Ergodic quantum systems are often quite alike, whereas nonergodic, fractal systems are unique and display characteristic properties. We explore one of these fractal systems, weakly bound dysprosium lanthanide molecules, in an external magnetic field. As recently shown, colliding ultracold magnetic dysprosium atoms display a soft chaotic behavior with a small degree of disorder. We broaden this classification by investigating the generalized inverse participation ratio and fractal dimensions for large sets of molecular wave functions. Our exact close-coupling simulations reveal a dynamic phase transition from partially localized states to totally delocalized states and universality in its distribution by increasing the magnetic field strength to only a hundred Gauss (or 10 mT). Finally, we prove the existence of nonergodic delocalized phase in the system and explain the violation of ergodicity by strong coupling between near-threshold molecular states and the nearby continuum.

}, doi = {https://doi.org/10.1126/sciadv.aap8308}, url = {https://arxiv.org/abs/1802.09586}, author = {Constantinos Makrides and Ming Li and Eite Tiesinga and Svetlana Kotochigova} } @article {2206, title = {Observation of bound state self-interaction in a nano-eV atom collider}, journal = {Nature Communications }, volume = {9}, year = {2018}, month = {2018/11/20}, abstract = {Quantum mechanical scattering resonances for colliding particles occur when a continuum scattering state couples to a discrete bound state between them. The coupling also causes the bound state to interact with itself via the continuum and leads to a shift in the bound state energy, but, lacking knowledge of the bare bound state energy, measuring this self-energy via the resonance position has remained elusive. Here, we report on the direct observation of self-interaction by using a nano-eV atom collider to track the position of a magnetically-tunable Feshbach resonance through a parameter space spanned by energy and magnetic field. Our system of potassium and rubidium atoms displays a strongly non-monotonic resonance trajectory with an exceptionally large self-interaction energy arising from an interplay between the Feshbach bound state and a different, virtual bound state at a fixed energy near threshold.

}, doi = {https://doi.org/10.1038/s41467-018-07375-8}, url = {https://arxiv.org/abs/1807.01174}, author = {Ryan Thomas and Matthew Chilcott and Eite Tiesinga and Amita B. Deb and Niels Kj{\ae}rgaard} } @article {2255, title = {Orbital quantum magnetism in spin dynamics of strongly interacting magnetic lanthanide atoms}, year = {2018}, abstract = {Laser cooled lanthanide atoms are ideal candidates with which to study strong and unconventional quantum magnetism with exotic phases. Here, we use state-of-the-art closed-coupling simulations to model quantum magnetism for pairs of ultracold spin-6 erbium lanthanide atoms placed in a deep optical lattice. In contrast to the widely used single-channel Hubbard model description of atoms and molecules in an optical lattice, we focus on the single-site multi-channel spin evolution due to spin-dependent contact, anisotropic van der Waals, and dipolar forces. This has allowed us to identify the leading mechanism, orbital anisotropy, that governs molecular spin dynamics among erbium atoms. The large magnetic moment and combined orbital angular momentum of the 4f-shell electrons are responsible for these strong anisotropic interactions and unconventional quantum magnetism. Multi-channel simulations of magnetic Cr atoms under similar trapping conditions show that their spin-evolution is controlled by spin-dependent contact interactions that are distinct in nature from the orbital anisotropy in Er. The role of an external magnetic field and the aspect ratio of the lattice site on spin dynamics is also investigated.

}, url = {https://arxiv.org/abs/1804.10102}, author = {Ming Li and Eite Tiesinga and Svetlana Kotochigova} } @article {2303, title = {A semiclassical theory of phase-space dynamics of interacting bosons}, year = {2018}, abstract = {We study the phase-space representation of dynamics of bosons in the semiclassical regime where the occupation number of the modes is large. To this end, we employ the van Vleck-Gutzwiller propagator to obtain an approximation for the Green\&$\#$39;s function of the Wigner distribution. The semiclassical analysis incorporates interference of classical paths and reduces to the truncated Wigner approximation (TWA) when the interference is ignored. Furthermore, we identify the Ehrenfest time after which the TWA fails. As a case study, we consider a single-mode quantum nonlinear oscillator, which displays collapse and revival of observables. We analytically show that the interference of classical paths leads to revivals, an effect that is not reproduced by the TWA or a perturbative analysis.

