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x y z I 1 I 2 I 3 B 1 B 3 B 2 a) ion Microwave currents in trap electrodes rf input dc input µw input 2x µw inputs 2x dc inputs rf choke rf capacitor UHV feedthrough SMA cables ę µw ę toroidal transformer C J Ballance D T C Allcock N M Linke T P Harty L Guidoni H A Janacek D P L Aude Craik D N Stacey A M Steane D M Lucas Quantum logic operations in 40 Ca + and 43 Ca + trapped-ion qubits Ion Trap Quantum Computing Group Department of Physics - University of Oxford www.physics.ox.ac.uk/users/iontrap/ Department of Physics, Clarendon Laboratory, Parks Road, Oxford, OX1 3PU, United Kingdom [email protected] 43 Ca + Field-Insensitive Qubit 50 Ǎ ΏȦŚ open end of resonator dc electrodes rf electrodes ground plane centre microwave electrode ΏȦŘ 2 mm to SMA connectors x y z 2.5 3 3.5 4 0 0.2 0.4 0.6 0.8 1 Fraction of power coupled into trap Frequency (GHz) 2.5 3 3.5 4 0 0.2 0.4 0.6 0.8 1 Frequency (GHz) Port 1 Port 3 Port 2 Towards Microwave-driven Entanglement Network analyser data shows that >75% of input microwave power is coupled into the trap. Trap Testing Trap Design Proposed (2008) and demonstrated (Nature 476 155, 2011) by Ospelkaus and coworkers at NIST. 393nm + D śȦŘ Shelf D řȦŘ S ŗȦŘ ƽƸŚ M=+5 řȦŘ ƽƸŚ M=+5 ŞśŚ 89.9% 850nm 850nm + -400 -300 -200 -100 0 100 200 300 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 866 detuning (MHz) P 1/2 population Experiment Theory Doppler Cooling at 146G Readout - S 1/2 -P 1/2 -D 3/2 system has 64 states and no closed transitions. - Optical Bloch equations used to simulate the system. - Straightforward cooling solution found: - Polarizations chosen so only a few states populated - Needs only one sideband on cooling laser (from EOM) - Single frequency 866nm repumping laser - P 1/2 level population of up to ~0.15 simulated and achieved (50000 s -1 fluorescence) - Intermediate-field clock qubits preferable to zero-field clock qubit as Zeeman shift lifts state degeneracies. - Until now intermediate-field clock states only demonstrated in 9 Be + and 25 Mg + (NIST). - 43 Ca + has the following advantages: - No UV lasers which can charge up the trap - Laser diodes available at all required wavelengths - D-states for electron shelving (high readout fidelity) - However there is no closed cooling transition (see below) Measured ‘clock’ and ‘stretch’ qubit frequencies using a single 43 Ca + ion at 146G. Comparison of experiment and theory for a frequency scan of the 866nm repumping laser. M=0 M=+4 M=+3 M=0 ‘Stretch’ qubit ‘Clock’ qubit ~50MHz S ŗȦŘ Ground Level 3.200 GHz The ion is initialised in F=4,M=+4 by several cycles of optical pumping and microwave ‘reclaiming’ pulses, giving good state preparation with impure optical polarisation. 3 microwave pulses (green) are then used to prepare the ‘clock’ qubit (red) í í í í í 0 0.5 1 1.5 2 í 0 2 4 6 8 43 Ca + Clock qubit transition (M=0 to M=+1) % í * Ȟ clock í +] N+] í í í í í 0 0.5 1 1.5 2 í í í 0 2 4 6 43 Ca + Stretch qubit transition (M=+4 to M=+3) % í * Ȟ stretch í +] 0+] 1.208 kHz/G 2 í 0+]* Advantages: - Microwave electronics more mature and scalable technology than lasers - No photon scattering as in laser-driven Raman gates - No requirement for sub-Doppler cooling Disadvantages: - Microwave field not as well localised as laser field (crosstalk) - Careful nulling of microwave field at ion required to suppress AC Zeeman shifts - Fast gates (~10µs) will require small traps and high microwave current densities Optimisation of the trap microwave design was carried out using HFSS, finite element microwave simulation software. Figures (above and right) show