Entropy, fidelity, and double orthogonality for resonance states in two-electron quantum dots

Pont, Federico M.; Osenda, Omar; Toloza, Julio H.; Serra, Pablo

doi:10.1103/physreva.81.042518

Cited by 25 publications

(40 citation statements)

References 41 publications

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“…Decay rates (inverse lifetimes) in QDs can be computed using different methods [25,30,35]. Here, we employed imaginary time propagation to arrive at the resonant state of setup C and then the state is let to evolve in real time to measure the total decay rate [25].…”

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confidence: 99%

Controlled energy-selected electron capture and release in double quantum dots

Pont¹,

Bande²,

Cederbaum³

2013

Phys. Rev. B

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Highly accurate quantum electron dynamics calculations demonstrate that energy can be efficiently transferred between quantum dots. Specifically, in a double quantum dot an incoming electron is captured by one dot and the excess energy is transferred to the neighboring dot and used to remove an electron from this dot. This process is due to long-range electron correlation and shown to be operative at rather large distances between the dots. The efficiency of the process is greatly enhanced by preparing the double quantum dot such that the incoming electron is initially captured by a two-electron resonance state of the system. In contrast to atoms and molecules in nature, double quantum dots can be manipulated to achieve this enhancement. This mechanism leads to a surprisingly narrow distribution of the energy of the electron removed in the process which is explained by resonance theory. We argue that the process could be exploited in practice. [2,[4][5][6][7] together with new phenomena handed down from the semiconductor nature of QDs [8-11] many of which endowed new technological applications to be cast into reality. In this work we concentrate on energy transfer between two QDs driven by long-range electron correlation and mediated by the capture of an electron.Electron capture in single QDs is an extensively studied topic [12][13][14] due to its relevance in the development of technological applications. The capture efficiency and its time scale depend substantially on temperature, carrier density, material and geometry of the QDs [13][14][15]. The capture and the later relaxation dynamics occur through diverse physical processes such as electronphonon interactions [13,14,16,17], multiple exciton generation [12] and Auger relaxation [15], all of which can be assessed using pump-probe schemes [10,[12][13][14]17]. Capture by optical phonon emission has been investigated in single [16,18,19] as well as in double QDs [18]. So far, electronically-induced inter-dot capture processes have not been considered at all. In the present work we use numerically exact quantum dynamics to show that electron capture by one QD in a DQD becomes possible by energy transfer to the neighboring QD due to long-range electron correlation. Originally, such processes were predicted to operate between atoms [20,21] where electron capture by one atom occurs while another electron is emitted from an atom in its environment and called interatomic electronic Coulombic capture (ICEC), a name which we would like to adopt also for QDs. For completeness we mention that energy transfer between quantum wells has been studied in a different context, see, e.g., [22,23].For explicit demonstration we study a system comprised of two different QDs which we call the left and right QDs and which are described by the model potentials discussed below. Let the left potential well support a one-electron level L 0 and the right one, R 0 . Although included in the calculation, the tunneling between L 0 and R 0 is vanishingly small due to the long inter-dot di...

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confidence: 99%

Controlled energy-selected electron capture and release in double quantum dots

Pont¹,

Bande²,

Cederbaum³

2013

Phys. Rev. B

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“…However, studies on the correlation in resonance states have not yet drawn much attention. Pont et al [34] proposed to associate the entanglement of a resonance state with a real part of a linear entropy computed from complexvalued eigenvalues of a reduced density matrixρ determined in the framework of the complex scaling method (CSM) [35][36][37][38]. Within the framework of this approach, the properties of two-electron one-dimensional (1D) quantum dots near the autoionization thresholds have recently been investigated in [39].…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, in a resonance case, the interpretation of the real and imaginary parts of the expectation value of log 2ρ (1 −ρ) as the entropy and its uncertainty, respectively, is problematic. Despite of this fact, we call the average values of the operators log 2ρ and1 −ρ as the complex-valued von Neumann and linear entropies, respectively, and, following to [34,39,40], use them to characterize the correlation in resonance states. The purpose of this brief paper is to determine the complex entropies for doubly excited resonance states of helium, 2s 2 1 S e and 2 p 2 1 S e , and compare the results obtained with the corresponding ones determined in different ways [27,28].…”

Section: Introductionmentioning

confidence: 99%

Doubly Excited Resonance States of Helium Atom: Complex Entropies

2016

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We provide a diagonal form of a reduced density matrix of S-symmetry resonance states of two electron systems determined under the framework of the complex scaling method. We have employed the variational Hylleraas type wavefunction to estimate the complex entropies in doubly excited resonance states of helium atom. Our results are in good agreement with the corresponding ones determined under the framework of the stabilization method (Lin and Ho in Few-Body Syst 56:157, 2015).

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“…was discussed for spherically symmetric two-electron QD [46], adopting the interpretation of its real part as the physical quantity and the imaginary part as the uncertainty of its measurement [16].…”

Section: B Two-particle Casementioning

confidence: 99%

Entanglement Properties of Bound and Resonant Few-Body States

Kuroś

Okopińska

2019

Quantum Systems in Physics, Chemistry and Biology - Theory, Interpretation, and Results

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Studying the physics of quantum correlations has gained new interest after it has become possible to measure entanglement entropies of few body systems in experiments with ultracold atomic gases. Apart from investigating trapped atom systems, research on correlation effects in other artificially fabricated few-body systems, such as quantum dots or electromagnetically trapped ions, is currently underway or in planning.Generally, the systems studied in these experiments may be considered as composed of a small number of interacting elements with controllable and highly tunable parameters, effectively described by Schrödinger equation. In this way, parallel theoretical and experimental studies of few-body models become possible, which may provide a deeper understanding of correlation effects and give hints for designing and controlling new experiments. Of particular interest is to explore the physics in the strongly correlated regime and in the neighborhood of critical points.Particle correlations in nanostructures may be characterized by their entanglement spectrum, i.e. the eigenvalues of the reduced density matrix of the system partitioned into two subsystems. We will discuss how to determine the entropy of entanglement spectrum of few-body systems in bound and resonant states within the same formalism. The linear entropy will be calculated for a model of quasi-one dimensional Gaussian quantum dot in the lowest energy states. We will study how the entanglement depends on the parameters of the system, paying particular attention to the behavior on the border between the regimes of bound and resonant states.

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Entropy, fidelity, and double orthogonality for resonance states in two-electron quantum dots

Cited by 25 publications

References 41 publications

Controlled energy-selected electron capture and release in double quantum dots

Controlled energy-selected electron capture and release in double quantum dots

Doubly Excited Resonance States of Helium Atom: Complex Entropies

Entanglement Properties of Bound and Resonant Few-Body States

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