1. QI@IC_061 of 34 Atomic Ions in Penning Traps for Quantum Information Processing Danny Segal QOLS Group, Blackett Laboratory. Current group members: R. C. Thompson, R. Castrejon-Pita, H.Ohadi, D. Crick and D M Segal Recent group members: A. Abdulla, M. Vogel, D. Winters, K. Koo, E. Phillips, R.Hendricks, H. Powell, J.Sudbery, S. de Echaniz, T.Freegarde.

2. QI@IC_062 of 34 Outline of Talk Introduction – the Penning Trap RF traps and Ion trapping – tools of the trade Quantum Information Processing in the Penning trap? Laser cooling in the Penning Trap Axialisation Laser Cooling of Ca + in a Penning Trap Scalability of Penning Trap QIP Conclusions

3. QI@IC_063 of 34 The Penning ion trap Three electrodes - hyperboloids of revolution –Generate pure quadrupole potential DC potential applied between endcaps and ring –This traps ions in the axial direction, radial motion unstable Potential V z Axial potential Radial potential B Large B field applied along the axis provides radial confinement (ions forced into cyclotron loops) Can trap single ions, Mg +, Be + Laser cooling + fluorescence detection

4. QI@IC_064 of 34 Penning Trap, Typical Parameters Use B~1T and V  few volts Trap internal diameter is 10 mm We trap Ca + ions from a small atomic beam oven, ionisation by e-beam Oscillation frequencies typically a few hundred kHz 70mm http://wswww.physik.uni- mainz.de/werth/g_fak/g-faktor.html

5. QI@IC_065 of 34 Q: How do you know you have a single ion? A: Quantum Jumps Ion cycles between states 1 and 2 high fluorescence rate Occasionally ion makes ‘quantum jump’ into state 3 (metastable state). Fluorescence switches off. The absence of a large number of 1-2 photons accompanies the absorption of a single 1-3 photon. Use to detect weak (narrow) trans. - Clock Strong transition Weak transition |1> |2> |3> QUBIT QJ in Ca + - signature of a single ion in an RF trap

6. QI@IC_066 of 34 Laser Cooling Laser cooling - Doppler effect – tune laser to red of transition – atoms absorb most strongly when moving towards the laser Blue detuning – laser ‘heating’ Trapped ions – only one laser beam required, ion already trapped! Peculiarities - laser cooling in the Penning trap – ions move on radial potential hill – need to add energy to make ions move to the top of the hill! Radial potential

7. QI@IC_067 of 34 Motional States Typical motional frequency in miniature rf trap 1MHz Ion acts as a quantum harmonic oscillator –Motional energy = (n+1/2) ħ  –Using ħ  /2 ~ ħ  gives ~10 for typical case Fundamental cooling limit for a trapped particle – state with n = 0 i.e. motional ground state. Excitation/emission spectrum is a carrier with sidebands spaced at the motional frequency In Lamb-Dicke regime (ion confined to less than ) only a single sideband is present For 2 ions there are 2 modes with different frequencies! For 3 ions… Potential V z Freq.

8. QI@IC_068 of 34 Sideband Cooling Tune laser to red sideband Spontaneous emission preferentially to state with same n. Ion pumped into motional g.s. When g.s. reached, ion decouples from radiation Speed up process with extra laser S 1/2 D 5/2 n=0 n=3 P 3/2 Speed-up laser Freq.

9. QI@IC_069 of 34 Quantum Computing DiVincenzo requirements –A scalable physical system with well characterised qubits –Ability to initialise in a particular quantum state –Long decoherence time –Universal set of quantum gates (single qubit rotations and two-qubit gate) –A qubit specific measurement capability

10. QI@IC_0610 of 34 Trapped ions for Quantum Computing Most work to date has concentrated on laser cooled ions in linear rf traps: –Each ion can be one qubit –Can be prepared in a particular quantum state –Internal and motional states manipulated coherently with lasers – Decoherence rates low – Ions interact via their normal modes of motion – Strings of well isolated laser cooled ions can be prepared and addressed individually – So far, gates, teleportation, atom- photon entanglement, entanglement of 8 ions… – BUT! Further scalability of this direct approach doubtful Blatt group, Innsbruck

11. QI@IC_0611 of 34 Quantum Computing in the Penning Trap? Decoherence is critical. Limitations in RF traps: –Ambient magnetic field fluctuations –The presence of the strong RF field –The proximity of the trap electrodes (e.g. patch potentials). tight confinement, high secular frequency, fast gate speed  Small rf traps In the Penning trap the conditions may be better: –Stable Magnetic field, use superconducting magnet, excludes ambient fields –Field free transition frequencies→ long lived qubits –No RF field –Can make a tight trap with larger electrodes –Lack of rf-heating  possibility of a planar array of ions But laser cooling not as effective in Penning trap –As a result, individual ions not as well localised T.B.Mitchell et al., Physics of Plasmas 6, 1751 (1999)

12. QI@IC_0612 of 34 Axialisation Originally performed in mass spectrometry - damping via buffer gas collisions Buffer gas cooling: cyclotron motion is cooled strongly by collisions –But the magnetron orbit is increased by the collisions A weak radial rf quadrupole drive at  c can be applied with a segmented ring electrode –This couples magnetron and cyclotron motions together so that the cyclotron cooling dominates –Leads to longer storage times when buffer gas cooling is applied We decided to use this with laser cooling –We wanted to see if we could cool a cloud strongly to give tighter localisation and higher density in a Penning trap

13. QI@IC_0613 of 34 Simulation of Axialisation Effect of quadrupole drive without damping Effect of quadrupole drive with damping

14. QI@IC_0614 of 34 Axialisation before optimisation of beam position Here the top image is a cooled cloud before axialisation The bottom image is after axialisation but without moving the laser beam Subsequently the laser beam position is no longer critical

15. QI@IC_0615 of 34 Single Mg + ion image with axialisation –the region in which the ion moves is now at most a few tens of  m across –gives an upper temperature limit of order 10mK allowing for diffraction –much better than otherwise possible in the Penning trap H.F. Powell, D.M. Segal, R.C. Thompson, PRL 89 093003-1 (2002).

