1. 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 Research University of Maryland

2. 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

3. Current-biased Josephson junction qubit* R I0I0 C IsIs V # Events IsIs Histogram I0I0 I switch 2  /e I V n=0 n=1 Shape of histogram depends on quantum 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)

4. Bias Current (  A) Response microwave: 5.5GHz, T=25mK |0>  |1> |1>  |2> Microwave Spectroscopy of Inter-level Transitions Microwave Radiation h  12 |0> |1> |2> Quantum Tunneling Smaller I Larger I Ramp I thru I o at very low temperatures

5. C J C J C c I 1 I 2 1.Fix-bias I 2 =I* 2.Ramp I 1 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 1Qubit 2 Coupling 2 Qubits  Entanglement

6. Spectroscopy of capacitively-coupled junction qubits*: Talk # H19.001 Quantum gates for capacitively-coupled Junction qubits: Talk # H19.003 Effect of current noise on resonant activation in the Josephson junction qubit: Talk #H19.002 Evidence for macroscopic quantum entanglement in 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.

7. 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

8. 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 ?

9. 22 11 High Low Escape from Well depends on Direction  Potential Landscape PePe  |00> 45°90°0°0° 45° 0°0° 1. Ground State |00> - the simplest case (unentangled state) V = (  o/2  ) d  /dt P e (  ) = escape probability

10. switching events in the two junctions will be anti-correlated High Low PePe  |00> 45°90°0°0° (|10> - |01>)/  2 junction 2 likely to tunnel, but not 1 junction 1 likely to tunnel, but not 2 22 11 0°0° 90°45° 2. First Excited State ( |01> - |10>)/  2

11. HighLow 22 11 0°0° 90°45° PePe  |00> 45°90°0°0° (|10> - |01>)/  2 (|10> + |01>)/  2 3. Second excited state: ( |01> + |10>)/  2 But….what does it mean to have a P e (  ) ? What does escape along any  correspond to, experimentally ?

12. Escape velocity v R along R in the Josephson phase plane --> decompose into projected escape velocities v R1 and v R2 22  R,2 R  R,1 D1 D2 11 For intermediate angles, |v R1 - v R2 | leads to a  T. For  = 45°: v R1 = v R2, No Delay  T between D1, D2 For  = 0° or 90°: no projection on other axis --> Long Delay  T vv t TT voltage = (  o/2  ) v  1 2 θ

13. Experimental Challenges in Correlations Experiment 1.Delays are short. 2.P e (45°) possibly small 3.Heating occurs after D1 detects 1st Escape  Results in Premature escape detected by D2. Experiment needs careful design!

14. 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