We demonstrate that releasing atoms into free space from an optical lattice does not deteriorate cavity-generated spin squeezing for metrological purposes. In this work, an ensemble of $500000$ spin-squeezed atoms in a high-finesse optical cavity with near-uniform atom-cavity coupling is prepared, released into free space, recaptured in the cavity, and probed. Up to $\sim 10$ dB of metrologically relevant squeezing is retrieved for $700\mu \mathrm{s}$ free-fall times, and decaying levels of squeezing are realized for up to 3 ms free-fall times. The degradation of squeezing results from loss of atom-cavity coupling homogeneity between the initial squeezed state generation and final collective state readout. A theoretical model is developed to quantify this degradation and this model is experimentally validated.

Quantum teleportation is one of the most pioneering features of the quantum world. Typically, the quality of a teleportation protocol is solely judged by its average fidelity. In this work, we analyze the performance of teleportation in terms of both fidelity and the deviation in fidelity. Specifically, we define a quantity called teleportability score, which incorporates contributions from both the fidelity and its deviation. It also takes into account the sensitivity one requires for a protocol in which the teleportation of a quantum state is required in one or many intermediate steps. We compute the teleportability score in the noiseless scenario and find that it increases monotonically with the entanglement content of the considered pure resource states. The result remains the same even if we consider an $n$-chain repeater-like configuration. However, in the presence of noise, the teleportability score can sometime display a nonmonotonic behavior with respect to the entanglement content of the initially shared resource state. Specifically, under local bit-flip and bit-phase-flip noise, less entangled states can have higher teleportability score for certain choices of system parameters. In the presence of global depolarizing noise, for low entangled resource states and high sensitivity requirements, the noisy states can have better a teleportability score in comparison to the noiseless scenario.

Quantum coherence is a crucial resource for quantum information processing. By employing the language of coherence orders largely applied in NMR systems, quantum coherence has been currently addressed in terms of multiple quantum coherences (MQCs). Here we investigate $\alpha$-MQCs, a class of multiple quantum coherences which is based on $\alpha$-relative purity, an information-theoretic quantifier analogous to quantum fidelity and closely related to Rényi relative entropy of order $\alpha$. Our framework enables linking $\alpha$-MQCs to Wigner-Yanase-Dyson skew information, an asymmetry monotone-finding application in quantum thermodynamics and quantum metrology. Furthermore, we derive a family of bounds on $\alpha$-MQCs, particularly showing that $\alpha$-MQCs define a lower bound to quantum Fisher information. We illustrate these ideas for quantum systems described by single-qubit states, two-qubit Bell-diagonal states, and a wide class of multiparticle mixed states. Finally, we investigate the time evolution of the $\alpha$-MQC spectrum and the overall signal of relative purity by simulating the time-reversal dynamics of a many-body all-to-all Ising Hamiltonian and comment on applications to physical platforms such as NMR systems, trapped ions, and ultracold atoms.

We have developed an experimental technique to study charge- and energy-flow processes in sub-eV collisions between oppositely charged, internally cold, ions of atoms, molecules, and clusters. Two ion beams are stored in separate rings of the cryogenic ion-beam storage facility DESIREE, and merged in a common straight section where a set of biased drift tubes is used to control the center-of-mass collision energy locally in fine steps. Here, we present measurements on mutual neutralization between ${\mathrm{Li}}^{+}$ and ${\mathrm{D}}^{-}$ where a time-sensitive imaging-detector system is used to measure the three-dimensional distance between the neutral Li and D atoms as they reach the detector. This scheme allows for direct measurements of kinetic-energy releases, and here it reveals separate populations of the $3s$ state and the $(3p+3d)$ states in neutral Li while the D atom is left in its ground state $1s$. The branching fraction of the $3s$ final state is measured to be $57.8\pm 0.7\%$ at a center-of-mass collision energy of $78\pm 13$ meV. The technique paves the way for studies of charge-, energy-, and mass-transfer reactions in single collisions involving molecular and cluster ions in well-defined quantum states.

In this work, we carry out an comprehensive study for the electron scattering with atomic argon in the framework of relativistic box-variational method. The phase shifts first are extracted from relativistic coupled-cluster-theory calculations. Then the properties including total elastic, momentum transfer, viscosity cross sections, and differential cross sections are evaluated and compared with available experimental and theoretical data. The validity and accuracy of present method are verified by the good agreement with experimental values, especially for the differential cross sections at small angle forward and backward scattering where obvious discrepancies exist between experiments and theories. The predicted scattering length of $-1.39 a_0$ for electron-argon system is only $2\%$ larger in magnitude than the most recent experimental estimate. In addition, the role of electron correlation effect are also investigated in these properties.

This paper presents a method for performing approximate optimal control simulations for quantum systems with multiple coupled degrees of freedom. The time evolution is simulated using the first-order Magnus expansion in the interaction picture, where the couplings between different degrees of freedom are treated as the perturbation. A numerical implementation procedure is presented that leverages upon pairwise couplings and the separability of the zeroth-order time evolution operator to achieve a reduced computational cost, which is analyzed with respect to the number of degrees of freedom. The formulation is compatible with gradient-free methods to optimize the control field, and a stochastic hill climbing algorithm is adopted for this purpose. As illustrations, optimal control simulations are performed for systems of two and three dipole-dipole-coupled molecular rotors under the influence of a control field. For the two-rotor system, the field is optimized to achieve either orientation or entanglement objectives. For the three-rotor system, the field is optimized either to orient all three rotors in the same direction or to orient one rotor in a particular direction while the other two rotors point in the opposite direction.

