Atoms in a Radio-Frequency-Dressed Optical Lattice

We load cold atoms into an optical lattice dramatically reshaped by radio-frequency coupling of state-dependent lattice potentials. This radio-frequency dressing changes the unit cell of the lattice at a subwavelength scale, such that its curvature and topology departs strongly from that of a simple sinusoidal lattice potential. Radio-frequency dressing has previously been performed at length scales from mm to tens of $\mu \mathrm{m}$, but not at the single-optical-wavelength scale. At this length scale significant coupling between adiabatic potentials leads to nonadiabatic transitions, which we measure as a function of lattice depth and dressing amplitude. We also investigate the dressing by measuring changes in the momentum distribution of the dressed states.

Figure 1

(a) The energy levels of ${}^{87}\mathrm{Rb}$ relevant to our lattice; the rf coupling can selectively address either $m_F$ transition due to the quadratic Zeeman shift. (b) Top two images: the bare lattice potentials for $m_F=\pm 1$, exhibiting approximately opposite light shifts. Bottom two images: the uppermost adiabatic potential, weakly dressed and strongly dressed. (c) From top: bare lattice potentials for $U\simeq 10E_R$; dressed adiabatic potentials at ${\omega }_{\mathrm{rf}}/2\pi =35.90\mathrm{MHz}$, $\Omega /2\pi =20\mathrm{kHz}$; dressed adiabatic potentials at ${\omega }_{\mathrm{rf}}/2\pi =35.90\mathrm{MHz}$, $\Omega /2\pi =205\mathrm{kHz}$. Note the significantly increased gap for stronger coupling.

Figure 2

(a) The width of the momentum distribution as a function of final dressing frequency, as measured by absorption imaging. The width is calculated as $Md/\hslash t_{\mathrm{TOF}}$, where $d$ is the Gaussian $1/e$ radius along one direction, corrected for the initial cloud size. The displayed uncertainties represent $1\sigma$ shot-to-shot scatter of five points. The shaded area represents predicted widths given the values and estimated uncertainties of the magnetic field [5.117(3) mT] and the depth of the bare lattice $U=10.0(5)E_R$. Also shown are the bare and dressed single-site potentials (solid lines) and ground-state wave functions (gray). (b, c) Sample images of the off-resonant (effectively bare) and dressed momentum distributions, respectively, (both at $\Omega /2\pi =205\mathrm{kHz}$) showing significant narrowing of the latter. (d, e) Examples of dressed momentum distributions created through faster ($>1\mathrm{MHz}/\mathrm{ms}$) rf ramps, such that higher vibrational states of the dressed lattice are populated.

Figure 3

Dressed-state losses as a function of calculated avoided-crossing gap $\Delta /2\pi$ for four bare lattice depths. Vertical bars represent uncertainties of fit; multiple points near a given $\Delta$ indicate scatter in multiple runs. The data are well represented by $\gamma (\Delta )=A{e}^{-B\Delta /2\pi }$, with $B=83(6)\mu \mathrm{s}$, $83(11)\mu \mathrm{s}$, $82(13)\mu \mathrm{s}$, and $100(30)\mu \mathrm{s}$ for $U=8E_R$, $10E_R$, $12E_R$, and $16E_R$, respectively. The scaling of the data does not change if plotted versus $\Omega$.

Figure 4

Dressed-state losses as a function of bare lattice depth $U$ at constant $\Omega /2\pi =205\mathrm{kHz}$ and dressing frequency 35.900(35.875) MHz for the first five (last four) depths, resulting in approximately constant gap $\Delta /2\pi \simeq 75\mathrm{kHz}$. Vertical bars represent uncertainties of fit; multiple points at a given depth represent the scatter in multiple runs. Horizontal bars represent known drifts in laser power; not shown is a constant systematic uncertainty in depth determination on the order of 5%. The data are well represented by a simple exponential fit $\gamma (U)=C{e}^{DU}$, yielding $C=1.2(4){\mathrm{s}}^{-1}$ and $D=0.27(3)E_R^{-1}$.