towards microwave entanglement generation for quantum simulation and computing
DESCRIPTION
towards microwave entanglement generation for quantum simulation and computing. Seb Weidt. IQsim13, Brighton. IQT group, University of Sussex. Experimental setup. Linear Paul trap. Drive frequency: 2 π x 20 MHz Ion-electrode separation: 310 μ m MHz MHz. Experimental setup. - PowerPoint PPT PresentationTRANSCRIPT
TOWARDS MICROWAVE ENTANGLEMENT
GENERATION FOR QUANTUM SIMULATION
AND COMPUTING
Seb Weidt
IQT group, University of SussexIQsim13, Brighton
Linear Paul trap
Experimental setup
Drive frequency: 2π x 20 MHzIon-electrode separation: 310 μm MHz MHz
Cooling 171Yb+
Experimental setup
2P1/2
2S1/2
3D[3/2]1/2
2D3/2
F=0
F=1
F=1
F=0
F=1
F=0
F=2
F=1369nm
935nm
2 GHz
1 GHz
12.6 GHz
Cooling 171Yb+
Experimental setup
2P1/2
2S1/2
3D[3/2]1/2
2D3/2
F=0
F=1
F=1
F=0
F=1
F=0
F=2
F=1369nm
935nm
2 GHz
1 GHz
12.6 GHz
State preparation
Experimental setup
2P1/2
2S1/2
F=0
F=1
F=1
F=0
F=1
F=0
F=2
F=1369nm
2 GHz 935nm
2 GHz
1 GHz
Optical pumping to 2S1/2 F=0 in ~ 20 μs
3D[3/2]1/2
2D3/2
Coherent manipulation
Experimental setup
2P1/2
2S1/2
F=0
F=1
F=1
F=0
F=1
F=0
F=2
F=1
12.6 GHz
3D[3/2]1/2
2D3/2
State detection
Experimental setup
2P1/2
2S1/2
3D[3/2]1/2
2D3/2
F=0
F=1
F=1
F=0
F=1
F=0
F=2
F=1369nm
935nm
2 GHz
1 GHz
State detection
Experimental setup
2P1/2
2S1/2
3D[3/2]1/2
2D3/2
F=0
F=1
F=1
F=0
F=1
F=0
F=2
F=1369nm
935nm
2 GHz
1 GHz
State detection
Experimental setup
2P1/2
2S1/2
3D[3/2]1/2
2D3/2
F=0
F=1
F=1
F=0
F=1
F=0
F=2
F=1369nm
935nm
2 GHz
1 GHz
State detection
Experimental setup
Threshold technique
Detection fidelity ~ 0.93
Increase collection efficiency for improvement
Ground state
GHz
𝜔𝐵±=
𝜇𝐵
ℏ 𝐵
Typical applied B ~ 10 Gauss MHz
2S1/2
F=1, mF = -1
F=1, mF = 0
F=1, mF = +1
F=0, mF = 0
𝜔0
𝜔𝐵+¿ ¿
𝜔𝐵−
Experimental setup
Ground state
𝜔0
𝜔𝐵+¿ ¿
𝜔𝐵−
𝜔𝐵±=
𝜇𝐵
ℏ 𝐵
Experimental setup
2S1/2
GHz
Typical applied B ~ 10 Gauss MHz
Ground state
𝜔0
𝜔𝐵+¿ ¿
𝜔𝐵−
𝜔𝐵±=
𝜇𝐵
ℏ 𝐵
Experimental setup
2S1/2
GHz
Typical applied B ~ 10 Gauss MHz
Motional coupling with a magnetic field gradient Add a magnetic field gradient
Gives a state dependent forceEffective Lamb-Dicke parameter
= 20 T/m, /2π = 100 kHz ⇒ = 0.04
Requires the use of magnetic field sensitive states
F. Mintert and C. Wunderlich, Phys. Rev. Lett. 87, 257904 (2001)A. Kromova et al., Phys. Rev. Lett. 108, 220502
𝜂𝑒𝑓𝑓 =(1.19×106𝑚𝑠− 32𝑇 −1)𝜕𝑧 𝐵
𝑣𝑧
32
Experimental setup
𝜔0
𝜔𝐵+¿ ¿
𝜔𝐵−
Fluctuations in the magnetic field causes dephasing
Gives rise to short coherence times
Experimental setup
