Variational theory for the ground state and collective excitations of an elongated dipolar condensate

We develop a variational theory for a dipolar condensate in an elongated(cigar shaped)confinement potential. Our formulation provides an effective one-dimensional extended meanfield theory for the ground state and its collective excitations. We apply our theory to investigate the properties of rotons in the system comparing the variational treatment to a full numerical solution. We consider the effect of quantum fluctuations on the scattering length at which the roton excitation softens to zero energy.     

Effects of Thermally Induced Roton-Like Excitation on the Superfluid Density of a Quasi-2D Dipolar Bose Condensed Gas

Using the Green's function approach, the density–density correlation function and the dielectric function in the random-phase approximation for a quasi-two-dimensional (quasi-2D) dipolar Bose gas are derived. From the pole of the density correlation function, by considering thermally induced roton-like excitations, the excitation spectrum of the system is calculated. It is shown that the position and depth of the roton minimum of the excitation spectrum are tunable by changing the temperature. To show how the position of the roton minimum influences the phenomenon of superfluidity, the superfluid density of the system is obtained and it is shown that the interplay of the thermal rotonization, contact and dipole–dipole interaction (DDI) can affect the superfluid fraction of a quasi-2D Bose gas. It is found that contact, DDI interactions, and thermally induced rotons enhance the fluctuations and reduce the superfluid density. In the absence of DDI and thermally induced rotons, the usual T³ dependence of superfluid density in 2D is obtained and the correction T⁴ term arises from DDI. It is shown that if the roton minimum is close to zero, the thermally induced rotons change the linear temperature dependence of the superfluid fraction, leading to a transition to nontrivial supersolid phase.     

Low-lying Collective Modes of a 1D Dipolar Quantum Gas in an Anharmonic Trap

The low-lying collective modes of an anharmonically confined one-dimensional ultracold dipolar Bose gas are investigated by using time-dependent variational method. The frequencies of dipole mode and breathing mode are obtained analytically in the full crossover regime from a Tonks-Girardeau gas to a dipolar density wave state. We find that the frequency shifts caused by quartic distortion of the potential can be amplified by interparticle interaction and the collapse and revival of the collective excitations can be observed in the anharmonic trap.     

On the mechanism of electromagnetic microwave absorption in superfluid helium

In experiments on electromagnetic (EM) wave absorption in the microwave range in superfluid (SF) helium [1?C3], a narrow EM field absorption line with a width on the order of (20?C200) kHz was observed against the background of a wide absorption band with a width of 30?C40 GHz at frequencies f ₀ ?? 110?C180 GHz corresponding to the roton gap energy ?? _r (T) in the temperature range 1.4?C2.2 K. Using the so-called flexoelectric mechanism of polarization of helium atoms (⁴He) in the presence of density gradients in SF helium (HeII), we show that nonresonance microwave absorption in the frequency range 170?C200 GHz can be due to the existence of time-varying local density gradients produced by roton excitations in the bulk HeII. The absorption bandwidth is determined by the roton-roton scattering time in an equilibrium Boltzmann gas of rotons, which is t _r-r ?? 3.4 × 10^?11 s at T = 1.4 K and decreases upon heating. We propose that the anomalously narrow microwave resonance absorption line in HeII at the roton frequency f ₀(T) = ??r(T)/2??? appears due to the following two factors: (i) the discrete structure of the spectrum of the surface EM resonator modes in the form of a periodic sequence of narrow peaks and (ii) the presence of a stationary dipole layer in HeII near the resonator surface, which forms due to polarization of ⁴He atoms under the action of the density gradient associated with the vanishing of the density of the SF component at the solid wall. For this reason, the relaxation of nonequilibrium rotons generated in such a surface dipole layer is strongly suppressed, and the shape and width of the microwave resonance absorption line are determined by the roton density of states, which has a sharp peak at the edge of the roton gap in the case of weak dissipation. The effective dipole moments of rotons in the dipole layer can be directed either along or across the normal to the resonator surface, which explains the experimentally observed symmetric doublet splitting of the resonance absorption line in an external dc electric field perpendicular to the resonator surface. We show that negative absorption (induced emission) of EM field quanta observed after triggering a Kapitza ??heat gun?? occurs when the occupation numbers for roton states due to ??pumping?? of rotons exceed the occupation numbers of EM field photons in the resonator.     

Dynamics of confined quantum fluids

We examine the static and dynamic properties of liquid ⁴He in confined geometries. Confinement is modeled by placing the liquid between two rigid, attractive walls with strengths corresponding to Geltech, Vycor, or glass. The liquid arranges itself in a series of layers, with increasing areal density it undergoes a sequence of layering transitions familiar from classical fluids. We identify “bulk” excitations that propagate throughout the film, and “layer” excitations that propagate only close to the substrate. Both have the typical phonon-roton dispersion relation, but the energy of the layer-roton minimum depends sensitively on the substrate strength, thus providing a mechanism for a direct measurement of this quantity. Bulk-like roton excitations are largely independent of the interaction between the matrix and the helium atoms. While the bulk-like rotons are very similar to their true bulk counterparts, the layer modes are not in close relation to two-dimensional rotons and should be regarded as a completely independent kind of excitation.     

