Experimental Qubits: E2 transition Interaction Hamiltonian Electric - - PowerPoint PPT Presentation

INTERACTING IONS IN THE LAB

Experimental Qubits: E2 transition

|0> |1> S1/2 D5/2 Electric quadrupole Ba+, Ca+ Sr+, Yb+ need to keep phase φ stable,

• ptical radiation: ω ≈ 5 ×1014 Hz

Interaction Hamiltonian  HL = 1 2 ΩR σ +e iφ + σ −e −iφ

( )

Qubits: E2 transition

Example |0> |1> S1/2 D5/2 Ba+, Ca+ Sr+, Yb+ Δω ω ≈ 10−14 Ca+

729 nm

• Ch. Roos et al. PRL 83, 4713 (1999)

Electric quadrupole

Elementary quantum logic using E2 transition

Example

Schindler et al., NJP 15, 123012 (2013)

• K. Mølmer and A. Sørensen, PRL 82, 1835 (1999).

Factoring using Shor‘s Algorithm

• Th. Monz et al., Science 351, 1068 (2016)

|0> |1> Raman transition:

9Be+, 25Mg+, 43Ca+

87Sr+, 111Cd+, 137Ba+, 171Yb+

Qubits: Hyperfine or Zeeman transition

ΩR ∝ Ω1Ω2 Δ  k1 −  k2 ≠ 

Be+ |0> |1>

9Be+, 25Mg+, 43Ca+

87Sr+, 111Cd+, 137Ba+, 171Yb+

Qubits: Hyperfine or Zeeman transition

Example

• C. Monroe et al., PRL 75 (1995)

Qubits: Hyperfine or Zeeman transition

Example: High fidelity gates

J.P. Gaebler et al., PRL 117 (2016)

Be+ Doppler cooling, repumping, detection Gate: Raman transitions

Trapped Ion Quantum Computer

Example

• S. Debnath et al. Nature 536, 63 (2016).

Qubits: E2 transition

Example |0> |1> S1/2 D5/2 Ba+, Ca+ Sr+, Yb+ Electric quadrupole Precise coherent operations demand:

• high phase stability,
• high absolute stability of centre frequency
• high amplitude stability

(need good beam quality, pointing stability, diffraction)

|0> |1>

9Be+, 25Mg+, 43Ca+

87Sr+, 111Cd+, 137Ba+, 171Yb+

Qubits: Hyperfine or Zeeman transition

Example Precise coherent operations demand:

• high phase stability,
• high absolute stability of centre frequency
• high amplitude stability

(need good beam quality, pointing stability, diffraction)

• Avoid spontaneous scattering

Quantum Information with Trapped Ions

Slide prepared by Dave Wineland

Magnetic Gradient Induced Coupling

MAGIC: Spin-Motion Coupling despite η≈ 0

|0> |1>

PRL 87 (2001). In “Laser Physics at the Limit”, Springer, 2002. quant-ph/0111158.

• Adv. At. Mol. Opt. Phys. 49 (2003). quant-ph/0305129

z z

MAGIC: Spin-Motion Coupling despite η≈ 0

|0> |1> B

PRL 87 (2001). In “Laser Physics at the Limit”, Springer, 2002. quant-ph/0111158.

• Adv. At. Mol. Opt. Phys. 49 (2003). quant-ph/0305129

MAGIC: Spin-Motion Coupling despite η≈ 0

|0> |1> B

PRL 87 (2001). In “Laser Physics at the Limit”, Springer, 2002. quant-ph/0111158.

• Adv. At. Mol. Opt. Phys. 49 (2003). quant-ph/0305129

ηeff = dz / Δz

Coupling internal and motional states

Semi-classical illustration

z z0 p p

|0> |1>

Spin-dependent force (magnetic gradient)

⊗

p p

Coupling internal and motional states

Semi-classical illustration. QM calculation

k p0

|0> |1>

⊗

dz z0 zz p p

dz Equilibrium shifted by dz = − ∂zω mν 2 Spin-dependent force (magnetic gradient)

⊗

z z0 p p PRL 87 (2001). Adv. At. Mol. Opt.Phys. 49, 295 (2003).

Coupling internal and motional states

Semi-classical illustration. QM calculation

k p0

dz z0 zz p p

dz

|0> |1>

⊗

κ ≡ dz z0 = z0 ∂zω ν η ' ≡η − iκ Effective Lamb-Dicke parameter: where Equilibrium shifted by dz = − ∂zω mν 2 Spin-dependent force (magnetic gradient)

PRL 87 (2001). Adv. At. Mol. Opt. Phys. 49, 295 (2003).

HI ∝σ + exp i η 'a + η '* a+

( )

⎡ ⎣ ⎤ ⎦ + h.c.

⊗

z z0 p p

RF

Coupling and Addressing Trapped Ions

AOMs EOMs Pinholes Doublers Sum-Frequency

RF

Coupling and Addressing Trapped Ions

AOMs EOMs Pinholes Doublers Sum-Frequency

RF

Coupling and Addressing Trapped Ions

Trapped Ions for QIS

Coupling and Addressing Qubits using Fundamental problems Technical challenges

• Stability of frequency

✔

• Stability of phase

✔

• Stability of intensity

✔

• Ambient fields
• Shuttling

✔

• Spontaneous scattering

✔

• Addressing errors

✔

• Thermal excitation

✔ ? RF-waves

?