pith. sign in

arxiv: 2308.07790 · v3 · submitted 2023-08-15 · ❄️ cond-mat.mes-hall · physics.optics· quant-ph

Structured beam controlled super-resolution in quantum dots via rapid adiabatic passage

Partha Das , Samit Kumar Hazra , Tarak Nath Dey This is my paper

Pith reviewed 2026-05-24 07:06 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall physics.opticsquant-ph
keywords super-resolution microscopyquantum dotsrapid adiabatic passagestructured beamsLaguerre-Gaussian beamsexciton-phonon couplingSTED microscopy
0
0 comments X

The pith

Rapid adiabatic passage with structured beams forms super-resolved spots in quantum dots and suppresses artifact rings.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that a two-level quantum dot interacting with two chirped structured beams under rapid adiabatic passage can produce a super-resolved focal spot when the beams have a suitably chosen spatiotemporal envelope. A variational master equation tracks the density matrix evolution including radiative and non-radiative decays to reveal how the envelope shapes the image. Bessel-modulated truncated Laguerre-Gaussian and super-Gaussian beams are used to eliminate the unwanted low-intensity rings that normally surround the spot. Temperature studies indicate that exciton-phonon coupling distorts the image at low pulse areas while decoupling at higher areas leaves the resolution intact. The approach is presented as a route to nanoscale imaging with quantum dots.

Core claim

A suitably chosen spatiotemporal envelope of the structured beams enables the formation of a super-resolved image. Unwanted low-intensity circular rings around the focal spot are suppressed using Bessel-modulated truncated structured Laguerre-Gaussian and super-Gaussian beams. At low pulse areas exciton-phonon coupling distorts the image, whereas at higher pulse areas exciton-phonon decoupling preserves the image resolution.

What carries the argument

Spatiotemporal envelope of Bessel-modulated truncated Laguerre-Gaussian and super-Gaussian beams under rapid adiabatic passage with chirping and time delay.

If this is right

  • Super-resolved spots appear when the spatiotemporal envelope of the structured beams is chosen appropriately.
  • Low-intensity rings are eliminated by switching to Bessel-modulated truncated Laguerre-Gaussian or super-Gaussian profiles.
  • Exciton-phonon coupling distorts the image at low pulse areas.
  • Exciton-phonon decoupling at higher pulse areas maintains the super-resolved image.
  • The scheme is proposed for nanoscale imaging and bioimaging applications.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same beam-shaping principle might reduce the high intensities required in conventional STED by replacing depletion with adiabatic passage.
  • Pulse-area tuning could serve as a practical control knob for temperature-stable imaging in real devices.
  • The numerical results point to an experimental test in which spot size is tracked while temperature and pulse area are varied independently.
  • The technique could be examined in other two-level emitters such as single atoms or molecules to check generality beyond quantum dots.

Load-bearing premise

The variational master equation for the density matrix accurately captures the mechanism of super-resolved spot formation under the chosen beam envelopes and temperature conditions.

What would settle it

Direct measurement of focal-spot width and surrounding ring intensity in a quantum-dot sample driven by the described beams at controlled temperatures and pulse areas would confirm or refute the predicted super-resolution and ring suppression.

Figures

Figures reproduced from arXiv: 2308.07790 by Partha Das, Samit Kumar Hazra, Tarak Nath Dey.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic diagram of two-level quantum dot system. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Excited state population as a function of pulse area [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Population transfer via RAP. The first pulse with pos [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Population of the excited state vs. spatial extent [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The 3-D intensity distribution of (a) SG beam of [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. FWHM of the spot is plotted against the intensity [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Dependence of beam intensity on spot formation. [PITH_FULL_IMAGE:figures/full_fig_p006_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. The modified population of the excited state is plot [PITH_FULL_IMAGE:figures/full_fig_p007_10.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Normalized peak intensities of Bessel-modulated SG [PITH_FULL_IMAGE:figures/full_fig_p007_9.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Spot size for higher coupling [PITH_FULL_IMAGE:figures/full_fig_p009_12.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Spot size for low coupling [PITH_FULL_IMAGE:figures/full_fig_p009_11.png] view at source ↗
read the original abstract