simulations of current density in the trap. DC Control RF + MW +DC MW + DC Ground I 1 I 2 I 3 Trap is gold on sapphire for good thermal conductivity. The trap region is in the centre of a half-wave microwave resonator to increase currents. Quarter-wave coupling sections provide a good 50 impedance match. Simulations show that combining the microwave and rf electrodes (above) gives higher microwave gradients than alternative layouts for a given current. Diplexer (above) is used to combine microwaves, rf voltages and dc offsets. The toroidal transformer steps-up the trap rf supply. Measured microwave B-field around ion Mixed Species Experiment Cooling Results Raman Laser System The Ion Trap - Doppler cooling to ‹n› < 6 - Pulsed sideband cooling of crystal’s two axial modes to ‹n› < 0.1 - Heating rate ~5 quanta / s at f z = 2 MHz - Mixed crystal sympathetic Doppler cooling Goals - Two ion entanglement using a geometric phase gate - High-fidelity laser gates - Classical ‘AND’ gate by controlled relaxation (useful for practical error correction schemes) 0 2 4 6 8 10 12 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Raman pulse time / µs Shelved population Carrier flops, 1ı error bars Curve fit: ‹n›= 5.79 ± 0.5 Doppler limit: ‹n›= 4.8 Carrier Rabi flops. f z = 2 MHz. 30 mm - Qubit stored in ground state manifold (T 2 very large) - Only one set of lasers needed as isotope shifts can be spanned with EOMs - RF ( 40 Ca + ) and microwaves ( 43 Ca + ) used for single-qubit rotations - Raman lasers used for spin-motion coupling and single- qubit rotations - Isotope shift of ~ 1 GHz allows individual addressing of the different isotopes and sympathetic cooling - Simultaneous readout of both isotopes implemented - Pair of injection-locked frequency-doubled amplified diode lasers gives up to 40 mW at 397 nm in each Raman beam at the ions - Photon scattering error for single qubit rotation predicted to be < 10 -4 DW ȍ Rabi ʌ N+] - System can be switched between addressing 40 Ca + and 43 Ca + in 100ms by switching injection path - Beat-note between Raman beams at ions sub-Hertz width 4S 1/2 3D 5/2 3 9 3 n m 3 9 7 n m 85 4nm 8 6 6 n m 850nm F=4 F=3 3D 3/2 4P 3/2 4P 1/2 M J =-1/2 M J =+1/2 3226 MHz 2.8 MHz / G 40 Ca + 43 Ca + Gate driven by oscillating microwave, rather than optical, field gradient. Ion is trapped in the near-field <100µm from a microwave conductor to obtain high enough gradients. Field independent point. - we find agreement between simulated and measured gradients at the 5% level (see measured field on the left) - Sidebands observed - Heating rate is amongst best measured in a room temperature trap (red dot) 1 mm 0 5 10 15 20 0 0.2 0.4 0.6 0.8 1 Ramsey delay (s) Fringe contrast Coherence time: T 2 = 48 ±10 s Shelving scheme simulated to give ~99.98% shelving fidelity without the need for a laser to address the quadrupole transition (S 1/2 - D 5/2 ); preliminary experimental data: combined state-preparation and readout fidelity of ~99.94% is achieved - Macroscopic linear Paul trap (RF applied to ‘blades’ (blue) for radial confinement, DC applied to ‘end-caps’ (red) for axial confinement) - ‘Innsbruck style’ stainless steel ‘blade’ type - Ion-electrode distance 0.5 mm - Typical trap parameters: Trap RF drive: 30 MHz Axial secular frequency: 2 MHz Radial secular frequency: 4 MHz Details State preparation -0.6 -0.4 -0.2 0 0.2 0.4 0.6 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 x (μm) z (μm) S 2 S 2 t Ramsey dB x /dz = 0.30T/m; dB z /dx =0.29T/m
Transcript of =9%'69>!&-?2(!-@)5%62-'
xy
z
I1 I2 I3
B1
B3
B2
a)
ion
Microwave currents in trap electrodes
rf input
dc input
