We calculate the excitation spectrum of a one-dimensional self-bound quantum droplet in a two-component bosonic mixture described by the Gross-Pitaevskii equation (GPE) with cubic and quadratic nonlinearities. The cubic term originates from the mean-field energy of the mixture proportional to the effective coupling constant $\delta g$, whereas the quadratic nonlinearity corresponds to the attractive beyond-mean-field contribution. The droplet properties are governed by a control parameter $\gamma \propto \delta g{N}^{2/3}$, where $N$ is the particle number. For large $\gamma >0$, the droplet features the flat-top shape with the discrete part of its spectrum consisting of plane-wave Bogoliubov phonons propagating through the flat-density bulk and reflected by edges of the droplet. With decreasing $\gamma$, these modes cross into the continuum, sequentially crossing the particle-emission threshold at specific critical values. A notable exception is the breathing mode, which we find to be always bound. The balance point $\gamma =0$ provides implementation of a system governed by the GPE with an unusual quadratic nonlinearity. This case is characterized by the ratio of the breathing-mode frequency to the particle-emission threshold equal to 0.8904. As $\gamma$ tends to $-\infty$, this ratio tends to 1 and the droplet transforms into the soliton solution of the integrable cubic GPE.

Established techniques for deterministically creating dark solitons in repulsively interacting atomic Bose-Einstein condensates (BECs) can only access a narrow range of soliton velocities. Because velocity affects the stability of individual solitons and the properties of soliton-soliton interactions, this technical limitation has hindered experimental progress. Here we create dark solitons in highly anisotropic cigar-shaped BECs with arbitrary position and velocity by simultaneously engineering the amplitude and phase of the condensate wave function, improving upon previous techniques which explicitly manipulated only the condensate phase. The single dark soliton solution present in true one-dimensional (1D) systems corresponds to the kink soliton in anisotropic three-dimensional systems and is joined by a host of additional dark solitons, including vortex ring and solitonic vortex solutions. We readily create dark solitons with speeds from zero to half the sound speed. The observed soliton oscillation frequency suggests that we imprinted solitonic vortices, which for our cigar-shaped system are the only stable solitons expected for these velocities. Our numerical simulations of 1D BECs show this technique to be equally effective for creating kink solitons when they are stable. We demonstrate the utility of this technique by deterministically colliding dark solitons with domain walls in two-component spinor BECs.

We report an increase of up to 60% on the count rates of the rare ${}^{81}\mathrm{Kr}$ and ${}^{85}\mathrm{Kr}$ isotopes in the Atom Trap Trace Analysis method by enhancing the production of metastable atoms in the discharge source. Additional atoms in the metastable $1s_5$ level (Paschen notation) are obtained via optically pumping the $1s_4–2p_6$ transition at 819 nm. By solving the master equation for the system, we identify this transition to be the most suitable one and can describe the measured increase in metastable population as a function of the 819-nm laser power. We calculate the previously unknown isotope shifts and hyperfine splittings of the $1s_4–2p_6$ transition in ${}^{81}\mathrm{Kr}$ and ${}^{85}\mathrm{Kr}$, and verify the results with count rate measurements. The demonstrated count-rate increase enables a corresponding decrease in the required sample sizes for ${}^{81}\mathrm{Kr}$ and ${}^{85}\mathrm{Kr}$ dating, a significant improvement for applications such as dating of ocean water and deep ice cores.

The canonical quantum formalism predicts that the interference pattern registered in multislit experiments should be a simple combination of patterns observed in two-slit experiments. This has been linked to the validity of Born's rule and verified in precise experiments with photons, nuclear spins, nitrogen-vacancy centers in diamond, and large molecules. Due to the expected universal validity of Born's rule, it is instructive to conduct similar tests with yet other physical systems. Here we discuss analogs of triple-slit experiment using atoms allowing tripod energy level configuration, as realizable, e.g., with alkaline-earth-metal-like atoms. We cover all the stages of the setup including various ways of implementing analogs of slit blockers. The precision of the final setup is estimated and offers improvement over the previous experiments.

