Introduction to Nonlinear Phenomena in Superfluid Liquids and Bose-Einstein Condensates: Helium, Semiconductors and Graphene (original) (raw)

Bose condensation and superfluidity of excitons in a high magnetic field

Physical Review B, 1994

In a high magnetic field, such that the distance between the Landau levels exceeds the binding energy of an exciton, an exciton gas in a semiconductor is capable of forming the Bose-Einstein condensate as well as a superfluid state even at a relatively high temperature. We consider the problem of excitonic interaction in a semiconductor in its multielectron formulation, starting from the second-quantization representation of the Hamiltonian of interacting electrons and holes in a high magnetic field. The expressions for the ground-state energy, the chemical potential, and the spectrum of elementary excitations of the system are obtained in a linear approximation in the concentration of excitons. It is shown that a system of excitons in a high magnetic field is similar to a weakly nonideal Bose gas. The existence and the stability of the Bose condensate due to an essential decrease of the interaction between excitons and an increase of their binding energy in a high magnetic field are established at a high density of excitons.

The Superfluid State of a Bose Liquid as a Superposition of a Single-Particle and Pair Coherent Condensates

arXiv (Cornell University), 2001

One considers the superfluid (SF) state of a Bose liquid with a strong repulsion between bosons, in which at T=0, along with a weak single-particle Bose-Einstein condensate (BEC), there exists an intensive pair coherent condensate (PCC), analogous to the Cooper condensate in a Fermi liquid with an attraction between the fermions. Such a PCC emerges in a system of bosons due to an oscillating sign-changing momentum dependence of the Fourier component of the pair interaction potential, which is characteristic of a certain family of repulsion potentials. In such cases, the Fourier component is negative in some domain of nonzero momentum transfer, which corresponds to an effective attraction. The collective effects of renormalization (``screening'') of the initial interaction lead to a suppression of the repulsion and an enhancement of the effective attraction. It is the ratio of the BEC density to the full density of the liquid n0/nll1n_0/n\ll 1n0/nll1 that is used as a small parameter---unlike in the Bogolyubov theory for a quasi-ideal Bose gas, in which the small parameter is the ratio of the number of supracondensate excitations to the number of particles in an intensive BEC, (n−n0)/n0ll1(n-n_0)/n_0\ll 1(nn_0)/n_0ll1. A closed system of nonlinear integral equations for the normal and anomalous self-energy parts is obtained, in the framework of a renormalized perturbation theory built on combined hydrodynamic and field variables. In the framework of the hard-spheres model, a spectrum of quasiparticles is obtained, which is in good accordance with the experimental spectrum of elementary excitations in superfluid 4^44He. The question of applicability of the Landau criterion in the absence of quantum vortices is discussed.

Bose-Einstein condensation and superfluidity of magnetobiexcitons in quantum wells' and graphene superlattices

2007

We propose the Bose-Einstein condensation (BEC) and superfluidity of quasi-two-dimensional (2D) spatially indirect magnetobiexcitons in a slab of superlattice with alternating electron and hole layers consisting from the semiconducting quantum wells (QWs) and graphene superlattice in high magnetic field. The two different Hamiltonians of a dilute gas of magnetoexcitons with a dipole-dipole repulsion in superlattices consisting of both QWs and graphene layers in the limit of high magnetic field have been reduced to one effective Hamiltonian a dilute gas of two-dimensional excitons without magnetic field. Moreover, for N excitons we have reduced the problem of 2N × 2 dimensional space onto the problem of N × 2 dimensional space by integrating over the coordinates of the relative motion of an electron (e) and a hole (h). The instability of the ground state of the system of interacting two-dimensional indirect magnetoexcitons in a slab of superlattice with alternating electron and hole layers in high magnetic field is established. The stable system of indirect quasi-two-dimensional magnetobiexcitons, consisting of pair of indirect excitons with opposite dipole moments is considered. The density of superfluid component ns(T) and the temperature of the Kosterlitz-Thouless phase transition to the superfluid state in the system of two-dimensional indirect magnetobiexcitons, interacting as electrical quadrupoles, are obtained for both QW and graphene realizations.

