12aTF-9 Laser probing of single-particle energy gap of a Bose gas in an optical lattice in the Mott insulator phase

Satoru Konabe, Tetsuro Nikuni, Masaaki Nakamura

We study single-particle excitations of a Bose gas in an optical lattice in the Mott-insulator phase. The characteristic feature of the single-particle spectrum in the Mott-insulator phase is the existence of an energy gap between the particle and hole excitations. We show that the single-particle excitation energies and associated energy gap in the Mott-insulator phase can be directly probed by an output-coupling experiment. We apply the general expression for the output current derived by Luxat and Griffin, which is given in terms of the single-particle Green's functions of a trapped Bose gas, to the Mott-insulator phase using the Bose-Hubbard model. The energy spectrum of the momentum-resolved output current exhibits two characteristic peaks corresponding to the particle and hole excitations, and thus it can be used to detect the transition point from the Mott insulator to superfluid phase where the energy gap disappears.

Satoru Konabe, Tetsuro Nikuni, Masaaki Nakamura

K. Ziegler

C. Fort, Nicole Fabbri, L. Fallani +2 more

We have used inelastic light scattering to study correlated phases of an array of one-dimensional interacting Bose gases. In the linear response regime, the observed spectra are proportional to the dynamic structure factor. In particular we have investigated the superfluid to Mott insulator crossover loading the one-dimensional gases in an optical lattice and monitoring the appearance of an energy gap due to finite particle-hole excitation energy. We attribute the low frequency side of the spectra to the presence of some superfluid and normal phase fraction between the Mott insulator regions with different fillings produced in the inhomogeneous systems. In the Mott phase we also investigated excitations to higher excited bands of the optical lattice, the spectra obtained in this case being connected to the single particle spectral function. In one-dimensional systems the effect of thermal fluctuations and interactions is enhanced by the reduced dimensionality showing up in the dynamic structure factor. We measured the dynamic structure factor of an array of one-dimensional bosonic gases pointing out the effect of temperature-induced phase fluctuations in reducing the coherence length of the system.

K. Ziegler

The Bose-Hubbard model of a twofold degenerate Bose gas is studied in an optical lattice with one particle per site and virtual tunneling to empty and doubly occupied sites. An effective Hamiltonian for this system is derived within a continued-fraction approach. The ground state of the effective model is studied in mean-field approximation for a modulated optical lattice. A dimerized mean-field state gives a Mott insulator whereas the lattice without modulations develops long-range correlated phase fluctuations due to a Goldstone mode. This result is discussed in comparison with the superfluid and the Mott-insulating state of a single-component hard-core Bose gas.

哲 小鍋