Entanglement and Quantum Correlations in Capacitively-coupled Junction Qubits

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Entanglement and Quantum Correlations in
Capacitively-coupled Junction Qubits
Roberto Ramos
Center for Superconductivity Research University
of Maryland
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
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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 (01gt 10gt)/?2

State of qubit 1 State of qubit 2
Correlations implied by entanglement
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Current-biased Josephson junction qubit
R. C. Ramos, et al., IEEE Trans. Appl.
Supercon. 11, 998 (2001)
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Microwave Spectroscopy of Inter-level Transitions
microwave 5.5GHz, T25mK
0gt?1gt
1gt?2gt
Response
Bias Current (?A)
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Coupling 2 Qubits ? Entanglement
I
I
1
2
C
C
C
c
J
J
Qubit 1 Qubit 2

• Fix-bias I2I
• Ramp I1 through I while shining microwaves
• If there is no coupling, then E(10gt) E(01gt)
  at I
• and their energies should cross.
• If coupled, E((01gt - 10gt)/?2) and E((01gt
  10gt)/?2)
• should have an avoided crossing.

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Details in U of Maryland Talks in Session H
Spectroscopy of capacitively-coupled junction
qubits Talk H19.001
Effect of current noise on resonant activation in
the Josephson junction qubit Talk H19.002
Quantum gates for capacitively-coupled Junction
qubits Talk H19.003
Evidence for macroscopic quantum entanglement in
capacitively-coupled junction qubits Talk
H19.013
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.
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?1 (01gt - 10gt)/?2
State of qubit 1 State of qubit 2
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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 ?
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Escape from Well depends on Direction ?
1. Ground State 00gt - the simplest case
(unentangled state)
Pe(?) escape probability
Potential Landscape
90
45
Pe
0
00gt
?
45
90
0
V (?o/2?) d?/dt
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2. First Excited State ( 01gt - 10gt)/?2
switching events in the two junctions will be
anti-correlated
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3. Second excited state ( 01gt 10gt)/?2
90
45
Pe
(10gt - 01gt)/?2
00gt
?2
0
(10gt 01gt)/?2
?1
?
45
90
0
But.what does it mean to have a Pe (?) ? What
does escape along any ? correspond to,
experimentally ?
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Escape velocity vR along R in the Josephson phase
plane --gt decompose into projected escape
velocities vR1 and vR2
D2
For ? 45 vR1 vR2, No Delay ?T between
D1, D2
?2
R
?R,2
?1
?
D1
For ? 0 or 90 no projection on other
axis --gt Long Delay ?T
?R,1
For intermediate angles, vR1 - vR2 leads to a
?T.
v?
voltage (?o/2?) v?
1
2
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Experimental Challenges in Correlations Experiment

• Delays are short.
• Pe(45) possibly small
• Heating occurs after D1 detects 1st Escape
• ? Results in Premature escape detected by
  D2.
• Experiment needs careful design!

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Conclusions and Future Work

• Analyzed effects of Macroscopic Quantum
  Entanglement
• in two coupled Josephson Phase Qubits
• Suggested experiments to observe effects of
  entanglement
• in this system
• Great potential to exploit this solid state
  system as a testbed
• for fundamental quantum mechanics