3589:
3012:
3584:{\displaystyle {\begin{aligned}\mathrm {i} \hbar {\frac {\partial }{\partial t}}c_{\mathrm {X} }^{\mathbf {k} ,\mathbf {k'} }=&\left({\tilde {\epsilon }}_{\mathbf {k} }-{\tilde {\epsilon }}_{\mathbf {k'} }\right)\,c_{\mathrm {X} }^{\mathbf {k} ,\mathbf {k'} }+S_{\mathrm {X} }^{\mathbf {k} ,\mathbf {k'} }\\&+{\Bigl (}1-f_{\mathbf {k'} }^{e}-f_{\mathbf {k'} }^{h}{\Bigr )}\sum _{\mathbf {l} }V_{\mathbf {l} -\mathbf {k} '}\,c_{\mathrm {X} }^{\mathbf {k} ,\mathbf {l} }-{\Bigl (}1-f_{\mathbf {k} }^{e}-f_{\mathbf {k} }^{h}{\Bigr )}\sum _{\mathbf {l} }V_{\mathbf {l} -\mathbf {k} '}\,c_{\mathrm {X} }^{\mathbf {l} ,\mathbf {k'} }\\&+D_{\mathrm {X,\,rest} }^{\mathbf {k} ,\mathbf {k'} }+T_{\mathrm {X} }^{\mathbf {k} ,\mathbf {k'} }\,.\end{aligned}}}
1341:
1688:
3969:
2634:
1358:
1045:
4013:
equally well originate from an electron–hole plasma or the presence of excitons. At first, this consequence of SLEs seems counterintuitive because in few-particle picture an unbound electron–hole pair cannot recombine and release energy corresponding to the exciton resonance because that energy is well below the energy an unbound electron–hole pair possesses.
2991:
2446:
2302:
572:
2459:
4183:
Semiconductors also can show several resonances well below the fundamental exciton resonance when phonon-assisted electron–hole recombination takes place. These processes are describable by three-particle correlations (or higher) where photon, electron–hole pair, and a lattice vibration, i.e., a
4012:
shows a discrete set of exciton resonances regardless which many-body state initiated the emission through the spontaneous-emission source. These resonances are directly transferred to excitonic peaks in the luminescence itself. This yields an unexpected consequence; the excitonic resonance can
1683:{\displaystyle \mathrm {i} \hbar {\frac {\partial }{\partial t}}\Pi _{\mathbf {k} ,\omega }=\left({\tilde {\epsilon }}_{\mathbf {k} }-\hbar \omega \right)\Pi _{\mathbf {k} ,\omega }+\Omega _{\mathbf {k} ,\omega }^{\mathrm {spont} }-\left(1-f_{\mathbf {k} }^{e}-f_{\mathbf {k} }^{h}\right)\left+T}
4020:
to the exciton resonance. Namely, when a high number of electronic states participate in the emission of a single photon, one can always distribute the energy of initial many-body state between the one photon at exciton energy and remaining many-body state (with one electron–hole pair removed)
1336:{\displaystyle \mathrm {i} \hbar {\frac {\partial }{\partial t}}\Delta \langle {\hat {B}}_{\omega }^{\dagger }{\hat {B}}_{\omega '}\rangle =(\hbar \omega '-\hbar \omega )\,\Delta \langle {\hat {B}}_{\omega }^{\dagger }{\hat {B}}_{\omega '}\rangle +\mathrm {i} \sum \limits _{\mathbf {k} }\left}
2310:
672:
3972:
Buildup of photon-assisted polarization (Î correlation) that is initiated by the spontaneous-emission source. The buildup occurs equally for all momentum states. In a many-body system, a photon (wave arrow) is generated collectively through multiple coupled Î -transition
2107:
4163:
The presented SLEs discussion does not specify the dimensionality or the band structure of the system studied. As one analyses a specified system, one often has to explicitly include the electronic bands involved, the dimensionality of wave vectors, photon, and
2850:
2306:
In its full form, the occupation dynamics also contains
Coulomb-correlation terms. It is straight forward to verify that the photon-assisted recombination destroys as many electron–hole pairs as it creates photons because due to the general conservation law
4184:
phonon, become correlated. The dynamics of phonon-assisted correlations are similar to the phonon-free SLEs. Like for the excitonic luminescence, also excitonic phonon sidebands can equally well be initiated by either electron–hole plasma or excitons.
4504:
Schwab, M.; Kurtze, H.; Auer, T.; Berstermann, T.; Bayer, M.; Wiersig, J.; Baer, N.; Gies, C.; Jahnke, F.; Reithmaier, J.; Forchel, A.; Benyoucef, M.; Michler, P. (2006). "Radiative emission dynamics of quantum dots in a single cavity micropillar".
4400:
Berstermann, T.; Auer, T.; Kurtze, H.; Schwab, M.; Yakovlev, D.; Bayer, M.; Wiersig, J.; Gies, C.; Jahnke, F.; Reuter, D.; Wieck, A. (2007). "Systematic study of carrier correlations in the electron–hole recombination dynamics of quantum dots".
68:
coupling among electronic excitations within a semiconductor. The SLEs are one of the most accurate methods to describe light emission in semiconductors and they are suited for a systematic modeling of semiconductor emission ranging from
4024:
In general, excitonic plasma luminescence explains many nonequilibrium emission properties observed in present-day semiconductor luminescence experiments. In fact, the dominance of excitonic plasma luminescence has been measured in both
4155:
degree of freedom. However, the SLEs often are the only (at low carrier densities) or more convenient (lasing regime) to compute luminescence accurately. Furthermore, the SLEs not only yield a full predictability without the need for
400:
2629:{\displaystyle \Omega _{\mathbf {k} ,\omega }^{\mathrm {spont} }=\mathrm {i} {\mathcal {F}}_{\omega }{\Bigl (}f_{\mathbf {k} }^{e}f_{\mathbf {k} }^{h}+\sum _{\mathbf {k'} }c_{\mathrm {X} }^{\mathbf {k} ,\mathbf {k'} }{\Bigr )}\,.}
4258:
4671:
Aßmann, M.; Veit, F.; Bayer, M.; Gies, C.; Jahnke, F.; Reitzenstein, S.; Höfling, S.; Worschech, L. et al. (2010). "Ultrafast tracking of second-order photon correlations in the emission of quantum-dot microresonator lasers".
3723:
Microscopically, the luminescence processes are initiated whenever the semiconductor is excited because at least the electron and hole distributions, that enter the spontaneous-emission source, are nonvanishing. As a result,
961:
3664:
2100:
321:
3713:
2830:
2781:
3776:
1873:
4562:
Rubel, O.; Baranovskii, S. D.; Hantke, K.; Heber, J. D.; Koch, J.; Thomas, P. V.; Marshall, J. M.; Stolz, W. et al. (2005). "On the theoretical description of luminescence in disordered quantum structures".
4420:
Shuvayev, V.; Kuskovsky, I.; Deych, L.; Gu, Y.; Gong, Y.; Neumark, G.; Tamargo, M.; Lisyansky, A. (2009). "Dynamics of the radiative recombination in cylindrical nanostructures with type-II band alignment".
2999:
because then spontaneously emitted light can return to the emitter (i.e., the semiconductor), either stimulating or inhibiting further spontaneous-emission processes. This term is also responsible for the
4021:
without violating the energy conservation. The
Coulomb interaction mediates such energy rearrangements very efficiently. A thorough analysis of energy and many-body state rearrangement is given in Ref.
