Optics and Photonics Journal, 2013, 3, 293-297 doi:10.4236/opj.2013.32B069 Published Online June 2013 (http://www.scirp.org/journal/opj) Intracavity Tunneling Introduced Transparency in Ultrastrong-coupling Regime Tao Wang, Rui Zhang, Chunxiao Zhou, Xuemei Su Physics College, Jilin University Changchun 130012, People’s Republic of China Email: [email protected] Received 2013 ABSTRACT Intracavity tunneling induced transparency in asymmetric double-quantum wells embedded in a microcavity in the ul- trastrong-coupling regime is investigated by the input-output theory developed by Ciuti and Carusotto. In this system a narrow spectra can be realized under anti-resonant terms of the external dissipation. Fano-interference asymmetric line profile is found in the absorption spectra. Keywords: Ultrastrong Coupling; Spectra Narrowing; Anti-resonant Terms; Fano-interferences 1. Introduction the cavity dynamics. The photonic mode is coupled to the external world mostly because of the finite reflectivity of Intersubband electronic transitions in doped semicon- the cavity mirrors, while the intersubband transition is ductor quantum wells play an important role in many re- coupled to other excitations in the semiconductor markable devices, such as quantum cascade lasers, quan- material-e.g., acoustic and optical phonons and free tum-well infrared photodetectors and ultrafast optical carriers in levels other than the ones involved in the modulators [1]. If semiconductor quantum wells in a mi- considered transition. In particular, the coupling to this crocavity were explored by using the intersubband tran- electronic bath allows one to electrically excite the sitions, it can achieve an ultrastrong light-matter cou- intersubband transitions and induce electroluminescence. pling regime where vacuum Rabi frequency becomes In the theory cavity field and electronic transition are comparable to the intersubband electronic transitions [2]. treated as two oscillators . The vacuum Rabi splitting of a In the ultrastrong coupling regime, the usual rotating- collection of oscillators in a single-mode cavity is wave approximation is not exact enough to explain the proportional to the square root of their number. So the experimental data and the antiresonant terms should be control of polariton coupling can be realized through the considered. The contribution of antiresonant terms can variation of carrier density. create many new effects such as back-reaction, photon In this paper we investigate quantum coherence in a blocked and two-mode squeezed vacuum [3]. multiple asymmetric double-well structure embedded in Quantum coherence is a fundamental problem in macrocavities. The cavity mode and the electronic excita- quantum mechanics and has been investigated for a long tions in each quantum well interact strongly in the ultras- time in atom physics and optics physics. Strong coupling trong-coupling regime and the intersubband transitions of is necessary for quantum coherence, but we still do not each quantum well are coupled by quantum tunneling which understand what will happen when the coupling strength can be tuned using bias voltage. Asymmetric semicon- reaches the ultrastrong-coupling region. The intersubband ductor double quantum well structure has been studied electronic transition in doped semiconductor quantum for many interesting phenomena such as lasers without wells embedded in a microcavity provide a chance to population inversion, tunneling induced transparency discuss and test the problem. (TIT) [5] and optical switching [6]. A full quantum description of the ultrastrong-coupling TIT is a typical interesting quantum coherence pheno- regime in doped semiconductor quantum wells microcavity mena similar as those of the idea of Electromagnetically has been developed by Ciuti and Carusotto [4] which can induced transparency (EIT) [7]. Recent years intracavity explicitly include the coupling to external dissipation EIT has attracted much attentions and has been studied baths including probe photons and injection electrons. experimentally in the multiatoms-cavity systems [8,9]. It The dissipation baths are not only responsible for damping has been shown that intracavity EIT results in an ultra- rates but also provide a way of exciting and observing narrow spectral linewidth which may be used for Copyright © 2013 SciRes. OPJ 294 T. WANG ET AL. frequency stabilization and high-resolution spectroscopic The photons mode is chosen to be resonant to the fun- measurements. When the intracavity dark state is induced damental cavity photon mode, whose frequency disper- by a coupling laser in the cavity and -type atomic system, c 22 sion is given by kkz , where is the cavity transmission spectrum exhibits three peaks: cav, k two side-bands associated with the multiatom