}, url = {https://arxiv.org/abs/1803.05122}, author = {Ranchu Mathew and Eite Tiesinga} } @article {2000, title = {Above threshold scattering about a Feshbach resonance for ultracold atoms in an optical collider}, journal = {Nature Communications}, volume = {8}, year = {2017}, month = {2017/09/06}, abstract = {Studies of magnetically tunable Feshbach resonances in ultracold atomic gases have predominantly been carried out in the zero collision-energy limit. Here, we explore above threshold collisions at well-defined energies in the vicinity of a narrow magnetic Feshbach resonance by means of a laser-based collider. Our experiment focuses on collisions between ground-state 87Rb atoms in the |F = 2,mF = 0i and |F = 1,mF = 1i hyperfine states, which have a known s-wave resonance at 9.040(7) G at threshold that strongly couples to inelastic channels, where 1 G = 10\−4 T. Using our collider we can track the magnetic field shift in resonance position as the energy is tuned. This presents a challenge due to the narrow width of the resonance in conjunction with inherent broadening mechanisms of the collider. We find, however, that the narrow Feshbach scattering feature becomes imprinted on the spatial distribution of atoms in a fashion that allows for an accurate determination of resonance position as a function of collision energy through a shift in center-of-mass position of the outgoing clouds. This shift has a dispersive line shape with a zero value at the resonance position. We obtain excellent agreement with theory on the resonance position.

}, doi = {10.1038/s41467-017-00458-y}, url = {https://arxiv.org/abs/1704.07109}, author = {Milena S. J. Horvath and Ryan Thomas and Eite Tiesinga and Amita B. Deb and Niels Kj{\ae}rgaard} } @article {2305, title = {Development of a new UHV/XHV pressure standard (cold atom vacuum standard)}, journal = {Metrologia}, volume = {54}, year = {2017}, month = {2017/11/3}, abstract = {The National Institute of Standards and Technology has recently begun a program to develop a primary pressure standard that is based on ultra-cold atoms, covering a pressure range of 1 x 10-6 to 1 x 10-10 Pa and possibly lower. These pressures correspond to the entire ultra-high vacuum range and extend into the extreme-high vacuum. This cold-atom vacuum standard (CAVS) is both a primary standard and absolute sensor of vacuum. The CAVS is based on the loss of cold, sensor atoms (such as the alkali-metal lithium) from a magnetic trap due to collisions with the background gas (primarily H2) in the vacuum. The pressure is determined from a thermally-averaged collision cross section, which is a fundamental atomic property, and the measured loss rate. The CAVS is primary because it will use collision cross sections determined from ab initio calculations for the Li + H2 system. Primary traceability is transferred to other systems of interest using sensitivity coefficients.

}, doi = {https://doi.org/10.1088/1681-7575/aa8a7b}, url = {https://arxiv.org/abs/1801.10120}, author = {Julia Scherschligt and James A Fedchak and Daniel S Barker and Stephen Eckel and Nikolai Klimov and Constantinos Makrides and Eite Tiesinga} } @article {1959, title = {Dispersive optical detection of magnetic Feshbach resonances in ultracold gases}, journal = {Physical Review A}, volume = {96}, year = {2017}, month = {2017/08/18}, pages = {022705}, abstract = {Magnetically tunable Feshbach resonances in ultracold atomic systems are chiefly identified and characterized through time consuming atom loss spectroscopy. We describe an off-resonant dispersive optical probing technique to rapidly locate Feshbach resonances and demonstrate the method by locating four resonances of\

We theoretically investigate trapping conditions for ultracold polar molecules in optical lattices, when external magnetic and electric fields are simultaneously applied. Our results are based on an accurate electronic-structure calculation of the polar\

Quenches in isolated quantum systems are currently a subject of intense study. Here, we consider quantum few-mode systems that are integrable in their classical mean-field limit and become dynamically unstable after a quench of a system parameter. Specifically, we study a Bose-Einstein condensate (BEC) in a double-well potential and an antiferromagnetic spinor BEC constrained to a single spatial mode. We study the time dynamics after the quench within the truncated Wigner approximation (TWA) and find that system relaxes to a steady state due to phase-space mixing. Using the action-angle formalism and a pendulum as an illustration, we derive general analytical expressions for the time evolution of expectation values of observables and their long-time limits. We find that the deviation of the long-time expectation value from its classical value scales as 1/O(ln N), where N is the number of atoms in the condensate. Furthermore, the relaxation of an observable to its steady state value is a damped oscillation and the damping is Gaussian in time. We confirm our results with numerical TWA simulations.

