Two-dimensional Superfluid Research Articles

Effective theory of chiral two-dimensional superfluids

We construct, to leading orders in the momentum expansion, an effective theory of a chiral $p_x + ip_y$ two-dimensional fermionic superfluid at zero temperature that is consistent with nonrelativistic general coordinate invariance. This theory naturally incorporates the parity and time reversal violating effects such as the Hall viscosity and the edge current. The particle number current and stress tensor are computed and their linear response to electromagnetic and gravitational sources is calculated. We also consider an isolated vortex in a chiral superfluid and identify the leading chirality effect in the density depletion profile.

Transitions and excitations in a superfluid stream passing small impurities

We analyze asymptotically and numerically the motion around a single impurity and a network of impurities inserted in a two-dimensional superfluid. The criticality for the breakdown of superfluidity is shown to occur when it becomes energetically favorable to create a doublet---the limiting case between a vortex pair and a rarefaction pulse on the surface of the impurity. Depending on the characteristics of the potential representing the impurity, different excitation scenarios are shown to exist for a single impurity as well as for a lattice of impurities. Depending on the lattice characteristics it is shown that several regimes are possible: dissipationless flow, excitations emitted by the lattice boundary, excitations created in the bulk, and the formation of large-scale structures.

The internal structure of a vortex in a two-dimensional superfluid with long healing length and its implications

We analyze the motion of quantum vortices in a two-dimensional spinless superfluid within Popov’s hydrodynamic description. In the long healing length limit (where a large number of particles are inside the vortex core) the superfluid dynamics is determined by saddle points of Popov’s action, which, in particular, allows for weak solutions of the Gross–Pitaevskii equation. We solve the resulting equations of motion for a vortex moving with respect to the superfluid and find the reconstruction of the vortex core to be a non-analytic function of the force applied on the vortex. This response produces an anomalously large dipole moment of the vortex and, as a result, the spectrum associated with the vortex motion exhibits narrow resonances lying within the phonon part of the spectrum, contrary to traditional view.

Light-cone effect and supersonic correlations in one- and two-dimensional bosonic superfluids

We study the spreading of density-density correlations in Bose-Hubbard models after a quench of the interaction strength, using time-dependent variational Monte Carlo simulations. It gives access to unprecedented long propagation times and to dimensions higher than one. In both one and two dimensions, we find ballistic light-cone spreading of correlations and extract accurate values of the light-cone velocity in the superfluid regime. We show that the spreading of correlations is generally supersonic, with a light-cone propagating faster than sound modes but slower than the maximum group velocity of density excitations, except at the Mott transition, where all the characteristic velocities are equal. Further, we show that in two dimensions the correlation spreading is highly anisotropic and presents nontrivial interference effects.

Holographic Vortex Liquids and Superfluid Turbulence

Superfluid turbulence is a fascinating phenomenon for which a satisfactory theoretical framework is lacking. Holographic duality provides a systematic approach to studying such quantum turbulence by mapping the dynamics of a strongly interacting quantum liquid into the dynamics of classical gravity. We use this gravitational description to numerically construct turbulent flows in a holographic superfluid in two spatial dimensions. We find that the superfluid kinetic energy spectrum obeys the Kolmogorov -5/3 scaling law, with energy injected at long wavelengths undergoing a direct cascade to short wavelengths where dissipation by vortex annihilation and vortex drag becomes efficient. This dissipation has a simple gravitational interpretation as energy flux across a black hole event horizon.

Exact Solution for Vortex Dynamics in Temperature Quenches of Two-Dimensional Superfluids

An exact analytic solution for the dynamics of vortex pairs is obtained for rapid temperature quenches of a superfluid film starting from the line of critical points below the critical temperature T(KT). An approximate solution for quenches at and above above T(KT) provides insights into the origin of logarithmic transients in the vortex decay, and is in general agreement with recent simulations of the quenched XY model. These results confirm that there is no "creation" of vortices whose density increases with the quench rate as predicted by the Kibble-Zurek theory but only monotonic decay of the thermal vortices already present at the initial temperature.

Higgs Mode in a Two-Dimensional Superfluid

We present solid evidence for the existence of a well-defined Higgs amplitude mode in two-dimensional relativistic field theories based on analytically continued results from quantum Monte Carlo simulations of the Bose-Hubbard model in the vicinity of the superfluid-Mott insulator quantum critical point, featuring emergent particle-hole symmetry and Lorentz invariance. The Higgs boson, seen as a well-defined low-frequency resonance in the spectral density, is quickly pushed to high energies in the superfluid phase and disappears by merging with the broad secondary peak at the characteristic interaction scale. Simulations of a trapped system of ultracold (87)Rb atoms demonstrate that the low-frequency resonance is lost for typical experimental parameters, while the characteristic frequency for the onset of a strong response is preserved.