This paper demonstrates cooling of the center-of-mass motion of 10-$\mu \mathrm{m}$-diameter optically levitated silica spheres to an effective temperature of $50\pm 22\mu \mathrm{K}$, achieved by minimizing the technical pointing noise of the trapping laser. This low noise leads to an acceleration and force sensitivity of $95\pm 41 \mathrm{n}g/\sqrt{\mathrm{Hz}}(g=9.8$ m/${\mathrm{s}}^2$) and $0.95\pm 0.11 \mathrm{aN}/\sqrt{\mathrm{Hz}}$, respectively, at frequencies near 50 Hz. This force sensitivity is comparable to that demonstrated for optically levitated nanospheres that are ${10}^4$ times less massive, corresponding to an acceleration sensitivity that is several orders of magnitude better. It is further shown that under these conditions the spheres remain stably trapped at pressures of $\sim {10}^{-7}$ mbar with no active cooling for periods longer than a day. Feedback cooling is still necessary in the moderate-pressure regime, motivating a comprehensive study of the loss mechanisms of the microspheres and providing better understanding of the requirements for feedback-free optical trapping in vacuum. This work can enable high-sensitivity searches for accelerations and forces acting on micron-sized masses, including those that could be produced by new physics beyond the standard model.

The electron-electron interaction correction of first order in $1/Z$ to the one-electron part of the nuclear recoil effect on binding energies in atoms and ions is considered within the framework of the rigorous quantum electrodynamics (QED) approach. The calculations to all orders in $\alpha Z$ are performed for the $1s^2$ state in heliumlike ions and the $1s^{2}2s$ and $1s^{2}2p_{1/2}$ states in lithiumlike ions in the range $Z=5–100$. The results obtained are compared with the Breit-approximation values. The performed calculations complete a systematic treatment of the QED nuclear recoil effect up to the first order in $1/Z$. The correction obtained is combined with the previously studied two-electron part as well as the higher-order electron-correlation corrections evaluated within the Breit approximation to get the total theoretical predictions for the mass shifts.

An array of 16 laser-pumped scalar Cs magnetometers was part of the neutron electric dipole moment (nEDM) experiment taking data at the Paul Scherrer Institute in 2015 and 2016. It was deployed to measure the gradients of the experiment's magnetic field and to monitor their temporal evolution. The originality of the array lies in its compact design, in which a single near-infrared diode laser drives all magnetometers that are located in a high-vacuum chamber, with a selection of the sensors mounted on a high-voltage electrode. We describe details of the Cs sensors' construction and modes of operation, emphasizing the accuracy and sensitivity of the magnetic-field readout. We present two applications of the magnetometer array directly beneficial to the nEDM experiment: (i) the implementation of a strategy to correct for the drift of the vertical magnetic-field gradient and (ii) a procedure to homogenize the magnetic field. The first reduces the uncertainty of the nEDM result. The second enables transverse neutron spin relaxation times exceeding 1500 s, improving the statistical sensitivity of the nEDM experiment by about 35% and effectively increasing the rate of nEDM data taking by a factor of 1.8.

We develop a model to describe the motional (i.e., external degree of freedom) energy spectra of atoms trapped in a one-dimensional optical lattice, taking into account both axial and radial confinement relative to the lattice axis. Our model respects the coupling between axial and radial degrees of freedom, as well as other anharmonicities inherent in the confining potential. We further demonstrate how our model can be used to characterize lattice light shifts in optical lattice clocks, including shifts due to higher-multipolar (magnetic dipole and electric quadrupole) and higher-order (hyperpolarizability) coupling to the lattice field. We compare results for our model with results from other lattice light shift models in the literature under similar conditions.

Recently it was shown that continuous matrix product states (cMPS) cannot express the continuum limit state of any matrix product state (MPS), according to a certain natural definition of the this last state. The missing element is a projector in the transfer matrix of the MPS. Here we provide a generalized ansatz of cMPS that is capable of expressing the continuum limit of any MPS. It consists of a sum of cMPS with different boundary conditions, each attached to an ancilla state. This ansatz can be interpreted as the concatenation of a state which is at the closure of the set of cMPS together with a standard cMPS. The first can be seen as a cMPS in the thermodynamic limit, or with matrices of unbounded norm. We provide several examples and discuss the result.