2441:{\displaystyle {\frac {\partial }{\partial t}}\sum _{\omega }\langle {\hat {B}}_{\omega }^{\dagger }{\hat {B}}_{\omega }\rangle =-{\frac {\partial }{\partial t}}\sum _{\mathbf {k} }f_{\mathbf {k} }^{e}}
2688:
2297:{\displaystyle \left.{\frac {\partial }{\partial t}}f_{\mathbf {k} }^{e}\right|_{\mathrm {L} }=\left.{\frac {\partial }{\partial t}}f_{\mathbf {k} }^{h}\right|_{\mathrm {L} }=-2\,\mathrm {Re} \left\,.}
585:
4135:, its dynamics is driven spontaneously, and it is directly coupled to three-particle correlations. Technically, the SLEs are more difficult to solve numerically than the SBEs due to the additional
373:
3017:
1916:
1729:
721:
204:
2986:{\displaystyle \Delta \Omega _{\omega }^{\mathrm {stim} }=\mathrm {i} \sum _{\omega '}{\mathcal {F}}_{\omega '}\,\Delta \langle {\hat {B}}_{\omega }^{\dagger }{\hat {B}}_{\omega '}\rangle }
4113:
4078:
4010:
3951:
3894:
3837:
2022:
902:
820:
785:
996:
3918:
values, the characteristic transition energy follows from the exciton energy, not the bare kinetic energy of an electron–hole pair. More mathematically, the homogeneous part of the
3597:-type in- and out-scattering of two electrons and two holes due to the Coulomb interaction. The second line contains the main Coulomb sums that correlate electron–hole pairs into
1987:
1953:
240:
1778:
3916:
3859:
3802:
2732:
2710:
743:
2712:
when electrons and holes are uncorrelated, i.e., plasma. Such form is to be expected for a probability of two uncorrelated events to occur simultaneously at a desired
4579:
Imhof, S.; Bückers, C.; Thränhardt, A.; Hader, J.; Moloney, J. V.; Koch, S. W. (2008). "Microscopic theory of the optical properties of Ga(AsBi)/GaAs quantum wells".
4378:
Li, Jianzhong (2007). "Laser cooling of semiconductor quantum wells: Theoretical framework and strategy for deep optical refrigeration by luminescence upconversion".
4153:
4133:
867:
847:
157:
4543:
Hader, J.; Hardesty, G.; Wang, T.; Yarborough, M. J.; Kaneda, Y.; Moloney, J. V.; Kunert, B.; Stolz, W. et al. (2010). "Predictive
Microscopic Modeling of VECSELs".
2836:
via their mutual
Coulomb attraction. Nevertheless, both the presence of electron–hole plasma and excitons can equivalently induce the spontaneous-emission source.
4485:; Gibbs, H.; Hoyer, W.; Kira, M.; Koch, S.; Prineas, J.; Stolz, H. (2004). "Excitonic Photoluminescence in Semiconductor Quantum Wells: Plasma versus Excitons".
567:{\displaystyle \mathrm {L} (\omega )={\frac {\partial }{\partial t}}\langle {\hat {B}}_{\omega }^{\dagger }{\hat {B}}_{\omega }\rangle =2\,\mathrm {Re} \left\,.}
1807:
260:
4652:
Gies, Christopher; Wiersig, Jan; Jahnke, Frank (2008). "Output
Characteristics of Pulsed and Continuous-Wave-Excited Quantum-Dot Microcavity Lasers".
4194:
907:
4277:
4160:
approximations but they also can be used as a systematic starting point for more general investigations such as laser design and disorder studies.
3593:
The first line contains the
Coulomb-renormalized kinetic energy of electron–hole pairs and the second line defines a source that results from a
2035:
787:
determines the corresponding electron–hole recombination operator defining also the microscopic polarization within semiconductor. Therefore,
331:
265:
49:
3961:
not the free-carrier energies. For low electron–hole densities, the
Wannier equation produces a set of bound eigenstates which define the
3604:
163:
4524:
Hader, J.; Moloney, J. V.; Koch, S. W. (2006). "Influence of internal fields on gain and spontaneous emission in InGaN quantum wells".
3727:
1824:
4800:
4781:
4762:
4743:
4724:
4705:
4366:
3669:
2786:
2737:
3601:
whenever the excitation conditions are suitable. The remaining two- and three-particle correlations are presented symbolically by
1732:
667:{\displaystyle \Pi _{\mathbf {k} ,\omega }\equiv \Delta \langle {\hat {B}}_{\omega }^{\dagger }{\hat {P}}_{\mathbf {k} }\rangle }
131:
that fully includes many-body interactions, quantized light field, and quantized light–matter interaction. Like almost always in
2641:
4819:
4633:
Böttge, C. N.; Kira, M.; Koch, S. W. (2012). "Enhancement of the phonon-sideband luminescence in semiconductor microcavities".
4595:
Feldtmann, T.; Schneebeli, L.; Kira, M.; Koch, S. (2006). "Quantum theory of light emission from a semiconductor quantum dot".
128:
104:
1023:
4042:
1744:
376:
336:
4325:; Gibbs, H. (1997). "Quantum Theory of Nonlinear Semiconductor Microcavity Luminescence Explaining "Boser" Experiments".
1878:
1696:
1346:
whose diagonal form reduces to the luminescence formula above. The dynamics of photon-assisted correlations follows from
4462:
Kira, M.; Jahnke, F.; Koch, S. (1998). "Microscopic Theory of
Excitonic Signatures in Semiconductor Photoluminescence".
4292:
4265:
3958:
112:
679:
4165:
168:
4302:
4282:
964:
4260:, and then continues toward higher-order photon-correlation effects. This approach can be applied to analyze the
4188:
1810:
61:
4083:
4048:
3980:
3921:
3864:
3807:
1992:
1736:
872:
790:
1814:
752:
85:
4033:
systems. Only when excitons are present abundantly, the role of excitonic plasma luminescence can be ignored.
2025:
970:
2734:
value. The possibility to have truly correlated electron–hole pairs is defined by a two-particle correlation
4824:
4451:
4443:
Kira, M.; Koch, S.W. (2006). "Many-body correlations and excitonic effects in semiconductor spectroscopy".
2029:
4614:
Baer, N.; Gies, C.; Wiersig, J.; Jahnke, F. (2006). "Luminescence of a semiconductor quantum dot system".