Splitting between quadrupole modes of dilute quantum gas in a two-dimensional anisotropic trap

We consider quadrupole excitations of quasi-two-dimensional interacting quantum gas in an anisotropic harmonic oscillator potential at zero temperature. Using the time-dependent variational approach, we calculate a few low-lying collective excitation frequencies of a two-dimensional anisotropic Bose gas. Within the energy weighted sum-rule approach, we derive a general dispersion relation of two quadrupole excitations of a two-dimensional deformed trapped quantum gas. This dispersion relation is valid for both statistics. We show that the quadrupole excitation frequencies obtained from both methods are exactly the same. Using this general dispersion relation, we also calculate the quadrupole frequencies of a two-dimensional unpolarized Fermi gas in an anisotropic trap. For both cases, we obtain analytic expressions for the quadrupole frequencies and the splitting between them for arbitrary value of trap deformation. This splitting decreases with increasing interaction strength for both statistics. For a two-dimensional anisotropic Fermi gas, the two quadrupole frequencies and the splitting between them become independent of the particle number within the Thomas-Fermi approach. Received 21 September 2001 and Received in final form 9 December 2001     

A model of Wigner liquid

A two-dimensional low-density system of charge carriers with strong Coulomb interaction, which can lead to the appearance of a short-wavelength soft mode (precursor of crystallization) is examined. This system provides elementary excitations of two types: Fermi excitations and Bose excitations with a gap in the spectrum. The latter excitations are similar to rotons in superfluid helium. A model involving the Fermi liquid and the soft mode is proposed, and interaction of different excitations with each other is described phenomenologically as in the Landau theory of Fermi liquid. By solving the derived equations, it was found that, as the temperature increases, the effective mass of Fermi excitations decreases and the gap in the Bose excitation spectrum increases.     

On the dispersion of the “roton” second sound in the superfluid helium

At sufficiently high frequencies of the sound when the energy equilibrium between the phonon and roton gases is not established in the superfluid helium there may propagate the second sound through the gas of rotons (“roton” second sound). In the systems of rotons the equilibrium with respect to the number of rotons can be not complete (the chemical potential is not exactly equal to zero). The dispersion of the roton second sound in these conditions is investigated.     

Rotons in interacting ultracold bose gases

In three dimensions, noninteracting bosons undergo Bose-Einstein condensation at a critical temperature, T(c), which is slightly shifted by ΔT(c), if the particles interact. We calculate the excitation spectrum of interacting Bose systems, (4)He and (87)Rb, and show that a roton minimum emerges in the spectrum above a threshold value of the gas parameter. We provide a general theoretical argument for why the roton minimum and the maximal upward critical temperature shift are related. We also suggest two experimental avenues to observe rotons in condensates. These results, based upon a path-integral Monte Carlo approach, provide a microscopic explanation of the shift in the critical temperature and also show that a roton minimum does emerge in the excitation spectrum of particles with a structureless, short-range, two-body interaction.     

Layer- and bulk-roton excitations of 4He in porous media

We examine the energetics of bulk- and layer-roton excitations of 4He in various porous medial such as aerogel, Geltech, or Vycor, in order to find out what conclusions can be drawn from experiments on the energetics about the physisorption mechanism. The energy of the layer-roton minimum depends sensitively on the substrate strength, thus providing a mechanism for a direct measurement of this quantity. On the other hand, bulklike roton excitations are largely independent of the interaction between the medium and the helium atoms, but the dependence of their energy on the degree of filling reflects the internal structure of the matrix and can reveal features of 4He at negative pressures. While bulklike rotons are very similar to their true bulk counterparts, the layer modes are not in close relation to two-dimensional rotons and should be regarded as a third, completely independent kind of excitation.     

Superfluid bose liquid with a suppressed BEC and an intensive pair coherent condensate as a model of 4He

One introduces a model of the superfluid state of a Bose liquid with repulsion between bosons, in which at T=0, along with a weak single-particle Bose-Einstein condensate, there exists an intensive pair coherent condensate, analogous to the Cooper condensate in a Fermi liquid with attraction between fermions. A closed system of nonlinear integral equations for the normal and anomalous self-energy parts is solved numerically, and a quasiparticle spectrum is obtained, which is in good agreement with the experimental spectrum of elementary excitations in superfluid 4He. It is shown that the roton minimum in the spectrum is associated with the negative minimum of the Fourier component of the pair interaction potential.     