Here we present an expanded analysis of a model for the manipulation and control of observables in a strongly correlated, many-body system, which was first presented by McCaul et al. [G. McCaul et al., Phys. Rev. Lett. 124, 183201 (2020)]. A field-free, nonlinear equation of motion for controlling the expectation value of an essentially arbitrary observable is derived, together with rigorous constraints that determine the limits of controllability. We show that these constraints arise from the physically reasonable assumptions that the system will undergo unitary time evolution, and has enough degrees of freedom for the electrons to be mobile. Furthermore, we give examples of multiple solutions to generating target observable trajectories when the constraints are violated. Ehrenfest theorems are used to further refine the model and provide a check on the validity of numerical simulations. Finally, the experimental feasibility of implementing the control fields generated by this model is discussed.

The dominant error sources for state-of-the-art laser-free trapped-ion entangling gates are decoherence of the qubit state and the ion motion. The effect of these decoherence mechanisms can be suppressed with additional control fields or with techniques that have the disadvantage of reducing gate speed. Here, we propose using a near-motional-frequency magnetic field gradient to implement a laser-free gate that is simultaneously resilient to both types of decoherence, does not require additional control fields, and has a relatively small cost in gate speed.

Josephson-junction based parametric amplifiers have become a ubiquitous component in superconducting quantum machines. Although parametric amplifiers regularly achieve near-quantum limited performance, they have many limitations, including low saturation powers, lack of directionality, and narrow bandwidth. The first is believed to stem from the higher order Hamiltonian terms endemic to Josephson junction circuits, and the latter two are direct consequences of the nature of the parametric interactions which power them. In this work, we attack both of these issues. First, we have designed a new, linearly shunted Josephson ring modulator (JRM), which nearly nullifies all fourth-order terms at a single flux bias point. Next, we achieve gain through a pair of balanced parametric drives. When applied separately, these drives produce phase-preserving gain (G) and gainless photon conversion (C); when applied together, the resultant amplifier (which we term GC) is a bidirectional, phase-sensitive, transmission-only amplifier with a large, gain-independent bandwidth. Finally, we have demonstrated the practical utility of the GC amplifier, as well as its quantum efficiency, by using it to read out a superconducting transmon qubit.

Studying dynamics is one of the most challenging areas of quantum many-body physics. In recent years, an attractive platform based on Rydberg atoms has been used to probe it since tunable interactions between Rydberg atoms enable a system to form interesting Hamiltonians. However, the observed dynamics generally differs from a desired Hamiltonian because an experimental system has various physical limitations and technical imperfections. In this work, to explain discrepancies from an ideal situation we modify the pure Hamiltonian to dissipative model including known imperfections, and the numerical model is compared with experimentally observed dynamics. As the experimental system, we use arrays with up to six atoms that are confined in one and two dimensions and coupled to $nD$-Rydberg states. By comparing results of the numerical simulation with observed dynamics, we analyze the contributions of individual imperfections to the obtained dynamics. Such analysis provides useful information for improving an experimental simulator and is an essential step for scaling up the number of atoms.

Small, out-of-equilibrium, and quantum systems defy simple thermodynamic expressions. Such systems are exemplified by molecular switches, which exchange heat with a bath. These molecules can photoisomerize, or change conformation, or switch, on absorbing light. The photoisomerization probability depends on kinetic details that couple the molecule's energetics to its dissipation. Therefore, a simple, general, thermodynamic-style bound on the photoisomerization probability seems out of reach. We derive such a bound using a resource theory. The resource-theory framework is a set of mathematical tools, developed in quantum information theory, used to generalize thermodynamics to small and quantum settings. From this toolkit has been derived a generalization of the second law, the thermomajorization preorder. We use thermomajorization to upper-bound the photoisomerization probability. Then, we compare the bound with an equilibrium prediction and with a Lindbladian model. We identify a realistic parameter regime in which the Lindbladian evolution saturates the thermomajorization bound. We also quantify the energy coherence in the electronic degree of freedom, and we argue that this coherence cannot promote photoisomerization. This work illustrates how quantum-information-theoretic thermodynamics can elucidate complex quantum processes in nature, experiments, and synthetics.

We analyze the Hamiltonian of a charged particle in a strong external infrared laser pulse including nondipole effects to first order in $1/c$. We consider the corresponding classical equations of motions in the high-intensity, long-wavelength limit and identify for linearly polarized fields an accurate nondipole strong-field-approximation Hamiltonian. This Hamiltonian is expressed in a mixed gauge with separate light-matter interaction terms depending either on coordinate or momentum operators. It can be transformed into a nondipole velocity gauge and nondipole length gauge version. The associated beyond dipole Volkov states are given. Implications for laser-assisted scattering, strong-field ionization, laser-assisted photoeletric effect, and attosecond streaking are outlined.

