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Science in China. Series G, Physics, mechanics & astronomy/Science in China. Series G, Physics, Mechanics & Astronomy

Two mode photon bunching effect as witness of quantum criticality in circuit QED

Ying Wang

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

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.

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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 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.
A local interaction between photons can be engineered by coupling a nonlinear system to a transmission line. The required transmission line can be conveniently formed from a chain of Josephson junctions. The nonlinearity is generated by side-coupling this chain to a Cooper pair box. We propose to probe the resulting photon-photon interactions via their effect on the current-voltage characteristic of a voltage-biased Josephson junction connected to the transmission line. Considering the Cooper pair box to be in the weakly anharmonic regime, we find that the dc current through the probe junction yields features around the voltages $2eV=n\ensuremath{\hbar}{\ensuremath{\omega}}_{s}$, where ${\ensuremath{\omega}}_{s}$ is the plasma frequency of the superconducting circuit. The features at $n\ensuremath{\ge}2$ are a direct signature of the photon-photon interaction in the system.
Two-qubit entanglement can be induced by a quantum data bus interacting with them. In this paper, with the quantum spin chain in the transverse field as an illustration of the quantum data bus, we show that such induced entanglement can be enhanced by the quantum phase transition (QPT) of the quantum data bus. We consider two external spins simultaneously coupled to a transverse field Ising chain. By adiabatically eliminating the degrees of the chain, the effective coupling between these two spins is obtained. The matrix elements of the effective Hamiltonian are expressed in terms of the dynamical structure factor (DSF) of the chain. The DSF is the Fourier transformation of the Green function of an Ising chain and can be calculated numerically by a method introduced by Derzhko and Krokhmalskii [Phys. Rev. B 56, 11659 (1997)]. Since all characteristics of QPT are embodied in the DSF, the dynamical evolution of the two external spins displays singularity in the vicinity of the critical point.
We propose a hybrid quantum architecture for engineering a photonic Mott insulator-superfluid phase transition in a two-dimensional (2D) square lattice of a superconducting transmission line resonator (TLR) coupled to a single nitrogen-vacancy (NV) center encircled by a persistent current qubit. The localization-delocalization transition results from the interplay between the on-site repulsion and the nonlocal tunneling. The phase boundary in the case of photon hopping with real-valued and complex-valued amplitudes can be obtained using the mean-field approach. Also, the quantum jump technique is employed to describe the phase diagram when the dissipative effects are considered. The unique feature of our architecture is the good tunability of effective on-site repulsion and photon-hopping rate, and the local statistical property of TLRs which can be analyzed readily using present microwave techniques. Our work opens new perspectives in quantum simulation of condensed-matter and many-body physics using a hybrid spin circuit-QED system. The experimental challenges are realizable using currently available technologies.
We propose a scheme to enable a controllable cross-Kerr interaction between microwave photons in a circuit quantum electrodynamics (QED) system. In this scheme we use two transmission-line resonators (TLRs) and one superconducting quantum interference device (SQUID) type charge qubit, which acts as an artificial atom. It is shown that in the dispersive regime of the circuit-QED system, a controllable cross-Kerr interaction can be obtained by properly preparing the initial state of the qubit, and a large cross-phase shift between two microwave fields in the two TLRs can then be reached. Based on this cross-Kerr interaction, we show how to create a macroscopic entangled state between the two TLRs.