Cavity Quantum Electrodynamics for Superconducting Electrical Circuits

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Presentation transcript:

Cavity Quantum Electrodynamics for Superconducting Electrical Circuits Alexandre Blais, Ren-Shou Huang, Andreas Wallraff, S.M. Girvin and R.J. Schoelkopf PRA 69, 062320 (2004) Dima Panna Shlomi Bouscher

Outline Cavity Quantum Electrodynamics - review Circuit Implementation of CQED Superconducting 1D cavity Artificial Atom- Cooper Pair Box Charging Effect Cooper Pair Box Physics Combined System

Motivation Macroscopic analog of atomic physics experiments Strong light matter coupling on chip Spontaneous emission inhibition Quantum computing and control

Cavity Quantum Electrodynamics (CQED) |𝑒 |𝑔 |𝑒 |𝑔 |0,𝑒 |1,𝑔

Circuit Implementation of Cavity QED Superconducting “Mirror” Superconducting Cavity Artificial Atom - Cooper Pair Box Superconducting “Mirror” Silicon Substrate

Circuit Implementation of CQED Niobium Silicon Substrate C L

Cooper Pair Box as an Artificial Atom – Josephson Junction Superconducting condensate composed of Cooper-pairs Condensate is non-dissipative and has some defined global phase Josephson Junction – SIS junction – 2 weakly linked SC condensates S I Josephson Junction

Cooper Pair Box as an Artificial Atom – Josephson Junction Junction dynamics described through two key relations: The First Josephson Relation The Second Josephson Relation S I Josephson Junction Josephson Energy: Physical meaning: Kinetic energy of charge carriers Moving through the junction CJ EJ

Cooper Pair Box as an Artificial Atom – DC SQUID Fine tuning 𝐸 𝐽 through magnetic flux Φ (DC-SQUID): Superconducting Island Josephson Junctions Source Electrode DC SQUID

Island and Charging Effect - - Island

Island and Charging Effect -q1 q1 -q2 q2 Vg Island - Island SOURCE GATE C Cg Vg L C (4π*L) Ec T 10um 1.1fF 70ueV 0.84K (3He) 1um 0.11fF 0.7meV 8.4K (LHe) 0.1um 0.011fF 7meV 84K (LN2) 0.01um 1.1aF 70meV 840K (spa)

Charge quantization on the island

Island Insulation R Island C Affecting charge while keeping it localized – Conflicting demands Island SOURCE R C Aluminum native oxide 1.5nm L J Zeng et.al., Journal of Physics D: Applied Physics, Volume 48, Number 39

CJ EJ Cooper Pair Box Combine Josephson junction with island structure Superconductor CJ EJ ,CJ N=-4 N=-2 N=0 N=2 N=4

Charge Qubit EJ1 ,CJ1 Cg EJ2 ,CJ2 Classical Equation of Motion Classical Lagrangian EJ1 ,CJ1 EJ2 ,CJ2 I Cg Vg

Charge Qubit Express Hamiltonian in the N basis State with a certain charge N is a “plane wave” in phase representation Final Hamiltonian Charging Energy Josephson Energy

Charge Qubit 1 10 50 Joesphson Energy lifts degeneracy

Two level system Island EJ1 ,CJ1 Cg EJ2 ,CJ2 Cooper Pair box mapped to a pseudospin -1/2 particle description EJ1 ,CJ1 EJ2 ,CJ2 I Cg Vg

Combined System

Combined System

Conclusion and Remarks Conventional QED system mapped to macroscopic QED system 1D Cavity offers strong dipole interaction due to field confinement Overall structure (relatively) simple to fabricate and scale up (multiple cavities and qubits) Multiple qubits can be placed in same cavity and addressed via different modes

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