Mehrtash Babadi

Competition between pairing and ferromagnetic instabilities in ultracold Fermi gases near Feshbach resonances.

We study the quench dynamics of a two-component ultracold Fermi gas from the weak into the strong interaction regime, where the short time dynamics are governed by the exponential growth rate of unstable collective modes. We obtain an effective interaction that takes into account both Pauli blocking and the energy dependence of the scattering amplitude near a Feshbach resonance. Using this interaction we analyze the competing instabilities towards Stoner ferromagnetism and pairing.

Dynamical Cooper pairing in nonequilibrium electron-phonon systems

We analyze Cooper pairing instabilities in strongly driven electron-phonon systems. The light-induced nonequilibrium state of phonons results in a simultaneous increase of the superconducting coupling constant and the electron scattering. We demonstrate that the competition between these effects leads to an enhanced superconducting transition temperature in a broad range of parameters. Our results may explain the observed transient enhancement of superconductivity in several classes of materials upon irradiation with high intensity pulses of terahertz light, and may pave new ways for engineering high-temperature light-induced superconducting states.

Dynamical stability of a many-body Kapitza pendulum

We consider a many-body generalization of the Kapitza pendulum: the periodically-driven sine–Gordon model. We show that this interacting system is dynamically stable to periodic drives with finite frequency and amplitude. This finding is in contrast to the common belief that periodically-driven unbounded interacting systems should always tend to an absorbing infinite-temperature state. The transition to an unstable absorbing state is described by a change in the sign of the kinetic term in the Floquet Hamiltonian and controlled by the short-wavelength degrees of freedom. We investigate the stability phase diagram through an analytic high-frequency expansion, a self-consistent variational approach, and a numeric semiclassical calculation. Classical and quantum experiments are proposed to verify the validity of our results.

The theory of parametrically amplified electron-phonon superconductivity

Ultrafast optical manipulation of ordered phases in strongly correlated materials is a topic of significant theoretical, experimental, and technological interest. Inspired by a recent experiment on light-induced superconductivity in fullerenes [M. Mitrano et al., Nature (London) 530, 461 (2016)], we develop a comprehensive theory of light-induced superconductivity in driven electron-phonon systems with lattice nonlinearities. In analogy with the operation of parametric amplifiers, we show how the interplay between the external drive and lattice nonlinearities lead to significantly enhanced effective electron-phonon couplings. We provide a detailed and unbiased study of the nonequilibrium dynamics of the driven system using the real-time Greens function technique. To this end, we develop a Floquet generalization of the Migdal-Eliashberg theory and derive a numerically tractable set of quantum Floquet-Boltzmann kinetic equations for the coupled electron-phonon system. We study the role of parametric phonon generation and electronic heating in destroying the transient superconducting state. Finally, we predict the transient formation of electronic Floquet bands in time- and angle-resolved photoemission spectroscopy experiments as a consequence of the proposed mechanism.

Far-from-Equilibrium Field Theory of Many-Body Quantum Spin Systems: Prethermalization and Relaxation of Spin Spiral States in Three Dimensions

We study theoretically the far-from-equilibrium relaxation dynamics of spin spiral states in the three dimensional isotropic Heisenberg model. The investigated problem serves as an archetype for understanding quantum dynamics of isolated many-body systems in the vicinity of a spontaneously broken continuous symmetry. We present a field-theoretical formalism that systematically improves on mean-field for describing the real-time quantum dynamics of generic spin-1/2 systems. This is achieved by mapping spins to Majorana fermions followed by a 1/N expansion of the resulting two-particle irreducible (2PI) effective action. Our analysis reveals rich fluctuation-induced relaxation dynamics in the unitary evolution of spin spiral states. In particular, we find the sudden appearance of long-lived prethermalized plateaus with diverging lifetimes as the spiral winding is tuned toward the thermodynamically stable ferro- or antiferromagnetic phases. The emerging prethermalized states are characterized by different bosonic modes being thermally populated at different effective temperatures, and by a hierarchical relaxation process reminiscent of glassy systems. Spin-spin correlators found by solving the non-equilibrium Bethe-Salpeter equation provide further insight into the dynamic formation of correlations, the fate of unstable collective modes, and the emergence of fluctuation-dissipation relations. Our predictions can be verified experimentally using recent realizations of spin spiral states with ultracold atoms in a quantum gas microscope [S. Hild, et al. Phys. Rev. Lett. 113, 147205 (2014)].

