content_image/395368.jpg content_image/395367.jpg
<img src='content_image/395368.jpg'>

quencies to one of the comb AO frequency shifters, we create two combs in one of the beams. When these combs are tuned to drive the red and blue sidebands (in conjunc- tion with the third frequency comb in the other beam), the ion experiences a spin-dependent force in a rotated basis as described in Ref. [23]. Ideally, when the fields are detuned from the sidebands by an equal and opposite amount δ = 2 η Ω, a decoupling of the motion and spin oc- curs at gate time t$_{g}$ = 2 π/δ, and the spin state evolve to the maximally entangled state | χ 〉 = |↓↓〉 + e iϕ |↑↑〉 . In the experiment, t$_{g}$ = 108 µ s ( N ∼ 8700 pulses). 

The entanglement is verified by the measurement of a fidelity-based entanglement witness [24]. The fidelity of the state ρ with respect to | χ 〉 is found by measur- ing the populations ρ$_{↑↑}$$_{,}$$_{↑↑}$ and ρ$_{↓↓}$$_{,}$$_{↓↓}$ and scanning the measurement phase angle φ in the parity signal Π( φ ) = T r [ σ (1) z σ (2) z R ( φ ) ⊗ $^{2}$ρR $^{†}$( φ ) ⊗ $^{2}$], where R ( φ ) is a π/ 2 rota- 

<img src='content_image/395367.jpg'>

tion on the Bloch sphere with phase φ [25]. The contrast of the parity signal, Π$_{C}$, is used to calculate the fidelity F = ( ρ$_{↑↑}$$_{,}$$_{↑↑}$ + ρ$_{↓↓}$$_{,}$$_{↓↓}$ ) / 2 + Π$_{C}$ / 4. The measured popula- tions of |↓↓〉 and |↑↑〉 together with the data shown in Fig. 5 yield a fidelity F = 0 . 86 ± 0 . 03, thereby signaling that the two ions are entangled after the application of the pulse train. 

We have demonstrated full control and entanglement of two atomic qubits using an optical frequency comb. This work represents a significant simplification over current methods for optical control of trapped ion qubits, and also points the way toward future advances with higher power laser pulses. For example, such pulses allow much larger detunings from resonance and a suppression of de- coherence from spontaneous emission [26] while main- taining gate speed. When only a few high-power pulses are used in ways similar to the experiment, it also be- comes possible to suppress sources of motional decoher- ence through the use of fast entanglement schemes [16]. 

This work is supported by the Army Research Office (ARO) with funds from the DARPA Optical Lattice Em- ulator (OLE) Program, IARPA under ARO contract, the NSF Physics at the Information Frontier Program, and the NSF Physics Frontier Center at JQI. 

∗ dhayes12@umd.edu 

[1] Th. Udem, R. Holzwarth, and T. W. H¨ ansch. Nature 416 , 233 (2002). 

[2] S. T. Cundiff and J. Ye. Rev. Mod. Phys. 75 , 325 (2003). 

[3] J. L. Hall. Rev. Mod. Phys. 78 , 1279 (2006). 

[4] T. W. H¨ ansch. Rev. Mod. Phys. 78 , 1297 (2006). 

[5] M. C. Stowe et al. Adv. At. Mol. Opt. Phys. 55 , 1 (2008). 

[6] M. C. Stowe et al. Phys. Rev. Lett. 96 , 153001 (2006). 

[7] M. C. Stowe, A. Pe’er, and J. Ye. Phys. Rev. Lett. 100 , 

