We have measured the quadratic Zeeman coefficient for the ${}^{1}S_0\leftrightarrow {}^{3}P_0$ optical clock transition in ${}^{27}\mathrm{Al}^{+}$, $C_2=-71.944\left(24\right)\mathrm{MHz}/{\mathrm{T}}^2$, and the unperturbed hyperfine splitting of the ${}^{25}\mathrm{Mg}^{+}{}^{2}S_{1/2}$ ground electronic state, $\mathrm{\Delta }W/h=1788762752.85\left(13\right)\mathrm{Hz}$, with improved uncertainties. Both constants are relevant to the evaluation of the ${}^{27}\mathrm{Al}^{+}$ quantum-logic clock systematic uncertainty. The measurement of $C_2$ is in agreement with a previous measurement and a recent calculation at the $1\sigma$ level. The measurement of $\mathrm{\Delta }W$ is in good agreement with a recent measurement and differs from a previously published result by approximately $2\sigma$. With the improved value for $\mathrm{\Delta }W$, we deduce an improved value for the nuclear-to-electronic $g$-factor ratio $g_I/g_J=9.299308313\left(60\right)\times {10}^{-5}$ and the nuclear $g$-factor for the ${}^{25}\mathrm{Mg}$ nucleus $g_I=1.86195782\left(28\right)\times {10}^{-4}$. Using the values of $C_2$ and $\mathrm{\Delta }W$ presented here, we derive a quadratic Zeeman shift of the ${}^{27}\mathrm{Al}^{+}$ quantum-logic clock of $\mathrm{\Delta }\nu /\nu =-(9241.8\pm 3.7)\times {10}^{-19}$, for a bias magnetic field of $B\approx 0.12\mathrm{mT}$.

We describe a diabatic protocol to prepare a strongly interacting Bose-Einstein condensate in a regime where neither an adiabatic ramp nor a direct diabatic quench is desirable. This protocol is expected to achieve a nearly unit population transfer to the strongly interacting ground state for realistic experimental parameters for ${}^{85}\mathrm{Rb}$. The protocol matches the initial and final density profiles by modifying the trap along with the scattering length during the quench. The protocol should reveal several properties of the strongly interacting Bose gas and enable further investigation of beyond-mean-field corrections to the Gross-Pitaevskii equation.

We study four- and higher order wave mixing of continuous coherent waves on a single superconducting artificial atom. Narrow side peaks of different orders of nonlinearity resulting from elastic multiphoton scattering on the atom are observed and investigated. We derive an analytical expression for the peak amplitudes and show that the ratio of any two adjacent peaks is a function of driving amplitudes and detuning. This is attributed to the photon distribution in the coherent states and provides a measure for characterization of photon statistics in nonclassical coherent waves. We also demonstrate an Autler-Townes-like splitting of side peaks, the magnitude of which scales with the scattering order.

We analyze analytically, semianalytically, and numerically the operation of a cross-resonance (CR) gate for superconducting qubits (transmons). We find that a relatively simple semianalytical method gives accurate results for the controlled-not (cnot) -equivalent gate duration and compensating single-qubit rotations. It also allows us to minimize the cnot gate duration over the amplitude of the applied microwave drive and find the dependence on the detuning between the qubits. However, full numerical simulations are needed to calculate the intrinsic fidelity of the CR gate. We decompose numerical infidelity into contributions from various physical mechanisms, thus finding the intrinsic error budget. In particular, at small drive amplitudes, the CR gate fidelity is limited by imperfections of the target-qubit rotations, while at large amplitudes it is limited by leakage. The gate duration and fidelity are analyzed numerically as functions of the detuning between qubits, their coupling, drive frequency, relative duration of pulse ramps, and microwave crosstalk. The effect of the echo sequence is also analyzed numerically. Our results show that the CR gate can provide intrinsic infidelity of less than ${10}^{-3}$ when a simple pulse shape is used.

We propose a generalization of the Feynman path integral using squeezed coherent states. We apply this approach to the dynamics of Bose-Einstein condensates, which gives an effective low-energy description that contains both a coherent field and a squeezing field. We derive the classical trajectory of this action, which constitutes a generalization of the Gross-Pitaevskii equation, at linear order. We derive the low-energy excitations, which provides a description of second sound in weakly interacting condensates as a squeezing oscillation of the order parameter. This interpretation is also supported by a comparison to a numerical c-field method.