4261:
4157:
3594:
1958:
1924:
1003:
999:
209:
89:
388:
4660:
2995:
that is particularly important when describing spontaneous emission in semiconductor microcavities and
1754:
4493:
108:
57:
17:
2841:
380:
136:
97:
81:
3899:
3842:
3785:
2715:
2693:
726:
4470:
4333:
1751:
photon-assisted polarizations are coupled with each other via the unscreened
Coulomb-interaction
2451:
Besides the terms already described above, the photon-assisted polarization dynamics contains a
4680:
4641:
4622:
4603:
4513:
4429:
4409:
4386:
3007:
To complete the SLEs, one must additionally solve the quantum dynamics of exciton correlations
4796:
4777:
4758:
4739:
4720:
4701:
4362:
4287:
2102:. These occupations are changed by spontaneous recombination of electrons and holes, yielding
4138:
4118:
852:
832:
142:
4016:
However, the excitonic plasma luminescence is a genuine many-body effect where plasma emits
132:
65:
4551:
1921:
The excitation level of a semiconductor is characterized by electron and hole occupations,
4482:
4322:
4297:
3968:
2783:; the corresponding probability is directly proportional to the correlation. In practice,
1027:
93:
2839:
As the semiconductor emits light spontaneously, the luminescence is further altered by a
4080:
are compared with the microscopic polarization within the SBEs. As the main difference,
64:
because the SLEs simultaneously includes the quantized light–matter interaction and the
3001:
1783:
245:
116:
4813:
746:
53:
45:
4173:
4169:
4026:
1030:. More specifically, a systematic derivation produces a set of equations involving
1011:
384:
41:
1780:. The three-particle correlations that appear are indicated symbolically via the
103:
light. At this level, one is often interested to control and access higher-order
4253:{\displaystyle \Delta \langle {\hat {B}}_{\omega }{\hat {B}}_{\omega '}\rangle }
4177:
4030:
3954:
1007:
1817:
of
Coulomb interaction, and additional highly correlated contributions such as
956:{\displaystyle \langle {\hat {B}}_{\omega }^{\dagger }P_{\mathbf {k} }\rangle }
4532:
111:. Such investigations are the basis of realizing and developing the field of
4736:
Quantum Theory of the Optical and Electronic Properties of Semiconductors
4191:. As a first step, one also includes two-photon absorption correlations,
2833:
2095:{\displaystyle \left(1-f_{\mathbf {k} }^{e}-f_{\mathbf {k} }^{h}\right)}
1743:. The Coulomb renormalization are identical to those that appear in the
829:
Many electron–hole pairs contribute to the photon emission at frequency
262:
signifies the operator nature of the quantity. The operator-combination
3962:
3598:
70:
3779:
2996:
324:
316:{\displaystyle {\hat {B}}_{\omega }^{\dagger }\,{\hat {B}}_{\omega }}
3659:{\displaystyle D_{\mathrm {X,\,rest} }^{\mathbf {k} ,\mathbf {k'} }}
88:
whereas the extensions of the SLEs include the possibility to study
107:
effects, distinct many-body states, as well as light–semiconductor
4321:
Kira, M.; Jahnke, F.; Koch, S.; Berger, J.; Wick, D.; Nelson, T.;
1740:
160:
100:
74:
3771:{\displaystyle \Omega _{\mathbf {k} ,\omega }^{\mathrm {spont} }}
1868:{\displaystyle \Omega _{\mathbf {k} ,\omega }^{\mathrm {spont} }}
392:
3804:
values that correspond to the excited states. This means that
2690:
describes the probability to find electron and hole with same
576:
As a result, the luminescence becomes directly generated by a
4187:
The SLEs can also be used as a systematic starting point for
3708:{\displaystyle T_{\mathrm {X} }^{\mathbf {k} ,\mathbf {k'} }}
2825:{\displaystyle c_{\mathrm {X} }^{\mathbf {k} ,\mathbf {k'} }}
2776:{\displaystyle c_{\mathrm {X} }^{\mathbf {k} ,\mathbf {k'} }}
2909:
2511:
2250:
1289:
1244:
977:
520:
2166:
2113:
2683:{\displaystyle f_{\mathbf {k} }^{e}\,f_{\mathbf {k} }^{h}}
904:
denotes that the correlated part of the expectation value
60:
light. This description established the first step toward
395:
is proportional to the temporal change in photon number,
4755:
Nitride Semiconductor Devices: Principles and Simulation
139:. For example, a light field corresponding to frequency
29:
Physical equations of light emission in semiconductors
4396:
4394:
4197:
4141:
4121:
4086:
4051:
3983:
3924:
3902:
3867:
3845:
3810:
3788:
3730:
3672:
3607:
3015:
2853:
2789:
2740:
2718:
2696:
2644:
2462:
2313:
2110:
2038:
1995:
1961:
1927:
1881:
1827:
1821:. The explicit form of a spontaneous-emission source
1786:
1757:
1699:
1361:
1048:
973:
910:
875:
855:
835:
793:
755:
729:
682:
588:
403:
339:
268:
248:
212:
171:
145:
2832:
becomes large when electron–hole pairs are bound as
368:{\displaystyle \langle {\hat {B}}_{\omega }\rangle }
1911:{\displaystyle \Omega _{\omega }^{\mathrm {stim} }}
1724:{\displaystyle {\tilde {\epsilon }}_{\mathbf {k} }}
4252:
4147:
4127:
4107:
4072:
4004:
3945:
3910:
3888:
3853:
3831:
3796:
3770:
3707:
3658:
3583:
2985:
2824:
2775:
2726:
2704:
2682:
2628:
2440:
2296:
2094:
2016:
1981:
1947:
1910:
1867:
1801:
1772:
1723:
1682:
1335:
990:
955:
896:
861:
841:
814:
779:
737:
715:
666:
566:
367:
315:
254:
234:
198:
151:
4793:Optics of Semiconductors and Their Nanostructures
3405:
3355:
3280:
3220:
2617:
2524:
716:{\displaystyle ({\hat {B}}_{\omega }^{\dagger })}
676:that describes a correlated emission of a photon
4698:Quantum Optics with Semiconductor Nanostructures
4168:. Many explicit examples are given in Refs. for
127:The derivation of the SLEs starts from a system
4738:(5th ed.). World Scientific. p. 216.
199:{\displaystyle {\hat {B}}_{\omega }^{\dagger }}
4439:
4437:
3861:values. Since the Coulomb interaction couples
387:(L). (This is the underlying principle behind
383:light spontaneously, commonly referred to as
8:
4247:
4201:
2980:
2929:
2385:
2339:
1213:
1162:
1126:
1075:
1026:needed to compute the luminescence spectrum
950:
911:
661:
613:
482:
436:
362:
340:
4108:{\displaystyle \Pi _{\omega ,\mathbf {k} }}
4073:{\displaystyle \Pi _{\omega ,\mathbf {k} }}
4005:{\displaystyle \Pi _{\omega ,\mathbf {k} }}
3946:{\displaystyle \Pi _{\omega ,\mathbf {k} }}
3889:{\displaystyle \Pi _{\omega ,\mathbf {k} }}
3832:{\displaystyle \Pi _{\omega ,\mathbf {k} }}
2017:{\displaystyle \Pi _{\mathbf {k} ,\omega }}
1733:Coulomb-renormalized single-particle energy
897:{\displaystyle \Pi _{\mathbf {k} ,\omega }}
815:{\displaystyle \Pi _{\mathbf {k} ,\omega }}
578:photon-assisted electron–hole recombination
4264:effects and to realize and understand the
4757:. Wiley-VCH Verlag GmbH \& Co. KGaA.
