We have studied the noise spectrum originating from electric current fluctuations of a multi-level quantum dot (QD) connected to two electronic reservoirs via two leads. In the confined mesoscopic region (QD) electrons cannot move freely to screen the Coulomb interactions. Therefore, when studying electronic properties in such systems the interactions must be taken into account. A self-consistent Hartree and Hartree-Fock calculation was performed to account for the electron-electron interactions in the multi-level QD, providing us with an effective noninteracting electronic system. The noise spectrum, obtained at zero bias and zero temperature, exhibits steps and dips (the latter occurring only for a non-symmetric dot coupling) as a function of the frequency. The obtained spectrum is consistent with the results for a similar configuration of a noninteracting two-level quantum dot [1] and a single-level quantum dot [2]. The steps, that indicate the internal QD's resonances with respect to the Fermi level, are shifted as a function of the interaction strength. The dips, which are formed due to interference between two levels that are at opposite sides of the Fermi level, are shifted as well with the interaction strength. Once an energy level has crossed the Fermi level, new dips appear in the noise. Even though the Fock term was crucial for the calculation of the ac conductance of a similar quantum dot connected only to one lead [3], we find no qualitative difference between the results from the Hartree and the Hartree-Fock approximations, in our system configuration.

[1] O. Entin-Wohlman, Y. Imry, S. A. Gurvitz, and A. Aharony, Phys. Rev. B 75, 193308 (2007).

[2] E. A. Rothstein, O. Entin-Wohlman, and A. Aharony, Phys. Rev. B 79, 075307 (2009).

[3] Z. Ringel, Y. Imry, and O. Entin-Wohlman, Phys.Rev. B 78, 165304 (2008).