We consider a two-component Bose gas in two dimensions at a low temperature with short-range repulsive interaction. In the coexistence phase where both components are superfluid, interspecies interactions induce a nondissipative drag between the two superfluid flows (Andreev-Bashkin effect). We show that this behavior leads to a modification of the usual Berezinskii-Kosterlitz-Thouless (BKT) transition in two dimensions. We extend the renormalization of the superfluid densities at finite temperature using the renormalization-group approach and find that the vortices of one component have a large influence on the superfluid properties of the other, mediated by the nondissipative drag. The extended BKT flow equations indicate that the occurrence of the vortex unbinding transition in one of the components can induce the breakdown of superfluidity also in the other, leading to a locking phenomenon for the critical temperatures of the two gases.

In this work we use the concept of quantum fingerprinting to develop a quantum communication protocol in the simultaneous message passing model that calculates the Hamming distance between two $n$-bit strings up to relative error $\epsilon$. The number of qubits communicated by the protocol is polynomial in $logn$ and $1/\epsilon$, while any classical protocol must communicate $\mathrm{\Omega }\left(\sqrt{n}\right)$ bits. Motivated by the relationship between Hamming distance and vertex distance in hypercubes, we apply the protocol to approximately calculate distances between vertices in graphs that can be embedded into a hypercube such that all distances are preserved up to a constant factor. Such graphs are known as ${\ell }_1$-graphs. This class includes all trees, median graphs, Johnson graphs, and Hamming graphs. Our protocol is efficient for ${\ell }_1$-graphs with low diameter, and we show that its dependence on the diameter is essentially optimal. Finally, we show that our protocol can be used to approximately compute ${\ell }_1$ distances between vectors efficiently.

We consider a qubit initialized in a superposition of its pointer states, exposed to pure dephasing due to coupling to a quasistatic environment, and subjected to a sequence of single-shot measurements projecting it on chosen superpositions. We show how with a few such measurements one can significantly diminish one's ignorance about the environmental state, and how this leads to an increase of coherence of the qubit interacting with a properly post-selected environmental state. We give theoretical results for the case of a quasistatic environment that is a source of an effective field of Gaussian statistics acting on a qubit, and for a nitrogen-vacancy center qubit coupled to a nuclear spin bath, for which the Gaussian model applies qualitatively provided one excludes from the environment nuclei that are strongly coupled to the qubit. We discuss the reason for which the most probable sequences of measurement results are the ones consisting of identical outcomes, and in this way we shed light on a recent experiment (D. D. Bhaktavatsala Rao et al., arXiv:1804.07111) on nitrogen-vacancy centers.

Weakly interacting Fermi gases exhibit rich collective dynamics in spin-dependent potentials, arising from correlations between spin degrees of freedom and conserved single-atom energies, offering broad prospects for simulating many-body quantum systems by engineering energy-space “lattices,” with controlled energy landscapes and site-to-site interactions. Using quantum-degenerate clouds of ${}^6\mathrm{Li}$, confined in a spin-dependent harmonic potential, we measure complex, time-dependent spin-density profiles, varying on length scales much smaller than the cloud size. We show that a one-dimensional mean-field model, without additional simplifying approximations, quantitatively predicts the observed fine structure. We measure the magnetic fields where the scattering lengths vanish for three different hyperfine state mixtures to provide constraints on the collisional (Feshbach) resonance parameters.

Photoprocesses of the endohedral fullerene ions ${\mathrm{Sc}}_3\mathrm{N}@{\mathrm{C}}_{80}^{+}$ and ${\mathrm{Sc}}_3\mathrm{N}@{\mathrm{C}}_{80}{}^{-}$ in the gas phase have been investigated in the photon energy ranges 30–50 eV and 280–420 eV. Single and double ionization as well as single ionization accompanied by the release of a ${\mathrm{C}}_2$ dimer were observed as a function of the photon energy for the positive parent ion and double detachment was measured for the negative parent ion. The emphasis of the experiments was on the specific effects of the encapsulated trimetallic nitride cluster ${\mathrm{Sc}}_3\mathrm{N}$ on the observed reactions. Clear evidence of photoexcitation near the Sc $L$ edge is obtained with the dominating contributions visible in the one- and two-electron-removal channels. $K$-vacancy production in the encapsulated central nitrogen atom is seen in the single ionization of ${\mathrm{Sc}}_3\mathrm{N}@{\mathrm{C}}_{80}^{+}$ but is much less pronounced in the photoionization-with-fragmentation channel. Comparison of the cross sections near the carbon $K$ edge with the corresponding channels measured previously in the photoionization of ${\mathrm{Lu}}_3\mathrm{N}@{\mathrm{C}}_{80}^{+}$ reveal strong similarities. Previously predicted sharp resonance features in the ionization of ${\mathrm{Sc}}_3\mathrm{N}@{\mathrm{C}}_{80}^{+}$ ions below the Sc $M$ edge are not confirmed. The experiments are accompanied by quantum-chemistry calculations in the Hartree-Fock approximation and by model calculations employing density functional theory (DFT).

