Heavy solitons in a fermionic superfluid

Overcrowding induces fast colloidal solitons in a slowly rotating potential landscape

Collective particle transport across periodic energy landscapes is ubiquitously present in many condensed matter systems spanning from vortices in high-temperature superconductors, frictional atomic sliding, driven skyrmions to biological and active matter. Here we report the emergence of fast solitons propagating against a rotating optical landscape. These experimentally observed solitons are stable cluster waves that originate from a coordinated particle exchange process which occurs when the number of trapped microparticles exceeds the number of potential wells. The size and speed of individual solitons rapidly increase with the particle diameter as predicted by theory and confirmed by numerical simulations. We show that when several solitons coexist, an effective repulsive interaction can stabilize their propagation along the periodic potential. Our experiments demonstrate a generic mechanism for cluster-mediated transport with potential applications to condensed matter systems on different length scales.

Fundamental dissipation due to bound fermions in the zero-temperature limit

The ground state of a fermionic condensate is well protected against perturbations in the presence of an isotropic gap. Regions of gap suppression, surfaces and vortex cores which host Andreev-bound states, seemingly lift that strict protection. Here we show that in superfluid 3He the role of bound states is more subtle: when a macroscopic object moves in the superfluid at velocities exceeding the Landau critical velocity, little to no bulk pair breaking takes place, while the damping observed originates from the bound states covering the moving object. We identify two separate timescales that govern the bound state dynamics, one of them much longer than theoretically anticipated, and show that the bound states do not interact with bulk excitations.

Jackiw-Rebbi states and trivial states in interfaced binary waveguide arrays with cubic-quintic nonlinearity

We systematically investigate two types of localized states-one is the optical analog of the quantum relativistic Jackiw-Rebbi states and the other is the trivial localized state-in interfaced binary waveguide arrays in the presence of cubic-quintic nonlinearity. By using the shooting method, we can exactly calculate the profiles of these nonlinear localized states. Like in the case with Kerr nonlinearity, we demonstrate that these localized states with cubic-quintic nonlinearity also have an extraordinary property, which completely differs from many well-known nonlinear localized structures in other media. Specifically, both the peak amplitude and transverse dimension of these nonlinear localized states can increase at the same time. Apart from that, we show that high values of the saturation nonlinearity parameter can help to generate and stabilize the intense localized states during propagation, especially in the case with a negative coefficient for the cubic nonlinearity term.

Creating oscillons and oscillating kinks in two scalar field theories

Oscillons are time-dependent, localized in space, extremely long-lived states in nonlinear scalar-field models, while kinks are topological solitons in one spatial dimension. In the present work, we show new classes of oscillons and oscillating kinks in a system of two nonlinearly coupled scalar fields in 1+1 spatiotemporal dimensions. The solutions contain a control parameter, the variation of which produces oscillons and kinks with a flat-top shape. The model finds applications in condensed matter, cosmology, and high-energy physics.

Majorana Corner Modes with Solitons in an Attractive Hubbard-Hofstadter Model of Cold Atom Optical Lattices

Higher-order topological superconductors hosting Majorana-Kramers pairs (MKPs) as corner modes have recently been proposed in a two-dimensional quantum spin Hall insulator proximity-coupled to unconventional cuprate or iron-based superconductors. Here, we show that such MKPs can be realized using a conventional s-wave superfluid with a soliton in cold atom systems governed by the Hubbard-Hofstadter model. The MKPs emerge in the presence of interaction at the "corners" defined by the intersections of line solitons and the one-dimensional edges of the system. Our scheme is based on the recently realized cold atom Hubbard-Hofstadter lattice and will pave the way for observing possible higher-order topological superfluidity with conventional s-wave superfluids or superconductors.

Flemish Strings of Magnetic Solitons and a Nonthermal Fixed Point in a One-Dimensional Antiferromagnetic Spin-1 Bose Gas

Thermalization in a quenched one-dimensional antiferromagnetic spin-1 Bose gas is shown to proceed via a nonthermal fixed point through annihilation of Flemish-string bound states of magnetic solitons. A possible experimental situation is discussed.

