Ultrafast Spin-Motion Entanglement and Interferometry with a Single Atom

We report entanglement of a single atom's hyperfine spin state with its motional state in a time scale of less than 3 ns. We engineer a short train of intense laser pulses to impart a spin-dependent momentum transfer of � 2@k. Using pairs of momentum kicks, we create an atomic interferometer and demonstrate collapse and revival of spin coherence as the motional wave packet is split and recombined. The revival after a pair of kicks occurs only when the second kick is delayed by an integer multiple of the harmonic trap period, a signature of entanglement and disentanglement of the spin with the motion. Such quantum control opens a new regime of ultrafast entanglement in atomic qubits. Trapped atomic ions are a leading platform for quantum information processing, with a well-developed toolkit for coherent spin manipulations (1). These tools have been used to experimentally demonstrate quantum algorithms (2,3), multiparticle entanglement (4,5), and quantum simu- lations (6,7), among other advances. To date, most coher- ent manipulations of trapped ions are performed in the weak excitation regime, in which the interaction between the ions and the laser fields is characterized by a Rabi frequencythat is much smaller than the motional trap frequency !t. Recent work has demonstrated coherent spin flips in the strong excitation regime, � � !t (8), using picosecond laser pulses (9) and near-field microwaves (10). However, motional control has not been observed in the strong excitation limit. In this Letter, we demonstrate ultrafast spin-motion entanglement, using a short train of picosecond pulses to drive stimulated Raman transitions. Each spin state receives a discrete kick in opposite directions. The mo- mentum transfer occurs in an interaction time of 2.7 ns, only 0.2% of the 1:27 � s trap oscillation period. A pair of such spin-dependent kicks, separated by an integer number of trap periods, creates an interferometer. The two spin components of the ion's wave function evolve along differ- ent paths in phase space after the first kick, and are then returned to their original position after the second. This is similar to other atomic interferometry experiments (11,12), with trap evolution playing the role of the atomic reflectors. Such spin-dependent kicks are a key building block for fast entanglement of multiple ion qubits via the Coulomb interaction (13,14). In contrast to motional gates using spectroscopically resolved sidebands, these gates may be performed faster than a trap oscillation period. This com- putational speed-up comes with the additional benefits that the entangling gates will be less sensitive to noise, inde- pendent of temperature, and more easily scaled to large crystals of ions (15). In addition to entangling gates, other applications of impulsive spin-dependent kicks include fast sideband cooling (16) and interferometry (8). To create the spin-dependent kick, two pulse trains are sent onto the ion from opposite directions, with pairs of pulses from each train arriving at the ion simultaneously. The two pulse trains have a relative frequency shift between them. The ion's response can be understood in either the frequency domain or the time domain; both are instructive. First, consider the spectrum seen by the ion. As sketched in Fig. 1, the combined spectrum contains frequency components that can drive stimulated Raman