Dipolar Bose-Einstein condensates are excellent platforms for studying supersolidity, characterized by coexisting density modulation and superfluidity. The realization of dipolar mixtures opens intriguing new scenarios, most remarkably the possibility of realizing a double supersolid, composed of two interacting superfluids. We analyze the complex excitation spectrum of a miscible trapped dipolar Bose mixture, showing that it provides key insights about the double-supersolid regime. We show that this regime may be readily probed experimentally by monitoring the appearance of a doublet of superfluid compressional modes, linked to the different superfluid character of each component. Additionally, the dipolar supersolid mixture exhibits a nontrivial spin nature of the dipolar rotons, the Higgs excitation, and the low-lying Goldstone modes. Interestingly, the analysis of the lowest-lying modes allows for monitoring the transition of just one of the components into the incoherent-droplet regime, whereas the other remains coherent, highlighting their disparate superfluid properties.

The Hubbard model is a paradigmatic model of strongly correlated quantum matter, thus making it desirable to investigate with quantum simulators such as ultracold atomic gases. Here we consider the problem of two atoms interacting in a quasi-one- or quasi-two-dimensional optical lattice, geometries which are routinely realized in quantum-gas-microscope experiments. We perform an exact calculation of the low-energy scattering amplitude which accounts for the effects of the transverse confinement as well as all higher Bloch bands. This goes beyond standard perturbative treatments and allows us to precisely determine the effective Hubbard on-site interaction for arbitrary $s$-wave scattering length (see source code available at https://github.com/HaydnAdlong/Hubbard-Interaction-Optical-Lattices). In particular, we find that the Hubbard on-site interaction displays lattice-induced resonances for scattering lengths on the order of the lattice spacing, which are well within reach of current experiments. Furthermore, we show that our results are in excellent agreement with spectroscopic measurements of the Hubbard interaction for a quasi-two-dimensional square optical lattice in a quantum-gas microscope. Our formalism is very general and may be extended to multiband models and other atomlike scenarios in lattice geometries, such as exciton-exciton and exciton-electron scattering in moiré superlattices.

Alkali-metal optically pumped magnetometers that utilize vapor cells containing high buffer-gas pressure and operate at elevated temperatures are prone to inaccuracies arising from the overlap of the average $F=I+1/2$ and $F=I-1/2$ ground-state Zeeman resonances. We employ density-matrix simulations and experiments to investigate how this hyperfine systematic error varies with spin polarization in a ${}^{87}\mathrm{Rb}$ free-induction-decay (FID) magnetometer. At low spin polarizations $P\le 0.5$, this effect causes single-frequency magnetic-field-extraction techniques to exhibit inaccuracies up to approximately 3.5 nT. Density-matrix simulations reveal that this bias can be traced to the relative amplitude and phase between the $F=I\pm 1/2$ hyperfine ground-state manifolds in the FID spin precession signal. We show that this systematic error can be mitigated using either a double-frequency fitting model that accounts for the relative amplitude and phase or synchronous-pulse pumping that minimizes the $F=1$ contribution to the FID signal. Theoretical simulations predict accuracies within 0.5 nT for both techniques across a wide range of spin polarizations, suggesting a sevenfold enhancement over single-frequency extraction methods. Our experiments validate this, showcasing a variation in the extracted field below 1 nT, a 3.5-fold improvement compared to single-frequency extraction methods. Furthermore, the mitigation techniques demonstrate agreement of the extracted magnetic field within 1.5 nT.

We propose a scheme achieving the ultimate quantum precision for the estimation of the transverse displacement between two interfering photons. Such a transverse displacement could be caused, for example, by the refracting properties of the propagation medium or by the orientation of a system of mirrors. By performing transverse-momentum sampling interference between polarization-entangled pairs of photons that propagate with different momenta, we show that it is possible to perform transverse-displacement estimation with a precision that increases with the difference of the transverse momenta of the photons. We show that the precision achieved with our scheme is independent of the value of the displacement, which is useful when tracking a variable displacement. Moreover, only for small displacements, we show that the estimation can be performed without the need for transverse-momentum-resolving detectors. More fundamentally, we demonstrate that it is the quantum interference arising from two-photon entanglement in the transverse momenta at the very heart of the foreseen quantum-limited sensitivity in the spatial domain.

