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The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics

Pancharatnam phase of two Cooper-pair boxes in a dissipative cavity

Mahmoud Abdel‐Aty, Waheeb Essa Alnaser

Published Apr 28, 2011• 1 citation
Publisher

Abstract

The time evolution of a single Cooper pair in the presence of another Cooper pair interacting with an electromagnetic field in a dissipative cavity is presented. The strong dependence of the dynamics of two superconducting charge qubits interacting with the microcavity field on the instantaneous phase shift experienced by the second qubit is demonstrated. The Pancharatnam phase is found to be more sensitive than the population dynamics to the phase shift. This leads us to suggest a new technique for controlling the system dynamics. Furthermore, although the atom is not directly coupled to the cavity modes, its coherent properties are found to be strongly influenced by dissipation, both qualitatively and quantitatively.

DOI
10.1080/14786435.2011.573816

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The time evolution of a single Cooper pair in the presence of another Cooper pair interacting with an electromagnetic field in a dissipative cavity is presented. The strong dependence of the dynamics of two superconducting charge qubits interacting with the microcavity field on the instantaneous phase shift experienced by the second qubit is demonstrated. The Pancharatnam phase is found to be more sensitive than the population dynamics to the phase shift. This leads us to suggest a new technique for controlling the system dynamics. Furthermore, although the atom is not directly coupled to the cavity modes, its coherent properties are found to be strongly influenced by dissipation, both qualitatively and quantitatively.
Abstract Quantum coherence represents a basic feature of a quantum system that is not present in the classical world. Here, we explore the dynamic behaviors of quantum coherence in two charge qubits who are strongly coupled with a single-mode dissipative cavity field. The results show that quantum coherence is sensitive to the coupled system parameters including qubit dissipation rate, initial qubit distribution angle, and coherent state intensity of the cavity field. Additionally, during the dynamic evolution, quantum coherence behaves periodically in the case of the qubit distribution angle, and this periodicity depends on the qubit dissipation rate. Also, the increasing coherent state intensity of cavity field can enhance the magnitude of quantum coherence, meaning that coherence resource in dissipative solid state quantum system can be controlled to some extent. This controllable coherence resource in engineering applications may quantify the advantage enabled in the superconducting circuit for processing the remarkable quantum information tasks.
We present the time evolution of a two-level atom interacting dispersively with an electromagnetic field in a dissipative cavity. We investigate the influence of dissipation on the entanglement of the two subsystems (atom+field).(\mathrm{atom}+\mathrm{field}).(atom+field). Simple but realistic, the model displays several nontrivial quantum features, which emerge when an environment is taken into account: the cavity is shown to have practically no influence in the coherence properties of the field from the qualitative point of view. On the other hand, although the atom is not directly coupled to the cavity modes, its coherent properties are strongly influenced by dissipation both qualitatively as well as quantitatively.
In cavity quantum electrodynamics (QED), the key physical systems include Fabry-Pérot cavity resonators and multilevel cold atoms. Since ultra-strong electromagnetic interaction between photons and quantized cavity modes occurs in cavity QED, many novel quantum optical effects such as optical Rabi oscillation, quantum collapse/revival of atomic-level population and atom-field quantum entanglement can be realized in such quantum microcavities. As is known in quantum optics, these schemes can be generalized to circuit QED, which is a circuit analog of cavity QED. Fundamental devices in circuit QED are superconducting coplanar waveguide microwave resonators and mesoscopic Cooper-pair boxes. Here, the coplanar waveguide resonator with photons stored can be identified as a resonant cavity and the Cooper-pair boxes with large electric dipoles play the role of multilevel cold atoms. Thus, all the quantum optical effects in conventional cavity QED can also be exhibited in the present superconducting circuit QED system. We consider the theoretical working mechanism of superconducting charge qubits based on tunable Josephson junction coupling. It can be found that an analog of optical Rabi oscillation in Cooper-pair boxes can be achieved by tuning an applied external magnetic field. Time evolution of energy levels in a Cooper-pair box, which is manipulated by a time-dependent magnetic flux through its Josephson-junction ring, is studied within the framework of time-dependent quantum mechanics.