Fluctuations in the magnetic field causes dephasing
coherence time of ~ 500 μs
Rabi oscillations using magnetic field sensitive state
Experimental setup
Dressed-states
Microwave dressed-states
Two microwave dressing fields
Ω𝜇𝑤❑ +¿¿
Ω𝜇𝑤❑ −
When = = :
N. Timoney, I. Baumgart, M. Johanning, A. F. Varon, M. B. Plenio, A. Retzker, and C. Wunderlich, Nature 476, 185 (2011)
Three eigenstates:𝜔0
𝜔𝐵+¿ ¿
𝜔𝐵−
Dressed qubit
Microwave dressed-states
N. Timoney, I. Baumgart, M. Johanning, A. F. Varon, M. B. Plenio, A. Retzker, and C. Wunderlich, Nature 476, 185 (2011)
Three eigenstates:√2 Ω𝜇𝑤
❑
Dressed qubit
√2 Ω𝜇𝑤❑
Insensitive to magnetic field fluctuations apart from at the splitting frequency
Insensitive to microwave power fluctuations
Form a qubit using and
Microwave dressed-states
N. Timoney, I. Baumgart, M. Johanning, A. F. Varon, M. B. Plenio, A. Retzker, and C. Wunderlich, Nature 476, 185 (2011)
Preparation
Microwave dressed-states
Optical pumping to prepare
Prep
S. C. Webster, S. Weidt, K. Lake, J. J. McLoughlin and W. K. Hensinger, Phys. Rev. Lett. 111, 140501 (2013)
π to Preparation
Microwave dressed-states
Microwave π-pulse to
Prep
S. C. Webster, S. Weidt, K. Lake, J. J. McLoughlin and W. K. Hensinger, Phys. Rev. Lett. 111, 140501 (2013)
Preparation
Microwave dressed-states
Partial STIRAP - Bare states mapped to dressed-states
Ω𝜇𝑤❑ +¿¿
Ω𝜇𝑤❑ −
π to Prep STIRAP
Ω𝜇𝑤❑
𝑡 th
S. C. Webster, S. Weidt, K. Lake, J. J. McLoughlin and W. K. Hensinger, Phys. Rev. Lett. 111, 140501 (2013)
Preparation
Microwave dressed-states
Partial STIRAP - Bare states mapped to dressed-states
Ω𝜇𝑤❑ +¿¿
Ω𝜇𝑤❑ −
Ω𝜇𝑤❑
𝑡
π to Prep STIRAP
th
S. C. Webster, S. Weidt, K. Lake, J. J. McLoughlin and W. K. Hensinger, Phys. Rev. Lett. 111, 140501 (2013)
Preparation
Microwave dressed-states
Partial STIRAP - Bare states mapped to dressed-states
Ω𝜇𝑤❑ +¿¿
Ω𝜇𝑤❑ −
Ω𝜇𝑤❑
𝑡
π to Prep STIRAP
th
Peak 25 kHzPulse width 450 μsPulse separation
356 μs
during hold 16 kHzS. C. Webster, S. Weidt, K. Lake, J. J. McLoughlin and W. K. Hensinger, Phys. Rev. Lett. 111, 140501 (2013)
Detection
Microwave dressed-states
Partial STIRAP - Bare states mapped to dressed-states
Ω𝜇𝑤❑ +¿¿
Ω𝜇𝑤❑ −
π to Prep STIRAP
th
Ω𝜇𝑤❑
𝑡
S. C. Webster, S. Weidt, K. Lake, J. J. McLoughlin and W. K. Hensinger, Phys. Rev. Lett. 111, 140501 (2013)
Detection
Microwave dressed-states
Microwave π-pulse tofollowed by state detection
π to Prep STIRAP π to
S. C. Webster, S. Weidt, K. Lake, J. J. McLoughlin and W. K. Hensinger, Phys. Rev. Lett. 111, 140501 (2013)
Lifetime measurement
Microwave dressed-states
Lifetime of = 550 ms
