All-optical scheme for detecting the possible Majorana signature based on QD and nanomechanical resonator systems

Majorana fermions(MFs) are exotic particles that are their own anti-particles. Currently, the search for MFs occurring as quasiparticle excitations in condensed matter systems has attracted widespread interest, because of their importance in fundamental physics and potential applications in topological quantum computation based on solid-state devices. Motivated by recent experimental progress towards the detection and manipulation of MFs in hybrid semiconductor/superconductor heterostructures, in this review, we present a novel proposal to probe MFs in all-optical domain. We introduce a single quantum dot(QD), a hybrid quantum dot-nanomechanical resonators(QD-NR) system, and a carbon nanotube(CNT) resonator implanted in a single electron spin system with optical pump-probe technology to detect MFs, respectively. With this scheme, a possible Majorana signature is investigated via the probe absorption spectrum and nonlinear optical Kerr effect, and the coupling strength between MFs and the QD or the single electron spin is also determined. In the hybrid QD-NR system, vibration of the NR will enhance the nonlinear optical effect, which makes the MFs more sensitive for detection. In the CNT resonator with a single electron, the single electron spin can be considered as a sensitive probe, and the CNT resonator behaved as a phonon cavity is robust for detecting of MFs. This optical scheme will provide another method for the detection MFs and will open the door for new applications ranging from robust manipulation of MFs to quantum information processing based on MFs.     

Transient electron population and optical properties in a semiconductor quantum well

We investigate the transient behaviors of the dispersion and the absorption in a three-level GaAs/AlGaAs semiconductor quantum well system. It is found that the Fano interference and the energy splitting affect the transient behaviors dramatically, which can be used to manipulate efficiently the gain-absorption coefficient and group velocity of the probe field. The dependence of transient electron population on the Fano interference and the energy splitting is also discussed.     

等离子体纳米结构中的Fano共振效应及其应用

Fano共振效应是一种具有非对称线型的共振散射现象,起源于共振过程和非共振过程的量子干涉效应。近年来,在等离子体纳米结构中Fano共振现象也被发现,并成为纳米光子学的一个研究热点。等离子体Fano共振通常具有较窄的光谱线宽,且不能直接与入射光耦合,只能局域在近场,强的近场局域特性可以获得巨大的表面电磁场增强。由于等离子体Fano共振独特的光学特性,已经被应用到单分子探测、高灵敏度传感、增强光谱、完美吸收、电磁诱导透明和慢光光子学器件等众多领域当中。     

Splitting of the Fano resonance by Coulomb interactions in a two-dot quantum ring

We study the splitting of the Fano resonance in a Aharonov–Bohm interferometer with a quantum dot in each of its arms. Both intra- and inter-dot Coulomb repulsions are taken into account by employing the Keldysh nonequilibrium Green’s function technique. The single narrow Fano resonance in the noninteracting case is split into two in the presence of either intra- or inter-dot Coulomb interaction. We find that four Fano peaks emerge in the conductance or local density of states spectra when the two kinds of interactions exist simultaneously. Such behavior holds true for the accompanying broad Breit–Wigner type resonance. We also show that the positions of the Fano peaks can be tuned with the aid of the magnetic flux penetrating through the ring, which might have practical applications in device design or quantum computation.     

Fano resonance sensing based on coupled sub-wavelength dielectric grating and periodic photonic crystal

Based on the diffraction effect of sub-wavelength dielectric grating and the optical property of periodic photonic crystal, a hybrid structure of sub-wavelength grating all-dielectric multilayer thin film containing periodic photonic crystal is proposed. The transmission property of the structure is simulated by finite element method (FEM). The result shows that the discrete state generated by the sub-wavelength waveguide grating will be coupled with the continuous state generated by the photonic crystal cavity and the Fano resonance can be formed. The Fano resonance sensing model based on structural parameters and resonance wavelength are established, the influence of structural parameters on the Fano resonance spectral curve is quantitatively analyzed by numerical simulations, and the dynamic detection of the refractive index of samples is realized. The above structure can realize the optical refractive index sensing with high figure of merit (FOM) value and provide an effective theoretical reference for the formation of Fano resonance in the all-dielectric hybrid structure.     

Mesoscopic Fano effect modulated by Rashba spin–orbit coupling and external magnetic field

By employing non-equilibrium Green's function method, the mesoscopic Fano effect modulated by Rashba spin–orbit (SO) coupling and external magnetic field has been elucidated for electron transport through a hybrid system composed of a quantum dot (QD) and an Aharonov–Bohm (AB) ring. The results show that the orientation of the Fano line shape is modulated by the Rashba spin–orbit interaction kRL$k_{R}L$ variation, which reveals that the Fano parameter q will be extended to a complex number, although the system maintains time-reversal symmetry (TRS) under the Rashba SO interaction. Furthermore, it is shown that the modulation of the external magnetic field, which is applied not only inside the frame, but also on the QD, leads to the Fano resonance split due to Zeeman effect, which indicates that the hybrid is an ideal candidate for the spin readout device.     

