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## Rapporteurs: Jean-Claude GARREAU – Universite ́ de Lille 1

### Citations

220 |
Bose-Einstein Condensation in Dilute Gases
- Pethick, Smith
- 2002
(Show Context)
Citation Context ...eld background: Gross-Pitaevskii theory The zeroth-order term in quantum and thermal fluctuations corresponds to the meanfield background. The latter is determined using the Gross-Pitaevskii approach =-=[147,277]-=-, adapted to the two-component mixture. It amounts to minimize the grand-canonical energy functional EMF ≡ 〈ψMF|Ĥ |ψMF〉 with the two-component Hartree-Fock ansatz |ψMF〉 = (â † 1) N1 √ N1! (â†2) N2 ... |

82 |
Observation of Feshbach resonances in a Bose-Einstein condensate
- Inouye, Andrews, et al.
- 1998
(Show Context)
Citation Context ...-photon Raman or radio-frequency coupling [236] or by Josephson coupling between two adjacent traps [255,259,271–273], whereas the two-body coupling can be controlled by Feshbach resonance techniques =-=[274]-=-. In the most general case, all coupling terms g1, g2, Figure 5.1: Coupled two-component Bose gas. The gas is made of bosonic particles of a single atomic species, which can be in two different intern... |

58 | Production of two overlapping Bose-Einstein condensates by sympathetic cooling, Phys - Myatt, Burt, et al. - 1997 |

37 | Oberthaler, “Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction”, Phys - Albiez, Gati, et al. - 2005 |

22 |
Low-temperature Bose-Einstein condensates in time-dependent traps: Beyond the U(1) symmetry-breaking approach, Phys
- Castin, Dum
- 1998
(Show Context)
Citation Context ...he non-conserving approach is sufficient if one is only interested in the quasi-particle part of the Bogoliubov spectrum. Orthogonal field operator Yet, the only subtle issue [see Sec. 2.2.2 and Ref. =-=[154,282]-=-] when using such an approach is that the field operators B̂σ(r) should be properly orthogonalized with respect to the (quasi)condensate wave function ψσ(r) ≡ eiθσ√nσ, which amounts to apply the subst... |

13 | Noise Thermometry with Two Weakly Coupled Bose-Einstein Condensates - Gati, Hemmerling, et al. |

13 | Low-dimensional trapped gases
- Petrov, M, et al.
(Show Context)
Citation Context ...e for perturbative expansion in the condensate or quasi-condensate regime, where the density fluctuations are suppressed by strongenough repulsive interactions but the phase fluctuations can be large =-=[154,156,158,270,276]-=-. 5.1.2 Meanfield background: Gross-Pitaevskii theory The zeroth-order term in quantum and thermal fluctuations corresponds to the meanfield background. The latter is determined using the Gross-Pitaev... |

12 |
Observations of density fluctuations in an elongated Bose gas: Ideal gas and quasicondensate
- Estève, Trebbia, et al.
- 2006
(Show Context)
Citation Context ...rnal states [236–238,280] and internal-state dependent imaging techniques [137]. The density profiles, fluctuations and correlation functions of each component are then found directly from the images =-=[283,284]-=-. The phase fluctuations and correlation functions of each component are found by time-of-flight [285, 286] or Bragg spectroscopy [229,287,288] techniques. The total and relative density profiles are ... |

10 |
Observation of phase fluctuations in elongated Bose-Einstein condensates
- Dettmer, Hellweg, et al.
- 2001
(Show Context)
Citation Context ...ctuations and correlation functions of each component are then found directly from the images [283,284]. The phase fluctuations and correlation functions of each component are found by time-of-flight =-=[285, 286]-=- or Bragg spectroscopy [229,287,288] techniques. The total and relative density profiles are then obtained by addition or subtraction of those of each component, which also provides their fluctuations... |