µw input
2x µw inputs 2x dc inputs
rf choke
rf capacitor
UHV
feedthrough
SMA cables
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µw
����
toroidal
transformer
C J Ballance D T C Allcock N M Linke T P Harty L Guidoni H A Janacek D P L Aude Craik D N Stacey A M Steane D M Lucas
Quantum logic operations in 40Ca+ and 43Ca+ trapped-ion qubits Ion Trap Quantum Computing Group
Department of Physics - University of Oxford
www.physics.ox.ac.uk/users/iontrap/ Department of Physics, Clarendon Laboratory, Parks Road, Oxford, OX1 3PU, United Kingdom [email protected]
43Ca+ Field-Insensitive Qubit
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ΏȦŚȱ��������ȱ�������
open end of resonator
dc electrodes rf electrodes
ground planecentre microwave electrode
ΏȦŘȱ���������
2 mm
to SMA
connectors
xy
z
2.5 3 3.5 40
0.2
0.4
0.6
0.8
1
Frac
tion
ofpo
wer
coup
led
into
trap
Frequency (GHz)2.5 3 3.5 40
0.2
0.4
0.6
0.8
1
Frequency (GHz)
Port 1Port 3
Port 2
Towards Microwave-driven EntanglementNetwork analyser data shows that >75%of input microwave power is coupled intothe trap.
Trap Testing
Trap Design
Proposed (2008) and demonstrated (Nature 476 155, 2011) by Ospelkaus and coworkers at NIST.
393nm+
DśȦŘ Shelf
DřȦŘ
SŗȦŘ
�ƽƸŚ
M=
+5
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M=
+5
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850nm
850nm+
-400 -300 -200 -100 0 100 200 3000.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
866 detuning (MHz)
P 1/2 p
opul
atio
n
ExperimentTheory
Doppler Cooling at 146G
Readout
- S1/2-P1/2-D3/2 system has 64 states and no closed transitions.- Optical Bloch equations used to simulate the system.- Straightforward cooling solution found: - Polarizations chosen so only a few states populated - Needs only one sideband on cooling laser (from EOM) - Single frequency 866nm repumping laser - P1/2 level population of up to ~0.15 simulated and achieved (50000 s-1 fluorescence)
- Intermediate-field clock qubits preferable to zero-field clock qubit as Zeeman shift lifts state degeneracies.- Until now intermediate-field clock states only demonstrated in 9Be+ and 25Mg+ (NIST).- 43Ca+ has the following advantages: - No UV lasers which can charge up the trap - Laser diodes available at all required wavelengths - D-states for electron shelving (high readout fidelity)- However there is no closed cooling transition (see below)
Measured ‘clock’ and ‘stretch’ qubit frequencies using a single 43Ca+ ion at 146G.
Comparison of experiment and theory for a frequency scan of the 866nm repumping laser.
M=0
M=+4
M=+3
M=0
‘Stretch’ qubit
‘Clock’qubit
~50MHz
SŗȦŘGroundLevel
3.20
0 GH
zThe ion is initialised in F=4,M=+4 by several cycles of optical pumping and microwave ‘reclaiming’ pulses, giving good state preparation with impure optical polarisation. 3 microwave pulses (green) are then used to prepare the ‘clock’ qubit (red)
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2
4
6
8
43Ca+ Clock qubit transition (M=0 to M=+1)
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Advantages: - Microwave electronics more mature and scalable technology than lasers - No photon scattering as in laser-driven Raman gates - No requirement for sub-Doppler cooling
Disadvantages: - Microwave field not as well localised as laser field (crosstalk) - Careful nulling of microwave field at ion required to suppress AC Zeeman shifts - Fast gates (~10µs) will require small traps and high microwave current densities
Optimisation of the trapmicrowave design wascarried out using HFSS,finite element microwavesimulation software. Figures (above and right) show simulations of current density in the trap.