We investigate the potential of tensor-network-based machine-learning methods to scale to large image and text datasets. We study how the mutual information between a subregion and its complement scales with the subsystem size $L$, similarly to approaches used in quantum many-body physics. Using various mutual information (MI) estimation methods, including an autoregressive network-based estimator, we find that simple image datasets exhibit area law scaling, suggesting efficient representation by two-dimensional tensor networks. More complex image datasets exceed the area law, indicating the need for generalized tensor network states or hybrid models. For Wikipedia text data, we observe power-law scaling $I\left(L\right)\propto L^{\nu }$ with $\nu \approx 0.82$, approaching a volume law. This implies that one-dimensional tensor networks with area law entanglement may not efficiently capture the structure of text. We introduce two models to reproduce this scaling: a quantum-inspired random pair toy model and a linguistically motivated Markovian dependency tree model. In the latter model, matching the observed MI scaling allows us to infer the word-word correlation length distribution in text.

A two-body interaction or force between quantum particles is ubiquitous in nature, and the microscopic description in terms of the bare two-body interaction is the basis for quantitatively describing interacting few- and many-body systems. Alternatively, the effective description in terms of an effective two-body interaction successfully captures the essence of the systems. However, for several important observations, the explanation in terms of an effective two-body interaction is not satisfactory, and the effective three-body interaction has played an essential role in understanding the systems. In this study, we investigate a few-body system comprising of ultracold bosons tightly confined in a deep optical lattice site, which is effectively described as zero-dimensional bosons. By combining an occupancy-resolving high-resolution laser spectroscopy with an inter-orbital Feshbach resonance controlling the bare two-body interaction over a wide range, we experimentally reveal the behaviors of few-atom systems in a strongly interacting regime. Our results, for which perturbative calculations do not provide proper explanations, serve as a valuable and precise benchmark for theoretical approaches to strongly interacting few-body systems. As one important illustration, we obtain a clear signature of an effective four-body interaction evidenced by the binding energies of four and more atoms. This work is an important step for our deeper understanding of strongly interacting few-body systems.

Using time-resolved UV-laser spectroscopy up to a few seconds in a cryogenic ion storage ring, we observe that coupling of the stretching and bending modes via Fermi resonance considerably affects the vibrational radiative cooling process of the linear triatomic molecular ion ${\mathrm{N}}_2{\mathrm{O}}^{+}$ isolated in vacuum. We state-selectively compare the cooling rates of vibrational states in the electronic ground states $X{}^2\mathrm{\Pi }_{3/2}$ and $X{}^2\mathrm{\Pi }_{1/2}$, only one of which is under Fermi resonance. The vibrational radiative cooling rate of the vibrational state ($v_1{v}_2{v}_3$) = (2 0 0) in the electronic ground state $X{}^2\mathrm{\Pi }_{3/2}$, which couples with (1 2 0) via Fermi resonance, is determined through the excitation to a predissociation channel. Here, $v_1$, $v_2$, and $v_3$ represent the vibrational quantum numbers of NN–O stretching, N–N–O bending, and N–NO stretching, respectively. We successfully find that the vibrational radiative cooling rate for the (2 0 0) state of $X{}^2\mathrm{\Pi }_{3/2}$ is significantly slower than that of $X{}^2\mathrm{\Pi }_{1/2}$ without the Fermi resonance coupling.

We introduce a polarization-agnostic method for Gaussian-modulated coherent-state (GCMS) continuous-variable quantum key distribution (CVQKD). Due to the random and continuous nature of the GCMS protocol, Alice, the transmitter, can encode two distinct quadratures in each of two orthogonal polarization modes, such that Bob, the receiver, measures valid GCMS quadratures in a single polarization mode even when polarization changes occur during transmission. This method does not require polarization correction in the optical domain, does not require monitoring both polarization modes, reduces loss by eliminating optical components, and avoids the noise injected by polarization correction algorithms.

Multipartite entanglement plays a critical role in various applications of quantum internet. In these applications, the entanglement is usually shared by the distant parties. Experimentally, the distributed entanglement should be estimated by only local measurements. Furthermore, for network experiments, it is desirable to employ measurement techniques that are straightforward to implement. In this paper, we propose a method to measure arbitrary multipartite single-photon path entangled states by only local measurements. By considering practically reasonable assumptions, our method is relatively easy to implement. We experimentally demonstrate the utility of this method by reconstructing the density matrix of a 3-qubit $W$ state.

We study the creation and breakdown of a quantized vortex shear layer forming between a stationary Bose-Einstein condensate and a stirred-in persistent current. Once turbulence is established, we characterize the progressive clustering of the vortices, showing that the cluster number follows a power-law decay with time, similar to decaying turbulence in other two-dimensional systems. Numerical study of the system demonstrates good agreement of the experimental data with a point vortex model that includes damping and noise. With increasing vortex number in the computational model, we observe a convergence of the power-law exponent to a fixed value.

