# Quantum phase transition and degeneracy of a circuit-QED vacuum

Abstract : We investigate theoretically the quantum vacuum properties of a transmission line resonator inductively coupled to a chain of $N$ superconducting qubits. We derive the quantum Hamiltonian for such circuit-QED system, showing that, due to the type and strength of the interaction, a quantum phase transition occurs in the limit of large $N$, with a twice degenerate quantum vacuum above a critical coupling. The phase diagram can be fully explored thanks to the controllable ultrastrong coupling of the qubits with the modes of the transmission line resonator. For finite values of $N$, an energy splitting occurs, which becomes exponentially small with increasing size and coupling.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-00418515
Contributor : Cristiano Ciuti <>
Submitted on : Wednesday, September 23, 2009 - 7:26:07 PM
Last modification on : Thursday, March 26, 2020 - 9:20:50 PM
Long-term archiving on: : Wednesday, September 22, 2010 - 1:30:25 PM

### Files

Josephson_vacuua_v35.pdf
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### Identifiers

• HAL Id : hal-00418515, version 2
• ARXIV : 0909.3505

### Citation

Pierre Nataf, Cristiano Ciuti. Quantum phase transition and degeneracy of a circuit-QED vacuum. 2009. ⟨hal-00418515v2⟩

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