibrium quantum dynamics of persistent currents experimentally.

We investigate the Rosen-Zener-Stückelberg interferometry of ultracold atoms in a sinusoidal-type periodical modulated, symmetrical double-well potential. Periodical modulation of the trapping potential barrier leads to an analog of light-assisted Rosen-Zener tunneling, with distinct signatures of the energy gap visible in the amount of particles transferred from one well to the other. Time-averaged atomic occupations in one well show nice interference patterns for multiple-period modulation. The condition for constructive interference is given by the requirements satisfied by the Stückelberg phase. Both integer and noninteger resonances ranging from $2n$ to $5n$ ($n$ is a positive integer) are predicted at certain modulating amplitudes. In particular, we find that the resonance profiles can change from a Fano-like line shape with weak modulation to a Lorentzian-like line shape with strong modulation. Our theory is generic for many other forms of periodical modulation fields and can be used to realize a time-domain multiple-slit interferometer.

The second-harmonic generation of Laguerre-Gaussian (LG) beams is investigated in this paper with a coupled equation set deduced from the nonlinear paraxial equations. Under the guidance of this coupled equation set, the conversion and propagation characteristics for individual LG modes in the second-harmonic (SH) generation process are studied quantitatively. Furthermore, we show that a periodic quasi-phase-matching crystal can be used as an integrated device to produce a controllable multimode SH source. By controlling the length or temperature of crystal each LG mode of the SH wave can be manipulated separately, instead of treating the SH wave as a whole. This method might be useful in mode division multiplexing system to expand the communication capacity, and thus has potential applications in optical communication.

The statistics of photon-subtracted and photon-added states has several important applications in quantum optics and quantum information science. In this study, we propose a scheme for a photon-subtraction operation with SU(1,1) beam splitters. We demonstrate that our scheme overcomes the exponential decaying trend of fidelity and works exceptionally well for quantum states with a large number of photons. Moreover, our scheme is effective even with realistic on-off photon detectors and the heralded single-photon source. Thus, our scheme can serve as a useful tool for manipulating the number of photons in bright coherent states and strongly squeezed states in the future.

The transition from the amplification of spontaneous emission to superfluorescence in a three-level and swept-gain medium excited by an x-ray free-electron-laser pulse is theoretically investigated. Given the specific timescale of an x-ray free-electron-laser pulse, we investigate the swept pumping process in detail, and our results show that the temporal structure of an x-ray free-electron-laser pulse plays a more critical role than its peak intensity does for producing population inversion. The typical watershed of two radiant regions depends on the optical depth of the gain medium for a given coherence time, namely, the particle number density and medium length are equally important. However, we find that medium length plays a more important role than particle density for making the forward-backward asymmetry. The transient gain length and the total medium length are identified as two important factors to observe length-induced backward transition. The present results suggest an application of parametric controls over a single-pass-amplified light source.

A quantum phase transition (QPT) in Hermitian systems is independent of the boundary condition in the thermodynamic limit. However, it may happen for a non-Hermitian system, that the QPT strongly depends on the boundary condition. We investigate the many-body ground-state property of a one-dimensional tight-binding ring with an embedded single asymmetrical dimer based on exact solutions. We employ a semilocalization state to describe a quantum phase that is a crossover from extended to localized state. The peculiar feature is that the decay length is of the order of the system size rather than fixed as a usual localized state. In addition, the spectral statistics is nonanalytic as asymmetrical hopping strengths vary, resulting a sudden charge of the ground state. The distinguishing feature of such a QPT is that the density of the ground-state energy varies smoothly due to unbroken symmetry. However, there are other observables, such as the ground-state center of mass and average current, which exhibit the behavior of second-order QPT. This behavior stems from time-reversal symmetry breaking of a macroscopic number of single-particle eigenstates.

We investigate spin squeezing for a one-axis twisting (OAT) model coupled to a general non-Markovian environment in a finite-temperature regime. Using the non-Markovian quantum state diffusion and master equation approach, we numerically study non-Markovian spin-squeezing generation in the OAT model. Our results show that the total spin number $N$, energy $k_{B}T$, and certain coefficients in the OAT model can play a crucial role in generating spin squeezing. In particular, it shows that the maximum spin squeezing can be significantly enhanced when the participating environment has a relatively long memory time.

