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Physical Review B

Magnetic-flux-driven quantum phase transition in superconducting qubits coupled with a nanomechanical resonator

Gang Chen, Zidong Chen, Jun‐Qi Li, Jiuqing Liang

Published Jun 27, 2007• 6 citations
Publisher

Abstract

In this Brief Report, we investigate the collective quantum dynamics of a solid-state system containing a superconducting quantum interference device (SQUID) coupled with a nanomechanical resonator. When the charging energy is much larger than the Josephson energy, the SQUID can act as an artificial two-level atom near the degeneracy point. Thus, we theoretically realize the Dicke model in quantum optics. Furthermore, we predict that a superradiant phase transition for this model can be driven by an experimentally controllable external magnetic flux. The essential features of quantum criticality, such as the scaling behavior, critical exponent, and universality, are also given. Finally, we propose to observe this quantum phase transition by measuring the ground-state Berry phase.

DOI
10.1103/physrevb.75.212508

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In this Brief Report, we investigate the collective quantum dynamics of a solid-state system containing a superconducting quantum interference device (SQUID) coupled with a nanomechanical resonator. When the charging energy is much larger than the Josephson energy, the SQUID can act as an artificial two-level atom near the degeneracy point. Thus, we theoretically realize the Dicke model in quantum optics. Furthermore, we predict that a superradiant phase transition for this model can be driven by an experimentally controllable external magnetic flux. The essential features of quantum criticality, such as the scaling behavior, critical exponent, and universality, are also given. Finally, we propose to observe this quantum phase transition by measuring the ground-state Berry phase.
In this paper, we propose an experimentally feasible scheme that the superconducting quantum interference devices are coupled with a high-quality cavity supporting a single-mode photon, to realize an effective Dicke model. By using several hundred artificial two-level atoms, the strong coupling regime can be successfully achieved. Moreover, in our proposal the superradiant phase transition for this model can be well controlled by the frequency of external magnetic flux when the superconducting charge qubits work at their optimal point, in which the qubits can be mostly immune from charge noise produced by uncontrollable charge fluctuations. Finally, we propose to observe this phase transition by detecting the intracavity intensity in terms of a heterodyne detector out of the cavity.
We propose an active mechanism for coupling the quantized mode of a nanomechanical resonator to the persistent current in the loop of a superconducting Josephson junction (or phase slip) flux qubit. This coupling is independently controlled by an external coupling magnetic field. The whole system forms a novel solid-state cavity quantum electrodynamics (QED) architecture in the strong coupling limit. This architecture can be used to demonstrate quantum optics phenomena and coherently manipulate the qubit for quantum information processing. The coupling mechanism is applicable for more generalized situations where the superconducting Josephson junction system is a multi-level system. We also address the practical issues concerning experimental realization.
At low temperature and low damping, the magnetic flux of a rf Superconducting QUantum Interference Device (SQUID) acts as a macroscopic quantum variable whose dynamic is described by a double well potential. A rf SQUID consists of a superconducting loop interrupted by a thin insulating barrier, known as a Josephson junction. The modified rf SQUID design discussed in this thesis has independent, in situ, controls that allow varying the barrier height between the potential wells and their relative tilt. This high level of control of the potential together with the capability to implement an experimental setup optimized to reduce coupling to external sources of noise, made this system ideal not only for tests of quantum transition at a macroscopic level, but also as a scalable solid state device for quantum computation. A variety of measurements of quantum phenomena are reported in this thesis, including microwave level spectroscopy, coherent oscillations, and macroscopic resonant tunneling (MRT). These measurements are compared with theoretical models to study the possible sources of decoherence in a rf SQUID qubit. The analysis confirmed that the main source of decoherence is not due to coupling to the external environment, but it can be linked to intrinsic low frequency flux noise. Work from many groups over the last several years has shown that the performance of a superconductive qubit is limited by coupling to spurious defects in the materials used for the device fabrication. In this work we analyze the possibility of using the MRT as a tool for future studies of effects of materials and fabrication process in the realization of improved qubits, and we also explore the feasibility for measurements of quantum phenomena that involve fast pulsing of the potential barrier height.
The quantum behaviour of mechanical resonators is a new and emerging field driven by recent experiments reaching the quantum ground state. The high frequency, small mass, and large quality-factor of carbon nanotube resonators make them attractive for quantum nanomechanical applications. A common element in experiments achieving the resonator ground state is a second quantum system, such as coherent photons or a superconducting device, coupled to the resonators motion. For nanotubes, however, this is a challenge due to their small size. Here, we couple a carbon nanoelectromechanical (NEMS) device to a superconducting circuit. Suspended carbon nanotubes act as both superconducting junctions and moving elements in a Superconducting Quantum Interference Device (SQUID). We observe a strong modulation of the flux through the SQUID from displacements of the nanotube. Incorporating this SQUID into superconducting resonators and qubits should enable the detection and manipulation of nanotube mechanical quantum states at the single-phonon level.
We investigate quantum phase transitions, quantum criticality, and Berry phase for the ground state of an ensemble of non-interacting two-level atoms embedded in a non-linear optical medium, coupled to a single-mode quantized electromagnetic field. The optical medium is pumped externally through a classical electric field, so that there is a degenerate parametric amplification effect, which strongly modifies the field dynamics without affecting the atomic sector. Through a semiclassical description the different phases of this extended Dicke model are described. The quantum phase transition is characterized with the expectation values of some observables of the system as well as the Berry phase and its first derivative, where such quantities serve as order parameters. It is remarkable that the model allows the control of the quantum criticality through a suitable choice of the parameters of the non-linear optical medium, which could make possible the use of a low intensity laser to access the superradiant region experimentally.
We study a system of two nanomechanical resonators embedded in a dc superconducting quantum interference device (SQUID). We show that the inductively coupled resonators can be treated as two entangled quantum memory elements with states that can be read from, or written on, by employing the SQUID as a displacement detector or switching additional external magnetic fields, respectively. We present a scheme to squeeze the even mode of the state of the resonators and, consequently, reduce the noise in the measurement of the magnetic flux threading the SQUID. We finally analyze the effect of dissipation on the squeezing using the quantum master equation, and show the qualitatively different behavior for the weak and strong damping regimes. Our predictions can be tested using current experimental capabilities.