Quantum coherence of hard-core bosons: Extended, glassy, and Mott 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.

Figure 1

(Color online) Noise correlations of HCBs in the glassy phase $(\lambda =2J)$ as $Q$ and $\nu$ vary.

Figure 2

(Color online) HCBs in the superfluid phase, $\lambda =0.5J$, top: Momentum distribution and bottom: noise correlations where the intensities of the central peaks are scaled by a factor of $1∕10$ to show the satellite dips.

Figure 3

For fixed $\lambda =0.5J$, The top figure displays the variation in superfluid fraction as $\nu$ varies. The bottom figure shows the variation in density as the chemical potential $\mu$ varies. The inset shows the number fluctuations. The grid lines are at ${\nu }_c^{(1,2)}$ and ${\overline{\nu }}_c^{(1,2)}$.

Figure 4

(Color online) HCBs noise correlation for$\lambda =0.5J$. In the inset we plot the visibility for the dominant peak (see text) as a function of $\nu$.