We investigate the transition from the many-body localized phase to the ergodic thermalized phase at an infinite temperature in an $XY$ spin chain with $L$ spins, which experiences power-law decaying interactions in the form of $V_{ij}\propto 1/{\left|i-j\right|}^{\alpha }$ ($i,j=1,...,L$) and a random transverse field. By performing large-scale exact diagonalization for the chain size up to $L=18$, we systematically analyze the energy gap statistics, the half-chain entanglement entropy, and the uncertainty of the entanglement entropy of the system at different interaction exponents $\alpha$. The finite-size critical scaling allows us to determine the critical disorder strength $W_c$ and the critical exponent $\nu$ at the many-body-localization phase transition, as a function of the interaction exponent $\alpha$ in the limit $L\to \infty$. We find that both $W_c$ and $\nu$ diverge when $\alpha$ decreases to a critical power of ${\alpha }_c\simeq 1.16\pm 0.17$, indicating the absence of many-body localization for $\alpha <{\alpha }_c$. Our result differs from the analytical prediction of ${\alpha }_c=3/2$ found in a previous work based on a scaling argument [A. L. Burin, Phys. Rev. B 92, 104428 (2015)], but is close to the recent numerical result ${\alpha }_c\approx 1$ obtained from quantum dynamics simulation [A. Safavi-Naini, M. L. Wall, O. L. Acevedo, A. M. Rey, and R. M. Nandkishore, Phys. Rev. A 99, 033610 (2019)].

We study numerically a one-dimensional mixture of spin-$\frac{1}{2}$ fermions and scalar bosons in the hard-core limit. Considering repulsive fermion-fermion and boson-fermion interactions, we find superfluid and insulator states, and determine the boundaries between them calculating several phase diagrams. We determine that, given a fermionic density ${\rho }_F$, the insulator states are located at the bosonic densities ${\rho }_B=1-{\rho }_F$ and $1-\frac{1}{2}{\rho }_F$, and emerge even in the absence of fermion-fermion coupling. In addition, the boson-fermion repulsion drives quantum phase transitions inside the insulator lobes with ${\rho }_B=1/2$. Our predictions could be observed in current cold-atom experimental platforms.

The quantum dynamics of population-balanced fractional vortices and population-imbalanced vortices in an effective two-state bosonic system, made of two coupled discrete circuits with few sites, is addressed within the Bose-Hubbard model. We show that, for low on-site interaction, the tunneling of quantized vortices between the rings performs a coherent, oscillating dynamics connecting current states with chiral symmetry. The vortex-flux transfer dually follows the usual sinusoidal particle current of the Josephson effect, in good agreement with a mean-field approximation. Within such a regime, the switch of persistent currents in the rings resembles flux-qubit features and is feasible for experimental realization. On the contrary, strong interatomic interactions suppress the chiral current and lead the system into fragmented condensation.

Trapped matter-wave interferometers (TMIs) present a platform for precision sensing within a compact apparatus, extending coherence time by repeated traversal of a confining potential. However, imperfections in this potential can introduce unwanted systematic effects, particularly when combined with errors in the associated beam-splitter operations. This can affect both the interferometer phase and visibility, and can make the performance more sensitive to other experimental imperfections. I examine the character and degree of these systematic effects, in particular within the context of two-dimensional TMIs applicable for rotation sensing. I show that current experimental control can enable these interferometers to operate in a regime robust against experimental imperfections.

We consider the ground states of binary atomic boson-boson and fermion-fermion mixtures confined in one-dimensional box potentials by simulating the systems using few-body models with $\delta$-function interactions and many-body models with density-density interactions. For boson-boson mixtures with strong interspecies repulsion, both models show sandwiched structures in the presence of mass imbalance but not in the equal-mass case. The structural difference between equal-mass and mass-imbalanced systems is due to the minimization of the interaction energy and the kinetic energies from the density distortion at the hard walls and at the phase-separation interface. The mass imbalance adjusts the kinetic energies and causes the lighter species to avoid the hard walls. For fermion-fermion mixtures, few-body simulations show mass-imbalance-induced structural changes in the strong-repulsion regime, while many-body simulations show two-chunk phase separation due to the strong bulk kinetic energy. For equal-mass mixtures with strong interspecies repulsion, the few-body and many-body models predict different structures because of the different treatments of kinetic and interaction energies.