Review of pseudogaps in strongly interacting Fermi gases

A central challenge in modern condensed matter physics is developing the tools for understanding nontrivial yet unordered states of matter. One important idea to emerge in this context is that of a 'pseudogap': the fact that under appropriate circumstances the normal state displays a suppression of the single particle spectral density near the Fermi level, reminiscent of the gaps seen in ordered states of matter. While these concepts arose in a solid state context, they are now being explored in cold gases. This article reviews the current experimental and theoretical understanding of the normal state of strongly interacting Fermi gases, with particular focus on the phenomonology which is traditionally associated with the pseudogap.

Two-terminal transport measurements with cold atoms

In recent years, the ability of cold atom experiments to explore condensed-matter-related questions has dramatically progressed. Transport experiments, in particular, have expanded to the point in which conductance and other transport coefficients can now be measured in a way that is directly analogous to solid-state physics, extending cold-atom-based quantum simulations into the domain of quantum electronic devices. In this topical review, we describe the transport experiments performed with cold gases in the two-terminal configuration, with an emphasis on the specific features of cold atomic gases compared to solid-state physics. We present the experimental techniques and the main experimental findings, focusing on-but not restricted to-the recent experiments performed by our group. We finally discuss the perspectives opened up by this approach, the main technical and conceptual challenges for future developments, and potential applications in quantum simulation for transport phenomena and mesoscopic physics problems.

Dynamics of Fragmented Condensates and Macroscopic Entanglement

The relative phase of the order parameters in the collision of two condensates can influence the outcome of their collision in the case of weak coupling. With increasing interaction strength, however, the initially independent phases of the two order parameters in the colliding partners quickly become phase locked, as the strong coupling favors an overall phase rigidity of the entire condensate, and upon their separation the emerging superfluid fragments become entangled.

Collective Modes of a Soliton Train in a Fermi Superfluid

We characterize the collective modes of a soliton train in a quasi-one-dimensional Fermi superfluid, using a mean-field formalism. In addition to the expected Goldstone and Higgs modes, we find novel long-lived gapped modes associated with oscillations of the soliton cores. The soliton train has an instability that depends strongly on the interaction strength and the spacing of solitons. It can be stabilized by filling each soliton with an unpaired fermion, thus forming a commensurate Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We find that such a state is always dynamically stable, which paves the way for realizing long-lived FFLO states in experiments via phase imprinting.

Kinetic theory of dark solitons with tunable friction

We study controllable friction in a system consisting of a dark soliton in a one-dimensional Bose-Einstein condensate coupled to a noninteracting Fermi gas. The fermions act as impurity atoms, not part of the original condensate, that scatter off of the soliton. We study semiclassical dynamics of the dark soliton, a particlelike object with negative mass, and calculate its friction coefficient. Surprisingly, it depends periodically on the ratio of interspecies (impurity-condensate) to intraspecies (condensate-condensate) interaction strengths. By tuning this ratio, one can access a regime where the friction coefficient vanishes. We develop a general theory of stochastic dynamics for negative-mass objects and find that their dynamics are drastically different from their positive-mass counterparts: they do not undergo Brownian motion. From the exact phase-space probability distribution function (i.e., in position and velocity), we find that both the trajectory and lifetime of the soliton are altered by friction, and the soliton can undergo Brownian motion only in the presence of friction and a confining potential. These results agree qualitatively with experimental observations by Aycock et al. [Proc. Natl. Acad. Sci. USA 114, 2503 (2017)] in a similar system with bosonic impurity scatterers.

Traveling Majorana Solitons in a Low-Dimensional Spin-Orbit-Coupled Fermi Superfluid

We investigate traveling solitons of a one- or two-dimensional spin-orbit-coupled Fermi superfluid in both topologically trivial and nontrivial regimes by solving the static and time-dependent Bogoliubov-de Gennes equations. We find a critical velocity v_{h} for traveling solitons that is much smaller than the value predicted using the Landau criterion due to spin-orbit coupling. Above v_{h}, our time-dependent simulations in harmonic traps indicate that traveling solitons decay by radiating sound waves. In the topological phase, we predict the existence of peculiar Majorana solitons, which host two Majorana fermions and feature a phase jump of π across the soliton, irrespective of the velocity of travel. These unusual properties of Majorana solitons may open an alternative way to manipulate Majorana fermions for fault-tolerant topological quantum computations.

