1,721,062 research outputs found
Polarization in a three-dimensional Fermi gas with Rabi coupling
No full textWe investigate the polarization of a two-component three-dimensional fermionic gas made of repulsive alkali-metal atoms. The two pseudo-spin components correspond to two hyperfine states which are Rabi coupled. The presence of Rabi coupling implies that only the total number of atoms is conserved and a quantum phase transition between states dominated by spin-polarization along different axses is possible. By using a variational Hartree-Fock scheme we calculate analytically the ground-state energy of the system and determine analytically and numerically the conditions under which there is this quantum phase transition. This scheme includes the well-known criterion for the Stoner instability. The obtained phase diagram clearly shows that the polarized phase crucially depends on the interplay among the Rabi coupling energy, the interaction energy per particle, and the kinetic energy per particle
Bright solitons in ultracold atoms
Full text linkWe review old and recent experimental and theoretical results on bright solitons in Bose-Einstein condensates made of alkali-metal atoms and under external optical confinement. First we deduce the three-dimensional Gross-Pitaevskii equation (3D GPE) from the Dirac-Frenkel action of interacting identical bosons within a time-dependent Hartree approximation. Then we discuss the dimensional reduction of the GPE from 3D to 1D, deriving the 1D GPE and also the 1D nonpolynomial Schr"odinger equation (1D NPSE). Finally, we analyze the bright solition solutions of both 1D GPE and 1D NPSE and compare these theoretical predictions with the available experimental data
Acoustic plasmons in graphene sandwiched between two metallic slabs
Full text linkWe study the effect of two metallic slabs on the collective dynamics of electrons in graphene positioned between the two slabs. We show that if the slabs are perfect conductors, the plasmons of graphene display a linear dispersion relation. The velocity of these acoustic plasmons crucially depends on the distance between the two metal gates and the graphene sheet. In the case of generic slabs, the dispersion relation of graphene plasmons is much more complicated, but we find that acoustic plasmons can still be obtained under specific conditions
Density of States for the Unitary Fermi Gas and the Schwarzschild Black Hole
Full text linkThe density of states of a quantum system can be calculated from its definition, but, in some cases, this approach is quite cumbersome. Alternatively, the density of states can be deduced from the microcanonical entropy or from the canonical partition function. After discussing the relationship among these procedures, we suggest a simple numerical method, which is equivalent in the thermodynamic limit to perform a Legendre transformation, to obtain the density of states from the Helmholtz free energy. We apply this method to determine the many-body density of states of the unitary Fermi gas, a very dilute system of identical fermions interacting with a divergent scattering length. The unitary Fermi gas is highly symmetric due to the absence of any internal scale except for the average distance between two particles and, for this reason, its equation of state is called universal. In the last part of the paper, by using the same thermodynamical techniques, we review some properties of the density of states of a Schwarzschild black hole, which shares the problem of finding the density of states directly from its definition with the unitary Fermi gas
Bose-Einstein Condensation on the Surface of a Sphere
Full text linkMotivated by the recent achievement of space-based Bose-Einstein condensates (BEC) with ultracold alkali-metal atoms under microgravity and by the proposal of bubble traps which confine atoms on a thin shell, we investigate the BEC thermodynamics on the surface of a sphere. We determine analytically the critical temperature and the condensate fraction of a noninteracting Bose gas. Then we consider the inclusion of a zero-range interatomic potential, extending the noninteracting results at zero and finite temperature. Both in the noninteracting and interacting cases the crucial role of the finite radius of the sphere is emphasized, showing that in the limit of infinite radius one recovers the familiar two-dimensional results. We also investigate the Berezinski-Kosterlitz-Thouless transition driven by vortical configurations on the surface of the sphere, analyzing the interplay of condensation and superfluidity in this finite-size system
Shift of the critical temperature in superconductors: a self-consistent approach