Guiding-center dynamics of vortex dipoles in Bose-Einstein condensates

A quantized vortex dipole is the simplest vortex molecule, comprising two counter-circulating vortex lines in a superfluid. Although vortex dipoles are endemic in two-dimensional superfluids, the precise details of their dynamics have remained largely unexplored. We present here several striking observations of vortex dipoles in dilute-gas Bose-Einstein condensates, and develop a vortex-particle model that generates vortex line trajectories that are in good agreement with the experimental data. Interestingly, these diverse trajectories exhibit essentially identical quasi-periodic behavior, in which the vortex lines undergo stable epicyclic orbits.

Structure and consequences of vortex-core states inp-wave superfluids

It is now well established that in two-dimensional chiral p-wave paired superfluids, the vortices carry zero-energy modes which obey non-abelian exchange statistics and can potentially be used for topological quantum computation. In such superfluids there may also exist other excitations below the bulk gap inside the cores of vortices. We study the properties of these subgap states, and argue that their presence affects the topological protection of the zero modes. In conventional superconductors where the chemical potential is of the order of the Fermi energy of a non-interacting Fermi gas, there is a large number of subgap states and the mini-gap towards the lowest of these states is a small fraction of the Fermi energy. It is therefore difficult to cool the system to below the mini-gap and at experimentally available temperatures, transitions between the subgap states, including the zero modes, will occur and can alter the quantum states of the zero-modes. We show that compound qubits involving the zero-modes and the parity of the occupation number of the subgap states on each vortex are still well defined. However, practical schemes taking into account all subgap states would nonetheless be difficult to achieve. We propose to avoid this difficulty by working in the regime of small chemical potential mu, near the transition to a strongly paired phase, where the number of subgap states is reduced. We develop the theory to describe this regime of strong pairing interactions and we show how the subgap states are ultimately absorbed into the bulk gap. Since the bulk gap vanishes as mu -> 0 there is an optimum value mu_c which maximises the combined gap. We propose cold atomic gases as candidate systems where the regime of strong interactions can be explored, and explicitly evaluate mu_c in a Feshbach resonant K-40 gas.

Single vortex–antivortex pair in an exciton-polariton condensate

In a homogeneous two-dimensional system at non-zero temperature, although there can be no ordering of infinite range, a superfluid phase is predicted for a Bose liquid. The stabilization of phase in this superfluid regime is achieved by the formation of bound vortex-antivortex pairs. It is believed that several different systems share this common behaviour, when the parameter describing their ordered state has two degrees of freedom, and the theory has been tested for some of them. However, there has been no direct experimental observation of the phase stabilization mechanism by a bound pair. Here we present an experimental technique that can identify a single vortex-antivortex pair in a two-dimensional exciton polariton condensate. The pair is generated by the inhomogeneous pumping spot profile, and is revealed in the time-integrated phase maps acquired using Michelson interferometry, which show that the condensate phase is only locally disturbed. Numerical modelling based on open dissipative Gross-Pitaevskii equation suggests that the pair evolution is quite different in this non-equilibrium system compared to atomic condensates. Our results demonstrate that the exciton polariton condensate is a unique system for studying two-dimensional superfluidity in a previously inaccessible regime.

Rotons in a Hybrid Bose-Fermi System

We calculate the spectrum of elementary excitations in a two-dimensional exciton condensate in the vicinity of a two-dimensional electron gas. We show that attraction of excitons due to their scattering with free electrons may lead to formation of a roton minimum. The energy of this minimum may go below the ground state energy which manifests breaking of the superfluidity. The Berezinsky-Kosterlitz-Thouless phase transition temperature decreases due to the exciton-exciton attraction mediated by electrons.

Light cone dynamics and reverse Kibble-Zurek mechanism in two-dimensional superfluids following a quantum quench

We study the dynamics of the relative phase of a bilayer of two-dimensional superfluids after the two superfluids have been decoupled. We find that on short time scales the relative phase shows "light cone" like dynamics and creates a metastable superfluid state, which can be supercritical. We also demonstrate similar light cone dynamics for the transverse field Ising model. On longer time scales the supercritical state relaxes to a disordered state due to dynamical vortex unbinding. This scenario of dynamically suppressed vortex proliferation constitutes a reverse-Kibble-Zurek effect. We study this effect both numerically using truncated Wigner approximation and analytically within a newly suggested time dependent renormalization group approach (RG). In particular, within RG we show that there are two possible fixed points for the real time evolution corresponding to the superfluid and normal steady states. So depending on the initial conditions and the microscopic parameters of the Hamiltonian the system undergoes a non-equilibrium phase transition of the Kosterlitz-Thouless type. The time scales for the vortex unbinding near the critical point are exponentially divergent, similar to the equilibrium case.

