Date post: | 19-Dec-2015 |
Category: |
Documents |
View: | 220 times |
Download: | 1 times |
Entanglement and Quantum Correlations in Capacitively-coupled Junction Qubits
Andrew Berkley, Huizhong Xu, Fred W. Strauch, Phil Johnson, Mark Gubrud, Sudeep Dutta, Bill Parsons, Joe Foley, Mohamed Abutaleb, James Anderson,
Chris Lobb, Fred Wellstood and Alex Dragt
Roberto Ramos
Center for Superconductivity ResearchUniversity of Maryland
Can we measure entanglement and quantum correlations of states in solid-state multi-qubit systems ?
Entangled States cannot be expressed as a direct product.
Example: (|01> ± |10>)/2
State of qubit 1 State of qubit 2
Correlations: implied by entanglement
Current-biased Josephson junction qubit*
RI0C
Is V
# Events
Is HistogramI0
Iswitch
2/e
I
V
n=0n=1
Shape of histogram depends onquantum state of junction
U()
|0>|1>
|2>
Quantum Tunneling
Thermal excitation
a|0>+b|1>
* R. C. Ramos, et al., IEEE Trans. Appl. Supercon. 11, 998 (2001)
Bias Current (A)
Res
pons
e -1.0
0.0
1.0
2.0
3.0
4.0
13.10 13.12 13.14 13.16 13.18 13.20 13.22 13.24
microwave: 5.5GHz, T=25mK
|0>|1>
|1>|2>
Microwave Spectroscopy of Inter-level Transitions
MicrowaveRadiation
h12
|0>
|1>|2>
QuantumTunneling
Smaller ILarger I
Ramp I thru Io at very low temperatures
CJCJCc
I1 I2
1. Fix-bias I2=I*
2. Ramp I1 through I* while shining microwaves
3. If there is no coupling, then E(|10>) = E(|01>) at I*
and their energies should cross.
If coupled, E((|01> - |10>)/2) and E((|01> + |10>)/2)
should have an avoided crossing.
Qubit 1 Qubit 2
Coupling 2 Qubits Entanglement
5.35
5.45
5.55
5.65
5.75
13.135 13.145 13.155 13.165Current I1 (A)
En
erg
y L
ev
el S
pa
cin
g (
Gh
z)
I*
|01>
|10>
|01>
|10>
0 -> 1 (|01> - |10>)/2
Spectroscopy of capacitively-coupledjunction qubits*: Talk # H19.001
Quantum gates for capacitively-coupledJunction qubits: Talk # H19.003
Effect of current noise on resonant activationin the Josephson junction qubit: Talk #H19.002
Evidence for macroscopic quantum entanglementin capacitively-coupled junction qubits:
Talk # H19.013
Details in U of Maryland Talks in Session H
* P. R. Johnson, et al. Rapid Communications, Phys Rev B 67, 020509(R) (2003);
R. C. Ramos, et. al. To appear in the June 2003 Issue of IEEE Trans on Appl Supercond.
If we see entanglement between states of coupled qubits separated by a distance of around 0.5 mm
This implies quantum correlations between measurements separated by macroscopic distances.
1 = (|01> - |10>)/2
State of qubit 1 State of qubit 2
These are entangled quantum states
• Einstein-Podolsky-Rosen (EPR) pairs
• Should exhibit correlations in their quantum
states that defy conventional notions of
locality
• A quantum mechanics effect !Einstein: “spooky action at a distance” !
Question: How to see quantum correlations in coupled Josephson phase qubits ?
2
1
High
Low
Escape from Well depends on Direction
Potential Landscape
Pe
|00>
45° 90°0°
90° 45°
0°
1. Ground State |00> - the simplest case (unentangled state)
V = (o/2) d/dt
Pe() = escape probability
switching events in the two junctions will be anti-correlated
High
Low
Pe
|00>
45° 90°0°
(|10> - |01>)/2
junction 2 likely to tunnel, but not 1
junction 1 likely to tunnel, but not 2
2 1
0°
90° 45°
2. First Excited State ( |01> - |10>)/2
High
Low
2
1
0°
90° 45°Pe
|00>
45° 90°0°
(|10> - |01>)/2
(|10> + |01>)/2
3. Second excited state: ( |01> + |10>)/2
But….what does it mean to have a Pe () ?
What does escape along any correspond to, experimentally ?
Escape velocity vR along R in the Josephson phase plane
--> decompose into projected escape velocities vR1 and vR2
2R,2
R
R,1
D1
D2
1
For intermediate angles, |vR1 - vR2 | leads to a T.
For = 45°: vR1 = vR2, No Delay T between D1, D2
For = 0° or 90°: no projection on other axis --> Long Delay T
v
t
Tvoltage = (o/2) v1
2
θ
Experimental Challenges in Correlations Experiment
1. Delays are short.
2. Pe(45°) possibly small
3. Heating occurs after D1 detects 1st Escape Results in Premature escape detected by D2.
Experiment needs careful design!