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Laser Physics

Noise correlations of fermions and hard core bosons in a quasi-periodic potential

Ana María Rey, Indubala I. Satija, C. W. Clark

Published Feb 1, 2007• 4 citations
Publisher

Abstract

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.

DOI
10.1134/s1054660x07020260

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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.
Finite size scalings of the momentum distribution and noise correlations are performed to study Mott insulator, Bose glass, and superfluid quantum phases in hard-core bosons (HCBs) subjected to quasiperiodic disorder. The exponents of the correlation functions at the superfluid to Bose-glass (SF-BG) transition are found to be approximately one half of the ones that characterize the superfluid phase. The derivatives of the peak intensities of the correlation functions with respect to quasiperiodic disorder are shown to diverge at the SF-BG critical point. This behavior does not occur in the corresponding free fermion system, which also exhibits an Anderson-like transition at the same critical point and thus provides a unique experimental tool to locate the phase transition in interacting bosonic systems. We also report on the absence of primary sublattice peaks in the momentum distribution of the superfluid phase for special fillings.
Noise correlations, such as those observable in the time of flight images of a released cloud, are calculated for hard-core bosonic (HCB) atoms. We find that the standard mapping of HCB systems onto spin-1/2 XY models fails in application to computation of noise correlations. This is due to the contribution of multiply occupied virtual states to noise correlations in bosonic systems. Such states do not exist in spin models. We use these correlations to explore quantum coherence of the ground states and re-address the relationship between the peaks present in noise correlation and the Mott phase. Our analysis points to distinctive new experimental signatures of the Mott phase. The importance of these correlations is illustrated in an example of a quasiperiodic potential that exhibits a localization transition. In this case, in contrast to the momentum distribution, the noise correlations reveal the presence of quasiperiodic order in the localized phase.
The theoretical framework of Hanbury Brown–Twiss interferometry (HBTI) is used to study integer and fractionally filled Mott insulator (MI) phases in period-2 optical superlattices. In contrast to the quasimomentum distribution, this second order interferometry pattern exhibits high contrast fringes in the insulating phases . Our detailed study of HBTI suggests that this interference pattern signals the various superfluid–insulator transitions and therefore can be used as a practical method to determine the phase diagram of the system. We find that in the presence of a confining potential the insulating phases become robust as they exist for a finite range of atom numbers. Furthermore, we show that in the trapped case, the HBTI interferogram signals the formation of the MI domains and probes the shell structure of the system.
Noise correlations, such as those observable in the time of flight images of a released cloud, are calculated for hard-core bosonic (HCBs) atoms. These second-order correlations are used to explore quantum coherence of strongly correlated bosons in the fermionized regime with and without external parabolic confinement. Our analysis points to distinctive new experimental signatures of the Mott phase. We also calculate noise correlations for the corresponding spin-1/2 XY model onto which the HCB system is standardly mapped. Our study shows important differences between the two systems due to the contribution of multiply occupied virtual states in HCBs. Such states do not exist in spin models. An interesting manifestation of such states is the breaking of particle–hole symmetry in HCB systems.
We investigate numerically the zero-temperature physics of the one-dimensional Bose-Hubbard model in an incommensurate cosine potential, recently realized in experiments with cold bosons in optical superlattices [L. Fallani et al., Phys. Rev. Lett. 98, 130404 (2007)]. An incommensurate cosine potential has intermediate properties between a truly periodic and a fully random potential, displaying a characteristic length scale (the quasiperiod) which is shown to set a finite lower bound to the excitation energy of the system at special incommensurate fillings. This leads to the emergence of gapped incommensurate band-insulator (IBI) phases along with gapless Bose-glass (BG) phases for strong quasiperiodic potential for both hard-core and soft-core bosons. Enriching the spatial features of the potential by the addition of a second incommensurate component appears to remove the IBI regions, stabilizing a continuous BG phase over an extended parameter range. Moreover, we discuss the validity of the local-density approximation in the presence of a parabolic trap, clarifying the notion of a local BG phase in a trapped system; we investigate the behavior of first- and second-order coherence upon increasing the strength of the quasiperiodic potential; and we discuss the ab initio derivation of the Bose-Hubbard Hamiltonian with quasiperiodic potential starting from the microscopic Hamiltonian of bosons in an incommensurate superlattice.