Controllable Optical Phase Shift Over One Radian from a Single Isolated Atom

Fundamental optics such as lenses and prisms work by applying phase shifts of several radians to incoming light, and rapid control of such phase shifts is crucial to telecommunications. However, large, controllable optical phase shifts have remained elusive for isolated quantum systems. We have used a single trapped atomic ion to induce and measure a large optical phase shift of $1.3\pm 0.1$ radians in light scattered by the atom. Spatial interferometry between the scattered light and unscattered illumination light enables us to isolate the phase shift in the scattered component. The phase shift achieves the maximum value allowed by atomic theory over the accessible range of laser frequencies, pointing out new opportunities in microscopy and nanophotonics. Single-atom phase shifts of this magnitude open up new quantum information protocols, in particular long-range quantum phase-shift-keying cryptography.

Figure 1

Configuration of experimental apparatus. A laser cooled ${}^{174}\mathrm{Yb}^{+}$ ion (red dot) is confined in a radio-frequency electric quadrupole trap generated by two tungsten needles. Resonant laser light at $\lambda =369.5\mathrm{nm}$ is incident along the optical axis of the imaging system (the left side of the figure) and weakly focused at the ion position, illuminating the ion with a plane wave. The transmitted light consists of a superposition of the scattering and driving field, with phase fronts depicted by lines in the vicinity of the ion. The transmitted light is imaged with a large aperture phase Fresnel lens [9, 11] and a weak refocusing lens (not shown) onto a cooled CCD camera at $585\times \mathrm{\text{magnification}}$. We acquire images of the transmitted light at several camera viewing planes. A secondary cooling beam (not shown) is incident orthogonal to the needle axis and the optical axis.

Figure 2

Spatial interferograms of the scattered wave. The theoretical prediction for each interferogram is shown to the right of the data. The image resolution is 370 nm, approximately equal to the illumination wavelength of 369.5 nm, and each image is $3.4\mu \mathrm{m}$ on a side. Each row of images corresponds to a fixed observation plane position. In terms of the object space coordinates, row I sits at the nominal plane of the ion and row II (respectively, III) at $1.7\mu \mathrm{m}$ (respectively, $3.3\mu \mathrm{m}$) upstream of the ion. The color bars at the right of the figure indicate the fractional change in transmission for the images in each row. The images are smoothed with a Gaussian filter of 40 nm width for ease of viewing, but only raw data are used for comparison with theory. (a) Data (left) and theory (right) at $-13\mathrm{MHz}$ detuning. (b) The same, but for $+9\mathrm{MHz}$ detuning.

Figure 3

Phase shift and normalized scattering probability of the scattered wave. (a) Phase of the scattered wave as a function of laser detuning. Each data point is obtained by fitting a series of spatial interferograms to the model. The data show a total phase shift of $1.3\pm 0.1$ radians. The uncertainty in determining spherical aberration imparts a common systematic error of $\pm 0.1\mathrm{rad}$ to all data points. This common-mode error does not affect the measurement of the phase shift. The data is well fit by semiclassical theory with the linewidth $\Gamma =34\pm 8\mathrm{MHz}$, with the fitted resonance position shifted $5\pm 2\mathrm{MHz}$ blue of the nominal resonance frequency. (b) Normalized scattering probability as a function of detuning. All values are normalized to the maximum scattering probability observed in the data. The theory curve is predicted from the fit to the phase shift. On resonance and at blue detuning, the scattering probability is lower than expected from the theory. The mechanical effects of the laser light are seen to be significant, including the broadening and redshift of the phase-shift data relative to the ideal case.