Optical Absorption of an Quantum Wells in Terahertz Plasmonic Microcavity*

MI Xianwu,MENG Fanbin,WU Hongwei

(1.College of Physical Science and Mechanical Engineering,Jishou University,Jishou 416000,Hunan China;2.Department of Physics and Information Engineering,Huaihua College,Huaihua 418000,Hunan China)

OpticalAbsorptionofanQuantumWellsinTerahertzPlasmonicMicrocavity*

MI Xianwu1,2,MENG Fanbin1,WU Hongwei1

(1.College of Physical Science and Mechanical Engineering,Jishou University,Jishou 416000,Hunan China;2.Department of Physics and Information Engineering,Huaihua College,Huaihua 418000,Hunan China)

An approach of solving excitonic absorption is presented for an asymmetric double quantum well driven by an intense terahertz field embedded in a semiconductor microcavity.The formalism relies on Zubarev’s Green functions,which allow us to handle the microcavity field and terahertz field as the photons and to fully account for the quantum aspect of the optical response of the asymmetric double quantum wells.Rich nonlinear dynamics behaviors of the replica peak and the Autler-Townes splitting are systematically studied in undoped asymmetric double quantum wells for taking account of the multiple factors,such as the detuning,coupling constant of the intense terahertz field,decay rate of the second electron subband,photon number of the intense terahertz field.The work provides a simple and convenient approach to deal with the microcavity-optical response of the asymmetric double quantum well in a fully quantum mechanical framework.

optical absorption,intense terahertz field,Autler-Townes splitting

1 Introduction

The optical properties of semiconductor quantum well (QW) have been reported many times in recent years[1-5].Particularly,the research topic of an external electric field being applied to the semiconductor QW has attracted great interest recently because it plays an important role in understanding various interesting phenomenon in semiconductor nanosize structure.A direct current (dc) electric field is applied along the semiconductor QW growth direction,the Franz-Keldysh effect (FKE)[6-7]and the quantum confine Stark effect (QCSE)[8]have been studied in semiconductor QW.For an ac electric field applied to QW modulates the interband absorption,in particular the electro-optic modulation by a terahertz (THz) electric field is of great interest.The development of THz field sources in recent years provides unique opportunities to investigate the effects of nonlinear optics such as ac-Stark effect[9],Rabi flopping[10-12]and dynamical FKE (DFKE)[13-14].The reason for applying THz field is the fact that the intersubband transition frequency in the conduction band or valence band fall in the frequency range of the THz field.

A large number of efforts on the theoretical and experimental studies of optical absorption in semiconductor QW system driven by an intense THz field are performed.Theoretical work on the optical absorption of the semiconductor quantum well has been based on various formulations,such as the density matrix approach[15-16],the semiconductor Bloch equation[17-18],the inhomogenous Schrodinger equation[19]as well as the master equation approach[20].Though much interesting phenomenon has been demonstrated by the above approaches,the quantum aspects of the optical response of semiconductor quantum well system remain unresolved due to the probe beam and THz field are treated as classical optical field in a semiclassical framework.Due to the development of the quantum mechanics and a deeper understanding of the theory of quantum dynamics,a full quantum Hamiltonian of optical field and interaction term between optical field and semiconductor QW system are obtained by M.Kira and S.W.Koch[21].Understanding of the quantum underlying of the light-QW interaction for the excitonic absorption in QW system is important to the calculation and analysis their absorption features.In full quantum framework,the Zubarev’s Green functions method[22]provide a convenient approach for modeling the optical response between the optical field and the semiconductor quantum well system.The approach becomes a powerful approach for describing the internal evolution of semiconductor quantum well system beyond the perturbation regime.The Zubarev’s Green function method has been successfully solved the problems of the statistic physics and linear response theory[23-24]as well as the optical absorption properties of plasmons-excitonic system[25].

In this paper,we adapt the Zubarev’s Green functions method to study the optical absorption properties of anasymmetric double quantum wells (ADQWs) driven by an intense terahertz field embedded in a semiconductor microcavity.In order to obtain the rich features of interband optical absorption,we set up a three-level system (TLS) in asymmetric double quantum well.The absorption peak shows symmetric evolution feature for the detuning changes from the negative value to the positive value.Autler-Townes (A-T) double peaks emerge for the detuning is zero (i.e.,the THz field frequency equal to the transition frequency between the first electron subband and the second electron subband) due to the optical Stark effect (OSE).When we increase the coupling strength of the THz field,the space between the two main peaks of the A-T splitting becomes very large.Similarly,the dip becomes deeper and the separation between the two main peaks becomes more pronounced for decreasing the decay rate of the second electron subband,increasing the photons numbers of the THz field for the THz field is near-resonant with the intersubband transition.Our results demonstrate the conclusion that the resonant splitting strength is proportional to the coupling strength and the photon number of the resonant THz field.This method may becomes an effective way for solving excitonic absorption in semiconductor QW and the model can be systematically extended to include more complicated structure.

