Misc Notes

“Axialization”

Penning trap couping cyclotron to magnetron modes because magnetron mode heats and has negative energy technically. So they couple the magnetron phonons to cyclotron mode to get rid of it that way.

Berry Phase

Phase accumulated when driving a mode around a loop in phase space - like in an MS gate. Equal to ½ the solid angle enclosed by loop.

Radial Mode Avoided Crossing

Von Neumann-Wigner Theorem: you need two independent parameters to vary for crossing of modes. They will approach, hybridize, and then separate.

The Hessian is a Hermitian matrix. The off diagonal terms are the Coulomb interaction. When you diagonal the Hessian, the eigenvalues do not cross because of these off diagonal terms. This Coulomb interaction is what prevents the crossings. Gap is 2x the coupling matrix element

Polarization Gradient Cooling

Sisyphus Cooling

MS vs. CZ Gate

MS:

• Bichromatic field (2 tones, BSB, RSB)

• Tones create state dependent force on ions

• 01 and 10 move in opposite directions - they cancel out

• 11 and 00 both ions move in the same direction - they pick up a phase

• This is virtually excited, so if the loop in phase space closers there is no residual spin motion entanglement

• Insensitive to heat because it is virtual

CZ:

• RSB pi pule on ion 1

  • |1> (n=0) → |0> (n=1)

  • Not resonant with |0>

• BSB 2pi pulse on |1> (n=1) to another state (aux transition) on ion 2

  • picks up -1 phase if and only if both ions were in |1> state, off resonant otherwise

• Then RSB pi pulse on ion 1 again to return to starting state.

• Only works when at full ground state (n=0)

Dynamic Decoupling

• Spin echo in MS gate to cancel slow noise and dephasing on qubit frequencies

  • Magnetic field drift

  • Laser phase noise

  • AC stark shift

    • T2 Errors

• Split the gate and flip in between

  • Two pi/2 pulses wit pi pulse on both qubits in between.

  • Error gets flipped, refocused, and canceled

    • Hahn Echo

• Can also modulate MS pulse to do same thing without interruption

Raman Carrier Drive

• Drive Raman intensity at w drives motional mode

  • Can do a gate this way

  • Can use instead of EOM/AOM when bandwidth or phase noise of those electronics is bad

• Drive Raman intensity at 2w creates squeeze states - faster gates/enhanced sensing

AM Gates

• Modulate amplitude of raman or microwave pulse to calcel spectator modes close to resonance

• Also can be used for pulse shaping - avoids sharper pulse edges

PM Gate

• Used for Dynamic Decoupling

• Robust against drift / miscalibration / noise

• Easier than AM Gates

FM GAtes

• Modulate frequency of raman or microwave pulse to suppress spectator modes getting excited

• Noise that is accumulated reverses and cancels out as frequency modulates

Mode Frequency Limits

• Ion chain will start to buckle as (w_rad / w_ax) gets too low

• As w_ax gets too high - ions get too close together - can not individually address

• As radial frequency gets too high - mode crowding becomes too close - must increase axial frequency

• “General limit” is ~30 MHz radial frequency if you really want to push it - this is huge and near the limit