When atoms or molecules are exposed to strong short-pulse infrared radiation, ionization as well as “frustrated tunneling ionization” can occur, in which some of the nearly freed electrons recombine into the initial ground or an excited bound state. We analyze the ellipticity dependence of the relative signals that are predicted in a single-active-electron (SAE) approximation, the validity of which is checked against a parameter-free multielectron $R$-matrix (close-coupling) with time-dependence approach. We find good agreement between the results from both models, thereby providing confidence in the SAE model potential to treat the process of interest. Comparison of the relative excitation probabilities found in our numerical calculations with the predictions of Landsman et al. [A. S. Landsman et al., New J. Phys. 15, 013001 (2013)] and Zhao et al. [Y. Zhao et al., Opt. Express 27, 21689 (2019)] reveals good agreement with the former for short pulses. For longer pulses, the ellipticity dependence becomes wider than that obtained from the Landsman et al. formula, but we do not obtain the increase compared to linearly polarized radiation predicted by Zhao et al.

The spin-orbit coupling (SOC) in degenerate Fermi gases can fundamentally change the fate of $s$-wave superfluids. Here we report the anomalous isothermal compressibility ${\kappa }_T$ in the degenerate Fermi gases with both SOC and Zeeman field. Starting from the Gibbs-Duhem equation, we show that ${\kappa }_T$ comes from both the explicit contribution of chemical potential and the implicit contribution of the order parameter. In the Bardeen-Cooper-Schrieffer (BCS) limit, ${\kappa }_T$ is determined by the explicit compressibility, which is proportional to the density of states at the Fermi surface; while in the Bose-Einstein condensate (BEC) regime it is determined by the implicit compressibility, which is uniquely given by the scattering length. Between these two limits, we find a pronouncedly enhanced compressibility in the gapless Weyl phase regime, which is attributed to a remanent effect of the instability of degenerate Fermi gases towards phase separation. This enhanced compressibility also leads to an anomaly in the exponent of pressure. A connection between this exponent and the polytropic index is established. These predictions can be measured from the anomaly in sound velocity, density fluctuation, and collective vibration frequencies.

We propose a translationally invariant metamirror for light filtering in reflection. The device consists of a thin transverse grating in the micron scale positioned in front of a flat mirror. We analyze the performance of such a photonic metamirror and find a modification of the angular spectrum of the reflected beams, leading to a significant reduction of the beam divergence for particular configurations. This study points toward a type of optical component, a flat metamirror with a filtering functionality and no alignment requirements, due to its translational invariance.

We studied numerically the generation of the two-color flat-top solitonic pulses, platicons, in the microresonator-based doubly resonant optical parametric oscillator. We revealed that if the signs of the group velocity dispersion (GVD) coefficients at interacting harmonics are opposite, platicon excitation is possible via pump amplitude modulation or controllable mode interaction approach. Upon pump frequency scan generation of platicons was observed at positive pump frequency detunings for the normal GVD at pump frequency and at negative detunings in the opposite case. Interestingly, we found the effect of the transformation of the flat-top platicon profile at half-frequency into the bell-shaped bright soliton profile upon frequency scan. For platicon excitation one needs simultaneous accurate matching of the microresonator free spectral ranges at interacting harmonics and resonant eigenfrequencies. Excitation conditions and platicon generation domains were found for the different generation methods, and properties of the generated platicons were studied for various combinations of the medium parameters.

Harmonic frequency combs, in which the lasing modes are separated by a period of tens of free spectral ranges from each other, have been recently discovered in quantum cascade lasers (QCLs). There is an ongoing debate how the harmonic combs can be formed and stable under continuous pumping. Here we reproduce the harmonic state of lasing in QCLs by space-time-domain numerical simulations and show that the corresponding optical wave has a frequency-modulated nature, with the fundamental beat note in the electron population being suppressed. To understand the physics behind the formation and stability of the harmonic state, we develop a frequency-domain linearized analytic theory which analyzes the stability of single-mode lasing with respect to the harmonic state formation and the instabilities of the resulting harmonic state. Our analysis shows how the instability of a single lasing mode can result in the growth of harmonic side modes. The coupling between the two side modes leads to enhancement of the gain for frequency-modulated waves as compared to the gain for amplitude-modulated waves. The dependence of the sideband gain spectrum on group-velocity dispersion is also studied. While the instability of a single lasing mode with respect to the growth of side bands separated by many free spectral ranges does not prove that the harmonic state can be self-starting, we analyze the instability of three strong harmonic modes and demonstrate that the harmonic state can be stable and self-supported.