4353:
4351:
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4347:
4345:
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4206:
4205:
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4098:
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4085:
4063:
4056:
4050:
3995:
3988:
3982:
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3929:
3923:
3903:
3901:
3879:
3872:
3866:
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3844:
3822:
3815:
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3736:
3735:
3729:
3693:
3685:
3684:
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3671:
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3636:
3635:
3620:
3613:
3612:
3606:
3573:
3561:
3553:
3552:
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3545:
3526:
3518:
3517:
3502:
3495:
3494:
3468:
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3436:
3427:
3426:
3415:
3414:
3404:
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3397:
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3390:
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3343:
3335:
3334:
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3290:
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3111:
3110:
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3028:
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3016:
3014:
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2925:
2914:
2908:
2907:
2895:
2886:
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2810:
2802:
2801:
2795:
2794:
2788:
2761:
2753:
2752:
2746:
2745:
2739:
2719:
2717:
2697:
2695:
2674:
2668:
2667:
2662:
2656:
2650:
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2622:
2616:
2615:
2603:
2595:
2594:
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2533:
2523:
2522:
2516:
2510:
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2503:
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2432:
2426:
2425:
2414:
2413:
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2367:
2360:
2355:
2344:
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2333:
2314:
2312:
2290:
2272:
2271:
2266:
2260:
2255:
2249:
2248:
2241:
2224:
2223:
2207:
2206:
2195:
2189:
2188:
2169:
2154:
2153:
2142:
2136:
2135:
2116:
2109:
2081:
2075:
2074:
2061:
2055:
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2037:
2001:
2000:
1994:
1973:
1967:
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1932:
1926:
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1880:
1846:
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1826:
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1701:
1698:
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1636:
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1598:
1575:
1574:
1569:
1549:
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1529:
1523:
1522:
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1472:
1471:
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1360:
1322:
1305:
1304:
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1202:
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1190:
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1115:
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1103:
1096:
1091:
1080:
1079:
1057:
1049:
1047:
982:
976:
975:
972:
943:
942:
932:
927:
916:
915:
909:
881:
880:
874:
854:
834:
799:
798:
792:
780:{\displaystyle {\hat {P}}_{\mathbf {k} }}
770:
769:
758:
757:
754:
730:
728:
704:
699:
688:
687:
681:
654:
653:
642:
641:
634:
629:
618:
617:
594:
593:
587:
560:
542:
541:
536:
530:
525:
519:
518:
510:
509:
492:
491:
476:
465:
464:
457:
452:
441:
440:
421:
404:
402:
356:
345:
344:
338:
307:
296:
295:
293:
287:
282:
271:
270:
267:
247:
226:
215:
214:
211:
190:
185:
174:
173:
170:
144:
4278:Coherent effects in semiconductor optics
3967:
991:{\displaystyle {\mathcal {F}}_{\omega }}
4314:
3025:
1435:
1367:
1149:
1135:
1054:
52:of electronic excitations, producing a
3839:is simultaneously generated for many
1024:single- and two-particle correlations
749:, i.e., an electronic vacancy. Here,
330:When the photon coherences, here the
242:, respectively, where the "hat" over
135:, it is most convenient to apply the
7:
4481:Chatterjee, S.; Ell, C.; Mosor, S.;
4452:doi:10.1016/j.pquantelec.2006.12.002
4041:Structurally, the SLEs resemble the
1982:{\displaystyle f_{\mathbf {k} }^{h}}
1948:{\displaystyle f_{\mathbf {k} }^{e}}
1350:Semiconductor luminescence equations
1037:Semiconductor luminescence equations
235:{\displaystyle {\hat {B}}_{\omega }}
34:semiconductor luminescence equations
18:Semiconductor-Luminescence Equations
1595:
1225:
164:creation and annihilation operators
4661:doi:10.1103/PhysRevLett.101.067401
4198:
4088:
4053:
3985:
3926:
3869:
3812:
3782:-assisted processes for all those
3762:
3759:
3756:
3753:
3750:
3732:
3679:
3630:
3627:
3624:
3621:
3614:
3547:
3512:
3509:
3506:
3503:
3496:
3454:
3329:
3182:
3147:
3049:
3034:
3030:
3021:
2926:
2887:
2877:
2874:
2871:
2868:
2858:
2854:
2796:
2747:
2589:
2504:
2494:
2491:
2488:
2485:
2482:
2464:
2400:
2396:
2320:
2316:
2268:
2228:
2225:
2208:
2175:
2171:
2155:
2122:
2118:
1997:
1902:
1899:
1896:
1893:
1883:
1859:
1856:
1853:
1850:
1847:
1829:
1793:
1674:
1638:
1585:
1582:
1579:
1576:
1566:
1498:
1495:
1492:
1489:
1486:
1468:
1447:
1386:
1376:
1372:
1363:
1301:
1266:
1220:
1159:
1072:
1063:
1059:
1050:
1022:In general, the SLEs includes all
877:
856:
795:
723:when an electron with wave vector
610:
590:
538:
496:
493:
427:
423:
405:
391:.) The corresponding luminescence
25:
4494:doi:10.1103/PhysRevLett.92.067402
1040:(photon-number-like correlations)
4791:Kalt, H.; Hetterich, M. (2004).
4099:
4064:
3996:
3937:
3904:
3880:
3847:
3823:
3790:
3737:
3695:
3686:
3646:
3637:
3563:
3554:
3528:
3519:
3470:
3461:
3437:
3428:
3416:
3392:
3372:
3344:
3336:
3312:
3303:
3291:
3263:
3238:
3198:
3189:
3163:
3154:
3125:
3100:
3065:
3056:
2812:
2803:
2763:
2754:
2720:
2698:
2669:
2651:
2605:
2596:
2573:
2552:
2535:
2469:
2427:
2415:
2273:
2190:
2137:
2076:
2056:
2002:
1989:, respectively. They modify the
1968:
1934:
1834:
1818:
1773:{\displaystyle V_{\mathbf {k} }}
1764:
1715:
1644:
1626:
1617:
1601:
1544:
1524:
1473:
1452:
1426:
1391:
1306:
1271:
1230:
944:
882:
800:
771:
731:
655:
595:
543:
511:
375:, vanish and the system becomes
84:, semiconductor luminescence is
4616:The European Physical Journal B
4471:doi:10.1103/PhysRevLett.81.3263
4445:Progress in Quantum Electronics
4334:doi:10.1103/PhysRevLett.79.5170
4166:exciton center-of-mass momentum
4037:Connections and generalizations
3719:Interpretation and consequences
1809:contributions – they introduce
1032:photon-number-like correlations
4734:Haug, H.; Koch, S. W. (2009).
4719:. Cambridge University Press.
4715:Kira, M.; Koch, S. W. (2011).
4681:doi:10.1103/PhysRevB.81.165314
4642:doi:10.1103/PhysRevB.85.094301
4623:doi:10.1140/epjb/e2006-00164-3
4604:doi:10.1103/PhysRevB.73.155319
4514:doi:10.1103/PhysRevB.74.045323
4430:doi:10.1103/PhysRevB.79.115307
4410:doi:10.1103/PhysRevB.76.165318
4387:doi:10.1103/PhysRevB.75.155315
4361:. Cambridge University Press.
4357:Kira, M.; Koch, S. W. (2011).
4230:
4211:
3116:
3092:
2963:
2939:
2373:
2349:
1875:and a stimulated contribution
1796:
1790:
1707:
1693:where the first contribution,
1677:
1671:
1418:
1353:(photon-assisted correlations)
1196:
1172:
1155:
1132:
1109:
1085:
921:
763:
710:
693:
683:
647:
623:
470:
446:
415:
409:
350:
301:
276:
220:
179:
1:
4043:semiconductor Bloch equations
1745:semiconductor Bloch equations
137:second-quantization formalism
4717:Semiconductor Quantum Optics
4552:doi:10.1109/JQE.2009.2035714
4359:Semiconductor Quantum Optics
4293:Quantum-optical spectroscopy
4266:quantum-optical spectroscopy
4189:semiconductor quantum optics
3959:generalized Wannier equation
3911:{\displaystyle \mathbf {k} }
3854:{\displaystyle \mathbf {k} }
3797:{\displaystyle \mathbf {k} }
3778:is finite and it drives the
2727:{\displaystyle \mathbf {k} }
2705:{\displaystyle \mathbf {k} }
1811:excitation-induced dephasing
824:photon-assisted polarization
738:{\displaystyle \mathbf {k} }
113:quantum-optical spectroscopy
62:semiconductor quantum optics
4700:. Woodhead Publishing Ltd.
2453:spontaneous-emission source
1018:Principal structure of SLEs
48:resulting from spontaneous
4841:
4772:Klingshirn, C. F. (2006).
4303:Semiconductor laser theory
4283:Cluster-expansion approach
4176:systems, and in Refs. for
1735:that is determined by the
965:cluster-expansion approach
159:is then described through
4545:IEEE J. Quantum Electron.
963:is constructed using the
82:vacuum-field fluctuations
80:Due to randomness of the
4565:J. Optoelectron. Adv. M.
4115:also has a photon index
3957:that are defined by the
2026:Coulomb renormalizations
1819:phonon-sideband emission
4654:Physical Review Letters
4581:Semicond. Sci. Technol.
