Incommensurate Superfluidity of Bosons in a Double-Well Optical Lattice

We study bosons in the first excited Bloch band of a double-well optical lattice, recently realized at NIST. By calculating the relevant parameters from a realistic nonseparable lattice potential, we find that in the most favorable cases, the boson lifetime in the first excited band can be several orders of magnitude longer than the typical nearest-neighbor tunneling time scales, in contrast with that of a simple single-well lattice. In addition, for sufficiently small lattice depths, the excited band has minima at nonzero momenta incommensurate with the lattice period, which opens a possibility to realize an exotic superfluid state that spontaneously breaks the time-reversal, rotational, and translational symmetries. We discuss possible experimental signatures of this novel state.

Figure 1

Excited-band dispersion for $V_0/E_R=-1.0$, $r=0.08$.

Figure 2

Contour plot of the excited-band dispersion for $V_0/E_R=-1.0$, $r=0.08$. Band minima are marked by “$\times$.”

Figure 3

Hubbard interaction parameters (in units of $E_R$) for $r=0.08$, $a_s/{\xi }_z=0.06$, and different lattice depths.

Figure 4

Boson lifetime in the first excited band for different filling factors $\nu$. Values of parameters are indicated.

Figure 5

Prediction of the density distribution in a time-of-flight experiment, for $V_0/E_R=-1.0$, $r=0.08$, and condensate wave vector $\mathbf{K}=(0.5,0.5)k_L$.