We investigate experimentally and theoretically the lasing behavior of dielectric microcavity lasers with chaotic ray dynamics. Experiments show multimode lasing for both $\mathsf{D}$-shaped and stadium-shaped wave-chaotic cavities. Theoretical calculations also find multimode lasing for different shapes, sizes, and refractive indices. While there are quantitative differences between the theoretical lasing spectra of the stadium and $\mathsf{D}$-cavity, due to the presence of scarred modes with anomalously high-quality factors, these differences decrease as the system size increases, and are also substantially reduced when the effects of surface roughness are taken into account. Lasing spectra calculations are based on steady-state ab initio laser theory, and indicate that gain competition is not sufficient to result in single-mode lasing in these systems.

We address the statistics of a simultaneous continuous weak linear measurement of two noncommuting variables on a few-state quantum system subject to a postselected evolution. The results of both postselected quantum measurement and simultaneous monitoring of two noncommuting variables differ drastically from the results of either classical or quantum projective measurement. We explore the peculiarities arising from the combination of the two. We concentrate on the distribution function of two measurement outcomes integrated over a time interval. We formulate a proper formalism for the evaluation of such distribution, and further compute and discuss the resulting statistics for idealized and experimentally relevant setups. We demonstrate the visibility and manifestations of the interference between initial and final states in the statistics of measurement outcomes for both variables in various regimes. We analytically predict the peculiarities at the circle ${\mathcal{O}}_1^2+{\mathcal{O}}_2^2=1$ in the distribution of measurement outcomes ${\mathcal{O}}_{1,2}$ in the limit of short measurement times and confirm this by numerical calculation at longer measurement times. We demonstrate analytically the anomalously large values of the time-integrated output cumulants in the limit of short measurement times and zero overlap between initial and final states, and give the detailed distributions for this case. We term this situation sudden jump. We present the numerical evaluation of the probability distributions for experimentally relevant parameters in several regimes and demonstrate that interference effects in the postselected measurement can be accurately predicted even if they are small.

Achieving high-fidelity control of quantum systems is essential for realization of a practical quantum computer. Composite pulse sequences which suppress different types of errors can be nested to suppress a wide variety of errors but the result is often not optimal, especially in the presence of constraints such as bandwidth limitations. Robust smooth pulse shaping provides flexibility but obtaining such analytical pulse shapes is a nontrivial problem and choosing the appropriate parameters typically requires a numerical search in a high-dimensional space. In this work, we extend a previous analytical treatment of robust smooth pulses to allow the determination of pulse parameters without numerical search. We also show that the problem can be reduced to a set of coupled ordinary differential equations which allows for a more streamlined numerical treatment.

We report a measurement of the radium ion's $7p{}^{2}P_{3/2}$ state branching fractions and improved theoretical calculations. With a single laser-cooled ${}^{226}{\mathrm{Ra}}^{+}$ ion we measure the $P_{3/2}$ branching fractions to the $7s{}^{2}S_{1/2}$ ground state $0.87678\left(20\right)$, the $6d{}^{2}D_{5/2}$ state $0.10759\left(10\right)$, and the $6d{}^{2}D_{3/2}$ state $0.01563\left(21\right)$.

We study the atom-exchange reaction involving Feshbach molecules in the overlapping Feshbach resonance at about 106.8 G in the ${}^{23}\mathrm{Na}{}^{40}\mathrm{K}$ system. We measure the reaction-rate coefficients as a function of the magnetic field in the exothermic regime. The measured reaction-rate coefficients in the current work and the reaction-rate coefficients measured in the previous work [Phys. Rev. A 100, 032706 (2019)] in the vicinity of the overlapping Feshbach resonance at a magnetic field of about 130 G can be quantitatively explained by a universal model using the three-body parameter. Our results indicate that the universality might exist in the atom-exchange reaction involving Feshbach molecules.