Vortex nucleation in a mesoscopic Bose superfluid and breaking of the parity symmetry

We analyze vortex nucleation in mesoscopic two-dimensional Bose superfluid in a rotating trap. We explicitly include a weakly anisotropic stirring potential, breaking thus explicitly the axial symmetry. As the rotation frequency passes the critical value ${\ensuremath{\Omega}}_{c}$, the system undergoes an extra symmetry change or breaking. Well below ${\ensuremath{\Omega}}_{c}$, the ground state is properly described by the mean-field theory with an even condensate wave function. Well above ${\ensuremath{\Omega}}_{c}$, the mean-field solution works also well, but the order parameter becomes odd. This phenomenon involves therefore a discrete parity symmetry breaking. In the critical region, the mean-field solutions exhibit dynamical instability. The true many-body state is a strongly correlated entangled state involving two macroscopically occupied modes (eigenstates of the single-particle density operator). We characterize this state in various aspects: (i) the eligibility for adiabatic evolution, (ii) its analytical approximation given by the maximally entangled combination of two single modes, and finally (iii) its appearance in particle detection measurements.

Supercritical superfluid and vortex unbinding following a quantum quench

We study the dynamics of the relative phase of a bilayer of two-dimensional superfluids after the two superfluids have been decoupled, using truncated Wigner approximation. On short time scales the relative phase shows ``light-cone''-like thermalization and creates a metastable superfluid state, which can be supercritical. On longer time scales this state relaxes to a disordered state due to dynamical vortex unbinding. This scenario of dynamically suppressed vortex proliferation constitutes a reverse-Kibble-Zurek effect. We observe dynamics of creation of vortex-antivortex pairs and their consequent motion. Our predictions can be directly measured in interference experiments [Z. Hadzibabic et al., Nature (London) 441, 1118 (2006)].

Two-dimensional fermionic superfluids, pairing instability, and vortex liquids in the absence of time reversal symmetry

We consider a generic two-dimensional system of fermionic particles with attractive interactions and no disorder. If time-reversal symmetry is absent, it is possible to obtain incompressible insulating states in addition to the superfluid at zero temperature. The superfluid-insulator phase transition is found to be second order in type-II systems using a perturbative analysis of Cooper pairing instability in quantum Hall states of unpaired fermions. We obtain the pairing phase diagram as a function of chemical potential (density) and temperature. However, a more careful analysis presented here reveals that the pairing quantum phase transition is always preempted by another transition into a strongly correlated normal state which retains Cooper pairing and cannot be smoothly connected to the quantum Hall state of unpaired fermions. Such a normal phase can be qualitatively viewed as a liquid of vortices, although it may acquire conventional broken symmetries. Even if it did not survive at finite temperatures its influence would be felt through strong quantum fluctuations below a crossover temperature scale. These conclusions directly apply to fermionic ultra-cold atom systems near unitarity, but are likely relevant for the properties of other strongly correlated superfluids as well, including high temperature superconductors.

Quantum tunneling of vortices in two-dimensional superfluids

We examine the problem of quantum vortex tunneling in the Gross-Pitaevskii model. The effect of gapless phonons is to produce a super-Ohmic quantum dissipation that renormalizes the effective tunneling parameters but does not destroy quantum coherence. The renormalization of the instanton frequency is computed within a specific model tunneling potential.

Room-temperature superfluidity in graphene bilayers

Because graphene is an atomically two-dimensional gapless semiconductor with nearly identical conduction and valence bands, graphene-based bilayers are attractive candidates for high-temperature electron-hole pair condensation. We present estimates which suggest that the Kosterlitz-Thouless temperatures of these two-dimensional counterflow superfluids can approach room temperature.

One-dimensional phase transitions in a two-dimensional optical lattice

A phase transition for bosonic atoms in a two-dimensional anisotropic optical lattice is considered. If the tunnelling rates in two directions are different, the system can undergo a transition between a two-dimensional superfluid and a one-dimensional Mott insulating array of strongly coupled tubes. The connection to other lattice models is exploited in order to better understand the phase transition. Critical properties are obtained using quantum Monte Carlo calculations. These critical properties are related to correlation properties of the bosons and a criterion for commensurate filling is established.

Modeling the Berezinskii-Kosterlitz-Thouless transition inNiGa2S4

In the two-dimensional superfluidity, the proliferation of the vortices and the antivortices results in a class of phase transition, the Berezinskii-Kosterlitz-Thouless (BKT) transition. This class of phase transition is also anticipated in the two-dimensional magnetic systems. However, its existence in the real magnetic systems still remains mysterious. Here we propose a phenomenological model to illustrate that the spin-freezing transition recently uncovered in the nuclear magnetic-resonance experiment on the ${\text{NiGa}}_{2}{\text{S}}_{4}$ compound is of BKT type. The spin-freezing state observed in the ${\text{NiGa}}_{2}{\text{S}}_{4}$ possesses the power-law decayed spin correlation.

Transition from a Two-Dimensional Superfluid to a One-Dimensional Mott Insulator

A two-dimensional system of atoms in an anisotropic optical lattice is studied theoretically. If the system is finite in one direction, it is shown to exhibit a transition between a two-dimensional superfluid and a one-dimensional Mott insulating chain of superfluid tubes. Monte Carlo simulations are consistent with the expectation that the phase transition is of Kosterlitz-Thouless type. The effect of the transition on experimental time-of-flight images is discussed.