We propose different spectroscopic methods to explore the nature of the thermal excitations of a trapped Bose condensed gas: 1) a four photon process to probe the uniform region in the trap center: 2) a stimulated Raman process in order to analyze the influence of a momentum transfer in the resulting scattered atom momentum distribution. We apply these methods to address specifically the energy spectrum and the scattering amplitude of these excitations in a transition between two hyperfine levels of the gas atoms. In particular, we exemplify the potential offered by these proposed techniques by contrasting the spectrum expected from the non-conserving Bogoliubov approximation, valid for weak depletion, to the spectrum of the finite-temperature extensions like the conserving generalized random phase approximation (GRPA). Both predict the existence of the Bogoliubov collective excitations but the GRPA approximation distinguishes them from the single-atom excitations with a gapped and parabolic dispersion relation and accounts for the dynamical screening of any external perturbation applied to the gas. We present two feasible experiments, one concerns the observation of the gap associated to this second branch of excitations and the other deals with this screening effect.
Molecular spectroscopy is used to probe a quantum degenerate gas of 7Li atoms. Several effects are investigated using both single-color and two-color (Raman) photoassociative spectroscopy. An unusual spectral shift with laser intensity is observed for single-color photoassociation and the intensity dependence agrees with theoretical predictions. Additionally, the prospects for altering the interactions between ground-state atoms is investigated for both the single-color and Raman schemes. The single-color scheme is found to be impractical experimentally (although feasible theoretically) while the Raman scheme may be experimentally feasible as well. The Raman spectra display an interesting lineshape which is found to reflect the rate for inelastic collisions involving ground-state molecules (produced via the Raman process) as well as the attractive mean-field interactions between atoms in the condensate. Under certain circumstances, a dispersive Raman lineshape is observed which may be due to coherence properties of both the condensate and the thermal gas. Additionally, the Raman lineshape appears to reflect the kinetic time scale for thermal atoms to enter the condensate via elastic collisions. The Raman technique is applied to studies of the condensate growth and collapse dynamics caused by attractive interactions between condensate atoms, and enables the first direct observations of this phenomenon.
We theoretically study a three-dimensional weakly interacting Bose gas with Raman-induced spin-orbit coupling at finite temperature. By employing a generalized Hartree-Fock-Bogoliubov theory with Popov approximation, we determine a complete finite-temperature phase diagram of three exotic condensation phases (i.e., the stripe, plane-wave, and zero-momentum phases), against both quantum and thermal fluctuations. We find that the plane-wave phase is significantly broadened by thermal fluctuations. The phonon mode and sound velocity at the transition from the plane-wave phase to the zero-momentum phase are thoughtfully analyzed. At zero temperature, we find that quantum fluctuations open an unexpected gap in sound velocity at the phase transition, in stark contrast to the previous theoretical prediction of a vanishing sound velocity. At finite temperature, thermal fluctuations continue to significantly enlarge the gap, and simultaneously shift the critical minimum. For a Bose gas of
87Rb atoms at the typical experimental temperature,
T=0.3T0, where
T0 is the critical temperature of an ideal Bose gas without spin-orbit coupling, our results of gap opening and critical minimum shifting in the sound velocity are qualitatively consistent with the recent experimental observation [Ji et al., Phys. Rev. Lett. 114, 105301 (2015)].