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Trilobite molecules are ultralong-range Rydberg molecules formed when a high angular momentum Rydberg electron scatters off of a ground-state atom. Their unique electronic structure and highly oscillatory potential energy curves support a rich variety of dynamical effects yet to be explored. We analyze the vibrational motion of these molecules using a framework of adiabatic wavepacket propagation dynamics and observe that for appropriate initial states, the trilobite potential acts as molecular diffraction grating. The quantum dynamic effects observed are explained using a Fourier analysis of the scattering potential and the associated scattered wavepacket. Furthermore, vibrational ground-states of the low angular momentum ultralong-range Rydberg molecules are found to be particularly suitable to prepare the relevant wavepackets. Hence, we propose a time resolved pump-probe scheme designed for the realization of the effect in question, and advertise the utilization of a single diatomic Rydberg molecule as a testbed for the study of exaggerated quantum dynamical phenomena., Comment: 9 pages, 6 figures

We investigate magneto-optical trap loss spectroscopy of Rydberg excited $^{85}$Rb ($66\leq n \leq 68~S_{1/2}$) atoms, placed inside a tailored microwave cavity. The cavity frequency at 13.053 GHz is in resonance with the $67S_{1/2} \rightarrow 66P_{3/2}$ transition, inducing a ladder multiphoton microwave Rydberg absorption and emission. The observed spectra are modeled with an extended Jaynes-Cumming formalism that accounts for multiphoton absorption from and emission into the cavity, the loss from the trap due to Rydberg excitation, and cavity imperfection. We calculate the average photons in each spectral feature and find evidence for fractional photon emission into the cavity modes. The microwave cavity Rydberg spectroscopy in this work should inform the application and technology development of Rydberg based sensors and hybrid Rydberg atom-superconducting resonator quantum gates.

We propose to simulate the anisotropic and chiral Dzyaloshinskii-Moriya (DM) interaction with Rydberg atom arrays. The DM Hamiltonian is engineered in a one-dimensional optical lattice or trap array with effective long-range Rydberg spins, interacting indirectly via a mobile mediator Rydberg atom. A host of XXZ and DM Hamiltonians can be simulated with out-of-phase sign periodic coupling strengths; for initial states in a stationary condensate, the DM interaction vanishes. This theory allows for determination of the DM interaction (DMI) vector components from first principles. The inherent anisotropy of the Rydberg-Rydberg interactions, facilitates the DMI coupling to be tuned so as to be comparable to the XXZ interaction. Our results make plausible the formation of non-trivial topological spin textures with Rydberg atom arrays., Comment: 4 pages, 2 figures

We propose to sympathetically slow and cool polar molecules in a cold, low-density beam using laser-cooled Rydberg atoms. The elastic collision cross sections between molecules and Rydberg atoms are large enough to efficiently thermalize the molecules even in a low density environment. Molecules traveling at 100 m/s can be stopped in under 30 collisions with little inelastic loss. Our method does not require photon scattering from the molecules and can be generically applied to complex species for applications in precision measurement, quantum information science, and controlled chemistry., Comment: 8 pages, 3 figures

This study concerns the two-body scattering of particles in a one-dimensional periodic potential. A convenient ansatz allows for the separation of center-of-mass and relative motion, leading to a discrete Schr\"odinger equation in the relative motion that resembles a tight-binding model. A lattice Green's function is used to develop the Lippmann-Schwinger equation, and ultimately derive a multi-band scattering K-matrix which is described in detail in the two-band approximation. Two distinct scattering lengths are defined according the limits of zero relative quasi-momentum at the top and bottom edges of the two-body collision band. Scattering resonances occur in the collision band when the energy is coincident with a bound state attached to another higher or lower band. Notably, repulsive on-site interactions in an energetically closed lower band lead to collision resonances in an excited band., Comment: 11 pages, 3 figures

We consider a BEC of rigid rotor molecules confined to quasi-2d through harmonic trapping. The molecules are subjected to an external electric field which polarizes the gas, and the molecules interact via dipole-dipole interactions. We present a description of the ground state and low-energy excitations of the system including an analysis of the mean-field energy, polarization, and stability. Under large electric fields the gas becomes fully polarized and we reproduce a well known density-wave instability which arises in polar BECs. Under smaller applied electric fields the gas develops an in-plane polarization leading to the emergence of a new global instability as the molecules "tilt". The character of these instabilities is clarified by means of momentum-space density-density structure factors. A peak at zero momentum in the spin-spin structure factor for the in-plane component of the polarization indicates that the tilt instability is a global phonon-like instability., Comment: 15 pages, 11 figures

We propose an experimentally realizable scheme to produce triatomic ultralong-range Rydberg molecules (TURM), formed in ultracold KRb traps. A near resonant coupling of the non-zero quantum defect Rydberg levels with the KRb molecule in N=0 and N=2 rotational levels, is engineered which exploits the unique Rydberg electron-molecule anisotropic dipole interaction. This near resonant coupling enhances the TURM binding and produces favorable Franck-Condon factors. Schemes for both postassium and rubidium excitations are demonstrated., Comment: 10 pages, 6 figures

Ultralong-range Rydberg trimer molecules are spectroscopically observed in an ultracold gas of Cs($nd_{3/2}$) atoms. The atomic Rydberg state anisotropy allows for the formation of angular trimer states, whose energies may not be obtained from integer multiples of dimer energies. These nonadditive trimers are predicted to coexist with Rydberg dimer lines. The existence of such effective three-body interactions is confirmed with observation of asymmetric line profiles and interpreted by a theoretical approach which includes relativistic spin interactions. Simulations of the observed spectra with and without angular trimer lines lends convincing support to the existence of effective three-body interactions., Comment: 10 pages, 7 figures