We theoretically investigate rapid adiabatic passage (RAP) based super-resolution microscopy in a two-level quantum dot (QD) system. The system consists of a QD interacting with two structured beams, accompanied by chirping and a time delay. The central concept of this work is inspired by the stimulated emission depletion (STED) microscopy technique. To understand the physical mechanism behind super-resolved spot formation, we employ a variational master equation for the density matrix, incorporating both radiative and non-radiative decay processes. A suitably chosen spatiotemporal envelope of the structured beams enables the formation of a super-resolved image. Unwanted low-intensity circular rings around the focal spot are suppressed using Bessel-modulated truncated structured Laguerre-Gaussian (LG) and super-Gaussian (SG) beams. We also study the temperature dependence of the imaging scheme. The numerical results confirm that at low pulse areas, exciton-phonon coupling distorts the image, whereas at higher pulse areas, exciton-phonon decoupling preserves the image resolution. Hence, the proposed scheme may open up new possibilities for nanoscale imaging and bioimaging applications using QDs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript theoretically studies rapid adiabatic passage (RAP) super-resolution in a two-level quantum dot using two chirped, time-delayed structured beams. A variational master equation incorporating radiative and non-radiative decay is solved numerically to show that suitably engineered spatiotemporal envelopes of Bessel-modulated truncated Laguerre-Gaussian and super-Gaussian beams produce a super-resolved focal spot while suppressing unwanted low-intensity rings. Numerical results are presented for the temperature dependence, claiming that exciton-phonon coupling distorts the image at low pulse area but decouples at high pulse area, thereby preserving resolution.

Significance. If the numerical results hold, the work offers a concrete proposal for combining RAP with structured light to achieve super-resolution in quantum dots while mitigating phonon-induced degradation at elevated temperatures. The explicit demonstration that particular beam truncations eliminate circular artifacts is a useful technical contribution that could be relevant for nanoscale and bioimaging applications.

major comments (2)
  1. [Numerical results (central paragraph)] The central claims (super-resolved spot formation and temperature-dependent decoupling) rest entirely on numerical integration of the variational master equation under position-dependent driving. No comparison to exact methods (HEOM), Redfield limits, or analytic high-pulse-area limits is supplied to establish the accuracy of the variational ansatz when both spatial inhomogeneity from the structured beams and phonon coupling are present simultaneously.
  2. [Numerical results (temperature-dependence paragraph)] The temperature-dependence results assert decoupling at high pulse area without reported error bars, convergence tests with respect to the variational parameters, or checks against the known low-temperature or zero-phonon limits of the model. This undermines the robustness of the claim that the imaging scheme remains effective at higher temperatures.
minor comments (2)
  1. [Abstract] The abstract and introduction would benefit from a brief statement of the specific pulse-area values and temperature range explored in the numerics.
  2. [Methods] Notation for the spatiotemporal envelopes (e.g., the precise definition of the Bessel modulation and truncation) should be introduced with an equation number in the methods section for reproducibility.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their careful reading of the manuscript and for the positive assessment of its potential significance. We address the two major comments point by point below.

read point-by-point responses

  1. Referee: [Numerical results (central paragraph)] The central claims (super-resolved spot formation and temperature-dependent decoupling) rest entirely on numerical integration of the variational master equation under position-dependent driving. No comparison to exact methods (HEOM), Redfield limits, or analytic high-pulse-area limits is supplied to establish the accuracy of the variational ansatz when both spatial inhomogeneity from the structured beams and phonon coupling are present simultaneously.

    Authors: We acknowledge that the absence of direct benchmarks against HEOM or Redfield limits for the combined spatial inhomogeneity and phonon coupling is a limitation. The variational master equation has been validated in prior literature for RAP in quantum dots, but we agree that explicit checks would be valuable. Full HEOM calculations with position-dependent structured beams are computationally prohibitive. In revision we will add a discussion of the analytic high-pulse-area limit, where the adiabatic condition ensures complete population inversion independent of phonon coupling strength, thereby supporting the decoupling observation. revision: partial

  2. Referee: [Numerical results (temperature-dependence paragraph)] The temperature-dependence results assert decoupling at high pulse area without reported error bars, convergence tests with respect to the variational parameters, or checks against the known low-temperature or zero-phonon limits of the model. This undermines the robustness of the claim that the imaging scheme remains effective at higher temperatures.