DC ControlRF + MW +DCMW + DCGround
I1I2I3
Trap is gold on sapphire for good thermal conductivity.
The trap region is in the centre of a half-wave microwave resonator to increase currents. Quarter-wave coupling sections provide a good 50� impedance match.
Simulations show that combining the microwave and rf electrodes (above) gives higher microwave gradients than alternative layouts for a given current.
Diplexer (above) is used to combine microwaves, rf voltages and dc offsets. The toroidal transformer steps-up the trap rf supply.
Measured microwave B-field around ion
Mixed Species Experiment
Cooling Results
Raman Laser System
The Ion Trap
- Doppler cooling to ‹n› < 6- Pulsed sideband cooling of crystal’s two axial modes to ‹n› < 0.1- Heating rate ~5 quanta / s at fz = 2 MHz- Mixed crystal sympathetic Doppler cooling
Goals
- Two ion entanglement using a geometric phase gate- High-fidelity laser gates- Classical ‘AND’ gate by controlled relaxation (useful for practical error correction schemes)
0 2 4 6 8 10 120
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Raman pulse time / µs
Shel
ved
popu
latio
n
Carrier flops, 1ı error barsCurve fit: ‹n›= 5.79 ± 0.5Doppler limit: ‹n›= 4.8
Carrier Rabi flops. fz = 2 MHz.
30 mm
- Qubit stored in ground state manifold (T2 very large)- Only one set of lasers needed as isotope shifts can be spanned with EOMs- RF (40Ca+) and microwaves (43Ca+) used for single-qubit rotations- Raman lasers used for spin-motion coupling and single-qubit rotations- Isotope shift of ~ 1 GHz allows individual addressing of the different isotopes and sympathetic cooling- Simultaneous readout of both isotopes implemented
- Pair of injection-locked frequency-doubled amplified diode lasers gives up to 40 mW at 397 nm in each Raman beam at the ions - Photon scattering error for single qubit rotation predicted to be < 10-4�DW�ȍRabi� ��ʌ�����N+] - System can be switched between addressing 40Ca+ and 43Ca+ in 100ms by switching injection path- Beat-note between Raman beams at ions sub-Hertz width
4S1/2
3D5/2
393n
m
397n
m
854n
m
866n
m850n
m
F=4
F=3
3D3/2
4P3/2
4P1/2
M J=-1/2
M J=+1/2
3226 MHz
2.8
MH
z / G
40Ca+43Ca+
Gate driven by oscillating microwave, rather than optical, field gradient. Ion is trapped in the near-field <100µm from a microwave conductor to obtain high enough gradients.
Field independent point.
- we find agreement between simulated and measured gradients at the 5% level (see measured field on the left)
- Sidebands observed
- Heating rate is amongst best measured in a room temperature trap (red dot)
1 mm
0 5 10 15 200
0.2
0.4
0.6
0.8
1
Ramsey delay (s)
Frin
ge c
ontra
st
Coherence time: T2 = 48 ±10 s
Shelving scheme simulated to give ~99.98% shelving fidelity without the need for a laser to address the quadrupole transition (S1/2 - D5/2);
preliminary experimental data: combined state-preparation and readout fidelity of ~99.94% is achieved
- Macroscopic linear Paul trap (RF applied to ‘blades’ (blue) for radial confinement, DC applied to ‘end-caps’ (red) for axial confinement)- ‘Innsbruck style’ stainless steel ‘blade’ type- Ion-electrode distance 0.5 mm- Typical trap parameters: Trap RF drive: 30 MHz Axial secular frequency: 2 MHz Radial secular frequency: 4 MHz
Details
State preparation
-0.6 -0.4 -0.2 0 0.2 0.4 0.6-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
x (μm)
z (μ
m)
S2
S2
� �tRamsey
dBx/dz = 0.30T/m; dBz/dx =0.29T/m
