Ultrafast Control of Spin and Motion of Trapped Atomic QubitsJ. Mizrahi, W.C. Campbell, C. Senko, C. Monroe

University of Maryland Department of Physics and National Institute of Standards and TechnologyJoint QuantumInstitute

Using Pulsed Lasers

2P1/2

2S1/2 ωHF = 12.6 GHz

2P3/2

369.5 nm laserwavelength: 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 shifts from 2P1/2 and 2P3/2 nearly cancel, making the differential AC Stark shift extremely small.

171Yb+ energy level diagram

Two Regimes:Weak Pulse Regime1

Individual pulses have very little eect on the spin state Many pulses add to produce frequency comb Raman transitions driven by teeth separated by hyperfine frequency Can perform tasks traditionally done by CW lasers, e.g. sideband cooling, Mølmer-Sørenson gate

Strong Pulse Regime2

Individual pulses have large effect on the spin state Raman transitions driven directly by very small number of pulses. Allows complete single qubit control in tens of picoseconds. Will allow extremely fast motional gates, which are faster than the trap period.

Weak pulse regime: two pulse trains, one withshifted comb teeth, drive Raman transitions.

Future Plans Counterpropagating pulses produce spin-dependent momentum kicks. Kicks are much faster than the trap period → pure vertical displacements in phase space. These kicks allow implementation 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-evolution location in phase-space. Motion factors, leaving spin-dependent phase → phase gate.

Fast gate scheme using spin-dependent kicks proposed in [3]. Fast gate proposed in [4].

x

p

initialposition

finalposition

|1⟩ path

|0⟩ path

REFERENCES:[1] D. Hayes et al., “Entanglement of Atomic Qubits Using an Optical Frequency Comb”, Phys. Rev. Lett. 104, 140501 (2010)[2] W.C. Campbell et al., “Ultrafast Gates for Single Atomic Qubits”, Phys. Rev. Lett. 105, 090502 (2010)[3] Garcia-Ripoll et al., “Speed Optimized Two-Qubit Gates with Laser Coherent Control Techniques for Ion Trap Quantum Computing”, Phys. Rev. Lett. 91, 157901 (2003)[4] Duan, "Scaling Ion Trap Quantum Computation through Fast Quantum Gates," Phys. Rev. Lett. 93, 100502 (2004).

100 50 0 50 1000.0

0.2

0.4

0.6

0.8

1.0lin ⊥ lin Delay Scan

Ramsey Zone Delay (ps)

Tran

sition

Pro

babi

lity

Ultrafast Single Qubit Control

mode-locked355 nm pulsed laser

variabledelay

pulsepicker

BSvacuumchamber

ion

0 200 400 600 800 1000 12000.0

0.2

0.4

0.6

0.8

1.0

Pulse Energy

Tran

sition

Pro

babi

lity

100 50 0 50 1000.0

0.2

0.4

0.6

0.8

1.0σ+ / σ+ Delay Scan

Ramsey Zone Delay (ps)

Tran

sition

Pro

babi

lity

This point correspondsto this Bloch sphere path

|↓⟩

|↑⟩

0.015 0.010 0.005 0.000 0.005 0.010 0.0150.0

0.2

0.4

0.6

0.8

1.0

Tran

sition

Pro

babi

lity

Microwave Detuning (MHz)

Microwave Ramsey Experiment

Ramsey experiment demonstrating pure σz rotation.

Blue: Two microwave π/2 pulses, free evolution in between. Red: Two microwave π/2 pulses, with σz rotation pulses and free evolution in between.

100 50 0 50 1000.0

0.2

0.4

0.6

0.8

1.0

σ+ / σ- Delay Scan

Ramsey Zone Delay (ps)

Tran

sition

Pro

babi

lity

∼50 ps π-pulse

This point is a pureσz rotation.

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 shift and spontaneous emission.

ωHFωHF ...

Single Pulse Qubit Rotation

72%

Spin flip vs. pulse energy for single 355 pulse.Limited by bandwidth -- Acts like Rabi floppingwith 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 shift, spontaneous emission.

Fast pulses + high power → Low noise, high speed operations.

Allow implementation of gates faster than trap frequency.

No carrier - envelope phase stablization necessary

Two Pulse Qubit Rotation

Variable Delay

π2 rotation π

2 rotation

Pure σz Rotation Pulse is split, with each half a π/2 pulse. Delay between pulses is controlled. Different polarizations lead to different behavior in the overlap region.

Green: Optical inteference region (Theory) Black: Thermal average of green (Theory)

12

34

x

p

If counterpropagating pulses have lin ⊥ lin polarizations, transitions only occur by absorbing from one pulse and emitting into the other. This gives the ion a momentum kick. In phase space, ion’s motional state diffracts. Sequences of counter- propagating lin ⊥ lin pulse pairs can produce true spin dependent kick.

320 330 340 350 360 370 3800.0010

0.0005

0.0000

0.0005

0.0010

Raman Laser Wavelength (nm)

Diffe

renti

al A

C St

ark

Shift

/ΩRa

man

355 nm:< 4 x 10-4

Motional State Behavior

↑

↓

↑

↓

↑

↓

↑

x

p

J1(θ)J0(θ)J1(θ)J2(θ)J3(θ)

J2(θ)J3(θ)

free evolutionpath