We propose the application of a coherence-based measure for non-Markovianity to study the dynamics of color centers in diamond, where the optical coherence between two orbital states is affected by interactions with a structured phonon bath. Although limited to pure dephasing, we show that this measure is well behaved at arbitrary temperatures and experimentally accessible through Ramsey spectroscopy. By taking realistic phonon spectral density functions into account, we use this quantity to show how non-Markovianity is affected by the presence of both bulk and quasilocalized phonon modes, as relevant for most defects in solids. Importantly, with only a minor modification the measure can be adapted to study the source of non-Markovianity in driven two-level systems and is thus applicable for a large class of systems modeled by the spin-boson Hamiltonian.

The quantum query model is one of the most important models in quantum computing. Several well-known quantum algorithms are captured by this model, including the Deutsch-Jozsa algorithm, the Simon algorithm, the Grover algorithm, and others. In this paper, we characterize the computational power of exact one-query quantum algorithms. It is proved that a total Boolean function $f:{\{0,1\}}^n\to \{0,1\}$ can be exactly computed by a one-query quantum algorithm if and only if $f\left(x\right)=x_{i_1}$ or $x_{i_1}\oplus x_{i_2}$ (up to isomorphism). Note that, unlike most work in the literature based on the polynomial method, our proof does not resort to any knowledge about the polynomial degree of $f$.

Einstein-Podolsky-Rosen (EPR) steering refers to the ability of one observer to convince a distant observer that they share entanglement by making local measurements. Determining which states allow a demonstration of EPR steering remains an open problem in general. Here, we outline and demonstrate a method of analytically constructing new classes of two-qubit states which are nonsteerable by arbitrary projective measurements, from consideration of local operations performed by the steering party on states known to be nonsteerable.

The orbital Feshbach resonance (OFR) is a recently developed scheme for magnetically tuning the interactions in closed-shell fermionic atoms. Remarkably, unlike the Feshbach resonances in alkali-metal atoms, the open and closed channels of the OFR are only very weakly detuned in energy. This leads to a unique effect whereby a medium in the closed channel can Pauli block—or frustrate—the two-body scattering processes. Here, we theoretically investigate the impact of frustration in the few- and many-body limits of the experimentally accessible three-dimensional ${}^{173}\mathrm{Yb}$ system. We find that by adding a closed-channel atom to the two-body problem the binding energy of the ground state is significantly suppressed, and by introducing a closed-channel Fermi sea to the many-body problem we can drive the system towards weaker fermion pairing. These results are potentially relevant to superconductivity in solid-state multiband materials, as well as to the current and continuing exploration of unconventional Fermi-gas superfluids near the OFR.

We investigate the early-time dynamics of a quasi-two-dimensional spin-1 antiferromagnetic Bose-Einstein condensate after a sudden quench from the easy-plane to the easy-axis polar phase. The postquench dynamics shows a crossover behavior as the quench strength $\tilde{q}$ is increased, where $\tilde{q}$ is defined as the ratio of the initial excitation energy per particle to the characteristic spin interaction energy. For a weak quench of $\tilde{q}<1$, long-wavelength spin excitations are dominantly generated, leading to the formation of irregular spin domains. With increasing $\tilde{q}$, the length scale of the initial spin excitations decreases, and we demonstrate that the long-wavelength instability is strongly suppressed for high $\tilde{q}>2$. The observed crossover behavior is found to be consistent with the Bogoliubov description of the dynamic instability of the initial spinor condensate.

We unravel the periodically driven dynamics of two repulsively interacting bosonic impurities within a bosonic bath upon considering either the impact of a finite pulse or continuous shaking of the impurities harmonic trap. Following a pulse driving of initially miscible components, we reveal a variety of dynamical response regimes depending on the driving frequency. At resonant drivings, the impurities decouple from their host, while if exposed to a high-frequency driving, they remain trapped in the bosonic gas. For continuous shaking, we showcase that in the resonantly driven regime the impurities oscillate back and forth within and outside the bosonic medium. In all cases, the bosonic bath is perturbed performing a collective dipole motion. Referring to an immiscible initial state, we unveil that for moderate driving frequencies the impurities feature a dispersive behavior while for a high-frequency driving they oscillate around the edges of the Thomas-Fermi background. Energy transfer processes from the impurities to their environment are encountered, especially for large driving frequencies. Additionally, coherence losses develop in the course of the evolution with the impurities predominantly moving as a pair.

