Coherent Spin Manipulation and ESR on Superfluid Helium Nanodroplets

Superfluid helium nanodroplets provide a versatile substrate to cool atoms and molecules, and to assemble weakly bound complexes. Absence of spin-relaxation mechanisms makes He nanodroplets ideal to isolate open-shell atoms and create a spin-polarized system. Here, we show the first coherent manipulation of such a system by resonant excitation of a magnetic-dipole transition. Observation of $\approx 50$ Rabi oscillations demonstrates coherent population transfer with minimal dephasing. Ours is also the first application of ESR spectroscopy to doped He nanodroplets. This unique environment results in extremely sharp lines and hyperfine-resolved spectra: those of single ${}^{39}\mathrm{K}$ and ${}^{85}\mathrm{Rb}$ dopant atoms presented here denote an increase of the Fermi contact interaction, which we can follow as a function of droplet size, reflecting the distortion of the valence-electron wave function due to the surrounding He.

Figure 1

Schematic diagram of ODMR on doped He nanodroplets. The pump laser beam ($A$ field) exciting an unpolarized ensemble creates a net spin polarization, which is coherently manipulated with a resonant microwave $C$ field. Because the probe beam ($B$ field) only excites spin-up atoms, a correlated change of fluorescence is observed.

Figure 2

Top: Stick spectrum of the six ESR transitions $|\Delta m_J|=1$, $\Delta m_I=0$ ($m_I=+5/2$, $+3/2$, $+1/2$, $-1/2$, $-3/2$, $-5/2$, from left to right) in free ${}^{85}\mathrm{Rb}$ atoms. Bottom: Shift of the ESR transitions due to the helium droplet (same colors as top panel, the traces are vertically offset by 3000 counts/s each; droplet size $\sim 8000$ He atoms; ${\nu }_0=9.44247\mathrm{GHz}$). The reference line from free atoms appears by definition at zero shift; the corresponding value of $B_0$ is indicated beside. Each trace is fitted (solid lines) with two Gauss functions, whose separation is used to calculate the absolute position of the transitions on the He droplet.

Figure 3

Relative change $\delta a/a$ versus droplet size $N$ of the hyperfine constant for ${}^{85}\mathrm{Rb}$ atoms. Values of $N$ for the experimental data (circles) are deduced from the nozzle temperatures reported on the top axis [24]. The solid line represents a $1/N$ dependence and is intended merely as a guide to the eye. The computed values (triangles) have been divided by a factor 4 to visually match the experimental points.

Figure 4

Rabi oscillations of ${}^{39}\mathrm{K}$ atoms ($m_I=+3/2$, $B_0=0.3404\mathrm{T}$, ${\nu }_0=9.442\mathrm{GHz}$) on helium droplets and their fit; the slow start at low $B_1$ can only be reproduced if a gradient of the static field $B_0$ is assumed. In order to limit the amount of fit parameters, we use $\overrightarrow{B}=[B_0+\frac{\partial B_0}{\partial x}(x-x_0)]\widehat{z}$. The choice is based on the fact that the portion of droplet beam irradiated in the cavity is a thin long cylinder; $x_0$ accounts for the possibility that the position where the field is resonant is offset from the center of the cavity.