}, doi = {10.1103/PhysRevA.96.013604}, url = {https://arxiv.org/abs/1705.01702}, author = {Ranchu Mathew and Eite Tiesinga} } @article {1781, title = {A Hubbard model for ultracold bosonic atoms interacting via zero-point-energy induced three-body interactions}, journal = {Physical Review A}, volume = {93}, year = {2016}, month = {2016/04/19}, pages = {043616}, abstract = {We show that for ultra-cold neutral bosonic atoms held in a three-dimensional periodic potential or optical lattice, a Hubbard model with dominant, attractive three-body interactions can be generated. In fact, we derive that the effect of pair-wise interactions can be made small or zero starting from the realization that collisions occur at the zero-point energy of an optical lattice site and the strength of the interactions is energy dependent from effective-range contributions. We determine the strength of the two- and three-body interactions for scattering from van-der-Waals potentials and near Fano-Feshbach resonances. For van-der-Waals potentials, which for example describe scattering of alkaline-earth atoms, we find that the pair-wise interaction can only be turned off for species with a small negative scattering length, leaving the 88Sr isotope a possible candidate. Interestingly, for collisional magnetic Feshbach resonances this restriction does not apply and there often exist magnetic fields where the two-body interaction is small. We illustrate this result for several known narrow resonances between alkali-metal atoms as well as chromium atoms. Finally, we compare the size of the three-body interaction with hopping rates and describe limits due to three-body recombination.

}, doi = {10.1103/PhysRevA.93.043616}, url = {http://journals.aps.org/pra/abstract/10.1103/PhysRevA.93.043616}, author = {Saurabh Paul and P. R. Johnson and Eite Tiesinga} } @article {1914, title = {Multiple scattering dynamics of fermions at an isolated p-wave resonance}, journal = {Nature Communications}, volume = {7}, year = {2016}, month = {2016/07/11}, pages = {12069}, abstract = {The wavefunction for indistinguishable fermions is anti-symmetric under particle exchange, which directly leads to the Pauli exclusion principle, and hence underlies the structure of atoms and the properties of almost all materials. In the dynamics of collisions between two indistinguishable fermions this requirement strictly prohibits scattering into 90 degree angles. Here we experimentally investigate the collisions of ultracold clouds fermionic\

We determine the exact time evolution of an initial Bardeen-Cooper-Schrieffer (BCS) state of ultra-cold atoms in a hexagonal optical lattice. The dynamical evolution is triggered by ramping the lattice potential up, such that the interaction strength Uf is much larger than the hopping amplitude Jf. The quench initiates collective oscillations with frequency |Uf|/(2π) in the momentum occupation numbers and imprints an oscillating phase with the same frequency on the order parameter Δ. The latter is not reproduced by treating the time evolution in mean-field theory. The momentum density-density or noise correlation functions oscillate at frequency |Uf|/2π as well as its second harmonic. For a very deep lattice, with negligible tunneling energy, the oscillations of momentum occupation numbers are undamped. Non-zero tunneling after the quench leads to dephasing of the different momentum modes and a subsequent damping of the oscillations. This occurs even for a finite-temperature initial BCS state, but not for a non-interacting Fermi gas. We therefore propose to use this dephasing to detect a BCS state. Finally, we predict that the noise correlation functions in a honeycomb lattice will develop strong anti-correlations near the Dirac point.

}, doi = {http://dx.doi.org/10.1103/PhysRevA.94.023607}, url = {http://arxiv.org/abs/1602.00979}, author = {Marlon Nuske and L. Mathey and Eite Tiesinga} } @article {1823, title = {Wannier functions using a discrete variable representation for optical lattices}, journal = {Physical Review A}, volume = {94}, year = {2016}, month = {2016/09/07}, pages = {033606}, abstract = {We propose a numerical method using the discrete variable representation (DVR) for constructing real-valued Wannier functions localized in a unit cell for both symmetric and asymmetric periodic potentials. We apply these results to finding Wannier functions for ultracold atoms trapped in laser-generated optical lattices. Following S. Kivelson [Phys. Rev. B\ 26, 4269 (1982)], for a symmetric lattice with inversion symmetry, we construct Wannier functions as eigenstates of the position operators\