Integrable model for density-modulated quantum condensates: Solitons passing through a soliton lattice

An integrable model possessing inhomogeneous ground states is proposed as an effective model of nonuniform quantum condensates such as supersolids and Fulde-Ferrell-Larkin-Ovchinnikov superfluids. The model is a higher-order analog of the nonlinear Schrödinger equation. We derive an n-soliton solution via the inverse scattering theory with elliptic-functional background and reveal various kinds of soliton dynamics such as dark soliton billiards, dislocations, gray solitons, and envelope solitons. We also provide the exact bosonic and fermionic quasiparticle eigenstates and show their tunneling phenomena. The solutions are expressed by a determinant of theta functions.

Cascade of Solitonic Excitations in a Superfluid Fermi gas: From Planar Solitons to Vortex Rings and Lines

We follow the time evolution of a superfluid Fermi gas of resonantly interacting ^{6}Li atoms after a phase imprint. Via tomographic imaging, we observe the formation of a planar dark soliton, its subsequent snaking, and its decay into a vortex ring, which, in turn, breaks to finally leave behind a single solitonic vortex. In intermediate stages, we find evidence for an exotic structure resembling the Φ soliton, a combination of a vortex ring and a vortex line. Direct imaging of the nodal surface reveals its undulation dynamics and its decay via the puncture of the initial soliton plane. The observed evolution of the nodal surface represents dynamics beyond superfluid hydrodynamics, calling for a microscopic description of unitary fermionic superfluids out of equilibrium.

Dynamics and Interaction of Vortex Lines in an Elongated Bose-Einstein Condensate

We study the real-time dynamics of vortices in a large elongated Bose-Einstein condensate (BEC) of sodium atoms using a stroboscopic technique. Vortices are produced via the Kibble-Zurek mechanism in a quench across the BEC transition and they slowly precess keeping their orientation perpendicular to the long axis of the trap as expected for solitonic vortices in a highly anisotropic condensate. Good agreement with theoretical predictions is found for the precession period as a function of the orbit amplitude and the number of condensed atoms. In configurations with two or more vortices, we see signatures of vortex-vortex interaction in the shape and visibility of the orbits. In addition, when more than two vortices are present, their decay is faster than the thermal decay observed for one or two vortices. The possible role of vortex reconnection processes is discussed.

Analytical solitonlike solutions and the dynamics of ultracold Fermi gases in a time-dependent three-dimensional harmonic potential

We present a theoretical study of solitonlike solutions and their dynamics of ultracold superfluid Fermi gases trapped in a time-dependent three-dimensional (3D) harmonic potential with gain or loss. The 3D analytical solitonlike solutions are obtained without introducing any additional integrability constraints used elsewhere. The propagation of both bright- and dark-soliton-like solutions is investigated. We show that the amplitudes of dark-soliton-like solutions exhibit periodic oscillation, whereas those of the bright-soliton-like ones do not show such behavior. Moreover, we highlight that the oscillation periods of dark-soliton-like solutions predicted by our approach are matched very well with those observed in a recent experiment carried out by Yefsah et al. [T. Yefsah, A. T. Sommer, M. J. H. Ku, L. W. Cheuk, W. Ji, W. S. Bakr, and M. W. Zwierlein, Nature (London) 499, 426 (2013)NATUAS0028-083610.1038/nature12338] in both Bose-Einstein condensation and unitarity regimes.

Chladni solitons and the onset of the snaking instability for dark solitons in confined superfluids

Complex solitary waves composed of intersecting vortex lines are predicted in a channeled superfluid. Their shapes in a cylindrical trap include a cross, spoke wheels, and Greek Φ, and trace the nodal lines of unstable vibration modes of a planar dark soliton in analogy to Chladni's figures of membrane vibrations. The stationary solitary waves extend a family of solutions that include the previously known solitonic vortex and vortex rings. Their bifurcation points from the dark soliton indicating the onset of new unstable modes of the snaking instability are predicted from scale separation for Bose-Einstein condensates (BECs) and superfluid Fermi gases across the BEC-BCS crossover, and confirmed by full numerical calculations. Chladni solitons could be observed in ultracold gas experiments by seeded decay of dark solitons.

Dark solitons with Majorana fermions in spin-orbit-coupled Fermi gases

We show that a single dark soliton can exist in a spin-orbit-coupled Fermi gas with a high spin imbalance, where spin-orbit coupling favors uniform superfluids over nonuniform Fulde-Ferrell-Larkin-Ovchinnikov states, leading to dark soliton excitations in highly imbalanced gases. Above a critical spin imbalance, two topological Majorana fermions without interactions can coexist inside a dark soliton, paving a way for manipulating Majorana fermions through controlling solitons. At the topological transition point, the atom density contrast across the soliton suddenly vanishes, suggesting a signature for identifying topological solitons.

