Quantum Simulations with Trapped Atomic Ions Yb crystal

Quantum Simulations with Trapped Atomic Ions Yb+ crystal ~5 mm

3 -layer geometry: • single rf electrode • scalable to larger structures, natural for junctions dc dc rf rf dc dc

171 Yb+ 2 S 1/2 | = |1, 0 | = |0, 0 hyperfine spin w. HF/2 p = 12 642 812 118 + 311 B 2 Hz (600 Hz/G @ 1 G)

171 Yb+ spin detection g/2 p = 20 MHz 2 P 2. 1 GHz 1/2 | z 0 369 nm 2 S Probability 1 0 5 10 15 20 # photons collected in 800 ms | | w. HF/2 p = 12 642 812 118 + 311 B 2 Hz (600 Hz/G @ 1 G) 25

171 Yb+ spin detection g/2 p = 20 MHz 2 P 2. 1 GHz 1/2 >99% detection efficiency | z 0 369 nm 2 S Probability 1 0 5 | z 10 15 20 # photons collected in 500 ms | | w. HF/2 p = 12 642 812 118 + 311 B 2 Hz (600 Hz/G @ 1 G) 25

171 Yb+ 2 P 2 P spin manipulation g/2 p = 20 MHz 3/2 D = 33 THz 1/2 355 nm (10 psec @ 100 MHz) 2 S 1/2 | | w. HF/2 p = 12 642 812 118 + 311 B 2 Hz (600 Hz/G @ 1 G)

National Ignition Facility: 351 nm (Livermore National Laboratory) Pavg ~ 5 W at 355 nm 10 psec pulses, 120 MHz rep rate 1 P(↑|↓) 0 picosecond spin control 0 10 20 pulse energy (n. J) 30 See talk by Jonathan Mizrahi (Sunday) J. Mizrahi, et al. , Ar. Xiv 1307. 0557 (2013)

Trapped Ion Quantum Computer (Cirac-Zoller) Internal states of these ions entangled Cirac and Zoller, Phys. Rev. Lett. 74, 4091 (1995) CM, et al. , Phys. Rev. Lett. 74, 4714 (1995) Q. Turchette, et al. , Phys. Rev. Lett. 81, 3631 (1998) F. Schmidt-Kaler, et al. , Nature 422, 408 (2003)

Cirac-Zoller: number states of the QHO • extreme cooling: requires a pure motional state • not scalable: mode density problem Better: “spin-dependent displacements” • only requires cooling to the Lamb-Dicke limit • “virtual” coupling to phonons Possible Mølmer & Sørensen (1999) Solano, de Matos Filho, Zagury (1999) Milburn, Schneider, James (2000)

global spin-dependent force F = F 0|↑ ↑| - F 0|↓ ↓|

spin-dependent force (171 Yb+) B(x) 1, -1 2 P 1, 1 1, 0 Magnetic field gradient 0, 0 1/2 1, -1 2 S 1, 1 1, 0 | 1/2 | 0, 0

spin-dependent force (171 Yb+) s+ 1, -1 2 P 1/2 1, 0 1, 1 0, 0 D Position-dependent AC Stark shift 369 nm g 1, -1 2 S 1, 1 1, 0 | 1/2 | 0, 0 s+

spin-dependent force (171 Yb+) 1, -1 2 P 1/2 1, 0 1, 1 0, 0 D 369 nm Red+blue sideband applied simultaneously g g | 1, 0 g 1, 1 1, -1 2 S 1/2 | 0, 0 Lamb-Dicke parameter

global spin-dependent oscillating force Lamb-Dicke approximation: simultaneous sidebands normal mode decomposition † normal mode transformation matrix: ion i, mode k

Aside: transverse Modes of an atom chain transverse modes. . . frequency axial modes transverse modes. . . frequency S. -L. Zhu et al. , Phys. Rev. Lett. 97, 050505 (2006) A. Serafini et al. , New J. Phys. 11, 023007 (2009) . . .

Raman spectrum of N=9 ions fluorescence ~ N( ) (Dk nominally along x) transverse y axial z Zig. Zag COM transverse x Zig. Zag 0 1 2 3 Raman beatnote (MHz) COM 4 5

global spin-dependent oscillating force carrier Raman beatnotes: w. HF ± m lower sidebands w. HF -m † upper sidebands frequency w. HF+m

† evolution operator † s n no o h p interaction between qubits (entangling gates etc. . )

How to avoid phonon creation? (1) Pick detuning m and time t wisely “FAST MOLMER” for all modes k e. g. : m near single mode k only → (m-wk)t = 2 p m m=1, 2, … S. -L. Zhu, et al. , Europhys Lett. 73 (4), 485 (2006).

“FAST MOLMER” p Rabi frequency x Beatnote frequency

How to avoid phonon creation? (1) Pick detuning m and time t wisely “FAST MOLMER” for all modes k e. g. : m near single mode k only → (m-wk)t = 2 p m m=1, 2, … S. -L. Zhu, et al. , Europhys Lett. 73 (4), 485 (2006). (2) “Adiabatically eliminate” phonons: |m - wk| >> h. W 0 “SLOW MOLMER”

“SLOW MOLMER” p Rabi frequency x Beatnote frequency

How to avoid phonon creation? (2) “Adiabatically eliminate” phonons: |m - wk| >> h. W 0 “SLOW MOLMER”