We point out the connection between the problem of formulating quantum mechanics in phase space and projecting the motion of a quantum-mechanical particle onto a particular Landau level. In particular, we show that lowest Landau-level wave functions, which are widely used in studies of quantum Hall effect, are actually phase-space wave functions in this context. We demonstrate the usefulness of this understanding by analyzing some simple problems, and propose other utilities.

We determine the quantum Cramér-Rao bound for the precision with which the oscillator frequency and damping constant of a damped quantum harmonic oscillator in an arbitrary Gaussian state can be estimated. This goes beyond standard quantum parameter estimation of a single-mode Gaussian state for which typically a mode of fixed frequency is assumed. We present a scheme through which the frequency estimation can nevertheless be based on the known results for single-mode quantum parameter estimation with Gaussian states. Based on these results, we investigate the optimal measurement time. For measuring the oscillator frequency, our results unify previously known partial results and constitute an explicit solution for a general single-mode Gaussian state. Furthermore, we show that with existing carbon nanotube resonators see J. Chaste et al. [Nat. Nanotechnol. 7, 301 (2012)] it should be possible to achieve a mass sensitivity of the order of an electron mass ${\mathrm{Hz}}^{-1/2}$.

Quantum-gate errors are a significant challenge for achieving precision measurements on noisy intermediate-scale quantum (NISQ) computers. This paper focuses on zero-noise extrapolation (ZNE), a technique that can be implemented on existing hardware, studying it in detail and proposing modifications to existing approaches. In particular, we consider identity insertion methods for amplifying noise because they are hardware agnostic. We build a mathematical formalism for studying existing ZNE techniques and show how higher order polynomial extrapolations can be used to systematically reduce depolarizing errors. Furthermore, we introduce a method for amplifying noise that uses far fewer gates than traditional methods. This approach is compared with existing methods for simulated quantum circuits. Comparable or smaller errors are possible with fewer gates, which illustrates the potential for empowering an entirely new class of moderate-depth circuits on near term hardware.

We construct a large family of planar maximally entangled (PME) states, which are a wider class of multipartite entangled states than absolutely maximally entangled (AME) states. These are states in which any half of the qudits are in a maximally mixed state, provided that they form a connected subset. We show that in contrast to AMEs, PMEs are easier to find and there are various PMEs for any even number of qudits. In particular, while it is known that no AME state of four qubits exists, we show that there are two distinct multiparameter classes of four-qubit PMEs. We also give explicit families of PMEs for any even number of particles and for any dimension. We also briefly mention the relevance of connectivity and underlying geometry to definition of a PME state. Here we have considered the simplest case of a one-dimensional graph.

In most experiments with atoms trapped in optical lattices, the transverse size of the optical lattice beams is of the order of tens of micrometers, and loading many atoms into smaller optical lattices has not been carefully investigated. We report trapping 1500 ${}^{171}\mathrm{Yb}$ atoms in a one-dimensional optical lattice generated by a narrow cavity mode at a distance of 0.14 mm from a mirror surface. The simplest approach of loading atoms from a mirror magneto-optical trap overlapped with the cavity mode allows the adjustment of the loading position by tuning a uniform bias magnetic field. The number of atoms trapped in the optical lattice exhibits two local maxima for different lattice depths, with a global maximum in the deeper lattice. These results open a way to quantum mechanical manipulation of atoms based on strong interaction with a tightly focused light field.

We consider the Bose gas on a $d$-dimensional anisotropic lattice employing the imperfect (mean-field) gas as a prototype example. We study the dimensional crossover arising as a result of varying the dispersion relation at finite temperature $T$. We analyze in particular situations where one of the relevant effective dimensionalities is located at or below the lower critical dimension, so that the Bose-Einstein condensate becomes expelled from the system by anisotropically modifying the lattice parameters controlling the kinetic term in the Hamiltonian. We clarify the mechanism governing this phenomenon. Subsequently we study the thermodynamic Casimir effect occurring in this system. We compute the exact profile of the scaling function for the Casimir energy. As an effect of strongly anisotropic scale invariance, the Casimir force below or at the critical temperature $T_c$ may be repulsive even for periodic boundary conditions. The corresponding Casimir amplitude is universal only in a restricted sense, and the power law governing the decay of the Casimir interaction becomes modified. We also demonstrate that, under certain circumstances, the scaling function is constant for sufficiently large values of the scaling variable, and in consequence is not an analytical function. At $T>T_c$ the Casimir-like interactions reflect the structure of the correlation function, and, for certain orientations of the confining walls, show exponentially damped oscillatory behavior so that the corresponding force is attractive or repulsive depending on the distance.

We investigate the macroscopic quantum tunneling of fermionic superfluids in the two-dimensional BCS-BEC crossover by using an effective tunneling energy which explicitly depends on the condensate fraction and the chemical potential of the system. We compare the mean-field effective tunneling energy with the beyond-mean-field one, finding that the mean-field tunneling energy is not reliable in the BEC regime of the crossover. Then we solve the Josephson equations of the population imbalance and the relative phase, calculating the frequency of tunneling oscillation both in the linear regime and in the nonlinear one. Our results show that the Josephson frequency is higher in the intermediate regime of the BCS-BEC crossover due to the peculiar behavior of the effective tunneling energy in the crossover.