We use Hanbury-Brown-Twiss interferometry (HBTI) to study various quantum phases of hard core bosons (HCBs) and ideal fermions confined in a one-dimensional quasi-periodic (QP) potential. For HCBs, the QP potential induces a cascade of Mott-like band-insulator phases in the extended regime, in addition to the Mott insulator, Bose glass, and superfluid phases. At critical filling factors, the appearance of these insulating phases is heralded by a peak to dip transition in the interferogram, which reflects the fermionic aspect of HCBs. On the other hand, ideal fermions in the extended phase display various complexities of incommensurate structures such as devil’s staircases and Arnold tongues. In the localized phase, the HCB and the fermion correlations are identical except for the sign of the peaks. Finally, we demonstrate that HBTI provides an effective method to distinguish Mott and glassy phases.
Quantum phases of hard core bosons (HCBs) confined in a one-dimensional quasiperiodic (QP) potential are studied within the theoretical framework of Hanbury-Brown-Twiss interferometry. The QP potential induces a cascade of Mott-like band-insulator phases in the extended regime, in addition to the Mott insulator, Bose glass, and superfluid phases. The new phases are incompressible and have zero superfluid fraction. At critical filling factors, the appearance of these insulating phases is heralded by a peak to dip transition in the interferogram, which reflects the fermionic aspect of HCBs. In the localized phase, the interference pattern exhibits an hierarchy of peaks at the reciprocal lattice vectors of the system. Our study demonstrates that in contrast to the momentum distribution, HBTI provides an effective method to distinguish Mott and glassy phases.
With Girardeau's Fermi-Bose mapping, we find the exact ground states of hard-core bosons residing in a one-dimensional periodic potential. The analysis of these ground states shows that when the number of bosons
N is commensurate with the number of wells
M in the periodic potential, the boson system is a Mott insulator whose energy gap, however, is given by the single-particle band gap of the periodic potential; when
N is not commensurate with
M, the system is a metal (not a superfluid). In fact, we argue that there may be no superfluid phase for any one-dimensional boson system in terms of Landau's criterion of superfluidity. The Kronig-Penney potential is used to illustrate our results.