    Authors: The calculations are deterministic numerical integrations of the master equation, so statistical error bars do not apply. We will incorporate convergence tests with respect to the variational parameters and additional curves for the zero-phonon (phonon-coupling-free) limit in the revised manuscript to strengthen the temperature-dependence claims. revision: yes

standing simulated objections not resolved
  • Direct numerical comparison to HEOM for the full spatially inhomogeneous driving fields, which remains computationally infeasible.

Circularity Check

0 steps flagged

No circularity: forward numerical simulation from standard master equation

full rationale

The paper performs numerical integration of a variational master equation driven by position-dependent structured-beam envelopes (LG/SG with Bessel modulation, chirp, delay). The super-resolved spot and temperature-dependent phonon decoupling emerge directly as outputs of that integration; no parameter is fitted to the target image and then re-predicted, no self-citation supplies a uniqueness theorem, and no ansatz is smuggled in. The derivation chain is therefore self-contained and does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central claim depends on the accuracy of the variational master equation and the ad-hoc selection of beam envelopes and pulse parameters; no new entities are postulated.

free parameters (3)
  • pulse area
    Varied to study low vs high regime where exciton-phonon coupling distorts or preserves resolution
  • spatiotemporal envelope parameters
    Suitably chosen to enable super-resolved spot and suppress rings
  • time delay and chirp rate
    Accompany the structured beams in the RAP protocol
axioms (2)
  • domain assumption Variational master equation with radiative and non-radiative decays accurately describes the QD density matrix dynamics under structured illumination
    Invoked to understand the physical mechanism behind super-resolved spot formation
  • domain assumption Exciton-phonon coupling strength follows standard temperature dependence in the QD system
    Used to interpret low-pulse-area distortion versus high-pulse-area decoupling

pith-pipeline@v0.9.0 · 5727 in / 1495 out tokens · 22556 ms · 2026-05-24T07:06:27.100832+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

65 extracted references · 65 canonical work pages

  1. [1]

    The excitation and de-excitation of two beams which couple the states |1⟩ and |2⟩ are respectively given as FIG

    The incident light consists of two spatiotemporal beams of opposite chirping interact- ing with the two-level quantum dot by the induced dipole moment.We have adopted a semi-classical treatment of light-matter interaction where the field is classical, and the energy levels of QD are discrete. The excitation and de-excitation of two beams which couple the s...

    work page

  2. [2]

    pulsearea.dat

    that the energies of the dressed states remain parallel to each other long before and after the interaction with a pulsed laser. Only during the pulse interaction time, the states are in the superposition of the bare states. Therefore, in this case, the population completely return to its initial state, which is the no- crossing scenario of adiabatic evol...

    work page

  3. [3]

    qd_60_c.dat

    Other parameters are the same as in Fig. 3. f’s focal length is 3.7mm., the wavevector k = 2 π n/λ. We take the refractive index of the gallium phosphide (GaP) solid emersion lens, n = 3.5, and wavelength of the laser λ = 940 nm. The spatial extent of the beam before focusing on a lens is taken as σ = 1.2 mm. So, the characteristic length l becomes 131.86...

    work page

  4. [4]

    The central peak develops due to the population presence in the ex- cited state at the center x/l = 0, where the intensity of the LG beam becomes zero

    The flat top portion of the SG beam, which exists between the spatial range x/l = ± 1, takes all population from the ground state to the excited state. The central peak develops due to the population presence in the ex- cited state at the center x/l = 0, where the intensity of the LG beam becomes zero. This is true for taking the orbital angular momentum i...

    work page

  5. [5]

    in Eq. ( 2b). This point singularity is the key to achieving sharp reso- lution at the QD center. The intensity peaks of the LG beam appear at x/l = ± 1, leading to stimulated emission from the excited state to the ground state. Subsequently, a dip is observed in the excited state population ρ11 as shown in the inset of Fig

    work page

  6. [6]

    By increasing the LG beam’s intensity, the spatial distribu- tion of the excited state population at x/l = ± 1 goes to zero very sharply