The realization of artificial gauge fields in ultracold atomic gases has opened up a path towards experimental studies of topological insulators and, as an ultimate goal, topological quantum matter in many-body systems. As an alternative to the direct implementation of two-dimensional lattice Hamiltonians that host the quantum Hall effect and its variants, topological charge-pumping experiments provide an additional avenue towards studying many-body systems. Here, we consider an interacting two-component gas of fermions realizing a family of one-dimensional superlattice Hamiltonians with onsite interactions and a unit cell of three sites, the ground states of which would be visited in an appropriately defined charge pump. First, we investigate the grand canonical quantum phase diagram of individual Hamiltonians, focusing on insulating phases. For a certain commensurate filling, there is a sequence of phase transitions from a band insulator to other insulating phases (related to the physics of ionic Hubbard models) for some members of the manifold of Hamiltonians. Second, we compute the Chern numbers for the whole manifold in a many-body formulation and show that, related to the aforementioned quantum phase transitions, a topological transition results in a change of the value and sign of the Chern number. We provide both an intuitive and a conceptual explanation and argue that these properties could be observed in quantum-gas experiments.

Optical cavities can induce photon-mediated interactions among intracavity-trapped atoms. Multimode cavities provide the ability to tune the form of these interactions, e.g., by inducing a nonlocal sign-changing term to the interaction. By accounting for the Gouy phase shifts of the modes in a nearly degenerate, confocal, Fabry-Pérot cavity, we provide a theoretical description of this interaction, along with additional experimental confirmation to complement that presented in the companion paper [Y. Guo et al., Phys. Rev. Lett. 122, 193601 (2019)]. Furthermore, we show that this interaction should be written in terms of a complex order parameter, allowing for a $\mathrm{U}\left(1\right)$ symmetry to emerge. This symmetry corresponds to the phase of the atomic density wave arising from self-organization when the cavity is transversely pumped above a critical threshold power. We show theoretically and experimentally how this phase depends on the position of the Bose-Einstein condensate within the cavity and discuss mechanisms that break the $\mathrm{U}\left(1\right)$ symmetry and lock this phase. We then consider alternative Fabry-Pérot multimode cavity geometries (i.e., beyond the confocal) and schemes with more than one pump laser and show that these provide additional capabilities for tuning the cavity-meditated interaction among atoms, including the ability to restore the $\mathrm{U}\left(1\right)$ symmetry despite the presence of symmetry-breaking effects. These photon-mediated interactions may be exploited for realizing quantum liquid crystalline states and spin glasses using multimode optical cavities.

The Hartree-Fock ground state of a homogeneous electron gas is never translation invariant, even at high densities. As proved by Overhauser, the (paramagnetic) free Fermi gas is always unstable under the formation of spin- or charge-density waves. We give here an explicit bound on the energy gain due to the breaking of translational symmetry. Our bound is exponentially small at high density, which justifies a posteriori the use of the noninteracting Fermi gas as a reference state in the large-density expansion of the correlation energy of the homogeneous electron gas. We are also able to discuss the positive temperature phase diagram and prove that the Overhauser instability only occurs at temperatures which are exponentially small at high density. Our work sheds a new light on the Hartree-Fock phase diagram of the homogeneous electron gas.

Ongoing efforts at the National Institute of Standards and Technology in creating a cold-atom vacuum standard device have prompted theoretical investigations of atom-molecule collision processes that characterize its operation. Such a device will operate as a primary standard for the ultrahigh-vacuum and extreme-high-vacuum regimes. This device operates by relating loss of ultracold lithium atoms from a conservative trap by collisions with ambient atoms and molecules to the background density and thus pressure through the ideal gas law. The predominant background constituent in these environments is molecular hydrogen ${\mathrm{H}}_2$. We compute the relevant $\mathrm{Li}+{\mathrm{H}}_2$ Born-Oppenheimer potential energy surface, paying special attention to its uncertainty. Coupled-channel calculations are then used to obtain total rate coefficients, which include momentum-changing elastic and inelastic processes. We find that inelastic rotational quenching of ${\mathrm{H}}_2$ is negligible near room temperature. For a ($T=300$)-K gas of ${\mathrm{H}}_2$ and 1.0-$\mu \mathrm{K}$ gas of Li atoms prepared in a single hyperfine state, the total rate coefficients are $6.0\left(1\right)\times {10}^{-9}{\mathrm{cm}}^3$/s for both ${}^6\mathrm{Li}$ and ${}^7\mathrm{Li}$ isotopes, where the number in parentheses corresponds to a one-standard-deviation combined statistical and systematic uncertainty. We find that a 10-K increase in the ${\mathrm{H}}_2$ temperature leads to a 1.9% increase in the rate coefficients for both isotopes. For Li temperatures up to 100 $\mu \mathrm{K}$, changes are negligible. Finally, a semiclassical Born approximation significantly overestimates the rate coefficients. The difference is at least ten times the uncertainty of the coupled-channel result.