4526:Applied Physics Letters
4487:Physical Review Letters
4464:Physical Review Letters
4327:Physical Review Letters
4148:{\displaystyle \omega }
4128:{\displaystyle \omega }
862:{\displaystyle \Delta }
842:{\displaystyle \omega }
152:{\displaystyle \omega }
4820:Semiconductor analysis
4262:resonance fluorescence
4254:
4149:
4129:
4109:
4074:
4006:
3974:
3947:
3912:
3890:
3855:
3833:
3798:
3772:
3709:
3660:
3585:
2987:
2826:
2777:
2728:
2706:
2684:
2630:
2442:
2298:
2096:
2018:
1983:
1949:
1912:
1869:
1803:
1774:
1725:
1684:
1337:
992:
957:
898:
863:
843:
822:can also be viewed as
816:
781:
739:
717:
668:
568:
379:, semiconductors emit
369:
317:
256:
236:
200:
153:
90:resonance fluorescence
4533:doi:10.1063/1.2372443
4255:
4150:
4130:
4110:
4075:
4007:
3971:
3948:
3913:
3891:
3856:
3834:
3799:
3773:
3710:
3661:
3586:
2988:
2827:
2778:
2729:
2707:
2685:
2631:
2443:
2299:
2097:
2030:Pauli-blocking factor
2019:
1984:
1950:
1918:are discussed below.
1913:
1870:
1804:
1775:
1747:(SBEs), showing that
1726:
1685:
1338:
1000:dipole-matrix element
993:
958:
899:
864:
844:
817:
782:
740:
718:
669:
569:
389:light-emitting diodes
370:
318:
257:
237:
201:
154:
115:which is a branch of
58:spontaneously emitted
4774:Semiconductor Optics
4195:
4139:
4119:
4084:
4049:
3981:
3922:
3900:
3865:
3843:
3808:
3786:
3728:
3670:
3605:
3013:
2851:
2787:
2738:
2716:
2694:
2642:
2460:
2311:
2108:
2036:
1993:
1959:
1925:
1879:
1825:
1784:
1755:
1697:
1359:
1046:
1004:interband transition
971:
908:
873:
853:
833:
791:
753:
727:
680:
586:
401:
337:
266:
246:
210:
169:
143:
4753:Piprek, J. (2007).
4696:Jahnke, F. (2012).
3767:
3704:
3655:
3572:
3537:
3479:
3402:
3382:
3349:
3277:
3252:
3207:
3172:
3074:
2955:
2882:
2821:
2772:
2679:
2661:
2614:
2562:
2545:
2499:
2437:
2365:
2265:
2200:
2147:
2086:
2066:
1978:
1944:
1907:
1864:
1590:
1554:
1534:
1503:
1327:
1264:
1188:
1101:
937:
709:
639:
535:
462:
292:
195:
66:Coulomb-interaction
4250:
4145:
4125:
4105:
4070:
4002:
3975:
3943:
3908:
3886:
3851:
3829:
3794:
3768:
3731:
3705:
3673:
3656:
3608:
3581:
3579:
3541:
3490:
3448:
3421:
3386:
3366:
3323:
3296:
3256:
3231:
3176:
3141:
3043:
2983:
2932:
2905:
2857:
2822:
2790:
2773:
2741:
2724:
2702:
2680:
2663:
2645:
2626:
2583:
2582:
2546:
2529:
2463:
2438:
2421:
2420:
2342:
2338:
2294:
2247:
2246:
2184:
2131:
2092:
2070:
2050:
2014:
1979:
1962:
1945:
1928:
1908:
1882:
1865:
1828:
1799:
1770:
1721:
1680:
1610:
1565:
1538:
1518:
1467:
1333:
1300:
1241:
1235:
1165:
1078:
988:
953:
914:
894:
859:
839:
812:
777:
745:recombines with a
735:
713:
686:
664:
616:
564:
517:
516:
439:
365:
327:-number operator.
313:
269:
252:
232:
196:
172:
149:
105:photon-correlation
4674:Physical Review B
4635:Physical Review B
4597:Physical Review B
4507:Physical Review B
4469:(15): 3263–3266.
4423:Physical Review B
4403:Physical Review B
4380:Physical Review B
4332:(25): 5170–5173.
4288:Photoluminescence
4233:
4214:
3410:
3285:
3119:
3095:
3041:
2966:
2942:
2891:
2566:
2409:
2407:
2376:
2352:
2329:
2327:
2237:
2182:
2129:
1802:{\displaystyle T}
1710:
1594:
1421:
1383:
1224:
1199:
1175:
1112:
1088:
1070:
1028:self-consistently
924:
766:
696:
650:
626:
505:
473:
449:
434:
353:
332:expectation value
304:
279:
255:{\displaystyle B}
223:
182:
133:many-body physics
16:(Redirected from
4832:
4806:
4787:
4768:
4749:
4730:
4711:
4683:
4669:
4663:
4650:
4644:
4631:
4625:
4612:
4606:
4593:
4587:
4577:
4571:
4560:
4554:
4541:
4535:
4522:
4516:
4502:
4496:
4479:
4473:
4460:
4454:
4441:
4432:
4418:
4412:
4398:
4389:
4376:
4370:
4355:
4336:
4319:
4259:
4257:
4256:
4251:
4246:
4245:
4244:
4235:
4234:
4226:
4222:
4221:
4216:
4215:
4207:
4158:phenomenological
4154:
4152:
4151:
4146:
4134:
4132:
4131:
4126:
4114:
4112:
4111:
4106:
4104:
4103:
4102:
4079:
4077:
4076:
4071:
4069:
4068:
4067:
4011:
4009:
4008:
4003:
4001:
4000:
3999:
3952:
3950:
3949:
3944:
3942:
3941:
3940:
3917:
3915:
3914:
3909:
3907:
3895:
3893:
3892:
3887:
3885:
3884:
3883:
3860:
3858:
3857:
3852:
3850:
3838:
3836:
3835:
3830:
3828:
3827:
3826:
3803:
3801:
3800:
3795:
3793:
3777:
3775:
3774:
3769:
3766:
3765:
3747:
3740:
3715:, respectively.
