Momentum dependent optical lattice induced by an artificial gauge potential

We propose an experimentally feasible method to generate a one-dimensional optical lattice potential in an ultracold Bose gas system that depends on the transverse momentum of the atoms. The optical lattice is induced by the artificial gauge potential generated by a periodically driven multilaser Raman process. We study the many-body Bose-Hubbard model in an effective 1D case and show that the superfluid–Mott-insulator transition can be controlled via tuning the transverse momentum of the atomic gas. Such a feature enables us to control the phase of the quantum gas in the longitudinal direction by changing its transverse motional state. We examine our prediction via a strong-coupling expansion to an effective 1D Bose-Hubbard model and a quantum Monte Carlo calculation and discuss possible applications.

Figure 1

$s$-band relative population of each momentum state along the $x$ axis with different $p_z$ at zero quasimomentum. The inset plot is the corresponding $p_z$-dependent 1D optical lattice potential.

Figure 2

Effective 1D on-site interaction, $U_{1\mathrm{D}}$ (blue line), and effective nearest-neighbor tunneling, $J_{1\mathrm{D}}$ (red line), with respect to the average transverse momentum, $\hslash {\overline{k}}_z$.

Figure 3

Phase diagram of the effective 1D TMDOL. The pink shaded area with a black solid line boundary is the $\overline{n}=1$ Mott lobe calculated from the strong coupling expansion of the effective 1D Bose-Hubbard model. Diamonds with error bars are QMC calculation results with system size $L=50a_L$ and temperature $k_{B}T=0.004E_r$. Note that all error bars are $\pm 0.005E_r$. The inset plot shows the corresponding effective 1D lattice potential for ${\overline{k}}_z=-4.73k_L$ (green line) and ${\overline{k}}_z=-2.49k_L$ (violet line), which correspond to the potentials for the green diamond and the violet diamond data points, respectively. Blue diamonds with errorbars are QMC results with different transverse momenta.

Figure 4

(a) Level diagram of the Raman process that we consider. Red solid, blue solid and red dashed arrows indicate lasers $a$, $b$, and $c$, respectively. (b) Laser configuration of the Raman process. The laser colors are the same as (a), with their polarizations indicated by the small arrows. The bias magnetic field is in the $+z$ direction, and the four black arrows represent the two-dimensional trapping lattice beams in $y\text{−}z$ plane.

Figure 5

$\overline{n}=2$ Mott lobe. The pink shaded area with black solid line boundaries is calculated from the occupation-independent Bose-Hubbard model, blue diamonds with error bars ($\pm 0.005Er$) are QMC calculation results, and black dashed lines are Bose-Hubbard model calculation results with a band mixing ground state $|{\psi }_g\rangle \approx 0.994|s\rangle +0.109|d\rangle$.