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!

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