Ω𝜇𝑤❑ +¿¿
Ω𝜇𝑤❑ −
Ω𝜇𝑤❑
𝑡 th
S. C. Webster, S. Weidt, K. Lake, J. J. McLoughlin and W. K. Hensinger, Phys. Rev. Lett. 111, 140501 (2013)
Qubit manipulation
Microwave dressed-states
𝜔0
𝜔𝐵+¿ ¿
𝜔𝐵−
One rf field coupling to will drive to as long as <<
Ω𝑟𝑓❑ Significant non-linear
Zeeman shift for small B-fields )
10 Gauss – 31 kHzΩ𝜇𝑤❑ +¿¿
Ω𝜇𝑤❑ −
Second order Zeeman shift
S. C. Webster, S. Weidt, K. Lake, J. J. McLoughlin and W. K. Hensinger, Phys. Rev. Lett. 111, 140501 (2013)
Rabi oscillations
Microwave dressed-states
S. C. Webster, S. Weidt, K. Lake, J. J. McLoughlin and W. K. Hensinger, Phys. Rev. Lett. 111, 140501 (2013)
1.4 kHzDressed coherence time 500 msBare coherence time 500 μs
Ramsey experiment
Microwave dressed-states
Arbitrary qubit rotations are possible
Detuned π/2 pulse
Freeprecession
Detuned π/2 pulse
S. C. Webster, S. Weidt, K. Lake, J. J. McLoughlin and W. K. Hensinger, Phys. Rev. Lett. 111, 140501 (2013)
Creating a magnetic field gradient
Microwave entanglement
6 mm
Four Samarium Cobalt permanent magnets
Microwave entanglement Individual addressing in frequency space
𝜔0
∆𝜔
∆𝜔
Magnetic field strength
2.03 MHzIon 1 Ion 2
Individual addressing in frequency space
Microwave entanglement
s 6 μm/2π 437 kHz
T/m0.004
∆𝜔
∆𝜔
2.03 MHzIon 1 Ion 2
Individual addressing in frequency space
Microwave entanglement
s 6 μm/2π 437 kHz
T/m0.004
∆𝜔
∆𝜔
2.03 MHzIon 1 Ion 2
Individual addressing in frequency space
Microwave entanglement
s 6 μm/2π 437 kHz
T/m0.004
∆𝜔
∆𝜔
Resolving motional sidebands
Microwave entanglement
(carrier) / (sideband) 50 kHz / 8 kHz/2π 168 kHz
24 T/m0.019
𝑣
Creation of Schrödinger cat state
Microwave entanglement
Re(α)
Im(α)
𝛼 (𝑡 )=𝜂𝑒𝑓𝑓 Ω𝜇𝜔
2𝛿(1−𝑒−𝑖 𝛿 𝑡 )
𝛿-
First demonstrated by Monroe et al. Science 272, 1131
𝑃 (0 )=12(1−𝑒− 12 |𝛼 ( 𝑡 )|
2
)
Apply Mølmer-Sørensen type spin operator
¿Coherent states will be displaced in phase space
¿
|− ⟩
K. Mølmer and A. Sørensen, Phys. Rev. Lett, 82:1835-1838, 1999
Driving detuned red and blue sideband
Creation of Schrödinger cat state
Microwave entanglement
t 120 μs41 kHz
/2π 267 kHz0.009
𝛿-
Creation of Schrödinger cat state
Microwave entanglement
Re(α)
Im(α)
No interference betweenwave packets
t 120 μs41 kHz
/2π 267 kHz0.009
Creation of Schrödinger cat state
Microwave entanglement
Interference betweenwave packets
t 120 μs41 kHz
/2π 267 kHz0.009
Im(α)
Re(α)
Creation of Schrödinger cat state
Microwave entanglement
Two-ion gate time ~ 15 ms
Coherence time ~ 500 μs
Combine magnetic field gradientwith dressed-state setup
t 120 μs41 kHz
/2π 267 kHz0.009