3714:
3712:
3711:
3706:
3703:
3702:
3701:
3689:
3683:
3682:
3665:
3663:
3662:
3657:
3654:
3653:
3652:
3640:
3634:
3633:
3590:
3588:
3587:
3582:
3580:
3571:
3570:
3569:
3557:
3551:
3550:
3536:
3535:
3534:
3522:
3516:
3515:
3483:
3478:
3477:
3476:
3464:
3458:
3457:
3446:
3445:
3444:
3440:
3431:
3420:
3419:
3409:
3408:
3401:
3396:
3395:
3381:
3376:
3375:
3359:
3358:
3348:
3347:
3339:
3333:
3332:
3321:
3320:
3319:
3315:
3306:
3295:
3294:
3284:
3283:
3276:
3271:
3270:
3269:
3251:
3246:
3245:
3244:
3224:
3223:
3211:
3206:
3205:
3204:
3192:
3186:
3185:
3171:
3170:
3169:
3157:
3151:
3150:
3139:
3135:
3134:
3133:
3132:
3131:
3121:
3120:
3112:
3105:
3104:
3103:
3097:
3096:
3088:
3073:
3072:
3071:
3059:
3053:
3052:
3042:
3040:
3029:
3024:
2992:
2990:
2989:
2984:
2979:
2978:
2977:
2968:
2967:
2959:
2954:
2949:
2944:
2943:
2935:
2924:
2923:
2922:
2913:
2912:
2904:
2903:
2890:
2881:
2880:
2865:
2831:
2829:
2828:
2823:
2820:
2819:
2818:
2806:
2800:
2799:
2782:
2780:
2779:
2774:
2771:
2770:
2769:
2757:
2751:
2750:
2733:
2731:
2730:
2725:
2723:
2711:
2709:
2708:
2703:
2701:
2689:
2687:
2686:
2681:
2678:
2673:
2672:
2660:
2655:
2654:
2635:
2633:
2632:
2627:
2621:
2620:
2613:
2612:
2611:
2599:
2593:
2592:
2581:
2580:
2579:
2561:
2556:
2555:
2544:
2539:
2538:
2528:
2527:
2521:
2520:
2515:
2514:
2507:
2498:
2497:
2479:
2472:
2447:
2445:
2444:
2439:
2436:
2431:
2430:
2419:
2418:
2408:
2406:
2395:
2384:
2383:
2378:
2377:
2369:
2364:
2359:
2354:
2353:
2345:
2337:
2328:
2326:
2315:
2303:
2301:
2300:
2295:
2289:
2285:
2284:
2283:
2276:
2264:
2259:
2254:
2253:
2245:
2231:
2213:
2212:
2211:
2205:
2201:
2199:
2194:
2193:
2183:
2181:
2170:
2160:
2159:
2158:
2152:
2148:
2146:
2141:
2140:
2130:
2128:
2117:
2101:
2099:
2098:
2093:
2091:
2087:
2085:
2080:
2079:
2065:
2060:
2059:
2023:
2021:
2020:
2015:
2013:
2012:
2005:
1988:
1986:
1985:
1980:
1977:
1972:
1971:
1954:
1952:
1951:
1946:
1943:
1938:
1937:
1917:
1915:
1914:
1909:
1906:
1905:
1890:
1874:
1872:
1871:
1866:
1863:
1862:
1844:
1837:
1808:
1806:
1805:
1800:
1779:
1777:
1776:
1771:
1769:
1768:
1767:
1730:
1728:
1727:
1722:
1720:
1719:
1718:
1712:
1711:
1703:
1689:
1687:
1686:
1681:
1664:
1660:
1659:
1658:
1651:
1650:
1635:
1634:
1633:
1629:
1620:
1609:
1608:
1607:
1589:
1588:
1573:
1559:
1555:
1553:
1548:
1547:
1533:
1528:
1527:
1502:
1501:
1483:
1476:
1463:
1462:
1455:
1445:
1441:
1431:
1430:
1429:
1423:
1422:
1414:
1402:
1401:
1394:
1384:
1382:
1371:
1366:
1342:
1340:
1339:
1334:
1332:
1328:
1326:
1321:
1320:
1309:
1299:
1298:
1293:
1292:
1282:
1281:
1274:
1263:
1258:
1257:
1248:
1247:
1234:
1233:
1223:
1212:
1211:
1210:
1201:
1200:
1192:
1187:
1182:
1177:
1176:
1168:
1145:
1125:
1124:
1123:
1114:
1113:
1105:
1100:
1095:
1090:
1089:
1081:
1071:
1069:
1058:
1053:
997:
995:
994:
989:
987:
986:
981:
980:
962:
960:
959:
954:
949:
948:
947:
936:
931:
926:
925:
917:
903:
901:
900:
895:
893:
892:
885:
869:notation within
868:
866:
865:
860:
848:
846:
845:
840:
821:
819:
818:
813:
811:
810:
803:
786:
784:
783:
778:
776:
775:
774:
768:
767:
759:
744:
742:
741:
736:
734:
722:
720:
719:
714:
708:
703:
698:
697:
689:
673:
671:
670:
665:
660:
659:
658:
652:
651:
643:
638:
633:
628:
627:
619:
606:
605:
598:
573:
571:
570:
565:
559:
555:
554:
553:
546:
534:
529:
524:
523:
515:
514:
499:
481:
480:
475:
474:
466:
461:
456:
451:
450:
442:
435:
433:
422:
408:
374:
372:
371:
366:
361:
360:
355:
354:
346:
322:
320:
319:
314:
312:
311:
306:
305:
297:
291:
286:
281:
280:
272:
261:
259:
258:
253:
241:
239:
238:
233:
231:
230:
225:
224:
216:
205:
203:
202:
197:
194:
189:
184:
183:
175:
158:
156:
155:
150:
73:luminescence to
21:
4840:
4839:
4835:
4834:
4833:
4831:
4830:
4829:
4810:
4809:
4803:
4790:
4784:
4771:
4765:
4752:
4746:
4733:
4727:
4714:
4708:
4695:
4692:
4690:Further reading
4687:
4686:
4670:
4666:
4651:
4647:
4632:
4628:
4613:
4609:
4594:
4590:
4578:
4574:
4561:
4557:
4542:
4538:
4523:
4519:
4503:
4499:
4480:
4476:
4461:
4457:
4442:
4435:
4419:
4415:
4399:
4392:
4377:
4373:
4356:
4339:
4320:
4316:
4311:
4298:Elliott formula
4274:
4237:
4223:
4204:
4193:
4192:
4137:
4136:
4117:
4116:
4087:
4082:
4081:
4052:
4047:
4046:
4039:
3984:
3979:
3978:
3925:
3920:
3919:
3898:
3897:
3868:
3863:
3862:
3841:
3840:
3811:
3806:
3805:
3784:
3783:
3726:
3725:
3721:
3694:
3668:
3667:
3645:
3603:
3602:
3578:
3577:
3562:
3527:
3481:
3480:
3469:
3435:
3422:
3310:
3297:
3262:
3237:
3209:
3208:
3197:
3162:
3124:
3109:
3085:
3084:
3080:
3078:
3064:
3033:
3011:
3010:
2970:
2956:
2915:
2906:
2896:
2849:
2848:
2811:
2785:
2784:
2762:
2736:
2735:
2714:
2713:
2692:
2691:
2640:
2639:
2604:
2572:
2508:
2458:
2457:
2399:
2366:
2319:
2309:
2308:
2267:
2236:
2232:
2174:
2168:
2165:
2164:
2121:
2115:
2112:
2111:
2106:
2105:
2043:
2039:
2034:
2033:
1996:
1991:
1990:
1957:
1956:
1923:
1922:
1877:
1876:
1823:
1822:
1782:
1781:
1758:
1753:
1752:
1731:, contains the
1700:
1695:
1694:
1691:
1643:
1637:
1624:
1611:
1600:
1564:
1560:
1511:
1507:
1446:
1411:
1410:
1406:
1385:
1375:
1357:
1356:
1344:
1313:
1286:
1265:
1250:
1240:
1236:
1203:
1189:
1138:
1116:
1102:
1062:
1044:
1043:
1020:
1006:, light-mode's
974:
969:
968:
967:. The quantity
938:
906:
905:
876:
871:
870:
851:
850:
849:; the explicit
831:
830:
794:
789:
788:
756:
751:
750:
725:
724:
678:
677:
640:
589:
584:
583:
537:
504:
500:
463:
426:
399:
398:
377:quasistationary
343:
335:
334:
323:determines the
294:
264:
263:
244:
243:
213:
208:
207:
167:
166:
141:
140:
125:
94:optical pumping
92:resulting from
30:
23:
22:
15:
12:
11:
5:
4838:
4836:
4828:
4827:
4825:Quantum optics
4822:
4812:
4811:
4808:
4807:
4802:978-3540383451
4801:
4788:
4783:978-3540383451
4782:
4769:
4764:978-3527406678
4763:
4750:
4745:978-9812838841
4744:
4731:
4726:978-0521875097
4725:
4712:
4707:978-0857092328
4706:
4691:
4688:
4685:
4684:
4664:
4645:
4626:
4621:(3): 411–418.
4607:
4588:
4572:
4555:
4536:
4531:(17): 171120.
4517:
4497:
4474:
4455:
4450:(5): 155–296.
