Exchange processes are responsible for the stability of elementary boson condensates with respect to their possible fragmentation. This remains true for composite bosons when single fermion exchanges are included but spin degrees of freedom are ignor
ed. We here show that their inclusion can produce a spin-fragmentation of a condensate of dark excitons, i.e., an unpolarized condensate with equal amount of dark excitons with spins (+2) and (-2). Quite surprisingly, for spatially indirect excitons of semiconductor bilayers, we predict that the condensate polarization can switch from unpolarized to fully polarized, depending on the distance between the layers confining electrons and holes. Remarkably, the threshold distance associated to this switching lies in the regime where experiments are nowadays carried out.
We study the dimer-dimer scattering length $a_4$ for a two-component Fermi mixture in which the different fermions have different masses $mus$ and $mds$. This is made in the framework of the exact field theoretical method. In the large mass ratio dom
ain the equations are simplified enough to lead to an analytical solution. In particular we link $a_4$ to the fermion-dimer scattering length $a_3$ for the same fermions, and obtain the very simple relation $a_4=a_3/2$. The result $a_4 simeq a_3/2$ is actually valid whatever the mass ratio with quite good precision. As a result we find an analytical expression providing $a_4$ with a fairly good precision for any masses. To dominant orders for large mass ratio it agrees with the literature. We show that, in this large mass ratio domain, the dominant processes are the repeated dimer-dimer Born scatterings, considered earlier by Pieri and Strinati. We conclude that their approximation, of retaining only these processes, is a fairly good one whatever the mass ratio.
We show that, near a Feshbach resonance, a strong p-wave resonance is present at low energy in atom-dimer scattering for $^6$Li-$^{40}$K fermionic mixtures. This resonance is due to a virtual bound state, in the atom-dimer system, which is present at
this low energy. When the mass ratio between the two fermionic elements is increased, this virtual bound state goes to a known real bound state which appears when the mass ratio reaches 8.17. This resonance should affect a number of physical properties. These include the equation of state of unbalanced mixtures at very low temperature but also the equation of state of balanced mixtures at moderate or high temperature. The frequency and the damping of collective modes should also provide a convenient way to evidence this resonance. Finally it should be possible to modify the effective mass of one the fermionic species by making use of an optical lattice. This would allow to study the strong dependence of the resonance as a function of the mass ratio of the two fermionic elements.
It has been recently suggested that the Bose-Einstein condensate formed by excitons in the dilute limit must be dark, i.e., not coupled to photons. Here, we show that, under a density increase, the dark exciton condensate must acquire a bright compon
ent due to carrier exchange in which dark excitons turn bright. This however requires a density larger than a threshold which seems to fall in the forbidden region of the phase separation between a dilute exciton gas and a dense electron-hole plasma. The BCS-like condensation which is likely to take place on the dense side, must then have a dark and a bright component - which makes it gray. It should be possible to induce an internal Josephson effect between these two coherent components, with oscillations of the photoluminescence as a strong proof of the existence for this gray BCS-like exciton condensate.
We consider an imbalanced mixture of two different ultracold Fermi gases, which are strongly interacting. Calling spin-down the minority component and spin-up the majority component, the limit of small relative density $x=nds /nus$ is usually conside
red as a gas of non interacting polarons. This allows to calculate, in the expansion of the total energy of the system in powers of $x$, the terms proportional to $x$ (corresponding to the binding energy of the polaron) and to $x^{5/3}$ (corresponding to the kinetic energy of the polaron Fermi sea). We investigate in this paper terms physically due to an interaction between polarons and which are proportional to $x^2$ and $x^{7/3}$. We find three such terms. A first one corresponds to the overlap between the clouds dressing two polarons. The two other ones are due to the modification of the single polaron binding energy caused by the non-zero density of polarons. The second term is due to the restriction of the polaron momentum by the Fermi sea formed by the other polarons. The last one results from the modification of the spin-up Fermi sea brought by the other polarons. The calculation of all these terms is made at the simplest level of a single particle-hole excitation. It is performed for all the possible interaction strengths within the stability range of the polaron. At unitarity the last two terms give a fairly weak contribution while the first one is strong and leads to a marked disagreement with Monte-Carlo results. The possible origins of this discrepancy are discussed.
We consider the problem of obtaining the scattering length for a fermion colliding with a dimer, formed from a fermion identical to the incident one and another different fermion. This is done in the universal regime where the range of interactions i
s short enough so that the scattering length $a$ for non identical fermions is the only relevant quantity. This is the generalization to fermions with different masses of the problem solved long ago by Skorniakov and Ter-Martirosian for particles with equal masses. We solve this problem analytically in the two limiting cases where the mass of the solitary fermion is very large or very small compared to the mass of the two other identical fermions. This is done both for the value of the scattering length and for the function entering the Skorniakov-Ter-Martirosian integral equation, for which simple explicit expressions are obtained.
Very recently Girardeau and Minguzzi [arXiv:0807.3366v2, Phys. Rev. A 79, 033610 (2009)] have studied an impurity in a one-dimensional gas of hard-core bosons. In particular they deal with the general case where the mass of the impurity is different
from the mass of the bosons and the impurity-boson interaction is not necessarily infinitely repulsive. We show that one of their initial step is erroneous, contradicting both physical intuition and known exact results. Their results in the general case apply only actually when the mass of the impurity is infinite.
We present an exact many-body theory of ultracold fermionic gases for the Bose-Einstein condensation (BEC) regime of the BEC-BCS crossover. This is a purely fermionic approach which treats explicitely and systematically the dimers formed in the BEC r
egime as made of two fermions. We consider specifically the zero temperature case and calculate the first terms of the expansion of the chemical potential in powers of the density $n$. We derive first the mean-field contribution, which has the expected standard expression when it is written in terms of the dimer-dimer scattering length $a_M$. We go next in the expansion to the Lee-Huang-Yang order, proportional to $n^{3/2}$. We find the far less obvious result that it retains also the same expression in terms of $a_M$ as for elementary bosons. The composite nature of the dimers appears only in the next term proportional to $n^2$.
We consider a single down atom within a Fermi sea of up atoms. We elucidate by a full many-body analysis the quite mysterious agreement between Monte-Carlo results and approximate calculations taking only into account single particle-hole excitations
. It results from a nearly perfect destructive interference of the contributions of states with more than one particle-hole pair. This is linked to the remarkable efficiency of the expansion in powers of hole wavevectors, the lowest order leading to perfect interference. Going up to two particle-hole pairs gives an essentially perfect agreement with known exact results. Hence our treatment amounts to an exact solution of this problem.
In ultracold gases many experiments use atom imaging as a basic observable. The resulting image is averaged over a number of realizations and mostly only this average is used. Only recently the noise has been measured to extract physical information.
In the present paper we investigate the quantum noise arising in these gases at zero temperature. We restrict ourselves to the homogeneous situation and study the fluctuations in particle number found within a given volume in the gas, and more specifically inside a sphere of radius $R$. We show that zero-temperature fluctuations are not extensive and the leading term scales with sphere radius $R$ as $R^2ln R$ (or $ln R$) in three- (or one-) dimensional systems. We calculate systematically the next term beyond this leading order. We consider first the generic case of a compressible superfluid. Then we investigate the whole Bose-Einstein-condensation (BEC)-BCS crossover crossover, and in particular the limiting cases of the weakly interacting Bose gas and of the free Fermi gas.