Dressed-state motional coupling
Microwave entanglement
𝜔0
𝜔𝐵+¿ ¿
𝜔𝐵−
Ω𝑟𝑓❑
Use rf field to drive motional sidebands in dressed-state qubit
Ω𝜇𝑤❑ +¿¿
Ω𝜇𝑤❑ −
Dressed-state motional coupling
Microwave entanglement
Ω𝑟𝑓❑
Ω𝜇𝑤❑ +¿¿
Ω𝜇𝑤❑ −
(carrier) / (sideband) 7 kHz / 1 kHz/2π 267 kHzGradient 24 T/m
0.009
|𝐷 ⟩ ❑→
|0 ′ ⟩
|𝑛⟩❑→
|𝑛+1
⟩
Microwave entanglement
Ω𝜇𝑤❑ +¿¿
Ω𝜇𝑤❑ −
Ω𝑟𝑓❑
Dressed-state motional coupling
(carrier) / (sideband) 7 kHz / 1 kHz/2π 267 kHzGradient 24 T/m
0.009
|𝐷 ⟩ ❑→
|0 ′ ⟩
|𝑛⟩❑→
|𝑛+1
⟩|𝑛
⟩❑→|𝑛−1
⟩
Microwave entanglement
Ω𝜇𝑤❑ +¿¿
Ω𝜇𝑤❑ −
Ω𝑟𝑓❑
Dressed-state motional coupling
(carrier) / (sideband) 7 kHz / 1 kHz/2π 267 kHzGradient 24 T/m
0.009
|𝐷 ⟩ ❑→
|0 ′ ⟩
|𝑛⟩❑→
|𝑛+1
⟩|𝑛
⟩❑→|𝑛−1
⟩
|𝑛 ⟩ ❑→|𝑛 ⟩
Microwave entanglement
Ω𝜇𝑤❑ +¿¿
Ω𝜇𝑤❑ −
Ω𝑟𝑓❑
Dressed-state motional coupling
(carrier) / (sideband) 7 kHz / 1 kHz/2π 267 kHzGradient 24 T/m
0.009
|𝐷 ⟩ ❑→
|0 ′ ⟩
|𝑛⟩❑→
|𝑛+1
⟩|𝑛
⟩❑→|𝑛−1
⟩
|𝑛 ⟩ ❑→|𝑛 ⟩
Microwave entanglement
Ω𝜇𝑤❑ +¿¿
Ω𝜇𝑤❑ −
Ω𝑟𝑓❑
Dressed-state motional coupling
(carrier) / (sideband) 7 kHz / 1 kHz/2π 267 kHzGradient 24 T/m
0.009
|𝐷 ⟩ ❑→
|0 ′ ⟩
|𝑛⟩❑→
|𝑛+1
⟩|𝑛
⟩❑→|𝑛−1
⟩
|𝑛 ⟩ ❑→|𝑛 ⟩
|𝑛⟩❑→
|𝑛−1
⟩
Microwave entanglement
Ω𝜇𝑤❑ +¿¿
Ω𝜇𝑤❑ −
Ω𝑟𝑓❑
Dressed-state motional coupling
(carrier) / (sideband) 7 kHz / 1 kHz/2π 267 kHzGradient 24 T/m
0.009
|𝐷 ⟩ ❑→
|0 ′ ⟩
|𝑛⟩❑→
|𝑛+1
⟩|𝑛
⟩❑→|𝑛−1
⟩
|𝑛 ⟩ ❑→|𝑛 ⟩
|𝑛⟩❑→
|𝑛−1
⟩|𝑛
⟩❑→|𝑛
+1
⟩
Microwave entanglement
Ω𝜇𝑤❑ +¿¿
Ω𝜇𝑤❑ −
Ω𝑟𝑓❑
Dressed-state motional coupling
(carrier) / (sideband) 7 kHz / 1 kHz/2π 267 kHzGradient 24 T/m
0.009
|𝐷 ⟩ ❑→
|0 ′ ⟩
|𝑛⟩❑→
|𝑛+1
⟩|𝑛
⟩❑→|𝑛−1
⟩
|𝑛 ⟩ ❑→|𝑛 ⟩
|𝑛⟩❑→
|𝑛−1
⟩|𝑛
⟩❑→|𝑛
+1
⟩
Microwave entanglement
Ω𝜇𝑤❑ +¿¿
Ω𝜇𝑤❑ −
Ω𝑟𝑓❑
Resilient to magnetic field fluctuationsBUT sensitive to magnetic field gradient
Dressed-state motional coupling|𝐷 ⟩ ❑
→|0 ′ ⟩
Arbitrary manipulation of magnetic field noise resilient dressed-state qubit
Creation of a strong magnetic field gradient Individual addressing and motional coupling using
bare states Creation of Schrödinger cat state Motional coupling using dressed-state qubit
Conclusion
The IQT GroupHead of Group:Dr. Winfried Hensinger
Postdocs:Dr. Simon WebsterDr. Gouri Giri
Research Assistants:Dr. Marcus HughesDr. James Siverns
PhD Students:Seb WeidtBjo LekitschKim LakeDarren De MotteJoe RandallEamon StandingDavid MurgiaTomas NavickasWe gratefully acknowledge funding from:
Ground state
𝜔0
𝜔𝐵+¿ ¿
𝜔𝐵−
Ω𝜇𝑤❑
Magnetic field insensitivequbit
Experimental setup
Rabi oscillations
Ω𝜇𝑤❑ =2𝜋×333 𝑘𝐻𝑧
Coherence time > 1s
Experimental setup
Creating a magnetic field gradient
Microwave entanglement
Four Samarium Cobalt permanent magnets
10 mm