4433:
4413:
4390:
4371:
4367:978-0521875097
4337:
4313:
4312:
4310:
4307:
4306:
4305:
4300:
4295:
4290:
4285:
4280:
4273:
4270:
4249:
4243:
4240:
4232:
4229:
4220:
4213:
4210:
4203:
4200:
4144:
4124:
4101:
4097:
4094:
4090:
4066:
4062:
4059:
4055:
4045:(SBEs) if the
4038:
4035:
3998:
3994:
3991:
3987:
3939:
3935:
3932:
3928:
3906:
3882:
3878:
3875:
3871:
3849:
3825:
3821:
3818:
3814:
3792:
3764:
3761:
3758:
3755:
3752:
3746:
3743:
3739:
3734:
3720:
3717:
3700:
3697:
3692:
3688:
3681:
3676:
3651:
3648:
3643:
3639:
3632:
3629:
3626:
3623:
3619:
3616:
3611:
3576:
3568:
3565:
3560:
3556:
3549:
3544:
3540:
3533:
3530:
3525:
3521:
3514:
3511:
3508:
3505:
3501:
3498:
3493:
3489:
3486:
3484:
3482:
3475:
3472:
3467:
3463:
3456:
3451:
3443:
3439:
3434:
3430:
3425:
3418:
3413:
3407:
3400:
3394:
3389:
3385:
3380:
3374:
3369:
3365:
3362:
3357:
3352:
3346:
3342:
3338:
3331:
3326:
3318:
3314:
3309:
3305:
3300:
3293:
3288:
3282:
3275:
3268:
3265:
3259:
3255:
3250:
3243:
3240:
3234:
3230:
3227:
3222:
3217:
3214:
3212:
3210:
3203:
3200:
3195:
3191:
3184:
3179:
3175:
3168:
3165:
3160:
3156:
3149:
3144:
3138:
3130:
3127:
3118:
3115:
3108:
3102:
3094:
3091:
3083:
3079:
3077:
3070:
3067:
3062:
3058:
3051:
3046:
3039:
3036:
3032:
3027:
3023:
3019:
3018:
3002:Purcell effect
2982:
2976:
2973:
2965:
2962:
2953:
2948:
2941:
2938:
2931:
2928:
2921:
2918:
2911:
2902:
2899:
2894:
2889:
2885:
2879:
2876:
2873:
2870:
2864:
2860:
2856:
2817:
2814:
2809:
2805:
2798:
2793:
2768:
2765:
2760:
2756:
2749:
2744:
2722:
2700:
2677:
2671:
2666:
2659:
2653:
2648:
2625:
2619:
2610:
2607:
2602:
2598:
2591:
2586:
2578:
2575:
2569:
2565:
2560:
2554:
2549:
2543:
2537:
2532:
2526:
2519:
2513:
2506:
2502:
2496:
2493:
2490:
2487:
2484:
2478:
2475:
2471:
2466:
2435:
2429:
2424:
2417:
2412:
2405:
2402:
2398:
2393:
2390:
2387:
2382:
2375:
2372:
2363:
2358:
2351:
2348:
2341:
2336:
2332:
2325:
2322:
2318:
2293:
2288:
2282:
2279:
2275:
2270:
2263:
2258:
2252:
2244:
2240:
2235:
2230:
2227:
2222:
2219:
2216:
2210:
2204:
2198:
2192:
2187:
2180:
2177:
2173:
2167:
2163:
2157:
2151:
2145:
2139:
2134:
2127:
2124:
2120:
2114:
2090:
2084:
2078:
2073:
2069:
2064:
2058:
2053:
2049:
2046:
2042:
2011:
2008:
2004:
1999:
1976:
1970:
1965:
1942:
1936:
1931:
1904:
1901:
1898:
1895:
1889:
1885:
1861:
1858:
1855:
1852:
1849:
1843:
1840:
1836:
1831:
1798:
1795:
1792:
1789:
1766:
1761:
1717:
1709:
1706:
1679:
1676:
1673:
1670:
1667:
1663:
1657:
1654:
1649:
1646:
1640:
1632:
1628:
1623:
1619:
1614:
1606:
1603:
1597:
1593:
1587:
1584:
1581:
1578:
1572:
1568:
1563:
1558:
1552:
1546:
1541:
1537:
1532:
1526:
1521:
1517:
1514:
1510:
1506:
1500:
1497:
1494:
1491:
1488:
1482:
1479:
1475:
1470:
1466:
1461:
1458:
1454:
1449:
1444:
1440:
1437:
1434:
1428:
1420:
1417:
1409:
1405:
1400:
1397:
1393:
1388:
1381:
1378:
1374:
1369:
1365:
1348:
1331:
1325:
1319:
1316:
1312:
1308:
1303:
1297:
1291:
1285:
1280:
1277:
1273:
1268:
1262:
1256:
1253:
1246:
1239:
1232:
1227:
1222:
1218:
1215:
1209:
1206:
1198:
1195:
1186:
1181:
1174:
1171:
1164:
1161:
1157:
1154:
1151:
1148:
1144:
1141:
1137:
1134:
1131:
1128:
1122:
1119:
1111:
1108:
1099:
1094:
1087:
1084:
1077:
1074:
1068:
1065:
1061:
1056:
1052:
1035:
1019:
1016:
985:
979:
952:
946:
941:
935:
930:
923:
920:
913:
891:
888:
884:
879:
858:
838:
809:
806:
802:
797:
773:
765:
762:
733:
712:
707:
702:
695:
692:
685:
663:
657:
649:
646:
637:
632:
625:
622:
615:
612:
609:
604:
601:
597:
592:
563:
558:
552:
549:
545:
540:
533:
528:
522:
513:
508:
503:
498:
495:
490:
487:
484:
479:
472:
469:
460:
455:
448:
445:
438:
432:
429:
425:
420:
417:
414:
411:
407:
364:
359:
352:
349:
342:
310:
303:
300:
290:
285:
278:
275:
251:
229:
222:
219:
193:
188:
181:
178:
148:
124:
123:Starting point
121:
117:quantum optics
46:semiconductors
28:
24:
14:
13:
10:
9:
6:
4:
3:
2:
4837:
4826:
4823:
4821:
4818:
4817:
4815:
4804:
4798:
4794:
4789:
4785:
4779:
4775:
4770:
4766:
4760:
4756:
4751:
4747:
4741:
4737:
4732:
4728:
4722:
4718:
4713:
4709:
4703:
4699:
4694:
4693:
4689:
4682:
4678:
4675:
4668:
4665:
4662:
4658:
4655:
4649:
4646:
4643:
4639:
4636:
4630:
4627:
4624:
4620:
4617:
4611:
4608:
4605:
4601:
4598:
4592:
4589:
4586:(12): 125009.
4585:
4582:
4576:
4573:
4569:
4566:
4559:
4556:
4553:
4549:
4546:
4540:
4537:
4534:
4530:
4527:
4521:
4518:
4515:
4511:
4508:
4501:
4498:
4495:
4491:
4488:
4484:
4478:
4475:
4472:
4468:
4465:
4459:
4456:
4453:
4449:
4446:
4440:
4438:
4434:
4431:
4427:
4424:
4417:
4414:
4411:
4407:
4404:
4397:
4395:
4391:
4388:
4384:
4381:
4375:
4372:
4368:
4364:
4360:
4354:
4352:
4350:
4348:
4346:
4344:
4342:
4338:
4335:
4331:
4328:
4324:
4318:
4315:
4308:
4304:
4301:
4299:
4296:
4294:
4291:
4289:
4286:
4284:
4281:
4279:
4276:
4275:
4271:
4269:
4267:
4263:
4241:
4238:
4227:
4218:
4208:
4190:
4185:
4181:
4179:
4175:
4171:
4167:
4161:
4159:
4142:
4122:
4095:
4092:
4060:
4057:
4044:
4036:
4034:
4032:
4028:
4022:
4019:
4014:
3992:
3989:
3973:correlations.
