3 January 2000

Ž .Physics Letters A 264 2000 346–349www.elsevier.nlrlocaterphysleta

Optical switching based on transparency in a semiconductordouble-quantum well

Xue-Mei Su b, Jin-Yue Gao a,b,c,)

a ( )CCAST World Laboratory , P.O. BOX 8730, Beijing 100080, PR Chinab Department of physics, Jilin UniÕersity, Jilin proÕince, Chuangchun 130023, PR China

c State Key Laboratory on Optoelectronics, Jilin UniÕersity, Jilin proÕince, Chuangchun 130023, PR China

Received 7 September 1999; received in revised form 17 November 1999; accepted 26 November 1999Communicated by P.R. Holland

Abstract

We propose a scheme for a photon switch in a semiconductor double-quantum well structure by quantum interference inintersubband transitions. q 2000 Published by Elsevier Science B.V. All rights reserved.

Recently, quantum interference in the form ofŽ . w xelectromagnetically induced transparency EIT 1

has been used to generate highly efficient schemesw xfor nonlinear optics 2 . The nonlinear optical pro-

cesses, which depend on quantum interference tocancel the absorption and dispersion of optical reso-nance to obtain unusually large nonlinear opticalsusceptibilities, have been experimentally observed

w xin atomic systems 3,4 . The implementation of EITin nonlinear semiconductor devices is very appealingfrom a more applied point of view, for their inherentadvantages such as large electric dipole momentsdue to the small effective electron mass, high nonlin-

w xear optical coefficients 5–7 and a great flexibilityin device design by choosing the materials and struc-ture dimensions. In this Letter, we propose a schemefor optical switch in a coherent coupled quantumwell based on the idea of optical switching in a

) Corresponding author. Fax:q 86-431-894-3967; e-mail:qol@mail.jlu.edu.cn

w xfour-level atomic system 8 and the facts of thetheories and experiments on Fano interference in

w xintersuband transitions 9–11 . In the Fano effectw x12 , two optical absorption paths from the groundstate to a common continuum interfere to produce anasymmetric absorption spectrum that falls to zeronear the absorption maximum. The switch works inrange of mid-IR when intersubband transitions inGaAsrAlGa, InGaAsrInAlAs and GaAsrAlGaAs

w xmaterial systems 9–11 are chosen. Near-infraredoptical switch in the 1.55–2 mm wavelength rangecan be also realized by utilizing appropriate quantumwell heterostructures, for example, using InGaAsrAlAs semiconductor material with which 1.798 mm

w xintersubband absorption was observed 13 .The prototype of double quantum well structure

that we envision is outlined in Fig. 1. The firstŽ .:subband 2 of the shallow well is resonant with

Ž .:the second subband 3 of the deep well by reso-nant tunneling via an ultra-thin potential-energy bar-rier connected to the two wells. For this coherent

: :coupling by tunneling, levels 2 and 3 split into a

0375-9601r00r$ - see front matter q 2000 Published by Elsevier Science B.V. All rights reserved.Ž .PII: S0375-9601 99 00831-2

( )X.-M. Su, J.-Y. GaorPhysics Letters A 264 2000 346–349 347

Fig. 1. Subband energy level diagram for double quantum wellsseparated by a thin tunneling barrier.

doublet. Adjusting the height and width of the tun-w xneling barrier with applied bias voltage 10 can

control the splitting on resonance. The lower andhigher subbands in the deep well and the narrow

: :well are denoted as level 1 and level 4 , respec-tively. v and v denote the frequencies of probep p

and switching pulses which are in resonance with the: : : :transition 1 to 3 and the transition 2 to 4 ,

respectively. The coherent coupling make the probev transparent when v is in absence. With thep s

switch-on of the beam, the quantum interference isdestroyed and therefore the probe light is absorbed.The semiconductor four-level system described hereis analogous to the four-state atomic system pro-

w xposed by Harris et.al 8 , which may function as anoptical switch where a pulse of light of one fre-quency will cause another pulse ‘on’ or ‘off’ at asecond frequency. The strong coupling effect be-

: :tween levels 2 and 3 in an atomic system isreplaced here by the coherent resonant tunneling insemiconductor.

In our four-level system, the dressed susceptibilitycan be calculated by solving the coupled amplitude

w xequations. They are 2 :

j)b s V b ,1 p 32

j) )b y jDv b s V b q jV b ,˜2 c 2 s 4 c 32

1Ž .j

b y jDv b s V b q jV b ,˜3 p 3 p 1 c 22j

b y jDv b s V b ,˜4 s 4 s 22

Ž .where b is1,2,3,4 stands for the probability am-i

plitude of the respective subband level and V andp

V are the respective field Rabi frequencies. Thes

1 1r2Ž .quantity V s G G represents the fact that asc 2 32

: :level 2 decays it drives 3 and vice versa. This: :term arises since both levels 2 and 3 couple to

w xthe same continuum and therefore to each other 14 .The complex detunings areDv sDv q jg˜ p p 13

sv y v yv q jg ,Ž .p 3 1 13

Dv sDv q jg˜ c c 12

s v yv y v yv q jg ,Ž . Ž .p c 2 1 12

Dv sDv q jg˜ s s 24

s v yv qv y v yv q jg ,Ž . Ž .p c 24 4 1 24

where the dephasing linewidth for the respectivetransitions comes from the intrasubband phonon scat-tering, electron–electron scattering, interface rough-ness scattering and alloy scattering contribution. Weneed to reduce this dephasing contribution as low aspossible, in order to raise the quality of Fano inter-ference by the lifetime broadening given by LO

w xphonon emission. Ref. 15 supplies a double-wellstructure to reduce the dephasing effect.