2 Model and Solution

In second quantization androtating wave approximation,the Hamiltonian of the investigated system which includes the TLS and the intense THz field can be written as

H=H0+Hinter,

(1)

where the first termH0includes the noninteracting Hamiltonian terms of the TLS and the intense THz field,and it can be described as

(2)

The interaction term between the intense THz field and the TLS is modeled by theHamiltonian

(3)

wheregdenotes the coupling constant for the THz field interacting with the TLS.The THz field induces the intersubband transition between the first electron subband and the second subband.

(4)

(5)

(6)

Due to the optical absorption spectrum being related to the retarded Zubarev’s Green functionσ(ω)∝-Im{《A|A+》ω+i0+},the optical absorption of the excitonXe1h1(the exciton is consistent with the first hole subband and the first electron subband) for the microcavity field coupling can be written as

(7)

(8)

the optical absorption of the excitonXe2h1(the exciton is consistent with the first hole subband and the second electron subband) for the microcavity field coupling can be written as before

(9)

3 Numerical Results and Discussions

Fig.1 Optical Absorption Spectrum of the Exciton Xe|h| for the Detuning Increasing from Δ=-0.05 eV to Δ=0.05 eV.The Parameters are =1.555 5 eV,g=0.02 eV,ωTHz=3.8 THz,nc1=nc2=0, nTHz=1,Γ1=0.05 eV,Γ2=0.02 eV

In Fig.1 absorption spectrum for the electron transition from the ground state (the first hole subband state) to the first electron subband are displayed for different detuning between the THz frequency and the intersubband transition frequency.The eigenenergies of the excitonXe1h1and the excitonXe2h1are 1.555 5 eV and 1.5712 eVby using thek·pperturbation theory.The frequency of the THz field is set to 3.8 THz,and the THz field is resonant with the two exciton due to the THz-photon energy ofωTHz=1 THz is 4.136 meV.A small replica peak of the second electron subband emerges at the location 1.49 eV,an absorption main peak emerges at the right side of the replica peak for the detuningΔ=-0.05 eV.Increasing the detuning toΔ=-0.01 eV,the replica peak increases in magnitude and moves to the absorption main peak.The replica peak translates into the left branch of the A-T double peaks and the absorption main peak evolves to the right branch for the detuning is increased to 0.00 eV(i.e,the THz frequency is tuned to the transition frequency between the first electron subband and the second electron subband).When increasing the detuning toΔ=0.01 eV,the symmetric double peaks translate into asymmetric shape,the replica peak and the absorption main peak is recovered.However,the replica peak emerges at the right side of the absorption main peak.The evolution laws are the fact that the THz frequency is decreased from the high-frequency to the low-frequency.If we continue to increase the detuning,the replica peak becomes more weak and moves to the right side,the absorption main peak recovery as the absorption peak of nonperturbative.

Fig.2 Optical Absorption Spectrum of the Exciton Xe2h1 for the Detuning Increasing from Δ=0.05 eV to Δ=-0.05 eV.The Parameters are =1.555 5 eV, g=0.02 eV,ωTHz=3.8 THz,nc1=nc2=0,nTHz=1, Γ1=0.05 eV,Γ2=0.02 eV

The optical absorption for the electron transition from the ground state to the second electron subband is showed in Fig.2.The evolve laws isopposite compared with the case of the Fig.1 for increasing the detuning fromΔ=-0.05 eV toΔ=0.05 eV.The replica peak of the first electron subband emerges at the right side of the absorption main peak forΔ=-0.05 eV.The magnitude of the absorption main peak is larger than the absorption peak of the excitonXe1h1due to the decay rate of the second electron subband being smaller than the decay rate of the first electron subband.The replica peak moves to the left side of the absorption main peak crossing the A-T double peaks for the detuning is a positive value.When the detuning isΔ=0.05 eV,the replica peak emerges at the location of 1.57 eV and the absorption main peak is recovered as the absorption main peak of the first absorption spectrum.

Theoptical absorption of the excitonsXe1h1,Xe2h1has been investigated for various detuning as above discussion.Next,we investigate the optical absorption properties of the first electron subband for various coupling constant of the THz field,decay rate of the second electron subband,photons numbers of the THz field.

Fig.3 shows optical absorption spectrum of the first electron subband for different decay rate of the second electron subband.The near-resonant THz field is applied (i.e,Δ=-0.005 eV).When the decay rate of the second electron is tuned toΓ2=2 meV,the optical absorption spectrum shows an asymmetric A-T double peaks.The absorption peaks are decreased in magnitude,the dip between the A-T double peaks becomes shallower and the asymmetric shape of the A-T double peaks become more pronounced for increasing the decay rate of the second electron subband.If increasing the decay rate toΓ2=50 meV,the dip fades away and the absorption peak is weak in magnitude.