Motivated by ongoing pump-probe spectroscopy experiments, this work develops a theoretical framework for describing the rovibrational wave-packet dynamics that ensues when a single weakly bound van der Waals trimer is exposed to a short, subpicosecond linearly polarized pump laser pulse. The intensity $I$ of the pump laser is chosen such that excitation and ionization of the electronic degrees of freedom are negligible, while excitation of the wave packet in the nuclear degrees of freedom is non-negligible. The numerical treatment, which takes advantage of the fact that the laser pulse is very short compared to typical molecular time scales, is based on a wave-packet decomposition that utilizes hyperspherical coordinates. The framework is applied to the extremely floppy bosonic helium trimer. A convergence analysis of the partial-wave decomposition is conducted. The kinetic-energy release and orientation dynamics are presented. While the dynamics of more strongly bound van der Waals trimers such as, e.g., the argon trimer, display negligible coupling between vibrational and rotational degrees of freedom, rendering a description within a rigid-body picture appropriate, those of weakly bound trimers display non-negligible coupling between vibrational and rotational degrees of freedom, rendering a description within a rigid-body picture inappropriate. It is shown that a model that constructs the helium trimer dynamics from the dynamics of the helium dimer captures a number of key characteristics of the alignment signal, including the interference between different angular momentum wave-packet components.

Controlling wave transmission is crucial for various applications. In this work we apply the concept of unitary control to manipulate multiport wave transmission. Unitary control aims to control the behaviors of a set of orthogonal waves simultaneously. The approach fully harnesses the capability of wavefront shaping techniques, with promising applications in communication, imaging, and photonic integrated circuits. Here we present a detailed theory of unitary control of wave transmission, focusing on two key characteristics: total (power) transmittance and direct (field) transmission. The total transmittance for an input port represents the fraction of total transmitted power with respect to the input power for a wave incident from an input port. The direct transmission for an input port denotes the complex transmission amplitude from that input port to its corresponding output port. We address two main questions: (i) the achievable total transmittance and direct transmission for each port and (ii) the configuration of unitary control to attain desired transmission values for each port. Our theory illustrates that unitary control enables uniform total transmittance and direct transmission across any medium. Furthermore, we show that reciprocity and energy conservation enforce direct symmetry constraints on wave transmission in both the forward and backward directions under unitary control.

While perturbation theories constitute a significant foundation of modern quantum system analysis, extending them from the Hermitian to the non-Hermitian regime remains a nontrivial task. In this work, we generalize the Rayleigh-Schrödinger perturbation theory to the non-Hermitian regime by employing a geometric formalism. This framework allows us to compute perturbative corrections to eigenstates and eigenvalues of Hamiltonians iteratively to any order. Furthermore, we observe that the recursion equation for the eigenstates resembles the form of the Girard-Newton formulas, which helps us uncover the general solution to the recursion equation. Moreover, we demonstrate that the perturbation method proposed in this paper reduces to the standard Rayleigh-Schrödinger perturbation theory in the Hermitian regime.

We simulate the Gross-Pitaevskii equation to model the development of turbulence in a quantum fluid confined by a cuboid box potential and forced by shaking along one axis. We observe the development of isotropic turbulence from anisotropic forcing for a broad range of forcing amplitudes and characterize the states through their Fourier spectra, vortex distributions, and spatial correlations. For weak forcing the steady-state wave-action spectrum exhibits a $k^{-3.5}$ scaling over wave number $k$; further decomposition uncovers the same power law in both compressible kinetic energy and quantum pressure, while the bulk superfluid remains phase coherent and free from extended vortices. As the forcing energy exceeds the chemical potential, extended vortices develop in the bulk, disrupting the $k^{-3.5}$ scaling. The spectrum then transitions to a $k^{-7/3}$ regime for compressible kinetic energy only, associated with dense vortex turbulence, and phase coherence limited to the healing length. The strong forcing regime is consistent with an inverse cascade of compressible energy driven by small-scale vortex annihilation.

Recently we introduced a local photon approach for modeling the quantized electromagnetic field in position space. Using this approach, we define the momentum of light in this paper as in quantum mechanics as the generator for spatial translation. Afterward, we analyze the momentum dynamics of photonic wave packets which transition from air into a denser dielectric medium. Our analysis shines new light onto the Abraham-Minkowski controversy, which highlights the intricacies involved in the characterization of the momentum of the electromagnetic field. Although our results align with Minkowski's theory and with the definition of the canonical momentum of light in quantum electrodynamics, there are also some crucial differences.