vacuum the dielectric constant of the cavity spacer and k s the Rabi splitting and a narrow central peak representing the z quantized photon wave vector along the growth direction, cavity dark-state resonance of the two-photon Raman which depends on the boundary conditions imposed by transition. the specific mirror structures. In the simplest case of me- Ulike atomic systems, semiconductor quantum well π embedded in a microcavity is easily use to realize the llic mirrors, kz , with Lcav he cavity thickness. ultrastrong coupling due to very large subband transition Lcav matrix elements [6]. In the asymmetric quantum wells The Hamiltonian of the present system is microcavity, the transmission spectrum is similar with Haabb† † cavkkk, 12 kk the multilevels atom-cavity system but is not symmetric kk and the narrow peak is not in the central position in the dd†† i ab ab† 13 kk 12,k kk kk ultrastrong-coupling regime. Intuitively the antiresonant kk terms reduce the simultaneous creation and annihilation †† †† i ad ad D aa aa (1) of the cavity photon and the electronic transition so the 13,kkkkk kkkkk dark state must be destroyed. However the zero-absorp- iabab †† 12,kkk kk tion at resonance is not changed by the aniresonant terms k in the ideal condition and can be used to reduce the ab- † † †† iadad Daa aa sorption induced by the aniresonant terms to zero. The 13,kkk kk k kk kk results mean that the intracavity TIT still hold even in the The first three terms describe the energy of the cavity ultrastrong-coupling regime. mode and the two intersunbband electronic transitions. The fouth term describe the resonant interactions be- 2. Model tween the cavity photons and the electronic transitions Figure 1 is the energy level diagram of the double quan- and the fifth terms is the antiresonant interactions be- tween them. a† is the creation operators of the cavity tum wells separated by a thin tunneling barrier. The deep k with in-plane wave vector k and energy and quantum well populates two-dimensional electron gas cav, k b† , d † are respectively the creation operato rs of the density (2DEG) in the first subband 1 at low tempera- k k tures with gas density. The energy splitting of the energy electronic excitation mode of wave vector k and en- ergy , . , are the vacuum Rabi subband 2 and 3 is caused by resonant tunneling. 12 13 12,k 13,k frequency of the cavity photon and the two electronic 12 , 13 are corresponding energies of the two in- tersubband transition energy from 1 to 2 and 3 . excitation which quantifies the strength of the light-matter If we denote with z the growth direction of the multiple dipole coupling and it can become a significant fraction of the intersubband transition. The explicit expression is quantum well structure, then the dipole moment of the ˆ ˆ ˆ ˆ 12 transition is aligned along z, i.e., dd12 12 z, dd13 13 z. 2 e2 Nf sin2 (2) The in-plane wave vector k is a conserved quantity. 12 3 ,k eff el QW 12 3 1 mL0 cav where NQW is the number of quantum wells present in the cavity, el NS el is the electron density per unit 1 area in the deep quantum wells, Nel is the number of 2 the electron in deep well and S is the quantization area. continuum eff Lcav is the effective length of the cavity mode, is the cavity dielectric constant, and 1 is the intracavity probe photon propagation angle. H are bilinear in the field operators and can be di- 3 2DEG agonalized through a Bogoliubov transformation. Three intersubband polariton annihilation operators can be in- troduced as following Figure 1. Subband energy level diagram for double quan- cwaxbydza † tum wells separated by a thin tunneling barrier. The deep j,,kjkkjkkjkkjk , , ,k (3) quantum well contains a two-dimensional electron gas in †† pb qd the lowest subband. jk,, k jk k Copyright © 2013 SciRes. OPJ T. WANG ET AL. 295 where j {1, 2, 3} . The Hamiltonian of the system can 1 Hdqph ph† be written as qk,,, qk qk k 2 3 ph † ph † H Ec † c (4) idq a a G j,,,kjkjk qk,, qk k qk , qk , k j1 k k phph † 1 where the constant term EG is the vacuum energy and Hdq qk,,, qk qk not considered here. The vectors k 2 T idq ph a† ph † a vwxyzpq ,,,, , (5) qk,, qk k qk , qk , k jk,,,,,,, jk jk jk jk jk jk k Inserting expression (5) into (1) and notes the Bose 1 Hdqel el † commutation rule 2 2,qk,2,,2,, qk qk k 2 † el†† el cc, jj, (6) idq b b j,,kjk kk , 2,qk , 2, qk , k 2, qk , 2, qk , k k imposes the normalization condition 1 Hdqel el † **** 3 3,qk , 3, qk , 3, qk , wwj,,kjk xx jkjk ,, y jkjk ,, y zz jkjk ,, k 2 (7) ** el†† el pp qq idq d d jk,, j k jk ,, j k jj, 3,,qk 3,, qk k 3,, qk 3,, qk k k We found five excitations should be taken into account 1 el el † which are related with the cavity mode and the two elec- Hdq qk,,, qk qk 2 tronic transitions and treated as ensembles of quantum k oscillators.