@article{WilkensIlluminatiKraemer2000,
  author    = {Wilkens, Martin and Illuminati, Fabrizio and Kr{\"a}mer, Meret},
  title     = {Transition temperature of the weakly interacting Bose gas: perturbative solution of the crossover equations in the canonical ensemble},
  year      = {2000},
  abstract  = {We compute the shift of the critical temperature Tc with respect to the ideal case for a weakly interacting uniform Bose gas. We work in the framework of the canonical ensemble, extending the criterion of condensation provided by the canonical particle counting statistics for the zero-momentum state of the uniform ideal gas. The perturbative solution of the crossover equation to lowest order in power of the scattering length yields (Tc - Tc0)/Tc0=-0,93ap 1/3, where Tc0 is the transition temperature of the corresponding ideal Bose gas , a is the scattering length, and p is the particle number density. This is at vaiance with the standard grand canonical prediction of a null shift of the critical temperature in the lowest perturbative order. The non-equevalence of statistical ensemble for the ideal Bose gas is thus confirm (at the lowestperturbative level) also in the presence of interactions.},
  language  = {en}
}
@article{IlluminatiNavezWilkens1999,
  author    = {Illuminati, Fabrizio and Navez, Patrick and Wilkens, Martin},
  title     = {Thermodynamic identities and paricle number fluctuations in weakly interacting Bose-Einstein condensates},
  year      = {1999},
  abstract  = {We derive exact thermodynamic identities relating the average number of condensed atoms and the root-mean- square fluctuations determined in different statistical ensembles for the weakly interacting Bose gas confined in a box. This is achieved by introducing the concept of auxiliary partition functions for model Hamiltonians that do conserve the total number of particles. Exploiting such thermodynamic identities, we provide the first, completely analytical prediction of the microcanonical particle number fluctuations in the weakly interacting Bose gas. Such fluctuations, as a function of the volume V of the box are found to behave normally, in contrast wiht the anomalous scaling behaviour V3/ 4 of the fluctuations in the ideal Bose gas.},
  language  = {en}
}
@article{AlbusGardinerIlluminatietal.2002,
  author    = {Albus, Alexander P. and Gardiner, Simon A. and Illuminati, Fabrizio and Wilkens, Martin},
  title     = {Quantum field theory of dilute homogeneous Bose-Fermi-mixtures at zero temperature : general formalismand beyond mean-field corrections},
  year      = {2002},
  abstract  = {We consider a dilute homogeneous mixture of bosons and spin-polarized fermions at zero temperature. We first construct the formal scheme for carrying out systematic perturbation theory in terms of single particle Green's functions. We introduce a new relevant object, the renormalized boson-fermion T-matrix which we determine to second order in the boson-fermion s-wave scattering length. We also discuss how to incorporate the usual boson-boson T-matrix in mean-field approximation to obtain the total ground state properties of the system. The next order term beyond mean- field stems from the boson-fermion interaction and is proportional to \$a_{scriptsize BF}k_{scriptsize F}\$. The total ground-state energy-density reads \$E/V =epsilon_{scriptsize F} + epsilon_{scriptsize B} + (2pihbar^{2}a_{ m BF}n_{scriptsize B}n_{scriptsize F}/m) [1 + a_{scriptsize BF}k_{scriptsize F}f(delta)/pi]\$. The first term is the kinetic energy of the free fermions, the second term is the boson-boson mean-field interaction, the pre-factor to the additional term is the usual mean-field contribution to the boson-fermion interaction energy, and the second term in the square brackets is the second-order correction, where \$f(delta)\$ is a known function of \$delta= (m_{scriptsize B} - m_{scriptsize F})/(m_{scriptsize B} + m_{scriptsize F})\$. We discuss the relevance of this new term, how it can be incorporated into existing theories of boson-fermion mixtures, and its importance in various parameter regimes, in particular considering mixtures of \$^{6}\$Li and \$^{7}\$Li and of \$^{3}\$He and \$^{4}\$He.},
  language  = {en}
}
@article{AlbusIlluminatiEisert2003,
  author    = {Albus, Alexander P. and Illuminati, Fabrizio and Eisert, Jens},
  title     = {Mixtures of bosonic and fermionic atoms in optical lattices},
  year      = {2003},
  language  = {en}
}
@article{IlluminatiAlbus2004,
  author    = {Illuminati, Fabrizio and Albus, Alexander P.},
  title     = {High-temperature atomic superfluidity in lattice Bose-Fermi mixtures},
  issn      = {0031-9007},
  year      = {2004},
  language  = {en}
}
@article{AlbusIlluminatiWilkens2003,
  author    = {Albus, Alexander P. and Illuminati, Fabrizio and Wilkens, Martin},
  title     = {Ground-state properties of trapped Bose-Fermi mixtures: Role of exchange correlation},
  year      = {2003},
  language  = {en}
}
@article{AlbusGiorginiIlluminatietal.2002,
  author    = {Albus, Alexander P. and Giorgini, S. and Illuminati, Fabrizio and Viverit, L.},
  title     = {Critical temperature of Bose-Einstein condensation in trapped atomic Bose-Fermi mixtures},
  year      = {2002},
  abstract  = {We calculate the shift in the critical temperature of Bose-Einstein condensation for a dilute Bose-Fermi mixture confined by a harmonic potential, to lowest order in both the Bose-Bose and Bose-Fermi coupling constans. The relativ importance of the effect on the critical temperature of the boson-fermion interactions is investigated as a function of the parameters of mixture. The possible relevance of the shift of the transition temperature in current experiments on trapped Bose-Fermi mixtures is discussed.},
  language  = {en}
}
@article{BreitenbachIlluminatiSchilleretal.1998,
  author    = {Breitenbach, Gerd and Illuminati, Fabrizio and Schiller, Stephan and Mlynek, J{\"u}rgen},
  title     = {Broadband detection of squeezed vacuum : a spectrum of quantum states},
  year      = {1998},
  abstract  = {We demonstrate the simultaneous quantum state reconstruction of the spectral modes of the light field emitted by a continuous wave degenerate optical parametric amplifier. The scheme is based on broadband measurement of the quantum fluctuations of the electric field quadratures and subsequent Fourier decomposition into spectral intervals. Applying the standard reconstruction algorithms to each bandwidth-limited quantum trajectory, a "spectrum" of density matrices and Wigner functions is obtained. The recorded states show a smooth transition from the squeezed vacuum to a vacuum state. In the time domain we evaluated the first order correlation function of the squeezed output field, showing good agreement with theory.},
  language  = {en}
}