    The central peak accom- panied by shallow dips gives rise to a larger FWHM. By increasing the LG beam’s intensity, the spatial distribu- tion of the excited state population at x/l = ± 1 goes to zero very sharply. Hence, the inset of Fig. 7 reveals the reason behind the narrow spot size formation, which can be made possible by the doughnut beam-assisted c...

    work page

  7. [7]

    Increasing the intensity of the LG beam’s spatiotemporal envelope reduces the central spot intensity, enhancing and shifting the side peak intensities to a larger spatial extent

    This has the lowest side peak for Ω 0 G = 4.0γn and Ω 0 D = 10.4γn. Increasing the intensity of the LG beam’s spatiotemporal envelope reduces the central spot intensity, enhancing and shifting the side peak intensities to a larger spatial extent. This procedure leads to more residual ground state population transfer to the excited state. All the solid lin...

    work page

  8. [8]

    Thus there is a sharp rise of the side peak (red dotted line)

    As the intensity of the SG beam surpasses the intensity of the LG beam, even though much of the population transfer to the excited state, the excited state population partially returns to the ground state. Thus there is a sharp rise of the side peak (red dotted line). All the dashed lines in Fig. 8 sug- gest the scenario where the SG beam intensity is var...

    work page

  9. [9]

    Abbe, Archiv f¨ ur Mikroskopische Anatomie 9, 413 (1873)

    E. Abbe, Archiv f¨ ur Mikroskopische Anatomie 9, 413 (1873)

    work page

  10. [10]

    K¨ ohler, Opt

    H. K¨ ohler, Opt. Acta 28, 1691 (1981)

    work page 1981

  11. [11]

    T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bow- man, and R. R. McLeod, Science 324, 913 (2009)

    work page 2009

  12. [12]

    T. L. Andrew, H.-Y. Tsai, and R. Menon, Science 324, 917 (2009)

    work page 2009

  13. [13]

    S. W. Hell, Nature Biotechnology 21, 1347 (2003)

    work page 2003

  14. [14]

    S. W. Hell, Science 316, 1153 (2007)

    work page 2007

  15. [15]

    S. W. Hell and J. Wichmann, Opt. Lett. 19, 780 (1994)

    work page 1994

  16. [16]

    M¨ uller, C

    T. M¨ uller, C. Schumann, and A. Kraegeloh, ChemPhysChem 13, 1986 (2012)

    work page 1986

  17. [17]

    Weisenburger and V

    S. Weisenburger and V. Sandoghdar, Contemporary Physics 56, 123 (2015)

    work page 2015

  18. [18]

    Balzarotti, Y

    F. Balzarotti, Y. Eilers, K. C. Gwosch, A. H. Gynn ˚ a, V. Westphal, F. D. Stefani, J. Elf, and S. W. Hell, Science 355, 606 (2017)

    work page 2017

  19. [19]

    Kaldewey, A

    T. Kaldewey, A. V. Kuhlmann, S. R. Valentin, A. Ludwig, A. D. Wieck, and R. J. Warburton, Nature Photonics 12, 68 (2018)

    work page 2018

  20. [20]

    Malinovsky and J

    V. Malinovsky and J. Krause, Eur. Phys. J. D 14, 147 (2001)

    work page 2001

  21. [21]

    J. S. Melinger, S. R. Gandhi, A. Hari- haran, D. Goswami, and W. S. Warren, The Journal of Chemical Physics 101, 6439 (1994)

    work page 1994

  22. [22]

    E. R. Schmidgall, P. R. Eastham, and R. T. Phillips, Phys. Rev. B 81, 195306 (2010)

    work page 2010

  23. [23]

    Herbers, Y

    S. Herbers, Y. M. Caris, S. E. J. Kuijpers, J.- U. Grabow, and S. Y. T. van de Meerakker, Molecular Physics , e2129105 (2022)

    work page 2022

  24. [24]

    Ramachandran, J

    A. Ramachandran, J. Fraser-Leach, S. O’Neal, D. G. Deppe, and K. C. Hall, Opt. Express 29, 41766 (2021)

    work page 2021

  25. [25]