Interaction of spherical colloidal particles in nematic media with degenerate planar anchoring

The interaction between two spherical colloidal particles with degenerate planar anchoring in a nematic media is studied by numerically minimizing the bulk Landau–de Gennes and surface energy using a finite element method. We find that the energy achieves its global minimum when the particles are in close contact and forming an angle θ = 28° ± 2 with respect to the bulk nematic director, in agreement with the experiments. Although the quadrupolar structure of the director field is preserved in the majority of configurations, we show that for smaller orientation angles and at smaller inter-particle separations, the axial symmetry of the topological defect-pairs is continuously broken, resulting in the emergence of an attractive interaction.

Density ordering instabilities of quasi-two-dimensional fermionic polar molecules in single-layer and multilayer configurations: Exact treatment of exchange interactions

We study the in-plane and out-of-plane density ordering instabilities of quasi-two-dimensional fermionic polar molecules in single-layer and multi-layer configurations. We locate the soft modes by evaluating linear response functions within the conserving time-dependent Hartree-Fock (TDHF). The short-range exchange effects are taken into account by solving the Bethe-Salpeter integral equation numerically. An instability phase diagram is calculated for both single-layer and multi-layer systems and the unstable wave-vector is indicated. In all cases, the in-plane density wave instability is found to precede the out-of-plane instability. The unstable wave-vector is found to be approximately twice the Fermi wave-vector of one of the subbands at a time and can change discontinuously as a function of density and dipolar interaction strength. In multi-layer configurations, we find a large enhancement of density wave instability driven by dilute quasiparticles in the first excited subband. Finally, we provide a simple qualitative description of the phase diagrams using a RPA-like approach. Compared to previous works done within the RPA approximation, we find that inclusion of exchange interactions stabilize the normal liquid phase further and increase the critical dipolar interaction strength corresponding to the onset of density-wave instability by over a factor of two.

Collective excitations of quasi-two-dimensional trapped dipolar fermions: Transition from collisionless to hydrodynamic regime

We study the collective excitations of polarized single-component quasi-two-dimensional dipolar fermions in an isotropic harmonic trap by solving the collisional Boltzmann-Vlasov (CBV) equation via the method of moments. We study the response to monopole and quadrupole perturbations of the trap potential and investigate thedynamicalcharacterofexcitationsineachcase.Simpleanalyticformulasarefoundusingthelinearizedscaling ansatzapproximationandaccuratenumericalresultsareobtainedbysatisfyingthefirsteightmomentsoftheCBV equation. Except for the lowest-lying monopole mode that is weakly affected by collisions, the quadrupole and the higher-order monopole modes undergo a transition from the collisionless regime to a dissipative crossover regime and finally approach the hydrodynamic regime upon increasing the dipolar interaction strength. For strong transverse confinement (2D limit), we predict the existence of a temperature window within which the characteristics of the collective modes become temperature independent. This plateau, which is a direct consequence of dipole-dipole scatterings, persists as long as the scattering energies remain in the near-threshold regime. The predictions of this work are expected to be observable in the current experiments.

Collective Phenomena in Quasi-Two-Dimensional Fermionic Polar Molecules: Band Renormalization and Excitons

We theoretically analyze a quasi-two-dimensional system of fermionic polar molecules trapped in a harmonic transverse confining potential. The renormalized energy bands are calculated by solving the Hartree-Fock equation numerically for various trap and dipolar interaction strengths. The intersubband excitations of the system are studied in the conserving time-dependent Hartree-Fock (TDHF) approximation from the perspective of lattice modulation spectroscopy experiments. We find that the excitation spectrum consists of both intersubband particle-hole excitation continua and antibound excitons whose antibinding behavior is associated to the anisotropic nature of dipolar interactions. The excitonic modes are shown to capture the majority of the spectral weight. We evaluate the intersubband transition rates in order to investigate the nature of the excitonic modes and find that they are antibound states formed from particle-hole excitations arising from several subbands. We discuss the sum rules in the context of lattice modulation spectroscopy experiments and utilize them to check the consistency of the obtained results. Our results indicate that the excitonic effects persist for interaction strengths and temperatures accessible in the current experiments with polar molecules.

Dynamical instabilities and transient short-range order in the fermionic Hubbard model

We study the dynamics of magnetic correlations in the half-filled fermionic Hubbard model following a fast ramp of the repulsive interaction. We use Schwinger-Keldysh self-consistent second-order perturbation theory to investigate the evolution of single-particle Greens functions and solve the non-equilibrium Bethe-Salpeter equation to study the dynamics of magnetic correlations. This approach gives us new insights into the interplay between single-particle relaxation dynamics and the growth of antiferromagnetic correlations. Depending on the ramping time and the final value of the interaction, we find different dynamical behavior which we illustrate using a dynamical phase diagram. Of particular interest is the emergence of a transient short-range ordered regime characterized by the strong initial growth of antiferromagnetic correlations followed by a decay of correlations upon thermalization. The discussed phenomena can be probed in experiments with ultracold atoms in optical lattices.