Fermionic quantum turbulence: Pushing the limits of high-performance computing.

Ultracold atoms provide a platform for analog quantum computer capable of simulating the quantum turbulence that underlies puzzling phenomena like pulsar glitches in rapidly spinning neutron stars. Unlike other platforms like liquid helium, ultracold atoms have a viable theoretical framework for dynamics, but simulations push the edge of current classical computers. We present the largest simulations of fermionic quantum turbulence to date and explain the computing technology needed, especially improvements in the Eigenvalue soLvers for Petaflop Applications library that enable us to diagonalize matrices of record size (millions by millions). We quantify how dissipation and thermalization proceed in fermionic quantum turbulence by using the internal structure of vortices as a new probe of the local effective temperature. All simulation data and source codes are made available to facilitate rapid scientific progress in the field of ultracold Fermi gases.

Atom Interferometric Imaging of Differential Potentials Using an Atom Laser.

Interferometry is a prime technique for modern precision measurements. Atoms, unlike light, have significant interactions with electric, magnetic, and gravitational fields, making their use in interferometric applications particularly versatile. Here, we demonstrate atom interferometry to image optical and magnetic potential landscapes over an area exceeding 240 µm×600 µm. The differential potentials employed in our experiments generate phase imprints in an atom laser that are made visible through a Ramsey pulse sequence. We further demonstrate how advanced pulse sequences can enhance desired imaging features, e.g., to image steep potential gradients. A theoretical discussion is presented that provides a semiclassical analysis and matching numerics.

Gravitational caustics in an atom laser.

Typically discussed in the context of optics, caustics are envelopes of classical trajectories (rays) where the density of states diverges, resulting in pronounced observable features such as bright points, curves, and extended networks of patterns. Here, we generate caustics in the matter waves of an atom laser, providing a striking experimental example of catastrophe theory applied to atom optics in an accelerated (gravitational) reference frame. We showcase caustics formed by individual attractive and repulsive potentials, and present an example of a network generated by multiple potentials. Exploiting internal atomic states, we demonstrate fluid-flow tracing as another tool of this flexible experimental platform. The effective gravity experienced by the atoms can be tuned with magnetic gradients, forming caustics analogous to those produced by gravitational lensing. From a more applied point of view, atom optics affords perspectives for metrology, atom interferometry, and nanofabrication. Caustics in this context may lead to quantum innovations as they are an inherently robust way of manipulating matter waves.

Negative-Mass Hydrodynamics in a Spin-Orbit-Coupled Bose-Einstein Condensate.

A negative effective mass can be realized in quantum systems by engineering the dispersion relation. A powerful method is provided by spin-orbit coupling, which is currently at the center of intense research efforts. Here we measure an expanding spin-orbit coupled Bose-Einstein condensate whose dispersion features a region of negative effective mass. We observe a range of dynamical phenomena, including the breaking of parity and of Galilean covariance, dynamical instabilities, and self-trapping. The experimental findings are reproduced by a single-band Gross-Pitaevskii simulation, demonstrating that the emerging features-shock waves, soliton trains, self-trapping, etc.-originate from a modified dispersion. Our work also sheds new light on related phenomena in optical lattices, where the underlying periodic structure often complicates their interpretation.

Vortex Pinning and Dynamics in the Neutron Star Crust.

The nature of the interaction between superfluid vortices and the neutron star crust, conjectured by Anderson and Itoh in 1975 to be at the heart vortex creep and the cause of glitches, has been a long-standing question in astrophysics. Using a qualitatively new approach, we follow the dynamics as superfluid vortices move in response to the presence of "nuclei" (nuclear defects in the crust). The resulting motion is perpendicular to the force, similar to the motion of a spinning top when pushed. We show that nuclei repel vortices in the neutron star crust, and characterize the force per unit length of the vortex line as a function of the vortex element to the nucleus separation.

Quantized superfluid vortex rings in the unitary Fermi gas.

In a recent article, Yefsah et al. [Nature (London) 499, 426 (2013)] report the observation of an unusual excitation in an elongated harmonically trapped unitary Fermi gas. After phase imprinting a domain wall, they observe oscillations almost an order of magnitude slower than predicted by any theory of domain walls which they interpret as a "heavy soliton" of inertial mass some 200 times larger than the free fermion mass or 50 times larger than expected for a domain wall. We present compelling evidence that this "soliton" is instead a quantized vortex ring, by showing that the main aspects of the experiment can be naturally explained within the framework of time-dependent superfluid density functional theories.

Strength of the vortex-pinning interaction from real-time dynamics.

We present an efficient and general method to compute vortex-pinning interactions--which arise in neutron stars, superconductors, and trapped cold atoms--at arbitrary separations using real-time dynamics. This method overcomes uncertainties associated with matter redistribution by the vortex position and the related choice of ensemble that plague the typical approach of comparing energy differences between stationary pinned and unpinned configurations: uncertainties that prevent agreement in the literature on the sign and magnitude of the vortex-nucleus interaction in the crust of neutron stars. We demonstrate and validate the method with Gross-Pitaevskii-like equations for the unitary Fermi gas, and demonstrate how the technique of adiabatic state preparation with time-dependent simulation can be used to calculate vortex-pinning interactions in fermionic systems such as the vortex-nucleus interaction in the crust of neutron stars.

Resonantly interacting fermions in a box.

We use two fundamental theoretical frameworks to study the finite-size (shell) properties of the unitary gas in a periodic box: (1) an ab initio quantum Monte Carlo (QMC) calculation for boxes containing 4 to 130 particles provides a precise and complete characterization of the finite-size behavior, and (2) a new density functional theory (DFT) fully encapsulates these effects. The DFT predicts vanishing shell structure for systems comprising more than 50 particles, and allows us to extrapolate the QMC results to the thermodynamic limit, providing the tightest bound to date on the ground-state energy of the unitary gas: ξ(S)≤0.383(1). We also apply the new functional to few-particle harmonically trapped systems, comparing with previous calculations.

Unitary Fermi supersolid: the Larkin-Ovchinnikov phase.

We present strong theoretical evidence that a Larkin-Ovchinnikov (LOFF/FFLO) pairing phase is favored over the homogeneous superfluid and normal phases in three-dimensional unitary Fermi systems. Using a density functional theory (DFT) based on the latest quantum Monte Carlo calculations and experimental results, we show that this phase is competitive over a large region of the phase diagram. The oscillations in the number densities and pairing field have a substantial amplitude, and a period some 3 to 10 times the average interparticle separation. Within the DFT, the transition to a normal polarized Fermi liquid at large polarizations is smooth, while the transition to a fully paired superfluid is abrupt.

Induced P-wave superfluidity in asymmetric fermi gases.

We show that two new intraspecies P-wave superfluid phases appear in two-component asymmetric Fermi systems with short-range S-wave interactions. In the BEC limit, phonons of the molecular BEC induce P-wave superfluidity in the excess fermions. In the BCS limit, density fluctuations induce P-wave superfluidity in both the majority and the minority species. These phases may be realized in experiments with spin-polarized Fermi gases.

Stability criteria for breached-pair superfluidity.

We present simple, concrete, two-fermion models that exhibit thermodynamically stable isotropic translationally invariant gapless superfluid states (breached-pair superfluidity). The mass ratio between the components and the momentum structure of the interaction are crucial for determining the stability of such states: idealized, momentum-independent ("contact") interactions are insufficient.