Fig.3 Optical Absorption Spectrum of the Exciton Xe1h1 for the Detuning Increasing from Δ=-0.05 eV to Δ=0.05 eV. The Parameters are =1.555 5 eV,g=0.02 eV,ωTHz=3.8 THz,nc1=nc2=0,nTHz=1,Γ1=0.5 eV,Γ2=0.02 eV

Fig.4 shows that the optical absorption spectrum of the first electron subband is dependent on the coupling constant of the THz field for the detuning is fixed atΔ=-0.005 eV.There is asymmetric A-T double peaks in the optical absorption spectrum for the coupling constant isg=0.01 eV.Dip associated to the asymmetric A-T splitting almost disappears for small values of the coupling constantg.When increasing the coupling constant,the dip becomes deeper and the separation between the two branches becomes more pronounced.The asymmetric shape of the A-T double peaks is remitted with increasing the coupling constant.

Fig.4 Optical Absorption Spectrum of the Exciton Xe1h1 for the Copuling Constant Between the THz and the ADQWs Increasing from g=-0.01 eV to g=0.04 eV.The Parameters are =1.555 5 eV, Δ=-0.005 eV,ωTHz=3.8 THz,nc1=nc2=0,nTHz=1,Γ1=0.5 eV,Γ2=0.02 eV

Fig.5 Plane-3dmensions Scheme of Absorption Spectrum for the Energy of the Microcavity Field from 1.3 eV to 1.8 eV and the THz Photons Number Increase from 0 to 10.The Parameters are =1.555 5 eV, Δ=0.00 eV,ωTHz=3.8 THz,nc1=nc2=0,g=0.02 eV,Γ1=0.5 eV,Γ2=0.02 eV

In Fig.5,we investigate the optical absorption of the first electron subband for various photon number of the THz field in the presence of resonant THz field (i.e,Δ=0.00 eV).The red region denotes that a single strong absorption peak emerges at the location of 1.555 5 eV.When increasing the THz photons number,the strong single absorption peak split into two small peaks.The two small peak is the A-T double peaks.The dip becomes deeper and the separation between the two branches becomes more pronounced for the THz photons number is increased fromnTHz=0 tonTHz=3.However,the depth of the dip keeps constant state and separation between the two branches is increased stilly with increasing the THz photons number fornTHz>3.The result is consistent with the conclusion of Rabi splitting in quantum optics.

4 Conclusions

In summary,we have presented the optical absorption properties of an asymmetric doublequantum well driven by an intense terahertz field embedded in a semiconductor microcavity based on the Zubarev’s Green functions method.The formalism shows the quantum process of the interaction between microcavity optical field and the ADQW system.Using realistic parameters,the optical absorption spectrum shows the A-T doublets for resonance THz field,replica peak for the non-resonance THz field by governing the detuning.The dip between the two branches becomes deeper and the separation between the two peaks of the A-T double peaks becomes more pronounced for decreasing the decay rate of the second electron subband,increasing the coupling constant of the THz field and increasing the THz photons number by the near-resonant THz field is applied.Particularly,our results verify the conclusion that the strength of the A-T splitting not only relates to the coupling constant of the near-resonant THz field,but also relates to the photons number.Our approach is likely to become a powerful tool for solving the optical absorption properties of semiconductor quantum well system which includes more complicated structure by governing the detuning.

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(责任编辑 陈炳权)

等离激元微腔中的量子阱太赫兹光吸收

米贤武1,2，孟凡斌2，吴宏伟2

(1.怀化学院物理与信息工程学院，湖南 怀化 418000；2.吉首大学物理科学与机械工程，湖南 吉首 416000)

利用Zubarev’s格林函数方法研究了强太赫兹电场作用下微腔中的双量子阱激子光吸收特性.将腔场和太赫兹场处理为光子，根据哈密顿量得到运动方程.研究考虑了失谐、太赫兹场耦合常数以及电子数的衰减率.研究发现，在强太赫兹场作用时，光谱呈现丰富的非线性效应，如出现复制峰和Autler-Townes分裂.该研究为微腔-量子阱系统量子光学响应提供了一个简单、方便的全量子理论处理方法.

光吸收；强太赫兹电场；Autler-Townes分裂

O47

A

1007-2985(2014)01-0029-07

date：2013-10-12

Project supported by the National Natural Science Foundation of China (11364020 );Hunan Provincial Education Department-Funded Project(10A100 )

Biography：Mi Xianwu(1973-),male,was born in Hunan,China,

the microelectronics and solid state electronics Ph. D degree from the graduate school of Chinese Academy of Sciences,research interests include theoretical aspects of semiconductor lasers and amplifiers and terahertz physics.

O47DocumentcodeA

10.3969/j.issn.1007-2985.2014.01.008