Strong-field ionization provides unique means to address complex dynamics of an electron in competing Coulomb and laser fields. A recent streak camera experiment [M. Kübel et al., Phys. Rev. Lett. 119, 183201 (2017).] analyzed asymmetries in the low-energy region of ejected electron momentum distributions and associated them with multiple rescattering of the electron on the parent ion. In this work we directly confirm the multiple-rescattering nature of the asymmetry in the low-energy region. Such electron-ion collisions cannot be described within one-dimensional simulations even taking into account focal-volume averaging. Using a time-dependent Schrödinger equation simulation in two dimensions supplemented by insights from the strong-field semiclassical approximation we identify the dominant interference features of the complex photoelectron momentum distributions and find their traces in the experiment. In particular, the holographic structures remain visible in experimental results averaged over the carrier-envelope phase (CEP). In the case of individual momentum distributions when the CEP or delay between the two pulses is varied, the structures arising due to rescattering events are influenced by interfering electrons ionized at the main peaks of the electric field. With an increase of experimental resolution, such structures record the electron dynamics on a sub-laser-cycle timescale.

We measure the photoelectron energy spectra from strong-field ionization of Kr in a two-color laser pulse consisting of a strong 400-nm field and a weak 800-nm field. The intensities of the main above-threshold ionization (ATI) and sideband peaks in the photoelectron energy spectra oscillate roughly oppositely with respect to the relative phase between the two-color components. We study the photoelectron interferometry in the strong-field ATI regime from the view of interference of different electron trajectories in order to extend reconstruction of attosecond harmonic beating by interference of two-photon transitions (RABBITT)-type analysis to the strong-field regime. Based on the strong-field approximation model, we obtain analytical expressions for the oscillations of both ATI and sideband peaks with the relative phase. A phase shift of $\pi /4$ with respect to the field maximum of the two-color laser pulse is revealed for the interference maximum in the main ATI peak without including the effect of the atomic potential.

A hollow spherical bubble containing thousands of spin-aligned triplet positronium (Ps) atoms in superfluid liquid ${}^4\mathrm{He}$ would be stable against breakup into smaller bubbles, and the Ps would form a Bose-Einstein condensate (BEC) with a number density of $\sim {10}^{20}{\mathrm{cm}}^{-3}$ and a BEC critical temperature $T_c\approx 300$ K. Estimates suggest that one could make such bubbles in the laboratory containing ${10}^5$ Ps atoms using presently known methods.

We demonstrate the emergence of the non-Abelian geometric potentials and thus the three-dimensional (3D) spin-orbit coupling (SOC) for ultracold atoms without using the laser beams. This is achieved by subjecting an atom to a periodic perturbation which is the product of a position-dependent Hermitian operator $\widehat{V}\left(\mathbf{r}\right)$ and a fast oscillating periodic function $f\left(\omega t\right)$ with a zero average. To have a significant spin-orbit coupling, we analyze a situation where the characteristic energy of the periodic driving is not necessarily small compared to the driving energy $\hslash \omega$. Applying a unitary transformation to eliminate the original periodic perturbation, we arrive at a non-Abelian (noncommuting) vector potential term describing the 3D SOC. The general formalism is illustrated by analyzing the motion of an atom in a spatially inhomogeneous magnetic field oscillating in time. A cylindrically symmetric magnetic field provides the SOC involving the coupling between the spin $\mathbf{F}$ and all three components of the orbital angular momentum (OAM) $\mathbf{L}$. In particular, the spherically symmetric monopole-type synthetic magnetic field $\mathbf{B}\propto \mathbf{r}$ generates the 3D SOC of the $\mathbf{L}·\mathbf{F}$ form, which resembles the fine-structure interaction of hydrogen atom. However, the strength of the SOC here goes as $1/r^2$ for larger distances, instead of $1/r^3$ as in atomic fine structure. Such a longer-ranged SOC significantly affects not only the lower states of the trapped atom, but also the higher ones. Furthermore, by properly tailoring the external trapping potential, the ground state of the system can occur at finite OAM, while the ground state of hydrogen atom has zero OAM.

