We describe and experimentally implement a single-ion local thermometry technique with absolute sensitivity adaptable to all laser-cooled atomic ion species. The technique is based on the velocity-dependent spectral shape of a quasi-dark resonance tailored by two driving fields in a $J\to J$ transition such that the two fields can be derived from the same laser source, leading to a negligible relative phase shift. We validated the method and tested its performance in an experiment on a single ${}^{88}\mathrm{Sr}^{+}$ ion cooled in a surface radio-frequency trap. We first applied the technique to characterize the heating rate of the surface trap. We then measured the stationary temperature of the ion as a function of cooling laser detuning in the Doppler regime. The results agree with theoretical calculations, with an absolute error smaller than 100 $\mu \mathrm{K}$ at 500 $\mu \mathrm{K}$, in a temperature range between 0.5 and 3 mK and in the absence of adjustable parameters. This simple-to-implement and reliable method opens the way to fast absolute measurements of single-ion temperatures in future experiments dealing with heat transport in ion chains or thermodynamics at the single-ion level.

We explore the influence of elliptical polarization on the (non)sequential two-photon double ionization of atomic helium with ultrashort extreme ultraviolet (XUV) light fields using time-dependent full ab initio simulations. The energy and angular distributions of photoelectrons are found to be strongly dependent on the ellipticity. The correlation minimum in the joint angular distribution becomes more prominently visible with increasing ellipticity. In a pump-probe sequence of two subsequent XUV pulses with varying ellipticities, polarization tagging allows us to discriminate between sequential and nonsequential photoionization. This clear separation demonstrates the potential of elliptically polarized XUV fields for improved control of electronic emission processes.

We introduce a type of model of two-component systems in one dimension that can be analyzed by the Bethe-ansatz approach. The interspecies interactions are tunable via Feshbach resonant interactions, and the Yang-Baxter equation for exact solvability is fulfilled by fine-tuning the resonant energies. Although the strict exact solvability beyond the level of two-body scatterings would require extra singular counterterms, the models introduced here can still be well described by the Bethe ansatz for relatively small densities. The resulting systems can be described by introducing intraspecies repulsive and interspecies attractive couplings $c_1$ and $c_2$. This kind of system admits two types of interesting solutions: In the regime with $c_1>c_2$, the ground state is a Fermi sea of two-strings, where the Fermi momentum $Q$ is constrained to be smaller than a certain value $Q^{*}$, and it provides an ideal scenario to realize the BCS-BEC crossover (from weakly attractive atoms to weakly repulsive molecules) in one dimension. In the opposite regime with $c_1<c_2$, the ground state is a single bright soliton even for fermionic atoms, which reveals itself as an embedded string solution.

We study the single-particle properties of a system formed by ultracold atoms loaded into the manifold of $l=1$ orbital angular momentum (OAM) states of an optical lattice with a diamond-chain geometry. Through a series of successive basis rotations, we show that the OAM degree of freedom induces phases in some tunneling amplitudes of the tight-binding model that are equivalent to a net $\pi$ flux through the plaquettes. These effects give rise to a topologically nontrivial band structure and protected edge states which persist everywhere in the parameter space of the model, indicating the absence of a topological transition. By taking advantage of these analytical mappings, we also show that this system constitutes a realization of a square-root topological insulator. In addition, we demonstrate that quantum interferences between the different tunneling processes involved in the dynamics may lead to Aharanov-Bohm caging in the system. All these analytical results are confirmed by exact diagonalization numerical calculations.

We show that bosonic atoms loaded into orbital angular momentum $l=1$ states of a lattice in a diamond-chain geometry provide a flexible and simple platform for exploring a range of topological effects. This system exhibits robust edge states that persist across the gap-closing points, indicating the absence of a topological transition. We discuss how to perform the topological characterization of the model with a generalization of the Zak's phase and we show that this system constitutes a realization of a square-root topological insulator. Furthermore, the relative phases arising naturally in the tunneling amplitudes lead to the appearance of Aharanov-Bohm caging in the lattice. We discuss how these properties can be realized and observed in ongoing experiments.

Recent advances in cooling techniques make possible the experimental study of quantum phase transitions, which are transitions near absolute zero temperature accessed by varying a control parameter. A paradigmatic example is the superfluid-Mott transition of interacting bosons on a periodic lattice. From the relativistic Ginzburg-Landau action of this superfluid-Mott transition we derive the elementary excitations of the bosonic system, which contain in the superfluid phase a gapped Higgs mode and a gapless Goldstone mode. We show that this energy spectrum is in good agreement with the available experimental data and we use it to extract, with the help of dimensional regularization, meaningful analytical formulas for the beyond-mean-field equation of state in two and three spatial dimensions. We find that, while the mean-field equation of state always gives a second-order quantum phase transition, the inclusion of Gaussian quantum fluctuations can induce a first-order quantum phase transition. This prediction is a strong benchmark for future experiments on quantum phase transitions.

