State Preparation and Dynamics of Ultracold Atoms in Higher Lattice Orbitals

We report on the realization of a multiorbital system with ultracold atoms in the excited bands of a 3D optical lattice by selectively controlling the band population along a given lattice direction. The lifetime of the atoms in the excited band is found to be considerably longer (10–100 times) than the characteristic time scale for intersite tunneling, thus opening the path for orbital selective many-body physics with ultracold atoms. Upon exciting the atoms from an initial lowest band Mott-insulating state to higher lying bands, we observe the dynamical emergence of coherence in 1D (and 2D), compatible with Bose-Einstein condensation to a nonzero momentum state.

Figure 1

(a) Schematic of anisotropic tunneling following an excitation along the $x$ direction into a $p$-wave orbital using stimulated Raman transitions. (b) Using adiabatic band mapping, the population of the lowest (i) and first excited band (ii) can be measured after a 16 ms TOF period [12, 14, 15]. Rabi oscillations between the $s$- and $p$-wave orbital demonstrate the coherent coupling. Black bars denote the $2\hslash k(t_{\mathrm{TOF}}/m)$ length scale.

Figure 2

Measured lifetime of the excited state $|100⟩$ with respect to (a) the total atom number for $V_x=40E_r$ and (b) the lattice depth $V_x$ along the excitation axis (for $4.5\times {10}^4\mathrm{\text{atoms}}$). The lifetime $\tau$ was determined from an exponential decay fit to the measured population dynamics $\propto e^{-t/\tau }$ (see inset) neglecting short time effects.

Figure 3

Emergence of 1D coherence in the first excited Bloch band: Directly after lowering the lattice depth to $V_{\mathrm{hold}}=17E_r$, the first excited band is still homogeneously populated (a) and the TOF image shows the Wannier function of the $|100⟩$ state as envelope (b). Within 1 ms hold time, the system relaxes to a nonzero momentum state (d) and shows interference structure (e), with the bar indicating the $2\hslash k(t_{\mathrm{TOF}}/m)$ length scale. (c),(f) Corresponding vertically integrated profiles with fits to the coherent contribution of the first excited state (red) and incoherent contributions of the vibrational ground state (blue) and first excited band (green). (g) Time evolution of the coherent and incoherent contributions at $V_{\mathrm{hold}}=20E_r$ (color code as above).

Figure 4

Time evolution of the measured interference pattern emerging out of the states (a) $|100⟩$ and (b) $|110⟩$ after the $x$ and $y$ axes were ramped down to $17E_R$ in $50\mu \mathrm{s}$ after the state preparation while the $z$ axis was kept at $55E_R$. In analogy to the 1D case, for zero hold time (a),(b) the corresponding Wannier product wave functions of $|100⟩$ and $|110⟩$ [(c),(d): theory] are visible, indicating an initial homogeneous occupation of the first excited Bloch band along (a) one and (b) two axes. The lowest energy states in the singly and doubly excited band are expected to yield gridlike (e), respectively, pointlike interference patterns (f) (both theory). White bars denote the $6\hslash k(t_{\mathrm{TOF}}/m)$ length scale.