10 |
Measurement of the spatial correlation function of phase fluctuating Bose-Einstein condensates
- Hellweg, Cacciapuoti, et al.
- 2003
(Show Context)
Citation Context ...ctuations and correlation functions of each component are then found directly from the images [283,284]. The phase fluctuations and correlation functions of each component are found by time-of-flight =-=[285, 286]-=- or Bragg spectroscopy [229,287,288] techniques. The total and relative density profiles are then obtained by addition or subtraction of those of each component, which also provides their fluctuations... |

8 |
Quantum mechanics
- Basdevant, Dalibard
- 2002
(Show Context)
Citation Context ...on operator δn̂σ/2 √ nσ plays the same role as the position operator X̂σ and the phase fluctuation operator √ nσδθ̂ plays the same role as the momentum operator P̂σ of the quantum harmonic oscillator =-=[281]-=-. 3In the case of a pure condensate with macroscopic occupation of a unique single-particle state, ψσ (assumed to be real-valued), the operator B̂σ represents the fluctuations of the field operator: ψ... |

7 |
Momentum distribution and correlation function of quasicondensates in elongated traps
- Gerbier, Thywissen, et al.
(Show Context)
Citation Context ...ns of each component are then found directly from the images [283,284]. The phase fluctuations and correlation functions of each component are found by time-of-flight [285, 286] or Bragg spectroscopy =-=[229,287,288]-=- techniques. The total and relative density profiles are then obtained by addition or subtraction of those of each component, which also provides their fluctuations and correlation functions. Finally,... |

6 |
de Gennes. Superconductivity of Metals and Alloys
- P-G
- 1995
(Show Context)
Citation Context ...resp. 2). 5.1.3 Excitations: Bogoliubov-de Gennes theory The low-energy spectrum of the collective excitations of the two-component Bose gas is then determined using the Bogoliubov-de Gennes approach =-=[131, 156, 270, 278, 279]-=-, which amounts to perform a perturbative expansion of Hamiltonian (5.1) in phase and density fluctuations. We write n̂σ = nσ + δn̂σ and θ̂σ = θσ + δθ̂σ, with nσ(r) and θσ(r) given by the mean-field G... |

4 |
Probing threebody correlations in a quantum gas using the measurement of the third moment of density fluctuations
- Armijo, Jacqmin, et al.
- 2010
(Show Context)
Citation Context ...rnal states [236–238,280] and internal-state dependent imaging techniques [137]. The density profiles, fluctuations and correlation functions of each component are then found directly from the images =-=[283,284]-=-. The phase fluctuations and correlation functions of each component are found by time-of-flight [285, 286] or Bragg spectroscopy [229,287,288] techniques. The total and relative density profiles are ... |

4 |
Ultracold Gases and Quantum
- Müller, Delande
- 2011
(Show Context)
Citation Context ...n exhaustive presentation, which would hardly fit into the present format, this short summary outlines the main ideas and gives a justification of all the results used in this manuscript. We refer to =-=[17,18,289,290]-=- for a more detailed presentation 1. We will consider the general situation of a single particle propagating in a disordered medium defined by a disordered potential, in arbitrary dimension d. The Ham... |

3 |
Second-order correlation function of a phase fluctuating Bose-Einstein condensate
- Cacciapuoti, Hellweg, et al.
- 2003
(Show Context)
Citation Context ...ns of each component are then found directly from the images [283,284]. The phase fluctuations and correlation functions of each component are found by time-of-flight [285, 286] or Bragg spectroscopy =-=[229,287,288]-=- techniques. The total and relative density profiles are then obtained by addition or subtraction of those of each component, which also provides their fluctuations and correlation functions. Finally,... |

2 |
localization of matter waves in correlated disorder:from 1D to 3D
- Anderson
(Show Context)
Citation Context ...n exhaustive presentation, which would hardly fit into the present format, this short summary outlines the main ideas and gives a justification of all the results used in this manuscript. We refer to =-=[17,18,289,290]-=- for a more detailed presentation 1. We will consider the general situation of a single particle propagating in a disordered medium defined by a disordered potential, in arbitrary dimension d. The Ham... |