Anomalous electric-field dependence of excitonic Fano-resonance spectra in semiconductor quantum-wells

Optical absorption spectra due to Fano resonance (FR) of an exciton in a quantum well with an external electric field perpendicular to the layer plane are presented, based on multi-channel scattering calculations incorporating a hole-subband mixing effect. Peak values of the calculated FR spectra exhibit anomalous field-dependent changes. These cannot be accounted for by the commonly-known quantum-confined Stark effect (QCSE) that has been applied exclusively to bound state spectra. This behavior, ascribable to correlation between Fano couplings and the QCSE, is revealed just in high-resolution spectra, otherwise the field-dependence results in nothing but the same as that of the bound-state spectra.     

Objectively discerning Autler-Townes splitting from electromagnetically induced transparency

Autler-Townes splitting (ATS) and electromagnetically induced transparency (EIT) both yield transparency in an absorption profile, but only EIT yields strong transparency for a weak pump field due to Fano interference. Empirically discriminating EIT from ATS is important but so far has been subjective. We introduce an objective method, based on Akaike's information criterion, to test ATS vs EIT from experimental data for three-level atomic systems and determine which pertains. We apply our method to a recently reported induced-transparency experiment in superconducting-circuit quantum electrodynamics.     

Structural control of Fano resonances in semiconductor heterostructures

Structural control of quantum interference in the optical intrasubband absorption spectrum of GaAs/AlGaAs multi-quantum wells is investigated theoretically. Our study shows that pronounced Fano resonances are in general difficult to obtain in quantum well heterostructures, with a presence of distinct Fano resonance features being the exception rather than the rule. Guided by an analogy to Young’s double-slit experiment, we design increasingly improved structures to display Fano resonances. Best results are achieved in structures where there is strong overlap between the ground-state wavefunction and scattering states associated with the uncoupled continuum. Alternatively one may use ionization via two or more resonances. In this case, resonances should not be separated by more than 25 meV to give significant effects. Moreover, we show that resonance features may also be induced without potential barriers to a continuum merely via orthogonality between bound and excited states.     

Quantum dots as scatterers in electronic transport: interference and correlations

Conductance through a system consisting of a wire with side-attached quantum dots is calculated. Such geometry of the device allows to study the coexistence of quantum interference, electron correlations and their influence on conductance. We underline the differences between ‘classical’ Fano resonance in which the resonant channel is of single-particle nature and ‘many-body’ Fano resonance with the resonant channel formed by Kondo effect. The influence of electron-electron interactions on the Fano resonance shape is also analyzed.     

Tunable optomechanically induced transparency and fast–slow light in a loop-coupled optomechanical system

We theoretically explore the tunability of optomechanically induced transparency(OMIT) phenomenon and fast–slow light effect in a loop-coupled hybrid optomechanical system in which two optical modes are coupled to a common mechanical mode. In the probe output spectrum, we find that the interference phenomena OMIT caused by the optomechanical interactions and the normal mode splitting(NMS) induced by the strong tunnel coupling between the cavities can be observed. We further observe that the tunnel interaction will affect the distance and the heights of the sideband absorption peaks. The results also show that the switch from absorption to amplification can be realized by tuning the driving strength because of the existence of stability condition. Except from modulating the tunnel interaction, the conversion between slow light and fast light also can be achieved by adjusting the optomechanical interaction in the output field. This study may provide a potential application in the fields of high precision measurement and quantum information processing.     

New polaron effect in magnetooptic phenomena in a quantum well

It is predicted that resonance coupling between two discrete electron energy levels corresponding to different size-quantization quantum numbers and different Landau quantum numbers can occur in a quantum well in a quantizing magnetic field. The resonance coupling is due to the interaction of an electron with LO phonons and results in the formation of polaron states of a new type. It is shown that for a certain value of the magnetic field, which depends on the splitting of the electron size-quantization levels, the absorption peak and the two-phonon resonance Raman scattering peak split into two components, the separation between which is determined by the electron-phonon coupling constant. The resonance coupling between size-quantization levels with the same Landau quantum numbers is also studied. The splitting of the peaks in this case is virtually independent of the magnetic field and can be observed in much weaker fields. The experimental observation of the effect will make it possible to determine the relative position of the electronic levels and the electron-phonon coupling constant. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 7, 511–515 (10 April 1997)     

Semiconductor-metal nanoparticle molecules: hybrid excitons and the nonlinear fano effect

Modern nanotechnology opens the possibility of combining nanocrystals of various materials with very different characteristics in one superstructure. Here we study theoretically the optical properties of hybrid molecules composed of semiconductor and metal nanoparticles. Excitons and plasmons in such a hybrid molecule become strongly coupled and demonstrate novel properties. At low incident light intensity, the exciton peak in the absorption spectrum is broadened and shifted due to incoherent and coherent interactions between metal and semiconductor nanoparticles. At high light intensity, the absorption spectrum demonstrates a surprising, strongly asymmetric shape. This shape originates from the coherent internanoparticle Coulomb interaction and can be viewed as a nonlinear Fano effect which is quite different from the usual linear Fano resonance.     