16. QI@IC_0616 of 34 Work with Ca + Mg + is good for preliminary studies, single laser required for laser cooling Ca + has more levels – metastable D 5/2 state to act as upper level of qubit transition Large Zeeman shifts complicate laser cooling 2  397nm lasers needed Many repumper frequencies needed All lasers are solid state (blue and infra-red diodes + Ti:sapphire for qubit transition) qubit

17. QI@IC_0617 of 34 Laser cooling of a multi-level ion in a Penning trap We have performed laser cooling in Penning trap of a heavy singly charged alkaline earth ion for the first time Temperature comparable with what we see in Mg + K.Koo, J. Sudbery, R.C. Thompson, D.M. Segal, PRA 69, 2004.

18. QI@IC_0618 of 34 Current Status of IC Experiment Have developed a ‘qubit’ laser with ~ 3kHz linewidth (H. Ohadi) Have applied axialisation to Ca + ions in the Penning trap Should allow us to work with single Ca + ions routinely… BUT Signal level per ion is lower in the Penning trap Possible causes –Trapped states –Trap impurities –Magnetic field instability Operate superconducting magnet trap with Ca + for future experiments Drive Rabi Oscillations, measure decoherence Ground state cooling Normal Axialised V trap =7.8V

19. QI@IC_0619 of 34 Scalability of Ion Trap QIP – shuttling in multiple traps For ions in a linear trap umber of modes = number of ions. For large number of ions sideband spectrum → spectrum of death Use multiple trap architecture Shuttle ions from trap to trap Perform gates in one location Recool ions using sympathetic cooling Going around corners is a key challenge!

20. QI@IC_0620 of 34 T - Junction trap – Monroe Group, Michigan http://tf.nist.gov/ion/workshop2006/monroe2.pdf

21. QI@IC_0621 of 34 Penning Trap QIP and scalability Employ axial chains of ions? –Radial confinement must be large and the axial confinement weak this calls for big B fields –5-10 ion crystals are feasible An axial stack of individual Penning traps would help, but scaling in 1-D is a limitation – ideally want 2D or 3D scaling Moving ions around corners in a Penning trap is complicated by the presence of the magnetic field. Employ 2-D crystals without shuttling? Employ arrays of traps connected in some other way?

22. QI@IC_0622 of 34 Scalability – Porras + Cirac They consider two-qubit ‘pushing gates’ between neighbouring ions Consider decoherence via anharmonic coupling to in-plane hot vibrational modes Show that high fidelities are possible Suggest it as a quantum simulator for interacting spin systems

23. QI@IC_0623 of 34 Scalability – interconnected traps Stahl et al Planar structure can make trap outside electrode structure (Stahl et al.) An array of such traps could be constructed and connections between traps made using superconducting wires Entanglement possible through energy exchange between remote ions.

24. QI@IC_0624 of 34 ‘Pad’ Trap Red electrodes – positive - act as ‘endcaps’ Blue electrodes – grounded – collectively act as ‘ring’ How good a trap is it? Why make it so complicated?

25. QI@IC_0625 of 34 Pad Trap - Axial and Radial Potentials

26. QI@IC_0626 of 34 Pad Traps Traps naturally scale into a 2-D trianglular array Ions can be loaded into traps or extracted through holes in ‘endcaps’ A stack of conventional Penning traps above one of these pad traps could act as the ‘entangling’ trap Shift ion array in radial plane

27. QI@IC_0627 of 34 Switch to alternative potentials for hopping A near linear potential results in ‘cycloid’ motion Time for cycloid loop is 1 cyclotron period ~ For B=10T, period = 260ns for Ca + Do ions remain ‘confined’ axially during hop? Assumes: 5mm between pad centres B=1T

28. QI@IC_0628 of 34 Axial potential along hop trajectory Ion accelerates and decelerates in potential along trajectory s Axial potential has minimum at z=0 all allong the trajectory

29. QI@IC_0629 of 34 Axial focusing of ions during hop Simulations for a range of initial conditions Ions start from centre of one trap with an initial velocity at angle ( ,  ) Axial potential ‘focuses’ ion to the centre of the second trap Top panel – 10meV Lower panel – 0.1meV

30. QI@IC_0630 of 34 Conclusions Single cold ions are routinely studied in conventional and linear radiofrequency traps, especially for studies in quantum information processing In the Penning trap the poor cooling of the magnetron motion was a limitation for work with cold ions Axialisation used with laser cooling seems to get over this problem –Colder and better localised ions –The Penning trap could become a serious candidate for QIP using this technique Scalability through multiple trap route or by using radial crystals