A method for mitigating the readout delay characteristic of Bragg-based atom interferometry is presented, utilizing an asymmetric Mach-Zehnder interferometer sequence to generate spatial fringes that are read out while still overlapped. The time of flight after the final beamsplitter is engineered to facilitate constructive overlap of the fringes on the output states. A noise analysis performed using a precision atom interferometer is presented, comparing the traditional separated symmetric scheme with that of the separated and overlapped asymmetric scheme showing no significant increase in short-term phase noise.

Single-particle dynamics of a spin-orbit-coupled Bose-Einstein condensate has recently been investigated in experiments that explore the physics of Landau-Zener tunneling and of the Zitterbewegung. In this paper, we study the influence of a nonlinearity due to interactions on these dynamics and show that the dispersion relation develops interesting loop structures. The atoms can move along the nonlinear dispersion curve in the presence of a weak acceleration force, and we show that the loops lead to straightforward nonlinear Landau-Zener tunneling. However, we find that for the Zitterbewegung, induced by a sudden quench in the spin-orbit-coupling parameters, the nonlinear dispersion is irrelevant.

We theoretically investigate the scattering of multiple Rayleigh nanoparticles in a microspheroid resonator which supports multiple polar whispering gallery modes. Different from a standard microsphere resonator in which polar modes with the same radial and angular mode numbers are degenerate, a spheroid resonator supports spectrally nondegenerate polar modes. The mode splitting, mode shift, and linewidth broadening of polar modes are deduced at the presence of multiple Rayleigh scatterers following the Weisskopf-Wigner semi-QED treatment. It is found that the radial, polar, and azimuthal coordinates of the nanoparticle can be inferred from the transmission spectra of the polar modes. In particular, the changes of both the mode shift and linewidth broadening show cosinoidal dependence on the azimuthal angle. Our scheme provides an efficient platform to locate the three-dimensional positions of multiple nanoparticles in a microcavity, which may push the microcavity sensing to sizing and further quantitative measurements.

Gain saturation is ubiquitous but has not been fully explored in the newly developed field of non-Hermitian optics. On the other hand, the nonclassical properties of light are highly relevant to the gain saturation that influences the quantum noise accompanying light amplification. In this paper, we systematically examine the gain saturation effects in a non-Hermitian system of coupled gain-loss waveguides. We explain the impact of gain saturation on a quantum light field dynamically evolving in the coupled system. In contrast to the ideal situation without gain saturation, one can achieve a quasisteady state under the gain saturation. Moreover, gain saturation reduces the influence of amplification noise and thereby better preserves such quantum features as entanglement. We illustrate the effects of gain saturation by examining the time evolution of the Wigner function, entanglement of the light fields, and the cross-correlation function between the two output modes. Significant differences exist between unsaturated and saturated situations, especially for low photon numbers.

The interplay between the nonclassical features and the parity-time ($\mathcal{PT}$) symmetry (or its breaking) is studied here by considering a $\mathcal{PT}$-symmetric system consisting of two cavities with gain and loss. The conditions for $\mathcal{PT}$ invariance are obtained for this system. The behavior of the average photon number corresponding to the gain and loss modes for different initial states (e.g., vacuum, NOON, coherent, and thermal states) has also been obtained. With the help of the number operators, quantum Zeno and anti-Zeno effects are studied, and the observed behavior is compared in $\mathcal{PT}$-symmetric (PTS) and $\mathcal{PT}$-symmetry-broken (PTSB) regimes. It has been observed that the relative phase of the input coherent fields plays a key role in the occurrence of these effects. Further, some nonclassicality features are witnessed using criteria based on the number operator(s). Specifically, intermodal antibunching, sum, and difference squeezing are investigated for specific input states. It is found that the various nonclassical features, including the observed quantum Zeno and anti-Zeno effects, are suppressed when one goes from the PTS to PTSB regime. In other words, the dominance of the loss or gain rate in the field modes over the coupling strength between them diminishes the nonclassical features of the system.

Although Lindblad developed a general Markovian theory for open-system dynamics while maintaining the positivity of the density matrix, a practical non-Markovian analog remains a significant problem. Here, we present an extension of Lindblad's theory through an ensemble of Lindbladian trajectories originating from different times in the system's history. This approach provides an account of the system's memory while preserving the positivity of the density matrix. We apply the theory to the Jaynes-Cummings model to capture non-Markovian dynamics in the weak and strong coupling regimes.

Among the 118 elements listed in the periodic table, there are nine superheavy elements (Mt, Ds, Mc, Rg, Nh, Fl, Lv, Ts, and Og) that have not yet been well studied experimentally because of their limited half-lives and production rates. How to classify these elements for further study remains an open question. For superheavy elements, although relativistic quantum-mechanical calculations for the single atoms are more accurate and reliable than those for their molecules and crystals, there is no study reported to classify elements solely based on atomic properties. By using cutting-edge machine learning techniques, we find the relationship between atomic data and classification of elements, and further identify that Mt, Ds, Mc, Rg, Lv, Ts, and Og should be metals, while Nh and Fl should be metalloids. These findings not only highlight the significance of machine learning for superheavy atoms but also challenge the conventional belief that one can determine the characteristics of an element only by looking at its position in the table.

