Fig. 3: Dispersion relation for increasing densities.

a Parabolic dispersion extracted from PL at densities well below the condensation threshold \({d}_{th}\). b–d Excitation spectrum for increasing pumping powers corresponding to \(P=0.9{P}_{th}\), \(P={P}_{th}\) and \(P=1.5{P}_{th}\) as extracted from the positions of the maxima in Fig. 2b, d, f, respectively. Best-fit parameters to Eq. (2) are \(\mu =\,\text{0.005}\, \text{meV}\,\), \(\mu =\,\text{0.04}\, \text{meV}\,\) and \(\mu =\,\text{0.1}\,\text{meV}\,\) in (b–d), respectively. The condensate wavevector is \({k}_{c}=0.03\ \upmu {{\rm{m}}}^{-1}\), \({k}_{c}=0.03\ \upmu {{\rm{m}}}^{-1}\) and \({k}_{c}=0.1\ \upmu {{\rm{m}}}^{-1}\) in b–d, respectively. The dashed-blue lines are the parabolic dispersion relations with the energy and momentum offsets given by \(\mu\) and \({k}_{c}\) as obtained from the fit of Eq. (2) to the data in each panel. The mass is extracted from the parabolic fitting of the data in (a). \(\Gamma =\,\text{0.005}\ \text{ps}^{-1}\,\) is used in (b–d).