Blue-Detuned Magneto-optical Trap of Molecules

Direct laser cooling of molecules has reached a phase-space density exceeding ${10}^{-6}$ in optical traps but with rather small molecular numbers. To progress toward quantum degeneracy, a mechanism that combines sub-Doppler cooling and magneto-optical trapping would facilitate near unity transfer of ultracold molecules from the magneto-optical trap (MOT) to a conservative optical trap. Using the unique energy level structure of YO molecules, we demonstrate the first blue-detuned MOT for molecules that is optimized for both gray-molasses sub-Doppler cooling and relatively strong trapping forces. This first sub-Doppler molecular MOT provides an increase of phase-space density by 2 orders of magnitude over any previously reported molecular MOT.

Figure 1

The basic physical mechanism of the BDM. GMC relies on a motion-induced Sisyphus mechanism through a light-induced Stark shift gradient in the molecular ground state of $X{}^2{\mathrm{\Sigma }}^{+}$. While most of the molecules are cold and, thus, remain in the dark state, fast-moving molecules can undergo nonadiabatic transitions to a bright state. These molecules lose kinetic energy as they climb the Stark potential hill. Near the intensity maximum, they will scatter a photon in a magnetic quadrupole field gradient which provides the MOT restoring force. Cooling is further enhanced in YO by coupling both ground-state manifolds in a $\mathrm{\Lambda }$-type configuration as shown diagrammatically. By detuning the two-photon resonance $\delta$, we can transition between robust coherent population trapping ($\delta =0$) and MOT restoring force ($\delta \ne 0$).

Figure 2

Relevant YO level structure and the transitions employed to address the hyperfine structure of $N=1$ rotational level of the main cooling laser for (a) dual-frequency MOT and (b) blue-detuned MOT.

Figure 3

Evolution of the blue-detuned MOT as a function of different hold times (13 ms in situ exposure). The magnetic field is ramped from 0 to $4\mathrm{G}/\mathrm{cm}$ over 40 ms and held constant for the remaining hold time, $\mathrm{\Delta }=0.44\mathrm{\Gamma }$ and $\delta /2\pi =-264\mathrm{kHz}$. Each camera image is $3.3\mathrm{mm}\times 3.3\mathrm{mm}$.

Figure 4

Variation of the (a) temperature ($T$), (b) spring constant ($\kappa$), and (c) damping rate ($\alpha /\mathrm{m}$) with intensity ($I$) of each sub-Doppler MOT hyperfine component, with a magnetic field gradient of $4\mathrm{G}/\mathrm{cm}$, $\mathrm{\Delta }=0.44\mathrm{\Gamma }$, and $\delta /2\pi =-264\mathrm{kHz}$. At optimal $I$ ($\approx 1–2I_{\mathrm{sat}}$), the damping rate is high but momentum diffusion remains sufficiently small for the lowest temperature. As $I$ increases further, dark states form more rapidly, suppressing the excited-state population, and $\kappa$ drops rapidly. The inset in (b) shows the excited-state population vs $I/I_{\mathrm{sat}}$ by solving the optical Bloch equations for a three-level system with the above parameters and is directly proportional to $\kappa$. We see good qualitative agreement. The red clover symbol represents a numerical simulation result based on a rate equation model. The model agrees strongly with the experimental data for low $I$.

Figure 5

Variation of (a) temperature ($T$), (b) quadrature size (${\sigma }^2$), (c) spring constant ($\kappa$), and (d) damping rate ($\alpha /m$) in the blue MOT with differential detuning ($\delta$), with a maximum magnetic field gradient of $4\mathrm{G}/\mathrm{cm}$, $\mathrm{\Delta }=0.44\mathrm{\Gamma }$, and $I=1.93I_{\mathrm{sat}}$. The variation of ${\sigma }^2$ and $\kappa$ vs $\delta$ shows the transition between BDM and GMC as a function of the excited-state population. The inset in (b) shows the inverse of the excited-state population which is proportional to dependence of quadrature size on $\delta$. There is good agreement as $\delta$ approaches 0; however, we see disagreement with this model as $\delta$ moves away from zero. This is most likely due to the fact that the model does not account for the close triplet of states in $X{}^2{\mathrm{\Sigma }}^{+}$, $G=1$.

Figure 6

The weak dependence of (a) temperature ($T$), (b) quadrature size (${\sigma }^2$), and (c) spring constant ($\kappa$) on one-photon detuning ($\mathrm{\Delta }$), with a magnetic field gradient of $4\mathrm{G}/\mathrm{cm}$, $\delta /2\pi =-264\mathrm{kHz}$, and $I=1.93I_{\mathrm{sat}}$. The inset in (b) shows the inverse of the excited-state population which is proportional to dependence of quadrature size on $\mathrm{\Delta }$, and we again see qualitative agreement.