Control of electronic and optical properties of a laser dressed double quantum dot molecule by lateral electric field

doi:10.1016/j.physe.2020.114362

Physica E: Low-dimensional Systems and Nanostructures

Volume 126, February 2021, 114362

https://doi.org/10.1016/j.physe.2020.114362 Get rights and content

Highlights

•
Double quantum dot molecule.
•
Intense Laser Field.
•
Electric Field.

Abstract

We study the confined states of a molecule formed by two laterally coupled quantum dots. The static electric field and incident plane wave laser field are considered with different polarization. The respective Shrödinger equation is obtained in the framework of the high-frequency limit of Floquet theory. It is shown that the electric field has a qualitative impact on the spatial symmetry of electronic states. An in-depth study of electric and laser field combined effects show a strong correlation between them. Additionally, we show that the linear, nonlinear and total optical absorption coefficients and relative refractive index of the considered structure can be effectively tuned by changing electric field strength and intense laser field parameter. Our results indicate the possibility of controlling the optical response of double quantum dots molecule for future applications in nanostructure-based quantum information science.

Introduction

An artificial molecule can be formed by two closely positioned quantum dots (QDs) resulting from the quantum tunneling. The coupling properties of such QD molecules (QDM) are in a focus of studies for optoelectronic and quantum information applications [1,2]. In particular, laterally coupled QDMs are candidates for constructing building blocks in the field of nanostructure-based quantum information science [3].

It is well known that the controllable tunnel coupling between QDs has technological importance [5]. Therefore, the tuning of coupling in double QDMs (DQDMs) has a great interest both from an experimental and theoretical point of view [4]. It has been demonstrated that by applying a lateral electric field on laterally coupled DQDM the electron localization can be readily controlled [3]. It was also pointed out that QDM can serve as single-photon emitters in a range of frequencies [6].

The effective controlling of one- and two-electron states in laterally coupled DQDMs with two-dimensional double parabolic confinement using the external electric and magnetic fields and changing the interdot distance have been investigated in Ref. [7]. In reverse, the application of a lateral electric field brings a superposition of localized states in separate QDs and a localized to a covalent diatomic molecular state transition.

Experiments show that the geometry of QDs in DQDMs is mostly elliptical rather than cylindrical [8]. We have already shown [9,10] that intense terahertz laser field (ILF) can induce and control the isotropic and anisotropic properties of quantum rings. Particularly, it can recover the physical properties in elliptical quantum rings that are specific to cylindrical symmetry. We have also shown that the electric field can cancel the degeneracy induced by IFL and, in turn, create new optical transitions [11]. Also, under ILF, Fock-Darwin states can be observed in anisotropic double QDs that are typical to single QDs with cylindrical symmetry [12]. In the current work, we analyze the effect of the electric field on the symmetry and coupling of laser field dressed electronic states in a DQDM. States are confined by parabolic confinement potential. A thorough analysis is done on the interplay between ILF and electric field effects. The key result is the possibility to control the symmetry of quantum states changing the direction and the strength of the electric field. ILF, in turn, can serve as means to supervise this change. The mentioned effects are also studied on the intraband optical properties of DQDM, such as on linear, nonlinear and total optical absorption coefficients and relative refractive index. The theoretical framework is given in Sec. 2, the analysis of results is presented in Sec. 3 and the conclusions are in Sec. 4.

Section snippets

Theoretical model

The confinement potential of DQDM is a sum of two-dimensional parabolic potential and Gaussian barrier [13]: $V (x, y) = \frac{1}{2} m (ω_{x}^{2} x^{2} + ω_{y}^{2} y^{2}) + V_{0} e^{- \frac{x^{2}}{R^{2}}},$ were ω_x(y) is the frequency of the confinement potential in x(y) direction, R and V₀ are the width and height of the Gaussian barrier, respectively. The single electron Hamiltonian of the system can be written as: $[\frac{1}{2 m} {(\hat{p} - \frac{e}{c} A (t))}^{2} + V_{F} (x, y)] Φ (x, y, t) = i ℏ \frac{\partial}{\partial t} Φ (x, y, t),$ where m is the electron effective mass, $\hat{p}$ is the momentum operator, e is the absolute value of the

Numerical results

We consider GaAs as the material for DQDM with m = 0.067m₀ (m₀ is the free electron mass), ε_h = 10.5, V₀ = 2 meV and R = 10 nm [13,24]. The eigenvalue equation Eq. (4) is solved in finite element method framework using COMSOL Multiphysics [27].

In Fig. 1 (symmetric - ℏω_x = ℏω_y = 3 meV) and Fig. 2 (asymmetric case - ℏω_x = 3 meV, ℏω_y = 2.7 meV) the confinement potential of the DQDM is given for varying ILF parameter α₀ and electric field strength F. As it is seen from the panels, in the case of

Final remarks

Summarizing, we have shown that the static electric field has a qualitative impact on the spatial symmetry of electronic states. Particularly, the change of the electric field direction can lead to the transformation of the quantum state symmetry, which can be controlled by an intense laser field. The symmetry transformation takes place also with the increment of the electric field of fixed direction. The later is expressed by the crossing of energy levels with electric field variation. Also,

Credit author statement

All the authors have equally contributed.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

MGB and VNM acknowledge the financial support by the Armenian State Committee of Science (Project no. 18T-1C223). LMP and DL acknowledge partial financial support from FONDECYT 1180905. DL acknowledges partial financial support from Centers of excellence with BASAL/CONICYT financing, Grant AFB180001, CEDENNA.

References (28)

M.G. Barseghyan et al.
Physica E
(2020)
M.G. Barseghyan et al.
Physica E
(2020)
R.L. Restrepo et al.
Physica E
(2013)
F. Ungan et al.
Physica E
(2019)
M.F. Doty et al.
Phys. Rev. Lett.
(2009)
A.N. Vamivakas et al.
Nature
(2010)
G.J. Beirne et al.
Phys. Rev. Lett.
(2006)
R.M. Abolfath et al.
Phys. Rev. Lett.
(2006)
X. Zhou et al.
J. Appl. Phys.
(2014)
A.J. Shields
Nat. Photon.
(2007)

V. Popsueva et al.

Phys. Rev. B

(2007)

J. Wu et al.

Quantum Dot Molecules

(2014)

T. Chakraborty et al.

Phys. Rev. B

(2018)

H.M. Baghramyan et al.

Sci. Rep.

(2018)

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Control of electronic and optical properties of a laser dressed double quantum dot molecule by lateral electric field

Highlights

Abstract

Introduction

Section snippets

Theoretical model

Numerical results

Final remarks

Credit author statement

Declaration of competing interest

Acknowledgments

Physica E

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Physica E

Physica E

Phys. Rev. Lett.

Nature

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