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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.

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Outline of Talk

Introduction – the Penning TrapRF traps and Ion trapping – tools of the tradeQuantum Information Processing in the Penning trap?Laser cooling in the Penning TrapAxialisationLaser Cooling of Ca+ in a Penning TrapScalability of Penning Trap QIPConclusions

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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

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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 2/)2/(2/

2/)2/(2/'

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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

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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

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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 ~ <n>ħ gives <n>~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.

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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

S1/2

D5/2

n=0n=3

P3/2

Speed-up laser Freq.

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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

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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

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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)

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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

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Simulation of Axialisation

Effect of quadrupole drive without damping

Effect of quadrupole drive with damping

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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

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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).

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Work with Ca+

• Mg+ is good for preliminary studies, single laser required for laser cooling

• Ca+ has more levels – metastable D5/2 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

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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.

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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

Vtrap=7.8V

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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!

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T - Junction trap – Monroe Group, Michigan

http://tf.nist.gov/ion/workshop2006/monroe2.pdf

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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?

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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

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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.

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‘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?

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Pad Trap - Axial and Radial Potentials

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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

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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

Padtrap.mpg

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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

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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

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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