Dynamical Superfluid-Insulator Transition in a Chain of Weakly Coupled Bose-Einstein Condensates

Physical Review Letters, 2002

We predict a dynammical classical superfluid-insulator transition (CSIT) in a Bose-Einstein condensate (BEC) trapped in an optical and a magnetic potential. In the tight-binding limit, this system realizes an array of weakly-coupled condensates driven by an external harmonic field. For small displacements of the parabolic trap about the equilibrium position, the BEC center of mass oscillates with the relative phases of neighbouring condensates locked at the same (oscillating) value. For large displacements, the BEC remains localized on the side of the harmonic trap. This is caused by a randomization of the relative phases, while the coherence of each individual condensate in the array is preserved. The CSIT is attributed to a discrete modulational instability, occurring when the BEC center of mass velocity is larger than a critical value, proportional to the tunneling rate between adjacent sites.

Bose-Einstein condensation and superfluidity of magnetoexcitons in bilayer graphene

Physical Review B, 2008

We propose the Bose-Einstein condensation (BEC) and superfluidity of quasi-two-dimensional (2D) spatially indirect magnetobiexcitons in a slab of superlattice with alternating electron and hole layers consisting from the semiconducting quantum wells (QWs) and graphene superlattice in high magnetic field. The two different Hamiltonians of a dilute gas of magnetoexcitons with a dipole-dipole repulsion in superlattices consisting of both QWs and graphene layers in the limit of high magnetic field have been reduced to one effective Hamiltonian a dilute gas of two-dimensional excitons without magnetic field. Moreover, for N excitons we have reduced the problem of 2N × 2 dimensional space onto the problem of N × 2 dimensional space by integrating over the coordinates of the relative motion of an electron (e) and a hole (h). The instability of the ground state of the system of interacting two-dimensional indirect magnetoexcitons in a slab of superlattice with alternating electron and hole layers in high magnetic field is established. The stable system of indirect quasi-two-dimensional magnetobiexcitons, consisting of pair of indirect excitons with opposite dipole moments is considered. The density of superfluid component ns(T ) and the temperature of the Kosterlitz-Thouless phase transition to the superfluid state in the system of two-dimensional indirect magnetobiexcitons, interacting as electrical quadrupoles, are obtained for both QW and graphene realizations.

Turbulence in a Bose-Einstein condensate of dipolar excitons in coupled quantum wells

Physical Review B, 2012

The nonlinear dynamics of a Bose-Einstein condensate (BEC) of dipolar excitons trapped in an external confining potential in coupled quantum wells is analyzed. It is demonstrated that under typical experimental conditions the dipolar exciton BEC can be described by a generalized Gross-Pitaevskii equation with the local interaction between the excitons, which depends on the exciton distribution function. It is shown that, if the system is pumped at sufficiently high frequencies, a steady turbulent state can be formed.

Superfluidity near phase separation in Bose-Fermi mixtures

The European Physical Journal B, 2009

We study the transition to fermion pair superfluidity in a mixture of interacting bosonic and fermionic atoms. The fermion interaction induced by the bosons and the dynamical screening of the condensate phonons due to fermions are included using the nonperturbative Hamiltonian flow equations. We determine the bosonic spectrum near the transition towards phase separation and find that the superfluid transition temperature may be increased substantially due to phonon damping. PACS. 67.85.De Dynamic properties of condensates; excitations, and superfluid flow -67.85.Fg Multicomponent condensates; spinor condensates -67.85.Pq Mixtures of Bose and Fermi gases -74.20.Fg BCS theory and its development

Superfluidity versus Bose-Einstein condensation in a Bose gas with disorder

Physical Review A, 2002

We investigate the phenomenon of Bose-Einstein condensation and superfluidity in a Bose gas at zero temperature with disorder. By using the Diffusion Monte-Carlo method we calculate the superfluid and the condensate fraction of the system as a function of density and strength of disorder. In the regime of weak disorder we find agreement with the analytical results obtained within the Bogoliubov model. For strong disorder the system enters an unusual regime where the superfluid fraction is smaller than the condensate fraction.