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Scaling quantum probe for quantum phase transition in macroscopic qubit array

Y. D. Wang, Fei Xue, Che Sun

Published Mar 2, 2006• 0 citations
OpenAlex

Abstract

Based on a superconducting circuit, we discuss the quantum phase transition of a qubit-array quantum Ising model with a quantum probe which is realized by the single mode quantized field in a superconducting transmission line resonator coupled to this qubit array. The scaling behavior of quantum probe near the critical point is analyzed for its quantum coherence. The critical index of decoherence factor is found to be 4.

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Based on a superconducting circuit, we discuss the quantum phase transition of a qubit-array quantum Ising model with a quantum probe which is realized by the single mode quantized field in a superconducting transmission line resonator coupled to this qubit array. The scaling behavior of quantum probe near the critical point is analyzed for its quantum coherence. The critical index of decoherence factor is found to be 4.
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.
Quantum phase transitions play an important role in many-body systems and have been a research focus in conventional condensed-matter physics over the past few decades. Artificial atoms, such as superconducting qubits that can be individually manipulated, provide a new paradigm of realising and exploring quantum phase transitions by engineering an on-chip quantum simulator. Here we demonstrate experimentally the quantum critical behaviour in a highly controllable superconducting circuit, consisting of four qubits coupled to a common resonator mode. By off-resonantly driving the system to renormalize the critical spin-field coupling strength, we have observed a four-qubit nonequilibrium quantum phase transition in a dynamical manner; that is, we sweep the critical coupling strength over time and monitor the four-qubit scaled moments for a signature of a structural change of the system's eigenstates. Our observation of the nonequilibrium quantum phase transition, which is in good agreement with the driven Tavis-Cummings theory under decoherence, offers new experimental approaches towards exploring quantum phase transition-related science, such as scaling behaviours, parity breaking and long-range quantum correlations.
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.
Analog quantum simulators can be used to study quantum correlation in novel many-body systems by emulating the Hamiltonian of these systems. One essential question in quantum simulation is to probe the properties of an emulated many-body system. Here we present a circuit QED scheme for probing such properties by measuring the spectrum of a superconducting resonator coupled to a quantum simulator. We first study a general framework of this approach and show that the spectrum of the resonator is directly related to the correlation function of the coupling operator between the resonator and the simulator. We then apply this scheme to a simulator of the transverse field Ising model implemented with superconducting qubits, where the resonance peaks in the resonator spectrum correspond to the frequencies of the elementary excitations. The effects of resonator damping, qubit decoherence, and resonator backaction are also discussed. This setup can be used to probe a broad range of many-body models.