Reconstruction of the wave functions of coupled nanoscopic emitters using a coherent optical technique

Richter, Marten; Schlösser, Felix J.V.; Schoth, Mario; Burger, Sven; Schmidt, Frank; Knorr, Andreas; Mukamel, Shaul

doi:10.1103/physrevb.86.085308

Cited by 17 publications

(20 citation statements)

References 50 publications

(101 reference statements)

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“…It is basically a sum over optical transition matrix elements between two local eigenstates, e.g., j and

j^{'}

at nanosystem k multiplied with the wave function overlap, e.g.,

c_{kj}^{* ν} c_{{kj}^{'}}^{ν^{'}}

of the delocalized states. We can select a specific coupling element, e.g.,

{bold p}_{g ν} false({bold r}_{k} false)

for a nanosystem k by manipulating the exciting electric field, so that

E false({bold r}_{i}, t false)

and thus

A false({bold r}_{i}, t false)

for

i \neq k

vanishes, i.e., the field is localized at nanosystem k (). This effectively restricts the sum in the local matrix elements to the contributions from nanosystem k .…”

Section: Adding Spatial Control To An Experimentsmentioning

confidence: 99%

“…This effectively restricts the sum in the local matrix elements to the contributions from nanosystem k . One application of this property maybe the extraction of delocalized wave functions expansion coefficients or wave functions overlaps from the local optical transition matrices, e.g.,

{bold p}_{g ν} false({bold r}_{i} false)

. To achieve this also the sum over the delocalized states in Eq.…”

Section: Adding Spatial Control To An Experimentsmentioning

confidence: 99%

“…For this purpose various spectroscopic schemes in coherent 2D spectroscopy exist, which allow to separate coherent transitions between

ν

ν^{'}

with different energies. If the energies of the coherences connected to

ν

ν^{'}

are separated well enough compared to the dephasing, we might be able to separate contributions from summands with different states

ν

().…”

Section: Adding Spatial Control To An Experimentsmentioning

confidence: 99%

“…Therefore, combining spectroscopy with localized excitation and detection is imminent. Experimental and theoretical studies exist and show that new properties are accessible like delocalized wave functions in spectroscopy ().…”

Section: Introductionmentioning

confidence: 99%

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Spatially localized spectroscopy for examining the internal structure of coupled nanostructures

Richter

2013

Phys. Status Solidi B

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Recent experimental progress in localized excitation with nanofields and localized detection for various observables (light intensities, photo electrons, etc.) at nanometer scales, suggest to rethink conventional spectroscopic schemes in terms of localized excitation and detection. In this paper, a systematic overview will be given, how the observables and Hamilton operators in case of localized excitation and detection need to be modified. The implications of localized excitation and detection are also illustrated using linear optics and pump probe spectroscopy.

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“…It is basically a sum over optical transition matrix elements between two local eigenstates, e.g., j and

j^{'}

at nanosystem k multiplied with the wave function overlap, e.g.,

c_{kj}^{* ν} c_{{kj}^{'}}^{ν^{'}}

of the delocalized states. We can select a specific coupling element, e.g.,

{bold p}_{g ν} false({bold r}_{k} false)

for a nanosystem k by manipulating the exciting electric field, so that

E false({bold r}_{i}, t false)

and thus

A false({bold r}_{i}, t false)

for

i \neq k

vanishes, i.e., the field is localized at nanosystem k (). This effectively restricts the sum in the local matrix elements to the contributions from nanosystem k .…”

Section: Adding Spatial Control To An Experimentsmentioning

confidence: 99%

{bold p}_{g ν} false({bold r}_{i} false)

. To achieve this also the sum over the delocalized states in Eq.…”

Section: Adding Spatial Control To An Experimentsmentioning

confidence: 99%

“…For this purpose various spectroscopic schemes in coherent 2D spectroscopy exist, which allow to separate coherent transitions between

ν

ν^{'}

with different energies. If the energies of the coherences connected to

ν

ν^{'}

are separated well enough compared to the dephasing, we might be able to separate contributions from summands with different states

ν

().…”

Section: Adding Spatial Control To An Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Spatially localized spectroscopy for examining the internal structure of coupled nanostructures

Richter

2013

Phys. Status Solidi B

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“…or localization alone [14]. We extend the reconstruction method for delocalized single excitons presented in [26] from single excitons to two excitons. In section 2, double-quantum coherence 2D spectroscopy is described [24].…”

Section: Introductionmentioning

confidence: 99%

Using localized double-quantum-coherence spectroscopy to reconstruct the two-exciton wave function of coupled quantum emitters

et al. 2013

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Coherent multidimensional spectroscopy allows us to inspect the energies and the coupling of quantum systems. Coupled quantum systems-such as a coupled semiconductor quantum dot or pigments in photosynthesis-form delocalized exciton and two-exciton states. A technique is presented to decompose these delocalized wave functions into the basis of individual quantum emitters. This quantum state tomography protocol is illustrated for three coupled InAs quantum dots. To achieve the decomposition of the wavefunction, we combine the double-quantum-coherence spectroscopy with spatiotemporal control, which allows us to localize optical excitations at a specific quantum dot. Recently, a protocol was proposed for single exciton states (Richter et al 2012 Phys . Rev. B 86 085308). In this paper, we extend the method presented by Richter et al with respect to: the reconstruction of two-exciton states, a detailed analysis process of reconstruction and the effect of filtering to enhance the quality of the reconstructed wave function.

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Theory of Spectroscopy and Light Emission of Semiconductors Nanostructures

Kühn

Carmele

Knorr

et al. 2020

Springer Series in Solid-State Sciences

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Reconstruction of the wave functions of coupled nanoscopic emitters using a coherent optical technique

Cited by 17 publications

References 50 publications

Spatially localized spectroscopy for examining the internal structure of coupled nanostructures

Spatially localized spectroscopy for examining the internal structure of coupled nanostructures

Using localized double-quantum-coherence spectroscopy to reconstruct the two-exciton wave function of coupled quantum emitters

Theory of Spectroscopy and Light Emission of Semiconductors Nanostructures

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