We report a continuum of pulselike soliton solutions to the generalized nonlinear Schrödinger equation with both quadratic and quartic dispersion and a Kerr nonlinearity. We show that the well-known nonlinear Schrödinger solitons, which occur in the presence of only negative (anomalous) quadratic dispersion, and pure-quartic solitons, which occur in the presence of only negative quartic dispersion, are members of a large superfamily, encompassing both. The members of this family, none of which are unstable, have exponentially decaying tails, which can exhibit oscillations. We find analytic solutions for positive quadratic dispersion and negative quartic dispersion and investigate the soliton dynamics. We also find evidence that a combination of the quadratic and quartic dispersion, rather than exclusively quadratic or quartic dispersion, is likely to improve the performance of soliton lasers.

In this article we investigate the connection between the chirality of interacting vortices and the appearance of radial structures in nonlinear wave mixing. Depending on the signs of their topological charges, the nonlinear mixing of optical vortices may produce a radial-angular coupling that generates a finite superposition of pure Laguerre-Gaussian modes carrying the resultant topological charge and a finite spectrum of radial orders. These radial modes evolve with different Gouy phases that determine the transformation from a hollow intensity distribution in the near field to a finite ring structure in the far field pattern. In this sense, we interpret the appearance of radial modes in nonlinear wave mixing as a diffraction of the up-converted beam through the effective amplitude-phase mask created by the pump beams. This interpretation is supported by comparison between the images produced by the nonlinear process and purely diffractive measurements with a spatial light modulator that mimics the amplitude-phase modulation produced in nonlinear wave mixing.

We show that recent high-precision measurements of relative on-site interaction energies $\mathrm{\Delta }U$ in a Mott insulator require a theoretical description beyond the standard Hubbard-model interpretation, when combined with an accurate coupled-channels calculation. In contrast to more sophisticated lattice models, which can be elaborate especially for parameter optimization searches, we introduce an easy to use effective description of $U$ valid over a wide range of interaction strengths modeling atomic pairs confined to single lattice sites. This concise model allows for a straightforward combination with a coupled-channels analysis. With this model we perform such a coupled-channels analysis of high-precision ${}^7\mathrm{Li}$ spectroscopic data on the on-site interaction energy $U$, which spans over four Feshbach resonances and provide an accurate and consistent determination of the associated resonance positions. Earlier experiments on three of the Feshbach resonances are consistent with this analysis. Moreover, we verify our model with a more rigorous numerical treatment of the two atom system in an optical lattice.

We theoretically define a complete class of partially coherent vortex beams of any radial and azimuthal order and characterize the behavior of their phase singularities and orbital angular momentum. These beams are shown to exhibit a coherence vortex supplement to the van Cittert–Zernike theorem, in which the vortex structure of the random beam reconstitutes upon propagation. This full characterization of a class of partially coherent Laguerre-Gauss beams of any order may find application in free-space optical communication, among other uses.

We investigate the subradiance properties of $n\ge 2$ multilevel fermionic atoms loaded into the lowest motional level of a single trap (e.g., a single optical lattice site or an optical tweezer). As pointed out in our previous work [A. Piñeiro Orioli and A. M. Rey, Phys. Rev. Lett. 123, 223601 (2019)], perfectly dark subradiant states emerge from the interplay between fermionic statistics and dipolar interactions. While previously we focused on the $n=2$ case, here we provide an in-depth analysis of the single-site dark states for generic filling $n$, and show a tight connection between generic dark states and total angular momentum eigenstates. We show how the latter can also be used to understand the full eigenstate structure of the single-site problem, which we analyze numerically. Apart from this, we discuss two possible schemes to coherently prepare dark states using either a Raman transition or an external magnetic field to lift the Zeeman degeneracy. Although the analysis focuses on the single-site problem, we show that multisite dark states can be trivially constructed in any geometry out of product states of single-site dark states. Finally, we discuss some possible implementations with alkaline-earth(-like) atoms such as ${}^{171}\mathrm{Yb}$ or ${}^{87}\mathrm{Sr}$ loaded into optical lattices, where they could be used for potential applications in quantum metrology and quantum information.