Quantum Dynamics with Spatiotemporal Control of Interactions in a Stable Bose-Einstein Condensate

Optical control of atomic interactions in quantum gases is a long-sought goal of cold atom research. Previous experiments have been hindered by rapid decay of the quantum gas and parasitic deformation of the trap potential. We develop and implement a generic scheme for optical control of Feshbach resonances which yields long quantum gas lifetimes and a negligible parasitic dipole force. We show that fast and local control of interactions leads to intriguing quantum dynamics in new regimes, highlighted by the formation of van der Waals molecules and localized collapse of a Bose condensate.

Figure 1

Illustration of optical control of Feshbach resonances. A Feshbach resonance occurs when a laser (yellow) brings a molecular energy level (blue surface) close to the atomic scattering threshold (red surface). Here, the atom-molecule coupling makes atomic interactions more attractive at higher laser intensity. When operating at the magic wavelength, the beam does not shift the energy of single atoms (see text).

Figure 2

Stable optical control of scattering length at a magic wavelength ${\lambda }_M$. (a) Theoretical polarizability of Cs atoms in the absolute ground state for ${\sigma }^{+}$ polarization [30]. The star marks the magic wavelength where polarizability is zero. (b) Measured polarizability (circle). A linear fit yields ${\lambda }_M=869.73(2)\mathrm{nm}$ (star). (c) Number of condensed atoms remaining over time with (circle) and without (square) exposure to OFR at a magnetic field of 48.19 G. We fit the decay dynamics (solid curves) and find that OFR exposure adds a one-body loss process with a time constant of 0.63(2) s [30] at intensity $I=225\mathrm{W}/{\mathrm{cm}}^2$. (d) Scattering length $a$ determined from the free expansion of BECs with (circle) and without (square) exposure to the OFR laser. When the scattering length becomes negative ($a<0$) the condensate collapses (cross). The solid curves derive from a single fit to all $a>0$ data using Eq. (2), which yields $\mathrm{\Delta }=157(3)\mathrm{mG}$, $B_0=47.766(4)\mathrm{G}$, and $\beta I=-38(1)\mathrm{mG}$. (e) In situ images of BECs at 47.97 G [dashed line in panel (d)] after ramping on the intensity of the OFR laser over 200 ms. Each image is the average of 10 trials. All error bars show standard error.

Figure 3

Interaction modulation spectroscopy. The BEC at 47.976 G is exposed for a hold time $t$ to the OFR laser, which is intensity modulated at frequency $\omega /2\pi$. We measure the number of condensed atoms remaining after exposure, normalized to the off-resonant number, under three conditions: (open circle) $t=100\mathrm{ms}$ with no optical lattice, (filled circle) $t=20\mathrm{ms}$ with a one dimensional optical lattice of depth $h\times 9.3\mathrm{kHz}$, (open triangle) $t=500\mathrm{ms}$ with no optical lattice. Resonances are observed at 0.89(1), 8.18(2), 133(7), 197(1), and 11 649(2) kHz, determined from fits (solid curve) to each resonance (Gaussian for 133 kHz, Lorentzian for others). The illustrations indicate the nature of each resonance. The van der Waals energy scale is $E_{\text{vd}\mathrm{W}}=h\times 2.7\mathrm{MHz}$ for Cs molecules.

Figure 4

Condensate dynamics with spatially modulated interactions. Time series of in situ images of BECs with $N=12000$ atoms after a quench from uniform $a=200a_0$ at 47.965 G to the spatially modulated $a$ shown in the top panels. The OFR beam has peak intensity of $115\mathrm{W}/{\mathrm{cm}}^2$ and a waist of $14\mu \mathrm{m}$, while the final magnetic fields are (a) 47.949 G, (b) 47.935 G, and (c) 47.925 G. Each image is the average of 6 or 7 trials. The red dashed lines show where $a$ equals zero. The white dashed lines in panel (c) guide the eye to the motion of the solitonic wave towards the trap center. (d) Illustration of the local collapse dynamics, in which the initial BEC (left) undergoes transverse compression followed by localized central collapse (right).