Three-Dimensional Matter-Wave Interferometry of a Trapped Single Ion

We report on a demonstration of Ramsey interferometry by three-dimensional motion with a trapped ${}^{171}{\mathrm{Yb}}^{+}$ ion. We applied a momentum kick to the ion in a direction diagonal to the trap axes to initiate three-dimensional motion using a mode-locked pulse laser. The interference signal was analyzed theoretically to demonstrate three-dimensional matter-wave interference. This work paves the way to realizing matter-wave interferometry using trapped ions.

Figure 1

(a) Phase-space diagrams of one-dimensional interference. (b) Experimental configuration (shown in inset) and results for one-dimensional interference. The light blue arrows represent the direction of the pulse laser beam. The laser pulses have a linear-perpendicular-linear polarization configuration and their polarizations are both orthogonal to the quantization axis (defined by the magnetic field $B$). Each data point represents an average of 900 measurements. (c) Measured interference fringes for a diagonal momentum kick. Pulse trains are introduced orthogonally. Both pulse trains are horizontally polarized. Each data point represents an average of 600 measurements.

Figure 2

Observed interference fringes at trap frequency $({\omega }_x,{\omega }_y,{\omega }_z)=2\pi \times [1229.0(8),1349.7(7),491.7(1)]\mathrm{kHz}$. (a) Blue points show the experimental results (each data point represents an average of 900 measurements) and the red solid line is the fitted curve. (b)–(e) show phase-space diagrams at the timings indicated in (a). The red, green, and purple circles represent the coherent state components in the $x$ direction, $y$ direction, and $z$ direction, respectively. For simplicity, phase space trajectories along the $x$, $y$, and $z$ axes are shown in a single phase-space diagram without scaling.

Figure 3

Axial trap frequency dependence of three-dimensional interference. The axial trap frequency is shifted by changing the voltage applied to the ion trap. Blue points represent an average of 900 or 600 measurements, and red solid lines are theoretical fits using Eq. (2). (a) ${\omega }_z=2\pi \times 491.7(1)$, (b) ${\omega }_z=2\pi \times 484.0(3)$, and (c) ${\omega }_z=2\pi \times 474.8(3)\mathrm{kHz}$.

Figure 4

Measured interference fringes for long interrogation times. Blue points represent an average of 300 measurements, and red solid lines are theoretical fits using Eq. (2) with an attenuation term $e^{-\gamma t}$.