We investigate the stability of nonequilibrium steady states of Bose-Einstein condensates with a local one-body loss in the presence of double potential barriers. We construct an exactly solvable mean-field model, in which the local loss and the potential barriers take the form of a delta function. Using the exact solutions of our model, we show that there are parameter regions in which two steady-state solutions are dynamically stable, i.e., the model exhibits bistability. We also find that unidirectional hysteresis phenomena appear when the local-loss rate is varied in some parameter region.

We study the phase separation in three-component bright vector solitons in a quasi-one-dimensional spin-orbit-coupled hyperfine spin $F=1$ ferromagnetic Bose-Einstein condensate upon an increase of the strength of spin-orbit (SO) coupling $p_x{\mathrm{\Sigma }}_z$ above a critical value, where $p_x$ is the linear momentum and ${\mathrm{\Sigma }}_z$ is the $z$ component of the spin-1 matrix. The bright vector solitons are demonstrated to be mobile and dynamically stable. The collision between two such vector solitons is found to be elastic at all velocities with the conservation of density of each vector soliton. The two colliding vector solitons repel at small separation and at very small colliding velocity, they come close and bounce back with the same velocity without ever encountering each other. This repulsion produced by SO coupling is responsible for the phase separation in a vector soliton for large strengths of SO coupling. The collision dynamics is found to be completely insensitive to the relative phase of the colliding solitons. However, in the absence of SO coupling, at very small velocity, the two colliding vector solitons attract each other and form a vector soliton molecule and the collision dynamics is sensitive to the relative phase as in scalar solitons. The present investigation is carried out through a numerical solution and an analytic variational approximation of the underlying mean-field Gross-Pitaevskii equation.

We present two alternative complete sets of static modes of a homogeneous dielectric sphere, for their use in the resonant-state expansion (RSE), a rigorous perturbative method in electrodynamics. Physically, these modes are needed to correctly describe the static electric field of a charge redistribution within the optical system due to a perturbation of the permittivity. We demonstrate the convergence of the RSE toward the exact result for a perturbation describing a size reduction of the basis sphere. We then revisit the quarter-sphere perturbation treated by Doost et al. [Phys. Rev. A 90, 013834 (2014)], where only a single static mode for each angular momentum was introduced, and show that using a complete set of static modes leads to a small though non-negligible correction of the RSE result, improving the agreement with finite-element simulations. As another example of applying the RSE with a complete set of static modes, we calculate the resonant states of a dielectric cylinder, also comparing the result with a finite-element simulation.

We predict a resonant enhancement of the nonlinear optical response of an interacting Rydberg gas under conditions of electromagnetically induced transparency. The enhancement originates from a two-photon process which resonantly couples electronic states of a pair of atoms dressed by a strong control field. We calculate the optical response for the three-level system by explicitly including the dynamics of the intermediate state. We find an analytical expression for the third-order susceptibility for a weak classical probe field. The nonlinear absorption displays the strongest resonant behavior on two-photon resonance where the detuning of the probe field equals the Rabi frequency of the control field. The nonlinear dispersion of the medium exhibits various spatial shapes depending on the interaction strength. Based on the developed model, we propose a realistic experimental scenario to observe the resonance by performing transmission measurements.

As four-wave-mixing-based photon-pair sources mature, accurate modeling of the photon-pair properties becomes important. Unlike spontaneous parametric down-conversion, four-wave mixing is accompanied by a number of parasitic effects such as nonlinear self- and cross-phase modulation. Currently, most modelings of photon-pair states are analytic in nature, which limits the number and type of effects that can be taken into account. In this work, we derive a complete, dual-pump evolution equation for the joint amplitude of photon pairs, wherein any desired effects can be included. We describe how to efficiently obtain numerical solution to this equation using a split-step approach. Lastly, we cover a few analytical solutions and compare two schemes for pure-photon generation under three different parasitic effects. We show how one scheme is highly sensitive to parasitic effects, while the other is very robust.

We propose and demonstrate phonon-number-resolving detection of the multiple local phonon modes in a trapped-ion chain. To mitigate the effect of phonon hopping during the detection process, the probability amplitude of each local phonon mode is mapped to the auxiliary long-lived motional ground states. Sequential state-dependent fluorescence detection is then performed. In the experiment, we have successfully observed the time evolution of two local phonon modes in two ions, including the phonon-number correlation between the two modes.