Theory of quantum dot cavity-qed
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1 Slide: 1 Theory of quantum dot cavity-qed -- LO-phonon induced cavity feeding and antibunching of thermal radiation -- Alexander Carmele, Julia Kabuss, Marten Richter, Andreas Knorr, and Weng W. Chow
2 OUTLINE Slide: 2 I: Introduction and Motivation II: Mathematical induction method III: Application: LO-phonon induced cavity feeding IV: Application: LO-phonon induced antibunching V: Conclusion
3 Jaynes-Cummings model Slide: 3 Cavity-QED with an atom, solved by the Jaynes-Cummings model 1 : Isolated two-level system (no losses) One-electron assumption One interaction: electron-light The simplest fully quantized model of interest (J.H. Eberly) 1 E. Jaynes and F. Cummings, Proc.IEEE 51, 89 (1963)
4 Jaynes-Cummings model Slide: 4 Cavity-QED with an atom, solved by the Jaynes-Cummings model 1 : Isolated two-level system (no losses) One-electron assumption One interaction: electron-light The simplest fully quantized model of interest (J.H. Eberly) analytically solvable, e.g. ha y ca c i(t) = cos 2 (M p N + 1 t) 1 E. Jaynes and F. Cummings, Proc.IEEE 51, 89 (1963)
5 Semiconductor nanostructures for device fabrication Slide: 5 Advantageous semiconductor QD properties for future technological applications in microcavity systems: Fixed emitter position, Cavity-emitter system ultra-small, tailorable coupling strength and optical properties Semiconductor QD cavity-qed: Theoretical simulations for device optimization are desirable BUT: more interactions need to be considered
6 Sanvitto et al., Appl.Phys.Lett. 86 (2005) Theory of quantum dot cavity-qed: Marquez et al., Appl.Phys.Lett. 78 (2001) Semiconductor QD cavity-qed Hamiltonian Slide: 6 QD, assumed as a 2-level system with one electron, interacts with the cavity photons, bulk LO-phonons, a classical pump field
7 Solving LO-phonon QD cavity-qed without factorization Slide: 7 for every possible combination of phonon, photon, and electron operators:
8 Solving LO-phonon QD cavity-qed without factorization Slide: 8 for every possible combination of phonon, photon, and electron operators: Using product rule for operators: and generalized commutation relations:
9 Solving LO-phonon QD cavity-qed without factorization Slide: 9 for every possible combination of phonon, photon, and electron operators: Using product rule for operators: and generalized commutation relations: their dynamics can be calculated:
10 General set of equations of motion Slide: 10 For example, in the case of LO-phonon assisted vacuum Rabi oscillations ( = 0 ) : E00 11 E20 00 E10 00 E00 00 E01 00 E02 00 T T T T T P ps 00 = hcyp c s i Phonon interaction: Photon interaction: P P E T P numerically solvable up to arbitrary accuracy, reproducing analytical solutions of the IBM and JCM
11 Slide: 11 LO-phonon induced cavity feeding
12 LO-phonon QD cavity-qed: additional anti-crossings Slide: 12 Probing with δ-pulse at 300K: 1 in preparation (2011)
13 Modified Rabi frequency due to phonon cavity feeding Slide: 13 Modified Rabi frequency 1 at the Stokes-position (2), assuming an excited QD and no cavity photon (vacuum Rabi oscillations): 3K 300K (i) Temperature dependence of frequency weak, but affects amplitude strongly (ii) Rabi frequency now determined by the LO-phonon coupling strength, also 1 in preparation (2011)
14 Modified Rabi frequency analytical expression Slide: 14 Modified Rabi frequency at the Stokes-position (2), assuming an excited QD and no cavity photon (vacuum Rabi oscillations):
15 Modified Rabi frequency analytical expression Slide: 15 Modified Rabi frequency at the Stokes-position (2), assuming an excited QD and no cavity photon (vacuum Rabi oscillations):
16 Modified Rabi frequency analytical expression Slide: 16 Modified Rabi frequency at the Stokes-position (2), assuming an excited QD and no cavity photon (vacuum Rabi oscillations):
17 Modified Rabi frequency analytical expression Slide: 17 Modified Rabi frequency at the Stokes-position (2), assuming an excited QD and no cavity photon (vacuum Rabi oscillations):
18 Slide: 18 LO-phonon enhanced anti-bunching
19 Quantum beating at resonance position Slide: 19 Quantum beating at resonance position (1): Vacuum Rabi oscillations: Thermal state: for a cavity field, prepared initially in the thermal state Impact small on Rabi oscillations
20 Quantum beating at resonance position Slide: 20 Quantum beating at resonance position (1): Intensity-intensity correlation function: Thermal state: for a cavity field, prepared initially in the thermal state Impact strong on correlation function:
21 LO-phonon enhances quantum optical features Slide: 21 Impact on intensity-intensity correlation function mean value: Thermal state: Cavity field is transformed into a nonclassical field via LO-phonon interaction 1 Semiconductor environment enforces non-classical light features 1 PRL 104, (2010)
22 Applications of the mathematical induction method Slide: 22 Systems, for which the induction method is successfully applied: 1. QD as a two-level system with one-electron (photon statistics) 1 2. QD as a three-level system (quantum coherence) 2 3. QD as a four-level system with two electrons (biexciton cascade) 3 1 PRL 104, (2010) 2 PSSB, accepted (2010) 3 PRB 81, (2010)
23 Conclusions Slide: 23 Systems, for which the induction method is successfully applied: 1. QD as a two-level system with one-electron (photon statistics) 1 2. QD as a three-level system (quantum coherence) 2 3. QD as a four-level system with two electrons (biexciton cascade) 3 Thank you for your attention!! 1 PRL 104, (2010) 2 PSSB, accepted (2010) 3 PRB 81, (2010)
24 Slide: 24 Theory for strongly coupled quantum dot cavity quantum electrodynamics -- Photon statistics and phonon signatures in quantum light emission --
25 Slide: 25
26 PPCE: general canonical statistical operator Slide: 26
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