Manipulating transmission and reflection properties of a photonic crystal doped with quantum dot nanostructures

We consider excitations that exist, in addition to phonons, in the ideal Bose gas at zero temperature. These excitations are vortex rings whose energy spectrum is similar to the roton one in liquid helium.     

Emission and absorption of phonons by rotons in superfluid helium

The roton spectrum of superfluid helium apparently has a threshold for phonon emission and absorption processes. We calculate the roton spectral function near the threshold for phonon emission in order to determine the effect of the phonon emission process on the roton line width. The spectral function develops a line shape anomaly due to a strong energy dependence of the roton self-energy. The line width is generally smaller than the sum of the phonon emission rate and the roton-roton collision rate. We also derive the ultrasonic attenuation due to the absorption of phonons by thermal rotons above the threshold.     

Dielectric properties of multiband electron systems II. Collective modes

Starting from the tight-binding dielectric matrix in the random phase approximation we examine the collective modes and electron-hole excitations in a two-band electronic system. For long wavelengths (q → 0), for which most of the analysis is carried out, the properties of the collective modes are closely related to the symmetry of the atomic orbitals involved in the tight-binding states. In insulators there are only inter-band charge oscillations. If atomic dipolar transitions are allowed, the corresponding collectivemodes reduce in the asymptotic limit of vanishing bandwidths to Frenkel excitons for an atomic insulator with weak on-site interactions. The finite bandwidths renormalize the dispersion of these modes and introduce a continuum of incoherent inter-band electron-hole excitations. The possible Landau damping of collective modes due to the presence of this continuum is discussed in detail. In conductors the intra-band charge fluctuations give rise to plasmons. If the atomic dipolar transitions are forbidden, the coupling of inter-band collective modes and plasmons tends to zero as q → 0. On the contrary, in dipolar conductors this coupling is strong and nonperturbative, due to the long range monopole-dipole interactions between intra-band and inter-band charge fluctuations. The resulting collective modes are hybrids of intra-band plasmons and inter-band dipolar oscillations. It is shown that the frequency of the lower hybridized longitudinal mode is proportional to the frequency of the transverse dipolar mode when the latter is small. The dielectric instability in a multi-band conductor is therefore characterized by the simultaneous softening of a transverse and a longitudinal mode, which is an important, directly measurable consequence of the present theory.     

Second harmonic generation of propagating collective excitations in Bose－Einstein condensates

We consider a possible second harmonic generation (SHG) of propagating collective excitations in a two-component Bose－Einstein condensate (BEC) with repulsive atom－atom interactions. We show that the phase-matching condition for the SHG can be fulfilled if the wave vectors and frequencies of the excitations are chosen adequately from different dispersion branches. We solve the nonlinear amplitude equations for the SHG derived using a method of multiple-scales and provide SHG solutions similar to those obtained for a SHG in nonlinear optical media. A possible experimental realization of the SHG for the propagating collective modes in a cigar-shaped two-component BEC is also discussed.     

Josephson effect in coherent roton aggregates

A localized microwave electromagnetic field in liquid helium behaves as a laser of rotons: it produces a coherent roton aggregate. We show that the whispering gallery mode of the dielectric resonator excites multiple coherent aggregates simultaneously and predict a Josephson effect between them. The superfluid velocity around the resonator acts as a “voltage across the weak link” in superconducting Josephson junctions. Josephson frequency-velocity relation agrees with existing experimental data.     

Electro-optical trap for dipolar excitons in a GaAs/AlAs Schottky diode with a single quantum well

An electro-optical trap for spatially indirect dipolar excitons has been implemented in a GaAs/AlAs Schottky diode with a 400-Å-wide single quantum well. In the presence of a bias voltage applied to a gate, the trap for excitons appears upon ring illumination of the structure by a continuous-wave or pulsed laser generating hot electron-hole pairs in the quantum well. A barrier for excitons collected inside the illuminated ring appears because of the screening of the applied electric field by nonequilibrium carriers directly in the excitation region. Excitons are collected inside the ring owing to the ambipolar drift of carriers and dipole-dipole exciton repulsion in the optical pump region. For dipolar excitons thus collected in the center of the ring electrooptical trap, a significant narrowing of the luminescence line that accompanies an increase in the density of excitations indicates the collective behavior of dipolar excitons.     

Collective excitations of harmonically trapped ideal gases

We theoretically study the collective excitations of an ideal gas confined in an isotropic harmonic trap. We give an exact solution to the Boltzmann-Vlasov equation; as expected for a single-component system, the associated mode frequencies are integer multiples of the trapping frequency. We show that the expressions found by the scaling ansatz method are a special case of our solution. Our findings are most useful in case the trap contains more than one phase: we demonstrate how to obtain the oscillation frequencies in case an interface is present between the ideal gas and a different phase.