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arXiv:cond-mat/0607401 · Physical Review A

Probing the superfluid–Mott-insulating shell structure of cold atoms by parametric excitations

Lilach Goren, Eros Mariani, Ady Stern

Published Jun 13, 2007• 8 citations
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Abstract

We study the effect of parametric excitations on systems of confined ultracold Bose atoms in periodically modulated optical lattices. In the regime where Mott insulating and superfluid domains coexist, we show that the dependence of the energy absorbed by the system on the frequency of the modulation serves as an experimental probe for the existence and properties of Mott insulating-superfluid domains.

DOI
10.1103/physreva.75.063612

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We study the effect of parametric excitations on systems of confined ultracold Bose atoms in periodically modulated optical lattices. In the regime where Mott insulating and superfluid domains coexist, we show that the dependence of the energy absorbed by the system on the frequency of the modulation serves as an experimental probe for the existence and properties of Mott insulating-superfluid domains.
In this paper, we consider a cloud of Bose atoms in an optical lattice subjected to a confinement. The equilibrium state of the system can show the coexistence of superfluid and Mott-insulating domains. We consider the surface waves at the interfaces between Mott-insulating and superfluid regions and derive their dispersion. Then, we calculate their contribution to the heat capacity of the system, showing how its low-temperature scaling is qualitatively affected by the presence/absence of the domain structure. This allows for an experimental test of the existence and properties of Mott insulator–superfluid domains, a currently open issue.
We present a detailed analysis of the dynamical response of ultracold bosonic atoms in a one-dimensional optical lattice subjected to a periodic modulation of the lattice depth. Following the experimental realization by Stöferle et al (2004 Phys. Rev. Lett. 92 130403), we study the excitation spectrum of the system as revealed by the response of the total energy as a function of the modulation frequency Ω. By using the Time Evolving Block Decimation algorithm, we are able to simulate one-dimensional systems comparable in size to those in the experiment, with harmonic trapping and across many lattice depths ranging from the Mott-insulator (MI) to the superfluid (SF) regime. Our results produce many of the features seen in the experiment, namely a broad response in the SF regime, and narrow discrete resonances in the MI regime. We identify several signatures of the SF–MI transition that are manifested in the spectrum as it evolves from one limit to the other.
We compute the energy absorbed by a one-dimensional system of cold bosonic atoms in an optical lattice subjected to lattice amplitude modulation periodic with time. We perform the calculation for the superfluid and the Mott insulator created by a weak lattice, and the Mott insulator in a strong lattice potential. For the latter case we show results for three-dimensional systems as well. Our calculations, based on bosonization techniques and strong-coupling methods, go beyond standard Bogoliubov theory. We show that the energy absorption rate exhibits distinctive features of low-dimensional systems and Luttinger liquid physics. We compare our results with experiments and find good agreement.
We present a nonperturbative analysis of a new experimental technique for probing ultracold bosons in an optical lattice by periodic lattice depth modulations. This is done using the time-dependent density-matrix renormalization group method. We find that sharp energy absorption peaks are not unique to the Mott insulating phase at commensurate filling but also exist for superfluids at incommensurate filling. For strong interactions, the peak structure provides an experimental measure of the interaction strength. Moreover, the peak height of the peaks at Planck's omega > or approximately 2U can be employed as a measure of the incommensurability of the system.
We propose an experimental setup of ultracold fermions in an optical lattice to determine the pairing gap in a superfluid state and the spin ordering in a Mott-insulating state. The idea is to apply a periodic modulation of the lattice potential and to use the thereby induced double occupancy to probe the system. We show by full time-dependent calculation using the adaptive time-dependent density-matrix renormalization-group method that the position of the peak in the spectrum of the induced double occupancy gives the pairing energy in a superfluid and the interaction energy in a Mott insulator, respectively. In the Mott insulator we relate the spectral weight of the peak to the spin ordering at finite temperature using perturbative calculations.