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arXiv:quant-ph/0603014 · Physical Review B

Detection mechanism for quantum phase transition in superconducting qubit array

Ying-Dan Wang, Fei Xue, Z. Song, Chang-Pu Sun

Published Nov 27, 2007• 34 citations
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Abstract

We describe a mechanism to detect quantum phase transition (QPT) in a system by a coherent probe weakly coupled to it. We illustrate this mechanism by a circuit QED architecture where a superconducting Josephson junction qubit array interacts with a one-dimensional superconducting transmission line resonator (TLR). The superconducting qubit array is modeled as an Ising chain in transverse field. Our investigation shows that the QPT phenomenon in the superconducting qubit array can be evidently revealed by the correlation spectrum of TLR output: At the critical point, the drastic broadening of spectrum indicates the occurrence of QPT. We also show the generalization of this mechanism to other QPT systems.

DOI
10.1103/physrevb.76.174519

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We describe a mechanism to detect quantum phase transition (QPT) in a system by a coherent probe weakly coupled to it. We illustrate this mechanism by a circuit QED architecture where a superconducting Josephson junction qubit array interacts with a one-dimensional superconducting transmission line resonator (TLR). The superconducting qubit array is modeled as an Ising chain in transverse field. Our investigation shows that the QPT phenomenon in the superconducting qubit array can be evidently revealed by the correlation spectrum of TLR output: At the critical point, the drastic broadening of spectrum indicates the occurrence of QPT. We also show the generalization of this mechanism to other QPT systems.
We suggest a scheme to probe critical phenomena at a quantum phase transition (QPT) using the quantum correlation of two photonic modes simultaneously coupled to a critical system. As an ex-perimentally accessible physical implementation,a circuit QED system is formed by a capacitively coupled Josephson junction qubit array interacting with one superconducting transmission line reso-nator (TLR). It realizes an Ising chain in the transverse field (ICTF) which interacts with the two mag-netic modes propagating in the TLR. We demonstrate that in the vicinity of criticality the originally in-dependent fields tend to display photon bunching effects due to their interaction with the ICTF. Thus,the occurrence of the QPT is reflected by the quantum characteristics of the photonic fields.
We consider a one-dimensional array of superconducting transmission line resonators (TLRs). The TLRs are coupled by current-biased Josephson junctions, which act as tunable couplers between each two nearest TLRs, and a superconducting qubit is fabricated in the center of each TLR. We show that some important quantum information processing, such as quantum state transfer and preparation of remote entanglement, can be achieved in this system, and we also propose a scheme for generating the W-class states.
Superconductivity provides a canonical example of a quantum phase of matter. When superconducting islands are connected by Josephson junctions in a lattice, the low-temperature state of the system can map to the celebrated XY model and its associated universality classes. This has been used to experimentally implement realizations of Mott insulator and Berezinskii-Kosterlitz-Thouless transitions to vortex dynamics analogous to those in type-II superconductors. When an external magnetic field is added, the effective spins of the XY model become frustrated, leading to the formation of topological defects (vortices). Here, we observe the many-body dynamics of such an array, including frustration, via its coupling to a superconducting microwave cavity. We take the design of the transmon qubit, but replace the single junction between two antenna pads with the complete array. This allows us to probe the system at 10 mK with minimal self-heating by using weak coherent states at the single (microwave) photon level to probe the resonance frequency of the cavity. We observe signatures of an ordered vortex lattice at rational flux fillings of the array.
Superconducting qubits connected in an array can form quantum many-body systems such as the quantum Ising model. By coupling the qubits to a superconducting resonator, the combined system forms a circuit QED system. Here, we study the nonlinear behavior in the many-body state of the qubit array using a semiclassical approach. We show that sudden switchings as well as a bistable regime between the ferromagnetic phase and the paramagnetic phase can be observed in the qubit array. A superconducting circuit to implement this system is presented with realistic parameters.