Magic trapping of ground and Rydberg states, which equalizes the AC Stark shifts of these two levels, enables increased ground-to-Rydberg state coherence times. We measure via photon storage and retrieval how the ground-to-Rydberg state coherence depends on trap wavelength for two different traps and find different optimal wavelengths for a one-dimensional optical lattice trap and a running wave optical dipole trap. Comparison to theory reveals that this is caused by the Rydberg electron sampling different potential landscapes. The observed difference increases for higher principal quantum numbers, where the extent of the Rydberg electron wave function becomes larger than the optical lattice period. Our analysis shows that optimal magic trapping conditions depend on the trap geometry, in particular for optical lattices and tweezers.

This article solves two major tasks that frequently arise in the theory of electron collisions with a target molecular cation. First, it extends the energy-dependent frame transformation (EDFT) treatment, which is needed to map fixed-nuclei electron-molecule scattering matrices into an energy-dependent laboratory-frame scattering matrix with vibrational channel indices. The EDFT mapping can now be carried out even when the target molecule possesses multiple low-energy potential curves, significantly transcending previous applications. Second, it implements a method to extract the rest of the full laboratory-frame scattering matrix, i.e., the columns and rows describing input and/or output dissociation channels. The treatment is benchmarked in this article against the essentially exact solution of a refined two-dimensional model of the singlet gerade $\mathrm{\Sigma }$ symmetry of ${\mathrm{H}}_2$. Our tests demonstrate that the theory accurately maps fixed-nuclei scattering information, of the type provided by existing electron-molecule computer codes, into a laboratory-frame scattering matrix that includes both ionization and dissociation. This treatment can provide a general framework applicable to a broad class of electron collision processes involving diatomic target ions, suitable for an accurate description of challenging processes such as dissociative recombination.

Even though the one-dimensional contact interaction requires no regularization, renormalization methods have been shown to improve the convergence of numerical calculations considerably. In this work, we compare and contrast these methods: “the running coupling constant” where the two-body ground-state energy is used as a renormalization condition, and two effective interaction approaches that include information about the ground as well as excited states. In particular, we calculate the energies and densities of few-fermion systems in a harmonic oscillator with the configuration-interaction method and compare the results based upon renormalized and bare interactions. We find that the use of the running coupling constant instead of the bare interaction improves convergence significantly. A comparison with an effective interaction, which is designed to reproduce the relative part of the energy spectrum of two particles, showed a similar improvement. The effective interaction provides an additional improvement if the center-of-mass excitations are included in the construction. Finally, we discuss the transformation of observables alongside the renormalization of the potential, and demonstrate that this might be an essential ingredient for accurate numerical calculations.

Crossed optical dipole traps (ODTs) provide three-dimensional confinement of cold atoms and other optically trappable particles. However, the need to maintain the intersection of the two trapping beams poses strict requirements on alignment stability and limits the ability to move the trap. Here we demonstrate a crossed ODT design that features inherent stability of the beam crossing, allowing the trap to move and remain aligned. The trap consists of a single high-power laser beam, imaged back onto itself at an angle to form a crossed trap. Self-aligning behavior results from employing an imaging system with positive magnification tuned precisely to unity. We employ laser-cooled samples of ${}^6\mathrm{Li}$ atoms to demonstrate that the trap remains well aligned over a 4.3-mm travel range along an axis approximately perpendicular to the plane containing the crossed beams. Our scheme can be applied to bring an atomic cloud held in a crossed ODT close to a surface or field source for various applications in quantum simulation, sensing, and information processing.

Plane electromagnetic waves in a Lorentzian dispersive medium (collection of classical oscillators) with a stepwise periodic modulation of oscillator density are considered. To account for the physical difference between the acts of involving new oscillators into motion and removing oscillators from the motion, different continuity conditions are used at the steps of the increase and decrease of the oscillator density. The continuity conditions are obtained from the general constitutive equations for an arbitrary nonmonotonic time dependence of the oscillator density. It is found that eigenmodes of the periodically modulated medium are decaying even for undamped oscillators. This leads to a decay of an initial wave energy after starting the modulation for any parameters of the modulation. The obtained results disprove many recent predictions that parametric amplification can occur in a Lorentzian medium with modulated oscillator density. Despite energy losses, promising wave transformation regimes, such as frequency multiplication and division with high-amplitude efficiency, are found.