We develop an analytical framework to study the synchronization of a quantum self-sustained oscillator to an external signal. Our unified description allows us to identify the resource on which quantum synchronization relies, and to compare quantitatively the synchronization behavior of different limit cycles and signals. We focus on the most elementary quantum system that is able to host a self-sustained oscillation, namely, a single spin 1. Despite the spin having no classical analog, we first show that it can realize the van der Pol limit cycle deep in the quantum regime, which allows us to provide an analytical understanding to recently reported numerical results. Moving on to the equatorial limit cycle, we then reveal the existence of an interference-based quantum synchronization blockade and extend the classical Arnold tongue to a snakelike split tongue. Finally, we derive the maximum synchronization that can be achieved in the spin-1 system, and construct a limit cycle that reaches this fundamental limit asymptotically.

Bistability of a nonlinear resonantly driven oscillator in the presence of external noise is analyzed using the classical Fokker–Planck equation in the quasienergy space with account for tunneling effects and by quantum master equation in quasienergy states representation. Two timescales responsible for different stages of this bistable system relaxation have been obtained. We found that the slow relaxation rate caused by fluctuation-induced transitions between different stable states can be enhanced by several orders of magnitude due to the tunneling effects. It was also revealed that tunneling between nearly degenerate quasienergy states and resonant multiphoton transitions between the genuine eigenstates of the nonlinear oscillator are just the similar effects. It was demonstrated that the quasienergy states in the bistability region corresponding to higher amplitude are squeezed. The degree of squeezing is determined by the ratio between nonlinearity and detuning, so that the uncertainty of one quadrature can be considerably smaller than the quantum limit. We found that tunneling effects can enhance the generation of output oscillator squeezed states. It was demonstrated that 1D Fokker–Planck equation is a quasiclassical limit of a quantum master equation.

We present an extended model for the lattice-induced light shifts of the clock frequency in optical lattice clocks, applicable to a wide range of operating conditions. The model extensions cover radial motional states with sufficient energies to invalidate the harmonic approximation of the confining potential. We reevaluate lattice-induced light shifts in our Yb optical lattice clock with an uncertainty of $6.1\times {10}^{-18}$ under typical clock operating conditions.

We derive an expression for the phase shift of an atom interferometer in a gravitational field taking into account both the finite duration of the light pulses and the effect of a small perturbing potential added to a stronger uniform gravitational field, extending the well-known results for rectangular pulses and at most quadratic potentials. These refinements are necessary for a correct analysis of present-day high-resolution interferometers.

The deuteron charge radius is calculated from the measurement of the Lamb shift in muonic deuterium, taking into account the electron vacuum polarization correction to the nuclear-structure effects. This correction is unexpectedly large and gives a mean-square charge-radii difference $r_d^2-r_p^2=3.81747\left(346\right){\mathrm{fm}}^2$, which is now consistent with that obtained from the ordinary H-D isotope shift in the $1S\text{−}2S$ transition. This suggests that the long-standing discrepancy in the proton charge radius obtained from electronic and muonic systems is due to an underestimated uncertainty in ordinary hydrogen spectroscopy.

We numerically study the universal scaling dynamics of an isolated one-dimensional ferromagnetic spin-1 Bose gas. Preparing the system in a far-from-equilibrium initial state, simultaneous coarsening and refining is found to enable and characterize the approach to a nonthermal fixed point. A macroscopic length scale which scales in time according to $L_{\mathrm{\Lambda }}\left(t\right)\sim t^{\beta }$, with $\beta \simeq 1/4$, quantifies the coarsening of the size of spin textures. At the same time kinklike defects populating these textures undergo a refining process measured by a shrinking microscopic length scale $L_{\lambda }\sim t^{{\beta }^{\prime }}$, with ${\beta }^{\prime }\simeq -0.17$. The combination of these scaling evolutions enables particle and energy conservation in the isolated system and constitutes a bidirectional transport in momentum space. The value of the coarsening exponent $\beta$ suggests the dynamics to belong to the universality class of diffusive coarsening of the one-dimensional $XY$ model. However, the universal momentum distribution function exhibiting nonlinear transport marks the distinction between diffusive coarsening and the approach of a nonthermal fixed point in the isolated system considered here. This underlines the importance of the universal scaling function in classifying nonthermal fixed points. Present-day experiments with quantum gases are expected to have access to the predicted bidirectional scaling.