Interaction Dependent Heating and Atom Loss in a Periodically Driven Optical Lattice

Periodic driving of optical lattices has enabled the creation of novel band structures not realizable in static lattice systems, such as topological bands for neutral particles. However, especially driven systems of interacting bosonic particles often suffer from strong heating. We have systematically studied heating in an interacting Bose-Einstein condensate in a driven one-dimensional optical lattice. We find interaction dependent heating rates that depend on both the scattering length and the driving strength and identify the underlying resonant intra- and interband scattering processes. By comparing the experimental data and theory, we find that, for driving frequencies well above the trap depth, the heating rate is dramatically reduced by the fact that resonantly scattered atoms leave the trap before dissipating their energy into the system. This mechanism of Floquet evaporative cooling offers a powerful strategy to minimize heating in Floquet engineered quantum gases.

Figure 1

Schematic of the experiment and frequency scan. (a) Two lattice beams with a linear out-of-plane polarization intersect at an angle of 120° to form a one-dimensional lattice of “pancakes.” By periodically modulating the frequency of one of the lattice beams, we can shake the lattice, i.e., modulate its position. (b) Normalized atom number after modulating for 50 (for $\omega /{\omega }_{10}>0.7$) or 100 ms (for $\omega /{\omega }_{10}<0.7$) with variable frequency at a driving strength of $\alpha \simeq 0.9$. Error bars indicate the standard error of the mean from four measurements per data point. The solid blue line shows the theoretically expected single-particle excitations to higher bands. Thin lines mark the resonance positions of single- and multiphoton transitions to higher bands labeled by $(b,\nu )$. In the frequency region from roughly $0.7{\omega }_{10}$ to $1.1{\omega }_{10}$, we observe a splitting of the BEC due to two degenerate minima in the lowest dressed band, which is included in the theory curve. The insets show raw quasimomentum images of the BEC. (c) Enlargement into the regime of small shaking frequencies with $\alpha =2.2$ and 200 ms shaking duration.

Figure 2

Loss rates in the presence of periodic driving. (a),(d) Effective loss rates for different driving amplitudes and scattering lengths. Each dot corresponds to a single lifetime measurement. The shaking frequency is (a)–(c) $\omega ={\omega }_l$ and (d)–(f) $\omega ={\omega }_h$. (b),(e) Crosscuts at fixed scattering lengths. The solid lines correspond to the theoretically predicted scattering rates, and error bars indicate fit uncertainties. (c),(f) Corresponding crosscuts at fixed driving strengths. Theory lines in (b),(c) assume $f\beta \hslash \omega =10$ to account for the thermalization of scattered atoms (see the text).

Figure 3

Examples of two-particle scattering channels. The lowest two bands of a schematic lattice dispersion are sketched by solid lines, and Floquet modes shifted by $-\hslash \omega (m=-1)$ are depicted by dashed lines. The condensate is represented by a large sphere, and scattered particles by small spheres. The pair of yellow wiggly arrows in (a) denotes a two-photon scattering process, where the atoms absorb two photons, while the red wiggly lines in (b),(c) denote a zero-photon (ordinary) collision between two atoms, and blue arrows describe single-photon interband transitions. (a) When the driving frequency is much smaller than the band gap, the dominant loss process are two-photon intraband collisions. (b),(c) For driving frequencies larger than the band gap, the leading (subleading) excitation channels combine one (two) single-photon interband transitions with zero-photon collisions. Note that only one photon number $m$ is associated with the whole system and not one per particle as suggested, for simplicity, in the diagrams.

Figure 4

Loss rates for large driving strengths and small frequencies. (a) When scanning the driving strength $\alpha$ at frequency ${\omega }_l$, we observe peaks in the loss rate whenever the effective tunneling $J_{\text{eff}}=J_0·{\mathcal{J}}_0(\alpha )$ goes through zero (dashed lines). The insets sketch the lowest band for positive and negative tunneling. (b) For a fixed driving strength $\alpha =1.1$, we observe a peak in the loss rate for driving frequencies close to the bandwidth of the lowest band. The solid line shows the theory scaled by $f\beta \hslash \omega$ with a temperature of 15 nK (see the text). The dashed black lines indicate one (two) times the effective bandwidth, below which the number of accessible states for two- (single-) photon scattering becomes reduced [45]. The dashed green line marks the frequency ${\omega }_l$. Error bars indicate fit errors.