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LUMINESCENCE ELSEVIER

Journal of Luminescence 72-74 (1997) 3055306

Quantum interference in exciton luminescence of coupled semiconductor quantum wells V.I. Yudson a,b,*, P. Reineker a a Abtriluny b Institute

of’ Spectroscopy.

Throrrtische Russian

Academy

Physik,

Unirersitiit

qf’ Sciences,

Ulm,

Troitzk,

89059

Alma

Mosc~ou~ req.

Germun?, 142092,

Russiun

Ftdertttiorz

Abstract We consider a single electron-hole pair excitation of an asymmetric undoped semiconductor double quantum well in the presence of an external electric field perpendicular to the well plane. Because there are two different ways for the transformation of, say, the left direct exciton to the right one (‘e, h’ or ‘h, e’ succession of tunneling events, respectively), the resulting effective coupling constant of the direct exciton states is determined by the interference of corresponding transition amplitudes. The coupling of the exciton states is monitored via the appearance of the luminescence with the frequencies of both transitions even if only one of them has been pumped. Changing the external field allows to manipulate the amplitudes of tunneling paths via their sensitivity to the difference of energy levels. Kqword~s:

Coupled quantum wells; Excitons

We consider a single electron-hole pair excitation of an asymmetric semiconductor double quantum well (DQW) in the presence of an external electric field perpendicular to the well plane. At negligible interwell tunneling there would exist only a spatially direct exciton confined to one of the wells. For differing optical transition frequencies, a resonant excitation of only one of the wells would not lead to a luminescence from the other one. However, in the presence of electron (e) and hole (h) tunneling, also two spatially indirect exciton states (with e and h located at different wells) enter the process. There is growing interest to study the electron, hole, and exciton tunneling in DQWs (see, e.g., Refs. [l-4] and references therein). Here we draw attention to a specific property of the DQWs with both electron and

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hole tunneling. Because there are two different ways for the transformation of, say, the left direct exciton to the right one (‘e, h’ or ‘h, e’ succession of tunneling events, respectively), the resulting effective coupling constant of the direct exciton states is determined by the quantum interference of the corresponding transition amplitudes. We restrict our consideration to a simplified mode1 with taking into account only the exciton subspace of the Hilbert space, i.e. the ground state IO), the left direct exciton state 1l), the right direct exciton state ]2), the indirect exciton state 13) with the electron and hole located in the right and the left QWs, respectively, and the indirect exciton state 14) with the electron and hole located in the left and right QWs. The state 11) (or 12)) is connected to the states (3) and 14) via the electron T, and hole rh tunnel matrix elements (or rh and 7’,), respectively. There are transition dipole moments ~1 and ~2 between the ground state IO) and the direct exciton states 11) and 12).

V.I. Yudson, P. Reinekrrl Journul of’ Luminescencr 72-74 i 1997) 305-306

306

We assume a strong static electric field F applied perpendicular to the DQW plane in the direction from the left QW to the right one. Due to this field, the energies Ej and Ed of the indirect exciton states 13) and 14) are far separated (by the value of the order +edF, respectively; d is the separation of the charges in the indirect states) from the energies El and E2 of the direct exciton states )1) and 12). We are interested in the effective coupling between the direct exciton states (1) and 12). Excluding the states 13) and 14) we arrive at the following effective system of equations: [E, + AI(E) - E]C, + T(E)C2 T(E)C,

+ [E2 + d2(E)

which determines positions Ci I 1) + the new states are terminant. InEqs.

= 0,

(1)

- E]C2 = 0,

(2)

the new states II) and jr) as superCz 12) of the bare ones. Energies E of given by the roots of the system de(l)and(2) d,(E)= T:/(E - E4)+

T;/(E - E3), A2(E) = T,2/(E - E3) + T;/(E - E4),

and the effective coupling T(E)

= T,T,

The two terms in Eq. (3) correspond to the two different paths of the direct exciton transfer between the QWs. The matrix element (3) determines relative fractions of bare states 11) and 12) in the new ones )l) and Ir). The hybridization of the states may differ significantly for the state /I) and 1~). Considering the case when the tunneling matrix elements are small as compared to the difference IEl - E2 1,we obtain Ir) = II) + T(EI)/(EI - E2)12) and /r) = 12)+

T(Ez)/(Ez - El )12) (where we omitted the terms describing the admixture of the states 13) and 14)). The amplitudes of the second terms in these superpositions depend on the relative positions of the energy levels El and E2 with respect to E3 and Ed. For instance, if the energy El is adjusted to the value (E3 + E4)/2, the transfer amplitude T(El) vanishes. It means that the coherent transition from the left direct exciton state to the right one is hindered due to the destructive interference of the two paths. At the same time, for the asymmetric DQW the transfer amplitude T(E2) may differ from zero. The coupling of the exciton states may be monitored via the appearance of the luminescence with the frequencies of both transitions if only one of them has been pumped. Changing the external field allows to manipulate the amplitudes of tunneling paths via their sensitivity to the difference of energy levels (indirect excitons are more sensitive to the electric field than the direct ones). The studied mechanism of the quantum paths interference is specific for the considered ‘four-excited-states’ system and is absent in the case when there is tunneling of only one type of the carriers (‘two-excited-states’ system).

References [I] G. Bastard, C. Delalande, R. Ferreira and H.W. Liu, J. Lumin. 44 (I 989) 247. [2] A.M. Fox, D.A.B. Miller, G. Livescu, J.E. Cunningham, J.E. Henry and W.Y. Jan, Phys. Rev. B 42 (1990) 1841. [3] B. Deveaud, A. Chomette, F. Clerot, P. Auvray, A. Regreny, R. Ferreira and G. Bastard, Phys. Rev. B 42 (1990) 7021. [4] S.A. Gurvitz, 1. Bar-Joseph and B. Deveaud, Phys. Rev. B 43 (1991) 14703.

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