Phase imprinting in equilibrating Fermi gases: the transience of vortex rings and other defects

We present numerical simulations of phase imprinting experiments in ultracold trapped Fermi gases, which were obtained independently and are in good agreement with recent experimental results. Our focus is on the sequence and evolution of defects using the fermionic time-dependent Ginzburg-Landau equation, which contains dissipation necessary for equilibration. In contrast to other simulations, we introduce small, experimentally unavoidable symmetry breaking, particularly that associated with thermal fluctuations and with the phase-imprinting tilt angle, and we illustrate their dramatic effects. As appears consistent with experiment, the former causes vortex rings in confined geometries to move to the trap surface and rapidly decay into more stable vortex lines. The latter aligns the precessing and relatively long-lived vortex filaments, rendering them difficult to distinguish from solitons.

Probing the topological properties of the Jackiw-Rebbi model with light

The Jackiw-Rebbi model describes a one-dimensional Dirac field coupled to a soliton field and can be equivalently thought of as a model describing a Dirac field with a spatially dependent mass term. Neglecting the dynamics of the soliton field, a kink in the background soliton profile yields a topologically protected zero-energy mode for the field, which in turn leads to charge fractionalisation. We show here that the model, in the first quantised form, can be realised in a driven slow-light setup, where photons mimic the Dirac field and the soliton field can be implemented–and tuned–by adjusting optical parameters such as the atom-photon detuning. Furthermore, we discuss how the existence of the zero-mode and its topological stability can be probed naturally by studying the transmission spectrum. We conclude by analysing the robustness of our approach against possible experimental errors in engineering the Jackiw-Rebbi Hamiltonian in this optical setup.

Observation of solitonic vortices in Bose-Einstein condensates

We observe solitonic vortices in an atomic Bose-Einstein condensate (BEC) after free expansion. Clear signatures of the nature of such defects are the twisted planar density depletion around the vortex line, observed in absorption images, and the double dislocation in the interference pattern obtained through homodyne techniques. Both methods allow us to determine the sign of the quantized circulation. Experimental observations agree with numerical simulations. These solitonic vortices are the decay product of phase defects of the BEC order parameter spontaneously created after a rapid quench across the BEC transition in a cigar-shaped harmonic trap and are shown to have a very long lifetime.

Motion of a solitonic vortex in the BEC-BCS crossover

We observe a long-lived solitary wave in a superfluid Fermi gas of (6)Li atoms after phase imprinting. Tomographic imaging reveals the excitation to be a solitonic vortex, oriented transverse to the long axis of the cigar-shaped atom cloud. The precessional motion of the vortex is directly observed, and its period is measured as a function of the chemical potential in the BEC-BCS crossover. The long period and the correspondingly large ratio of the inertial to the bare mass of the vortex are in good agreement with estimates based on superfluid hydrodynamics that we derive here using the known equation of state in the BEC-BCS crossover.

Resistive flow in a weakly interacting Bose-Einstein condensate

We report the direct observation of resistive flow through a weak link in a weakly interacting atomic Bose-Einstein condensate. Two weak links separate our ring-shaped superfluid atomtronic circuit into two distinct regions, a source and a drain. Motion of these weak links allows for creation of controlled flow between the source and the drain. At a critical value of the weak link velocity, we observe a transition from superfluid flow to superfluid plus resistive flow. Working in the hydrodynamic limit, we observe a conductivity that is 4 orders of magnitude larger than previously reported conductivities for a Bose-Einstein condensate with a tunnel junction. Good agreement with zero-temperature Gross-Pitaevskii simulations and a phenomenological model based on phase slips indicate that the creation of excitations plays an important role in the resulting conductivity. Our measurements of resistive flow elucidate the microscopic origin of the dissipation and pave the way for more complex atomtronic devices.

Many-body matter-wave dark soliton

The Gross-Pitaevskii equation--which describes interacting bosons in the mean-field approximation--possesses solitonic solutions in dimension one. For repulsively interacting particles, the stationary soliton is dark, i.e., is represented by a local density minimum. Many-body effects may lead to filling of the dark soliton. Using quasiexact many-body simulations, we show that, in single realizations, the soliton appears totally dark although the single particle density tends to be uniform.

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.