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Physical Review B

Period-voltage-driven quantum phase transition of superconducting charge qubits

Gang Chen, Jun‐Qi Li, Jiuqing Liang

Published Aug 15, 2007• 3 citations
Publisher

Abstract

In this paper, we employ an experimentally feasible scheme to realize a uniaxial spin model in superconducting charge qubits connected in parallel to a common superconducting inductance. Furthermore, we demonstrate that this nonlinear spin model with nonzero parallel field can give rise to a second-order phase transition under periodic modulation. It is shown that, when the amplitude of the periodically driven gate voltage in our proposal is varied, this second-order phase transition occurs from a normal to a deformed phase in the resonant case. Furthermore, in this system the adiabatic and cyclic conditions needed to generate the geometric phase can be easily implemented, and therefore this predicted phase transition could be detected in experiments by measuring the ground-state geometric phase.

DOI
10.1103/physrevb.76.054512

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In this paper, we employ an experimentally feasible scheme to realize a uniaxial spin model in superconducting charge qubits connected in parallel to a common superconducting inductance. Furthermore, we demonstrate that this nonlinear spin model with nonzero parallel field can give rise to a second-order phase transition under periodic modulation. It is shown that, when the amplitude of the periodically driven gate voltage in our proposal is varied, this second-order phase transition occurs from a normal to a deformed phase in the resonant case. Furthermore, in this system the adiabatic and cyclic conditions needed to generate the geometric phase can be easily implemented, and therefore this predicted phase transition could be detected in experiments by measuring the ground-state geometric phase.
In this letter we predict a novel second-order quantum phase transition of two-component Bose-Einstein condensates coupled with a periodically driven laser field in the resonant case. It is shown that this quantum phase transition from the normal to the tunneling phases can be controlled by the interspecies nonlinear interaction tuned via the magnetic-field–dependent Feshbach resonance technique. Furthermore, it is also demonstrated that this quantum phase transition can be detected by measuring the ground-state population imbalance between two condensates.
We present a superconducting circuit in which non-Abelian geometric transformations can be realized using an adiabatic parameter cycle. In contrast to previous proposals, we employ quantum evolution in the ground state. We propose an experiment in which the transition from non-Abelian to Abelian cycles can be observed by measuring the pumped charge as a function of the period of the cycle. Alternatively, the non-Abelian phase can be detected using a single-electron transistor working as a charge sensor.
To achieve robust gate operations on superconducting charge qubits, we theoretically propose a feasible scheme to realize geometric quantum computation via coherent pulses. Only by adiabatically tuning the microwave pulses applied to the gate capacitance can the Berry phases associated with the system be acquired, from which we construct a universal set of geometric gates. Combining the geometric approach with the coherent pulse technique, robust quantum operations aimed at combating noise errors may be implemented experimentally.
We propose a method of controlling the dc-SQUID (superconducting quantum interference device) system by changing the gate voltages, which controls the amplitude of the fictitious magnetic fields , and the externally applied current that produces the piercing magnetic flux for the dc-SQUID system. We have also introduced a physical model for the dc-SQUID system. Using this physical model, one can obtain the non-adiabatic geometric phase gate for the single qubit and the non-adiabatic conditional geometric phase gate (controlled NOT gate) for the two qubits. It is shown that when the gate voltage and the externally applied current of the dc-SQUID system satisfies an appropriate constraint condition, the charge state evolution can be controlled exactly on a dynamic phase free path. The non-adiabatic evolution of the charge states is given as well.
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.
We propose a method of controlling the dc-SQUID (superconducting quantum interference device) systemby changing the gate voltages, which controls the amplitude of the fictitious magnetic fields Bz, and the externallyapplied current that produces the piercing magnetic fiux φx for the dc-SQUID system. We have also introduced aphysical model for the dc-SQUID system. Using this physical model, one can obtain the non-adiabatic geometric phasegate for the single qubit and the non-adiabatic conditional geometric phase gate (controlled NOT gate) for the twoqubits. It is shown that when the gate voltage and the externally applied current of the dc-SQUID system satisfies anappropriate constraint condition, the charge state evolution can be controlled exactly on a dynamic phase free path. Thenon-adiabatic evolution of the charge states is given as well.