We investigate the properties of Lindblad equations on $d$-dimensional lattices supporting a unique steady-state configuration. We consider the case of a time evolution weakly symmetric under the action of a finite group $G$, which is also a symmetry group for the lattice structure. We show that in such case the steady state belongs to a relevant subspace, and provide an explicit algorithm for constructing an orthonormal basis of such set. As explicitly shown for a spin-1/2 system, the dimension of such subspace is extremely smaller than the dimension of the set of square operators. As a consequence, by projecting the dynamics within such set, the steady-state configuration can be determined with a considerably reduced amount of resources. We demonstrate the validity of our theoretical results by determining the exact structure of the steady-state configuration of the two-dimensional $XYZ$ model in the presence of uniform dissipation, with and without magnetic fields, up to a number of sites equal to 12. Although in this work we consider explicitly only spin-1/2 systems, our approach can be exploited in the characterization of arbitrary spin systems and fermion and boson systems (with truncated Fock space), as well as many-particle systems with degrees of freedom having different statistical properties.

We consider the quantum implementations of two classical iterative solvers for a system of linear equations, including the row (Kaczmarz) method which utilizes a row of the coefficient matrix in each iteration step, and the column (coordinate descent) method which uses a column instead. These two methods are widely applied in big data science due to their simple iteration schemes. We propose fast quantum algorithms for these two approaches by constructing efficient unitary operators in each iteration step based on the block-encoding technique. The construction is based on the unitaries to prepare the quantum states of rows or columns of the coefficient matrix. If the quantum states are efficiently prepared, for example, by qRAM, then the quantum iterative methods achieve an exponential speedup in the problem size $n$ over the classical versions. Meanwhile the dependence on the number of steps is linear, which is the same as the classical counterparts. The complexity of the quantum iterative linear solvers is $O({\kappa }_s^2(logn)\left(log\frac{1}{\epsilon }\right))$, where ${\kappa }_s$ is the scaled condition number, and $\epsilon$ is the error. The quantum iterative linear solvers do not depend on Hamiltonian simulations and quantum phase estimation, and also work for the dense case.

It has been recently shown that an interferometric measurement may allow for subwavelength resolution of incoherent light. Whereas this holds for noiseless detectors, one could expect that the resolution is in practice limited by the signal-to-noise ratio. Here I present a qualitative assessment of the ultimate resolution limits that can be achieved using noisy detectors. My analysis indeed indicates that the signal-to-noise ratio represents a fundamental limit to quantum imaging, and the reduced resolution scales with the square root of the signal-to-noise ratio. For example, a signal-to-ratio of $20\mathrm{dB}$ is needed to resolve one order of magnitude below the wavelength.

Quantum steering describes a phenomenon whereby one system can immediately influence another via local measurements. It can be detected by violating the powerful and useful steering criterion based on a general entropic uncertainty relation. This criterion can be straightforwardly evaluated by using probability distributions from a finite set of measurements. Herein, we experimentally verify the steering criterion by means of the two-photon Werner-like states and three Pauli measurements. The results indicate that quantum steering can be captured by the criterion in a convenient way. In particular, there is no need to perform the usual quantum state tomography in the experiment, which greatly reduces experimental resources. Moreover, we demonstrate that the criterion is stronger than the linear one for detecting quantum steering of the Werner-like states.

Using numerical solutions of the time-dependent Schrödinger equation we show that in oriented molecules one can control the polarization of molecular high-order harmonic generation (MHOHG) by intense linearly polarized pulses. For oriented triangular molecules, ${\mathrm{H}}_3{}^{+}/{\mathrm{H}}_3{}^{2+}$, one obtains even-order harmonics perpendicular to the laser polarization, whereas all odd-order harmonics have the same polarization as the laser polarization. For ${\mathrm{H}}_2{}^{+}/{\mathrm{H}}_2$ we show that only odd-order harmonics are generated for any orientation and their polarization is nearly parallel to the molecular axis. We describe these phenomena based on perturbation theory. Redshifts of the MHOHG spectra occur due to laser induced electron localization in non-Born-Oppenheimer dissociating molecules, reflecting the effect of nuclear dynamics. The numerical results illustrate the sensitivity of harmonic polarization to molecular geometry and nuclear dynamics.

We study the driven critical dynamics of the quantum link model, whose Hamiltonian describes the one-dimensional U(1) lattice gauge theory. We find that combined topological defects emerge after the quench and they consist of both gauge field and matter field excitations. Furthermore, the ratio of gauge field and matter field excitation is $1/2$ due to the constraint of the Gauss' law. We show that the scaling of these combined topological defects satisfies the usual Kibble-Zurek mechanism. We also verify that both the electric flux and the entanglement entropy satisfy the finite-time scaling theory in the whole driven process. Possible experimental realizations are discussed.