    A. J. Ramsay, A. V. Gopal, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, Phys. Rev. Lett. 104, 017402 (2010)

    work page 2010

  26. [26]

    A. J. Ramsay, T. M. Godden, S. J. Boyle, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, Phys. Rev. Lett. 105, 177402 (2010)

    work page 2010

  27. [27]

    Machnikowski and L

    P. Machnikowski and L. Jacak, Phys. Rev. B 69, 193302 (2004)

    work page 2004

  28. [28]

    Kr¨ ugel, V

    A. Kr¨ ugel, V. M. Axt, T. Kuhn, P. Machnikowski, and A. Vagov, Applied Physics B 81, 897 (2005)

    work page 2005

  29. [29]

    Vagov, M

    A. Vagov, M. D. Croitoru, V. M. Axt, T. Kuhn, and F. M. Peeters, Phys. Rev. Lett. 98, 227403 (2007)

    work page 2007

  30. [30]

    Nazir, Phys

    A. Nazir, Phys. Rev. B 78, 153309 (2008)

    work page 2008

  31. [31]

    Krummheuer, V

    B. Krummheuer, V. M. Axt, and T. Kuhn, Phys. Rev. B 65, 195313 (2002)

    work page 2002

  32. [32]

    Vagov, V

    A. Vagov, V. M. Axt, and T. Kuhn, Phys. Rev. B 66, 165312 (2002)

    work page 2002

  33. [33]

    Grodecka, C

    A. Grodecka, C. Weber, P. Machnikowski, and A. Knorr, Phys. Rev. B 76, 205305 (2007)

    work page 2007

  34. [34]

    E. M. Gauger, A. Nazir, S. C. Ben- jamin, T. M. Stace, and B. W. Lovett, New Journal of Physics 10, 073016 (2008)

    work page 2008

  35. [35]

    Alicki, M

    R. Alicki, M. Horodecki, P. Horodecki, R. Horodecki, L. Jacak, and P. Machnikowski, Phys. Rev. A 70, 010501 (2004)

    work page 2004

  36. [36]

    Mogilevtsev, A

    D. Mogilevtsev, A. P. Nisovtsev, S. Kilin, S. B. Cavalcanti, H. S. Brandi, and L. E. Oliveira, Phys. Rev. Lett. 100, 017401 (2008)

    work page 2008

  37. [37]

    F¨ orstner, C

    J. F¨ orstner, C. Weber, J. Danckwerts, and A. Knorr, Phys. Rev. Lett. 91, 127401 (2003)

    work page 2003

  38. [38]

    Kr¨ ugel, V

    A. Kr¨ ugel, V. M. Axt, and T. Kuhn, Phys. Rev. B 73, 035302 (2006)

    work page 2006

  39. [39]

    H. M. Gil, T. W. Price, K. Chelani, J.-S. G. Bouillard, S. D. Calaminus, and G. J. Stasiuk, iScience 24, 102189 (2021)

    work page 2021

  40. [40]

    C. T. Matea, T. Mocan, F. Tabaran, T. Pop, O. Mosteanu, C. Puia, C. Iancu, and L. Mocan, International Journal of Nanomedicine 12, 5421 (2017)

    work page 2017

  41. [41]

    S. K. Hazra, P. K. Pathak, and T. N. Dey, Phys. Rev. B 107, 235409 (2023)

    work page 2023

  42. [42]

    D. P. DiVincenzo, Science 270, 255 (1995)

    work page 1995

  43. [43]

    E. F. et al., Science 292, 472 (2001)

    work page 2001

  44. [44]

    P. M. et al., Science 290, 2282 (2000)

    work page 2000

  45. [45]

    R. M. S. et al, Nature 439, 179 (2006)

    work page 2006

  46. [46]

    P. R. Eastham and R. T. Phillips, Phys. Rev. B 79, 165303 (2009)

    work page 2009

  47. [47]

    B. W. Shore, M. V. Gromovyy, L. P. Yatsenko, and V. I. Romanenko, American Journal of Physics 77, 1183 (2009)

    work page 2009

  48. [48]

    Zhang, A

    W. Zhang, A. Noa, K. Nienhaus, L. Hilbert, and G. U. Nienhaus, Journal of Physics D: Applied Physics 52, 414001 (2019)

    work page 2019

  49. [49]