In this paper, we study the distinguishability of arbitrary dimensional generalized Bell states under one-way local operations and classical communication (LOCC). We introduce an admissible solutions set and a nonadmissible solutions set for each set of generalized Bell states. Any element that exists in the admissible solution set but not in the nonadmissible one implies the one-way LOCC distinguishablity of a given set. This criterion is very convenient in the following two aspects: both solution sets can be calculated easily and, once the criterion can be applied successfully for a given set, it immediately presents an explicit distinguishing strategy. Furthermore, Fan's results in Phys. Rev. Lett. 92, 177905 (2004) can also be deduced as special cases of our results. For the case no such element exists, we disprove a conjecture proposed by Yang et al. in Quantum Inf. Process. 17, 29 (2018) by presenting a counterexample.

Quantum simulation of fermionic systems is a promising application of quantum computers, but to program them, we need to map fermionic states and operators to qubit states and quantum gates. While quantum processors may be built as two-dimensional qubit networks with couplings between nearest neighbors, standard fermion-to-qubit mappings do not account for that kind of connectivity. In this work we concatenate the (one-dimensional) Jordan-Wigner transform with specific quantum codes defined under the addition of a certain number of auxiliary qubits. This yields a class of mappings with which any fermionic system can be embedded in a two-dimensional qubit setup, fostering scalable quantum simulation. Our technique is demonstrated on the two-dimensional Fermi-Hubbard model, which we transform into a local Hamiltonian. What is more, we adapt the Verstraete-Cirac transform and Bravyi-Kitaev superfast simulation to the square lattice connectivity and compare them to our mappings. An advantage of our approach in this comparison is that it allows us to encode and decode a logical state with a simple unitary quantum circuit.

For multipartite states, we consider a notion of $D$ symmetry. For a system of $N$ qubits, it coincides with the usual permutational symmetry. In the case of $N$ qudits ($d\ge 3$), the $D$ symmetry is stronger than the permutational one. For the space of all $\mathrm{D}$-symmetric vectors in ${\left({\mathbb{C}}^d\right)}^{\otimes N}$, we define a basis composed of vectors $\left\{\right|R_{N,d;k}\rangle :0\le k\le N(d-1)\}$ which are analogs of Dicke states. The aim of this paper is to discuss the problem of separability of $D$-symmetric states which are diagonal in the basis $\left\{\right|R_{N,d;k}\rangle \}$. We show that if $N$ is even and $d\ge 2$ is arbitrary then a positive partial transposition property is a necessary and sufficient condition of separability for $D$-invariant diagonal states. In this way, we generalize results obtained by Yu [Phys. Rev. A 94, 060101(R) (2016)] and Wolfe and Yelin [Phys. Rev. Lett. 112, 140402 (2014)]. Our strategy is to use some classical mathematical results on a moment problem.

The Fano resonance, with a unique asymmetric line shape, is a well-known manifestation of quantum interference with numerous promising applications for light-harvesting devices. Here we report an experimental observation of the Fano effect in an ultracold atom-molecule coupled system realized by photoassociation near a magnetically tunable $d$-wave Feshbach resonance. Our result shows that, compared to ubiquitous single-peak Fano-type line shapes, the coupled Fano resonances feature a two-peak profile. We develop a theory of coupled Fano resonances which agrees very well with the experimental results. This work may open a new perspective for tuning ultracold collisional interaction using the Fano resonance and studying bound states in continuum.

In measurements of relative phases in photoionization processes, the contribution of continuum-continuum (CC) couplings to the atomic (Wigner) phases, corresponding to attosecond time delays, is currently accounted for only by theoretical models. Here, we introduce a measurement scheme that is sensitive to phase differences of CC transitions after photoionization in the presence of an optical field. The method allows us to separate CC transitions from the ionization process and can help in testing existing theoretical models. It is based on a multicolor interferometer, similar to the RABBITT (reconstruction of attosecond beating by interference of two-photon transitions) method. The key idea involves the comparison of two measurements with different orders of CC transitions. The scheme is illustrated by an ab initio calculation on atomic hydrogen.

We examine the effect that the subtraction of multiple photons has on the statistical characteristics of a light field. In particular, we are interested in the question whether an initial state transforms into a lasing state, i.e., a (phase-diffused) coherent state, after infinitely many photon subtractions. This question is discussed in terms of the Glauber P representation $P\left(\alpha \right)$, the photon number distribution $P\left[n\right]$, and the experimentally relevant autocorrelation functions $g^{\left(m\right)}$. We show that a thermal state does not converge to a lasing state, although all of its autocorrelation functions at zero delay time converge to one. This contradiction is resolved by the analysis of the involved limits, and a general criterion for an initial state to reach at least such a pseudo-lasing state ($g^{\left(m\right)}\to 1$) is derived, revealing that they can be generated from a large class of initial states.