Full text linkWithin the Ginzburg-Landau functional framework for the superconducting transition, we analyze the fluctuation-driven shift of the critical temperature. In addition to the order parameter fluctuations, we also take into account the fluctuations of the vector potential above its vacuum. We detail the approximation scheme to include the fluctuating fields contribution, based on the Hartree-Fock-Bogoliubov-Popov framework. We give explicit results for d = 2 and d = 3 spatial dimensions, in terms of easily accessible experimental parameters such as the Ginzburg-Levanyuk number Gi(d), which is related to the width of the critical region where fluctuations cannot be neglected, and the Ginzburg-Landau parameter κ, defined as the ratio between the magnetic penetration length and the coherence one
Collisionless sound of bosonic superfluids in lower dimensions
No full textThe superfluidity of low-temperature bosons is well established in the collisional regime. In the collisionless regime, however, the presence of superfluidity is not yet fully clarified, in particular in lower spatial dimensions. Here, we compare the Vlasov-Landau equation, which does not take into account the superfluid nature of the bosonic system, with the Andreev-Khalatnikov equations, which instead explicitly contain a superfluid velocity. We show that recent experimental data of the sound mode in a two-dimensional collisionless Bose gas of Rb87 atoms are in good agreement with both theories, but the sound damping is better reproduced by the Andreev-Khalatnikov equations below the Berezinskii-Kosterlitz-Thouless critical temperature Tc, while above Tc the Vlasov-Landau results are closer to the experimental ones. For one-dimensional bosonic fluids, where experimental data are not yet available, we find larger differences between the sound velocities predicted by the two transport theories and, also in this case, the existence of a superfluid velocity reduces the sound damping
Quantum and thermal fluctuations in the dynamics of a resistively and capacitively shunted Josephson junction
No full textWe theoretically investigate the phase and voltage correlation dynamics, which includes both the deterministic contribution and stochastic fluctuations, under a current noise generated by a resistor including thermal and quantum fluctuations in a resistively and capacitively shunted Josephson junction. An external current is found to shift and intensify the deterministic contributions in phase and voltage. In addition to effects of external current, we observe the relaxation of autocorrelation functions of phase and voltage, which includes the variances due to the current noise, to finite values in the long-time limit. In particular, we find that the asymptotic correlations depend on the resistance as a consequence of quantum effects. We also find an earlier decay of coherence at a higher temperature in which thermal fluctuations dominate over quantum ones. These theoretical predictions can be tested in the next future experiments
Effects of long-range hopping in the Bose-Hubbard model
No full textWe investigate the effects of an extended Bose-Hubbard model with a long-range hopping term on the Mott insulator-superfluid quantum phase transition. We consider the effects of a power-law decaying hopping term, and we show that the Mott phase is shrunk in the parameters' space. We provide an exact solution for one-dimensional lattices and also two reliable approximations for higher dimensions. Finally, we extend these results to a more realistic situation in which long-range hopping is made by a combination of power-law and screening terms, studying the main effects on the Mott lobes
Gaussian quantum fluctuations in the superfluid-Mott-insulator phase transition
No full textRecent advances in cooling techniques make possible the experimental study of quantum phase transitions, which are transitions near absolute zero temperature accessed by varying a control parameter. A paradigmatic example is the superfluid-Mott transition of interacting bosons on a periodic lattice. From the relativistic Ginzburg-Landau action of this superfluid-Mott transition we derive the elementary excitations of the bosonic system, which contain in the superfluid phase a gapped Higgs mode and a gapless Goldstone mode. We show that this energy spectrum is in good agreement with the available experimental data and we use it to extract, with the help of dimensional regularization, meaningful analytical formulas for the beyond-mean-field equation of state in two and three spatial dimensions. We find that, while the mean-field equation of state always gives a second-order quantum phase transition, the inclusion of Gaussian quantum fluctuations can induce a first-order quantum phase transition. This prediction is a strong benchmark for future experiments on quantum phase transitions
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