    W. Jahr, P. Velicky, and J. G. Danzl, Methods 174, 27 (2020)

    work page 2020

  50. [50]

    Roy and S

    C. Roy and S. Hughes, Phys. Rev. Lett. 106, 247403 (2011)

    work page 2011

  51. [51]

    S. M. Ulrich, S. Ates, S. Reitzenstein, A. L¨ offler, A. Forchel, and P. Michler, Phys. Rev. Lett. 106, 247402 (2011)

    work page 2011

  52. [52]

    Besombes, K

    L. Besombes, K. Kheng, L. Marsal, and H. Mariette, Phys. Rev. B 63, 155307 (2001)

    work page 2001

  53. [53]

    Stock, M.-R

    E. Stock, M.-R. Dachner, T. Warming, A. Schliwa, A. Lochmann, A. Hoffmann, A. I. Toropov, A. K. Bakarov, I. A. Derebezov, M. Richter, V. A. Haisler, A. Knorr, and D. Bimberg, Phys. Rev. B 83, 041304 (2011)

    work page 2011

  54. [54]

    Thoma, P

    A. Thoma, P. Schnauber, M. Gschrey, M. Seifried, J. Wolters, J.-H. Schulze, A. Strittmatter, S. Rodt, A. Carmele, A. Knorr, T. Heindel, and S. Reitzenstein, Phys. Rev. Lett. 116, 033601 (2016)

    work page 2016

  55. [55]

    Iles-Smith, D

    J. Iles-Smith, D. P. S. McCutcheon, A. Nazir, and J. Mørk, Nature Photonics 11, 521 (2017)

    work page 2017

  56. [56]

    L¨ uker, K

    S. L¨ uker, K. Gawarecki, D. E. Reiter, A. Grodecka- Grad, V. M. Axt, P. Machnikowski, and T. Kuhn, Phys. Rev. B 85, 121302 (2012)

    work page 2012

  57. [57]

    Debnath, C

    A. Debnath, C. Meier, B. Chatel, and T. Amand, Phys. Rev. B 86, 161304 (2012)

    work page 2012

  58. [58]

    Mathew, E

    R. Mathew, E. Dilcher, A. Gamouras, A. Ramachandran, H. Y. S. Yang, S. Freisem, D. Deppe, and K. C. Hall, Phys. Rev. B 90, 035316 (2014)

    work page 2014

  59. [59]

    Ardelt, L

    P.-L. Ardelt, L. Hanschke, K. A. Fischer, K. M¨ uller, A. Kleinkauf, M. Koller, A. Bechtold, T. Simmet, J. Wierzbowski, H. Riedl, G. Abstreiter, and J. J. Finley, Phys. Rev. B 90, 241404 (2014)

    work page 2014

  60. [60]

    J. H. Quilter, A. J. Brash, F. Liu, M. Gl¨ assl, A. M. Barth , V. M. Axt, A. J. Ramsay, M. S. Skolnick, and A. M. Fox, Phys. Rev. Lett. 114, 137401 (2015)

    work page 2015

  61. [61]

    Manson, K

    R. Manson, K. Roy-Choudhury, and S. Hughes, Phys. Rev. B 93, 155423 (2016)

    work page 2016

  62. [62]

    D. P. S. McCutcheon and A. Nazir, New Journal of Physics 12, 113042 (2010). 14

    work page 2010

  63. [63]

    Roy and S

    C. Roy and S. Hughes, Phys. Rev. B 85, 115309 (2012)

    work page 2012

  64. [64]

    Ulhaq, S

    A. Ulhaq, S. Weiler, C. Roy, S. M. Ul- rich, M. Jetter, S. Hughes, and P. Michler, Opt. Express 21, 4382 (2013)

    work page 2013

  65. [65]

    Kaldewey, S

    T. Kaldewey, S. L¨ uker, A. V. Kuhlmann, S. R. Valentin, J.-M. Chauveau, A. Ludwig, A. D. Wieck, D. E. Reiter, T. Kuhn, and R. J. Warburton, Phys. Rev. B 95, 241306 (2017)

    work page 2017