We show that indirect spin-spin interactions between effective spin-1/2 systems can be realized in two parallel 1D optical lattices loaded with polar molecules and/or Rydberg atoms. The effective spin can be encoded into low-energy rotational states of polar molecules or long-lived states of Rydberg atoms, tightly trapped in a deep optical lattice. The spin-spin interactions can be mediated by Rydberg atoms, placed in a parallel shallow optical lattice, interacting with the effective spins by charge-dipole (for polar molecules) or dipole-dipole (for Rydberg atoms) interaction. Indirect XX, Ising and XXZ interactions with interaction coefficients $J^{\bot}$ and $J^{zz}$ sign varying with interspin distance can be realized, in particular, the $J_{1}-J_{2}$ XXZ model with frustrated ferro-(antiferro-)magnetic nearest (next-nearest) neighbor interactions.

We calculate vibrational spectra of ultralong-range Cs(32p) Rydberg molecules which form in an ultracold gas of Cs atoms. We account for the partial-wave scattering of the Rydberg electrons from the ground Cs perturber atoms by including the full set of spin-resolved ${}^{1,3}S_J$ and ${}^{1,3}P_J$ scattering phase shifts, and allow for the mixing of singlet (S=0) and triplet (S=1) spin states through Rydberg electron spin-orbit and ground electron hyperfine interactions. Excellent agreement with observed data in Sa{\ss}mannshausen et al. [Phys. Rev. Lett. 113, 133201(2015)] in line positions and profiles is obtained. We also determine the spin-dependent permanent electric dipole moments for these molecules. This is the first such calculation of ultralong-range Rydberg molecules in which all of the relativistic contributions are accounted for., Comment: 9 pages, 6 figures

We analyze in detail the possibility to use charge-dipole interaction between a single polar molecule or a 1D molecular array and a single Rydberg atom to read out rotational populations. The change in the Rydberg electron energy is conditioned on the rotational state of the polar molecules, allowing for realization of a CNOT quantum gate between the molecules and the atom. Subsequent readout of the atomic fluorescence results in a non-destructive measurement of the rotational state. We study the interaction between a 1D array of polar molecules and an array or a cloud of atoms in a Rydberg superatom (blockaded) state and calculate the resolved energy shifts of Rb(60s) with KRb and RbYb molecules, with N=1, 3, 5 molecules. We show that collective molecular rotational states can be read out using the conditioned Rydberg energy shifts.

We examine a system of three-bosons confined to two dimensions in the presence of a perpendicular magnetic field within the framework of the adiabatic hyperspherical method. For the case of zero-range, regularized pseudo-potential interactions, we find that the system is nearly separable in hyperspherical coordinates and that, away from a set of narrow avoided crossings, the full energy eigenspectrum as a function of the 2D s-wave scattering length is well described by ignoring coupling between adiabatic hyperradial potentials. In the case of weak attractive or repulsive interactions, we find the lowest three-body energy states exhibit even/odd parity oscillations as a function of total internal 2D angular momentum and that for weak repulsive interactions, the universal lowest energy interacting state has an internal angular momentum of $M=3$. With the inclusion of repulsive higher angular momentum we surmise that the origin of a set of ``magic number'' states (states with anomalously low energy) might emerge as the result of a combination of even/odd parity oscillations and the pattern of degeneracy in the non-interacting lowest Landau level states., Comment: 12 pages, 8 figures

We present an analytic Bogoliubov description of a BEC of polar molecules trapped in a quasi-2D geometry and interacting via internal state-dependent dipole-dipole interactions. We derive the mean-field ground-state energy functional, and we derive analytic expressions for the dispersion relations, Bogoliubov amplitudes, and dynamic structure factors. This method can be applied to any homogeneous, two-component system with linear coupling, and direct, momentum-dependent interactions. The properties of the mean-field ground state, including polarization and stability, are investigated, and we identify three distinct instabilities: a density-wave rotonization that occurs when the gas is fully polarized, a spin-wave rotonization that occurs near zero polarization, and a mixed instability at intermediate fields. These instabilities are clarified by means of the real-space density-density correlation functions, which characterize the spontaneous fluctuations of the ground state, and the momentum-space structure factors, which characterize the response of the system to external perturbations. We find that the gas is susceptible to both density-wave and spin-wave response in the polarized limit but only a spin-wave response in the zero-polarization limit. These results are relevant for experiments with rigid rotor molecules such as RbCs, $\Lambda$-doublet molecules such as ThO that have an anomalously small zero-field splitting, and doublet-$\Sigma$ molecules such as SrF where two low-lying opposite-parity states can be tuned to zero splitting by an external magnetic field., Comment: 21 pages, 18 figures, comments welcome

We perform a comparative analysis of different computational approaches employed to explore the electronic structure of ultralong-range Rydberg molecules. Employing the Fermi pseudopotential approach, where the interaction is approximated by an $s$-wave bare delta function potential, one encounters a non-convergent behavior in basis set diagonalization. Nevertheless, the energy shifts within the first order perturbation theory coincide with those obtained by an alternative approach relying on Green's function calculation with the quantum defect theory. A pseudopotential that yields exactly the results obtained with the quantum defect theory, i.e. beyond first order perturbation theory, is the regularized delta function potential. The origin of the discrepancies between the different approaches is analytically motivated., Comment: 9 pages, 1 figure