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Physical Review B

Berry phase of two coupled quantum dots

Xiao-Zhong Yuan, Ka-Di Zhu

Published Aug 31, 2006• 13 citations
Publisher

Abstract

The Berry phase of two coupled quantum dots is investigated. The coupled quantum dots are embedded in a high-$Q$ single mode cavity and coupled to the common phonon fields. We show how the Berry phase depends on the environmental temperatures.

DOI
10.1103/physrevb.74.073309

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The Berry phase of two coupled quantum dots is investigated. The coupled quantum dots are embedded in a high-QQQ single mode cavity and coupled to the common phonon fields. We show how the Berry phase depends on the environmental temperatures.
We investigate the dynamical behavior of entanglement in a system made of two solid-state emitters, as two quantum dots, embedded in two separated microcavities. In these solid-state systems, in addition to the coupling with the cavity mode, the emitter is coupled to a continuum of leaky modes providing additional losses and is also subjected to a phonon-induced pure dephasing mechanism. We model this physical configuration as a multipartite system composed of two independent parts each containing a qubit embedded in a single-mode cavity, exposed to cavity losses, spontaneous emission and pure dephasing. We study the time evolution of entanglement of this multipartite open system, finally applying this theoretical framework to the case of currently available solid-state quantum dots in microcavities.
We predict dominating cooperative two-photon emission from two quantum dots coupled with a single-mode photonic crystal cavity. The cooperative two-photon emission occurs when excitons in two off-resonantly coupled quantum dots decay simultaneously. The interaction with a common cavity field leads to cavity-induced two-photon emission which is strongly inhibited by electron-phonon coupling. The interaction with a common phonon bath produces phonon-induced two-photon emission which increases on increasing temperature. For identical quantum dots, cavity-induced two-photon emission is negligible, but phonon-induced two-photon emission could be large.
We propose a feasible experiment to investigate quantum effects in geometric phases, arising when a classical source drives not a single quantum system, but two interacting ones. In particular, we show how to observe a signature of the quantization of the electromagnetic field through a vacuum effect in Berry's phase. To do so, we describe the interaction of an atom and a quantized cavity mode altogether driven by an external quasiclassical field. We also analyze the semiclassical limit recovering the usual Berry's phase results.
We report a new type of coupling between quantum dot excitons mediated by the strong single-photon field in a high-finesse micropillar cavity. Coherent exciton coupling is observed for two dots with energy differences of the order of the exciton-photon coupling. The coherent coupling mode is characterized by an anticrossing with a particularly large line splitting of 250 microeV. Because of the different dispersion relations with temperature, the simultaneous photonic coupling of quantum dot excitons can be easily distinguished from cases of sequential strong coupling of two quantum dots.
The Berry phase has universal applications in various fields. Here, we explore the coupling effect on the Berry phase of a two-level system adiabatically driven by a rotating classical field and interacting with a single quantized mode. Our simulations clearly reveal that the Berry phase change is quadratic proportional to the coupling constant if it is less than the level spacing between neighboring instantaneous eigenstates. Remarkably, if the nearest neighbouring level spacing is comparable with the coupling constant, this simple quadratic dependence is lost. Around this resonance, the Berry phase can be significantly tuned by slightly adjusting the parameters, such as the coupling constant, the frequency of the quantized mode, and the transition frequency. These numerical results, agreeing well with the perturbation theory calculations, provide an alternative approach to tune the Berry phase near the resonance, which is useful in quantum information science, i.e. designing quantum logic gates.
The voltage-controlled Berry phases in two vertically coupled InGaAs/GaAs quantum dots are investigated theoretically. It is found that Berry phases can be changed dramatically from 0 to 2π (or 2π to 0) only by simply applying an external voltage. Under realistic conditions, as the tunneling is varied from 0.8 eV to 0.9 eV via a bias voltage, the Berry phases are altered obviously, and this can be detected in an interference experiment. The scheme is expected to be useful in constructing quantum computation based on geometric phases in an asymmetrical double quantum dot controlled by voltage.