Anisotropic light shift and magic polarization of the intercombination line of dysprosium atoms in a far-detuned dipole trap

We characterize the anisotropic differential ac-Stark shift for the Dy $626\mathrm{nm}$ intercombination transition, induced in a far-detuned $1070\mathrm{nm}$ optical dipole trap, and observe the existence of a “magic polarization” for which the polarizabilities of the ground and excited states are equal. From our measurements we extract both the scalar and tensorial components of the dynamic dipole polarizability for the excited state, ${\alpha }_E^{\text{s}}=188\left(12\right){\alpha }_{\text{0}}$ and ${\alpha }_E^{\text{t}}=34\left(12\right){\alpha }_{\text{0}}$, respectively, where ${\alpha }_{\text{0}}$ is the atomic unit for the electric polarizability. We also provide a theoretical model allowing us to predict the excited state polarizability and find qualitative agreement with our observations. Furthermore, we utilize our findings to optimize the efficiency of Doppler cooling of a trapped gas, by controlling the sign and magnitude of the inhomogeneous broadening of the optical transition. The resulting initial gain of the collisional rate allows us, after forced evaporation cooling, to produce a quasipure Bose-Einstein condensate of ${}^{162}\mathrm{Dy}$ with $3\times {10}^4$ atoms.

Figure 1

Center-of-mass displacement resonance. Schematic drawing: a near-resonant ($626\mathrm{nm}$) beam is applied to a cold atomic sample optically trapped around the focal point of a 1070 nm laser beam propagating along the $x$ axis. The magnetic field bias is orientated in a plane perpendicular to the optical beam propagation axis, forming an angle $\theta$ with the polarization vector ${\mathbf{e}}_{\text{L}}$. Two orientations of $\mathbf{B}$ are represented: the initial vertical orientation (${\mathbf{B}}_{\text{i}}$) and the value corresponding to the resonance curve shown in the main panel (${\mathbf{B}}_{\theta }$). The beam is applied for a short duration and accelerates the atoms, leading to a displacement of the cloud center-of-mass (CoM), measured after time of flight (ToF) represented by the dashed lines (see top panels). The center-of-mass displacement (${\delta }_{\text{CoM}}$) is plotted as a function of the laser frequency $\nu$ for $\theta ={80}^{\circ }$ and fitted using Eq. (7) with the free parameter $\mathrm{\Delta }\alpha \left(\theta \right)$. The error bars denote the rms. deviation of three independent measurements.

Figure 2

Differential light shift as a function of the relative angle $\theta$. Top panels: CoM resonances as a function of the trap depth experienced in $\left|g\right.〉$ (see legend) for three different angles: $0^{\circ },{55}^{\circ },\text{and}{100}^{\circ }$. The CoM values have been shifted with respect to each other for clarity. The error bars denote the rms deviation of three independent measurements. Main panel: $\mathrm{\Delta }\alpha$ as a function of $\theta$. The solid line corresponds to a fit based on the energy difference between excited and ground states following the diagonalization of $\widehat{H}$ given in Eq. (2) with $\mathrm{\Delta }{\alpha }^{\text{s}}$ and $\mathrm{\Delta }{\alpha }^{\text{t}}$ as free parameters. Inset: Differential polarizability as a function of $\theta$ using Eq. (5) and the theoretical values given in Sec. 2. The shaded region represents the differential polarizability uncertainty.

Figure 3

Doppler cooling efficiency as a function of $\theta$ and gain in phase-space density: Cooling efficiency for (a) $\theta ={50}^{\circ }$ and (b) $\theta ={75}^{\circ }$ as a function of the cooling beam frequency $\nu$, for $s_0=0.5$ and a pulse time $\tau =20$ ms. The vertical red dashed line indicates the transition resonance at the trap center. (c) Detuning from the trap center for which the minimal temperature is recorded ($\mathrm{\Delta }{\omega }_{\text{min}}$) as a function of $\theta$. The black dashed line indicates the zero-detuning limit. (d) Collisional rate, ${\mathrm{\Gamma }}_{\text{col.}}$, as a function of $\theta$. An optimum is visible for $\theta ={70}^{\circ }$ corresponding to a small, positive differential light shift. The horizontal dashed red line corresponds to the value of ${\mathrm{\Gamma }}_{\text{col.}}$ prior to the Doppler cooling stage. The error bars denote the rms deviation of three independent measurements.

Figure 4

Condensation of ${}^{162}\mathrm{Dy}$: (a) Schematic representation of the evaporation procedure in the optical dipole trap. (b) Phase-space density, $\varpi$, as a function of the atom number $N$ in logarithmic scale. (c) Two-dimensional picture and integrated profile of a dipolar Bose-Einstein condensate with a condensed fraction of $50\%$. The solid line corresponds to a Gaussian plus parabolic fit.