3970:
3966:
3964:
3960:
3956:
3955:eigenenergies
3953:dynamics has
3933:
3930:
3876:
3873:
3819:
3816:
3781:
3744:
3741:
3718:
3716:
3698:
3690:
3674:
3649:
3641:
3617:
3609:
3600:
3596:
3591:
3574:
3566:
3558:
3542:
3538:
3531:
3523:
3499:
3491:
3487:
3485:
3473:
3465:
3449:
3441:
3432:
3423:
3411:
3398:
3387:
3383:
3378:
3367:
3363:
3360:
3350:
3340:
3324:
3316:
3307:
3298:
3286:
3273:
3266:
3257:
3253:
3248:
3241:
3232:
3228:
3225:
3215:
3213:
3201:
3193:
3177:
3173:
3166:
3158:
3142:
3136:
3128:
3113:
3106:
3089:
3081:
3075:
3068:
3060:
3044:
3037:
3008:
3005:
3003:
2998:
2993:
2974:
2971:
2960:
2951:
2946:
2936:
2919:
2916:
2900:
2897:
2892:
2883:
2862:
2846:
2845:
2843:
2837:
2835:
2815:
2807:
2791:
2766:
2758:
2742:
2675:
2664:
2657:
2646:
2638:Intuitively,
2636:
2623:
2608:
2600:
2584:
2576:
2567:
2563:
2558:
2547:
2541:
2530:
2517:
2500:
2476:
2473:
2455:
2454:
2449:
2433:
2422:
2410:
2403:
2391:
2388:
2380:
2370:
2361:
2356:
2346:
2334:
2330:
2323:
2304:
2291:
2286:
2280:
2277:
2261:
2256:
2242:
2238:
2233:
2220:
2217:
2214:
2202:
2196:
2185:
2178:
2161:
2149:
2143:
2132:
2125:
2103:
2088:
2082:
2071:
2067:
2062:
2051:
2047:
2044:
2040:
2031:
2027:
2009:
2006:
1974:
1963:
1940:
1929:
1919:
1887:
1841:
1838:
1820:
1816:
1812:
1787:
1759:
1750:
1746:
1742:
1738:
1737:bandstructure
1734:
1704:
1690:
1668:
1665:
1661:
1655:
1652:
1647:
1630:
1621:
1612:
1604:
1591:
1570:
1561:
1556:
1550:
1539:
1535:
1530:
1519:
1515:
1512:
1508:
1504:
1480:
1477:
1464:
1459:
1456:
1442:
1438:
1432:
1415:
1407:
1403:
1398:
1395:
1379:
1354:
1351:
1347:
1343:
1329:
1323:
1317:
1314:
1310:
1295:
1283:
1278:
1275:
1260:
1254:
1251:
1237:
1216:
1207:
1204:
1193:
1184:
1179:
1169:
1152:
1146:
1142:
1139:
1129:
1120:
1117:
1106:
1097:
1092:
1082:
1066:
1041:
1038:
1034:
1033:
1029:
1025:
1017:
1015:
1013:
1009:
1008:mode function
1005:
1001:
998:contains the
983:
966:
939:
933:
928:
918:
889:
886:
836:
827:
825:
807:
804:
760:
748:
705:
700:
690:
674:
644:
635:
630:
620:
607:
602:
599:
581:
579:
574:
561:
556:
550:
547:
531:
526:
506:
501:
488:
485:
477:
467:
458:
453:
443:
430:
418:
412:
396:
394:
390:
386:
382:
378:
357:
347:
333:
328:
326:
308:
298:
288:
283:
273:
249:
227:
217:
191:
186:
176:
165:
162:
146:
138:
134:
130:
122:
120:
118:
114:
110:
106:
102:
99:
95:
91:
87:
83:
78:
76:
72:
67:
63:
59:
55:
51:
50:recombination
47:
43:
39:
35:
27:
19:
4795:. Springer.
4792:
4776:. Springer.
4773:
4754:
4735:
4716:
4697:
4676:
4673:
4667:
4656:
4653:
4648:
4637:
4634:
4629:
4618:
4615:
4610:
4599:
4596:
4591:
4583:
4580:
4575:
4567:
4564:
4558:
4547:
4544:
4539:
4528:
4525:
4520:
4509:
4506:
4500:
4489:
4486:
4483:Khitrova, G.
4477:
4466:
4463:
4458:
4447:
4444:
4425:
4422:
4416:
4405:
4402:
4382:
4379:
4374:
4358:
4329:
4326:
4323:Khitrova, G.
4317:
4186:
4182:
4174:quantum-wire
4170:quantum-well
4162:
4040:
4027:quantum-well
4023:
4018:collectively
4017:
4015:
3976:
3965:resonances.
3722:
3592:
3009:
3006:
2994:
2847:
2844:contribution
2840:
2838:
2637:
2456:
2452:
2450:
2305:
2104:
1920:
1748:
1692:
1355:
1352:
1349:
1345:
1042:
1039:
1036:
1031:
1021:
1012:vacuum-field
828:
823:
675:
582:
577:
575:
397:
385:luminescence
329:
126:
109:entanglement
79:
42:luminescence
37:
33:
31:
26:
4178:quantum-dot
4031:quantum-dot
3977:Therefore,
1014:amplitude.
129:Hamiltonian
40:) describe
4814:Categories
4309:References
2842:stimulated
381:incoherent
86:incoherent
4570:(1): 115.
4248:⟩
4239:ω
4231:^
4219:ω
4212:^
4202:⟨
4199:Δ
4180:systems.
4143:ω
4123:ω
4093:ω
4089:Π
4058:ω
4054:Π
3990:ω
3986:Π
3931:ω
3927:Π
3896:with all
3874:ω
3870:Π
3817:ω
3813:Π
3745:ω
3733:Ω
3595:Boltzmann
3433:−
3412:∑
3384:−
3364:−
3351:−
3308:−
3287:∑
3254:−
3229:−
3117:~
3114:ϵ
3107:−
3093:~
3090:ϵ
3035:∂
3031:∂
3026:ℏ
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2972:ω
2964:^
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2568:∑
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2257:ω
2243:ω
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2176:∂
2172:∂
2123:∂
2119:∂
2068:−
2048:−
2010:ω
1998:Π
1888:ω
1884:Ω
1842:ω
1830:Ω
1815:screening
1794:Π
1708:~
1705:ϵ
1675:Π
1656:ω
1639:Π
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1436:ℏ
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1368:ℏ
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1252:ω
1226:∑
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1197:^
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1173:^
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1160:Δ
1153:ω
1150:ℏ
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1136:ℏ
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1118:ω
1110:^
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1086:^
1076:⟨
1073:Δ
1064:∂
1060:∂
1055:ℏ
984:ω
951:⟩
934:†
929:ω
922:^
912:⟨
890:ω
878:Π
857:Δ
837:ω
808:ω
796:Π
764:^
706:†
701:ω
694:^
662:⟩
648:^
636:†
631:ω
624:^
614:⟨
611:Δ
608:≡
603:ω
591:Π
551:ω
539:Π
532:⋆
527:ω
507:∑
483:⟩
478:ω
471:^
459:†
454:ω
447:^
437:⟨
428:∂
424:∂
413:ω
363:⟩
358:ω
351:^
341:⟨
309:ω
302:^
289:†
284:ω
277:^
228:ω
221:^
192:†
187:ω
180:^
147:ω
71:excitonic
4272:See also
4242:′
3699:′
3650:′
3599:excitons
3567:′
3532:′
3474:′
3442:′
3317:′
3267:′
3242:′
3202:′
3167:′
3129:′
3069:′
2975:′
2920:′
2901:′
2834:excitons
2816:′
2767:′
2609:′
2577:′
2028:and the
2024:via the
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1631:′
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1143:′
1121:′
98:coherent
4550:: 810.
3963:exciton
1739:of the
4799:
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4704:
4679:(16).
4602:(15).
4428:(11).
4408:(16).
4385:(15).
4365:
3780:photon
2997:lasers
1010:, and
325:photon
75:lasers
4659:(6).
4640:(9).
4512:(4).
4492:(6).
1741:solid
161:Boson
101:laser
96:with
4797:ISBN
4778:ISBN
4759:ISBN
4740:ISBN
4721:ISBN
4702:ISBN
4363:ISBN
4172:and
4029:and
3666:and
1955:and
1002:for
747:hole
393:flux
206:and
54:flux
38:SLEs
32:The
4657:101
1749:all
56:of
44:of
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4638:85
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