Ultrafast Control of Spin and Moon of Trapped Atomic Qubits J. Mizrahi, W.C. Campbell, C. Senko, C. Monroe University of Maryland Department of Physics and Naonal Instute of Standards and Technology Joint Quantum Institute Using Pulsed Lasers 2 P 1/2 2 S 1/2 ω HF = 12.6 GHz 2 P 3/2 369.5 nm laser wavelength: 355 nm 33 THz 67 THz |↓〉 |↑〉 Advantages of 355 nm ● 3rd harmonic of YAG, so high power systems are readily available. ● High power allows very large detuning (33 THz) ● Spontaneous emission negligible ● AC Stark shiſts from 2 P 1/2 and 2 P 3/2 nearly cancel, making the differenal AC Stark shiſt extremely small. 171 Yb + energy level diagram Two Regimes: Weak Pulse Regime 1 ● Individual pulses have very little effect on the spin state ● Many pulses add to produce frequency comb ● Raman transions driven by teeth separated by hyperfine frequency ● Can perform tasks tradionally done by CW lasers, e.g. sideband cooling, Mølmer-Sørenson gate Strong Pulse Regime 2 ● Individual pulses have large effect on the spin state ● Raman transions driven directly by very small number of pulses. ● Allows complete single qubit control in tens of picoseconds. ● Will allow extremely fast moonal gates, which are faster than the trap period. Weak pulse regime: two pulse trains, one with shiſted comb teeth, drive Raman transions. Future Plans ● Counterpropagang pulses produce spin-dependent momentum kicks. ● Kicks are much faster than the trap period → pure vercal displacements in phase space. ● These kicks allow implementaon of a gate faster than the trap frequency. ● Gates work by rapidly enclosing an area in phase space in a spin-dependent way, then returning to the free-evoluon locaon in phase-space. Moon factors, leaving spin-dependent phase → phase gate. Fast gate scheme using spin- dependent kicks proposed in [3]. Fast gate proposed in [4]. x p inial posion final posion |1〉 path |0〉 path REFERENCES: [1] D. Hayes et al., “Entanglement of Atomic Qubits Using an Opcal Frequency Comb”, Phys. Rev. Le. 104, 140501 (2010) [2] W.C. Campbell et al., “Ultrafast Gates for Single Atomic Qubits”, Phys. Rev. Le. 105, 090502 (2010) [3] Garcia-Ripoll et al., “Speed Opmized Two-Qubit Gates with Laser Coherent Control Techniques for Ion Trap Quantum Compung”, Phys. Rev. Le. 91, 157901 (2003) [4] Duan, "Scaling Ion Trap Quantum Computaon through Fast Quantum Gates," Phys. Rev. Le. 93, 100502 (2004). 100 50 0 50 100 0.0 0.2 0.4 0.6 0.8 1.0 lin ⊥ lin Delay Scan Ramsey Zone Delay (ps) Transion Probability Ultrafast Single Qubit Control mode-locked 355 nm pulsed laser variable delay pulse picker BS vacuum chamber ion 0 200 400 600 800 1000 1200 0.0 0.2 0.4 0.6 0.8 1.0 Pulse Energy Transion Probability 100 50 0 50 100 0.0 0.2 0.4 0.6 0.8 1.0 σ+ / σ+ Delay Scan Ramsey Zone Delay (ps) Transion Probability This point corresponds to this Bloch sphere path |↓〉 |↑〉 0.015 0.010 0.005 0.000 0.005 0.010 0.015 0.0 0.2 0.4 0.6 0.8 1.0 Transion Probability Microwave Detuning (MHz) Microwave Ramsey Experiment Ramsey experiment demonstrang pure σ z rotaon. Blue: Two microwave π/2 pulses, free evoluon in between. Red: Two microwave π/2 pulses, with σ z rotaon pulses and free evoluon in between. 100 50 0 50 100 0.0 0.2 0.4 0.6 0.8 1.0 σ+ / σ- Delay Scan Ramsey Zone Delay (ps) Transion Probability ∼50 ps π-pulse This point is a pure σ z rotaon. Conclusions ● Pulsed lasers allow very fast, very clean qubit control. ● Complete arbitrary control of a trapped ion qubit in tens of picoseconds, with negligible AC Stark shiſt and spontaneous emission. ω HF ω HF . . . Single Pulse Qubit Rotaon 72% Spin flip vs. pulse energy for single 355 pulse. Limited by bandwidth -- Acts like Rabi flopping with a detuning. Strong pulse regime spectra for 1, 2, 5, and 20 pulses. ● Pulses are very short (1-10 ps) → large bandwidth (0.1-1 THz) → large frequency gaps are easily bridged. ● Extremely high power readily available → Efficient frequency doubling and tripling, large detunings OK → Reduced AC Stark shiſt, spontaneous emission. ● Fast pulses + high power → Low noise, high speed operaons. ● Allow implementaon of gates faster than trap frequency. ● No carrier - envelope phase stablizaon necessary Two Pulse Qubit Rotaon Variable Delay π 2 rotaon π 2 rotaon Pure σz Rotaon ● Pulse is split, with each half a π/2 pulse. ● Delay between pulses is controlled. ● Different polarizaons lead to different behavior in the overlap region. Green: Opcal inteference region (Theory) Black: Thermal average of green (Theory) 1 2 3 4 x p ● If counterpropagang pulses have lin ⊥ lin polarizaons, transions only occur by absorbing from one pulse and eming into the other. ● This gives the ion a momentum kick. ● In phase space, ion’s moonal state diffracts. ● Sequences of counter- propagang lin ⊥ lin pulse pairs can produce true spin dependent kick. 320 330 340 350 360 370 380 0.0010 0.0005 0.0000 0.0005 0.0010 Raman Laser Wavelength (nm) Differenal AC Stark Shiſt/Ω Raman 355 nm: < 4 x 10 -4 Moonal State Behavior ↑ ↓ ↑ ↓ ↑ ↓ ↑ x p J 1 (θ) J 0 (θ) J 1 (θ) J 2 (θ) J 3 (θ) J 2 (θ) J 3 (θ) free evoluon path