Andreev-Fano Effect in a Hybrid Normal-Metal/Superconductor Interferometer

We report on a new type of Fano effect, named as Andreev-Fano effect, in a hybrid normal-metal/supeeconductor (N/S) interferometer embedded with a quantum dot. Compared with the conventional Fano effect, AndreevFano effect has some new features related to the characteristics of Andreev reflection. In the Iinear response regime, the line shape is the square of the conventional Fano shape, while in the nonlinear transport, a sharp resonant structure is superposed on an expanded interference pattern, which is qualitatively different from the conventional Fano effect. The phase dependence of the hybrid N/S interferometer is also distinguished from those of all-N or all-S interferometers.     

Andreev-Fano Effect in a Hybrid Normal-Metal/Superconductor Interferometer

We report on a new type of Fano effect, named as Andreev-Fano effect, in a hybrid normal-metal/superconductor (N/S) interferometer embedded with a quantum dot. Compared with the conventional Fano effect, Andreev-Fano effect has some new features related to the characteristics of Andreev reflection. In the linear response regime, the line shape is the square of the conventional Fano shape, while in the nonlinear transport, a sharp resonant structure is superposed on an expanded interference pattern, which is qualitatively different from the conventional Fano effect. The phase dependence of the hybrid N/S interferometer is also distinguished from those of all-N or all-S interferometers.     

Tunable Fano resonances and plasmonic hybridization of gold triangle–rod dimer nanostructure

A gold dimer structure consisting of a notched triangle nanoslice and a rectangle nanorod is proposed to produce distinct Fano resonance. Owing to the coupling between the dipole plasmon mode of the nanorod and the dipole or quadrupole plasmon mode of the nanoslice, the extinction spectrum with a deep Fano dip is formed and can be well fitted by the Fano interference model for different geometry parameters. In addition, Fano resonance of the gold dimer nanostructure also intensely depends on the polarization direction of incident light. Moreover, Fano resonance of the triangle–rod trimer is also analyzed by adding another nanorod into the former dimer and exhibits the splitting of plasmonic resonant peak in high order coupling modes. The plasmonic hybridizations in these nanostructures have been analyzed for revealing the physical origin of the Fano resonance.     

Nearly Perfect Absorbers Operating Associated with Fano Resonance in the Infrared Range

We fabricate a three-layer metamaterial of metal patterns/dielectric/metal films.The optical properties associated with Fano resonance of the metamaterials are investigated experimentally and theoretically.The results indicate that the introduction of Fano resonance due to symmetry breaking leads to a much wider absorption range.Furthermore,the amplitude and phase of reflection can be modulated effectively by adjusting various free parameters using the proposed structure.     

外力驱动下耦合弹簧振子的法诺共振

法诺共振是物理体系中普遍存在的一种非对称共振现象,它最早起源于量子物理,其微观图像是原子谱线中窄的分离态与宽的连续态之间的相干干涉.本文利用经典力学体系中两个弹簧振子的耦合,使其中一个弹簧振子受到周期性外力的驱动,成功类比了量子力学中的法诺共振现象.通过分析每个弹簧振子的动力学方程,严格求解它们的振动公式,从而得到每个弹簧振子的振幅和位相与外部驱动力频率之间的关系.结果表明,耦合体系中受外力驱动的那个弹簧振子既可以发生非对称的法诺共振,又可以发生对称的洛仑兹共振,而另一个弹簧振子只能发生洛仑兹共振.本文的推导与分析能够使读者更好地理解法诺共振现象及其激发条件.     

Resonant-state Expansion of the Green’s Function of Open Quantum Systems

Our series of recent work on the transmission coefficient of open quantum systems in one dimension will be reviewed. The transmission coefficient is equivalent to the conductance of a quantum dot connected to leads of quantum wires. We will show that the transmission coefficient is given by a sum over all discrete eigenstates of the Hamiltonian, without a background integral. An apparent “background” is in fact not a background but generated by tails of various resonance peaks. By using the expression, we will show that the Fano asymmetry of a resonance peak is caused by the interference between various discrete eigenstates. In particular, a broad resonance can strongly skew the peak of a nearby sharp resonance.     

Optical Properties of Metal-Dielectric Structures Based on Photon-Crystal Opal Matrices

Optical properties of novel metal–dielectric nanocomposite materials based on opal matrices have been investigated. The position of optical resonances of nanocomposites, obtained by embedding of silver into the opal matrix by the electrothermodiffusion method, is explained by the Bragg diffraction, and an asymmetric form of resonance curves is attributed to the Fano resonance. An anomalous transmission and absorption of light by hybrid plasmon-photonic layered heterostructures, which is apparently associated with excitation of surface plasmon-polaritons, propagating along “metal–dielectric” interfaces, was revealed.