We assume that the probe field is weak enoughthat the probability amplitude b s1. In steady1

state, we drop all the derivatives of the probabilityŽ .amplitudes in Eq. 1 and use the definition of the

Ž . Ž . Ž .polarization P v s´ x v E v . The expres-p 0 p p

sion of the susceptibility at the probe frequency isx vŽ .p

2V y2 Dv Dv˜ ˜s c s

sK 2 22 Dv Dv Dv y V Dv y2 V Dv˜ ˜ ˜ ˜ ˜c s p s p c s

2Ž .2

where the constant KsN m r"´ , m is the13 0 i j

corresponding effective dipole moment. We neglectDv and Dv as compared to their respectivep s

linewidths and get g sg by choosing the widths23 13

of quantum wells and doped concentration at theŽ .collector region. Inserting Dv sDv v sv ,p c 2 3

2 Ž .the golden rule transition rates W sV r 2g ,p p 132 Ž . 2 Ž .W sV r 2g , W sV r 2g into the expres-c c 23 s s 24

Ž .sion 2 , and combining it with Maxwell’s equations,we obtain the power loss at the probe frequency:

W qg W q2W qg qDv 2Ž . Ž .s 12 s c 12 p2aLsNLs13 2 2W q2W qg qDvŽ .s c 12 p

3Ž .

( )X.-M. Su, J.-Y. GaorPhysics Letters A 264 2000 346–349348

where s is defined as the absorption cross section.13Ž .The power transmission exp y2aL can be com-Ž .puted at various W from Eq. 3 . The critical W iss s

obtained when the power loss 2aLs1.Next we consider W , W being pulse and askings p

Ž .for the conditions for which Eq. 3 remains valid.We neglect the frequency detuning as compared tothe corresponding linewidths and drop the deriva-

:tives of the probability amplitudes of states 3 and:4 because they vary slowly as compared to the

Ž .linewidths in Eq. 3 . These equations are

j)b s V b1 p 32

j) )b qg b s V b q jV b2 12 2 s 4 c 32

4Ž .j

g b s V b q jV b13 3 p 1 c 22j

g b s V b24 4 s 22

We obtain here the equations similarly to Harris’. IfŽ .Eq. 3 is required to be valid for the pulse fields, the

w xcondition will be 8

1 EV ) 1p<

)V E t Wp c

That is to say, the maximum rate of variation ofprobe pulse and therefore the switch bandwidth is setby the adjustable golden rule transition rate W , inc

other words, the switch may open or close with aw xspeed equal to W 8 .c

To estimate the possibility for our semiconductorswitching in experiment, or in virtual use, we choosea GaAs–Al Ga As quantum well structure to bex 1yx

w xour material, which is the same as in Ref. 10 wheretunneling induced transparency is obtained in experi-ment. We depict the probe power transmission virusthe detuning Dv in Fig. 2. All the parameters arep

taken as the above virtual sample with an opticalŽ .depth NLs s10. In Fig. 2 a it is shown that the13

Ž .switch is open W s0 . The switch is closed whensŽ Ž ..W s0.2W shown in b . The results tell us thats c

our design for optical switch in coupled doublequantum well is utilizable.

We should emphasize two points about the resultsshown in Fig. 2. One is that the power transmission

Fig. 2. Power transmission as a function of the detuning Dvpw x Ž .using experimental data in Ref. 10 . a the switch is open

Ž . Ž . .W s0 and b the switch is closed W s0.2W . The others s c

parameter is NLs s10.13

at open state is below 100% because of relativelylarge dephasing rate g . In an atomic system, state12:2 is metastable because of its little g . The semi-12

conductor structure tunneling by an additional barrierw xnext to the deeper well 15 is better than the one that

we used. The other point we should emphasize is thecritical value chosen for switching at the closed state.When W s0.2W , the Rabi frequency of the switch-s c

ing field V ;0.1V is in the order of 1011 Hz,s c

which is large enough to be imaginable in an atomicsystem. In our semiconductor design, a very large

Ž y8 .electric dipole moment ;10 cm requires theintensity of the switching pulse for critical weak tobe in the order of 106 Wrcm2.

In summary, we have presented a weak opticalswitch in DQW semiconductor. It is much morepractical than the atomic system for its flexibledesign and the controllable interference strength. Werealized this with a Fano-type interference in inter-subband transitions by resonant tunneling. It’s amethod to realize one light controls another in semi-conductor.

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