The line shape of resonances in the overlapping regime is studied by using the eigenvalues and eigenfunctions of the effective Hamiltonian of an open quantum system. A generalized expression $\tilde q_k(E)$ for the Fano parameter of the resonance state $k$ is derived that contains the interaction of the state $k$ with neighboured states $l\ne k$ via the continuum. It is energy dependent since the coupling coefficients between the state $k$ and the continuum show a resonance-like behaviour at the energies of the neighboured states $l\ne k$. Under certain conditions, the energy dependent $\tilde q_k(E)$ are equivalent to the generalized complex energy independent Fano parameters that are introduced by Kobayashi et al. in analyzing experimental data. Long-lived states appear mostly isolated from one another in the cross section, also when they are overlapped by short-lived resonance states. The $\tilde q_k(E)$ of narrow resonances allow therefore to study the complicated interplay between different time scales in the regime of overlapping resonance states by controlling them as a function of an external parameter.
Fano resonances and bound states with energy in the continuum are ubiquitous phenomena in different areas of physics. Observations, however, have been limited so far to single-particle processes. In this work we experimentally investigate the multi-particle case and observe Fano interference in a non-interacting two-particle Fano-Anderson model by considering propagation of two-photon states in engineered photonic lattices. We demonstrate that the quantum statistics of the particles, either bosonic or fermionic, strongly affects the decay process. Remarkably, we find that the Fano resonance, w…
It is well known that in open quantum systems resonances can coalesce at an exceptional point, where both the energies {\em and} the wave functions coincide. In contrast to the usual behaviour of the scattering amplitude at one resonance, the coalescence of two resonances invokes a pole of second order in the Green's function, in addition to the usual first order pole. We show that the interference due to the two pole terms of different order gives rise to patterns in the scattering cross section which closely resemble Fano-Feshbach resonances. We demonstrate this by extending previous work on…
Fano resonances are proposed to perform a measurement of a spin state (whether it is up or down) of a single electron in a quantum dot via a spin-polarized current in an adjacent quantum wire. Rashba-like spin-orbit interaction in a quantum dot prohibits spin-flip events (Kondo-like phenomenon). That ensures the measurement to be non-demolishing.
We explain the phenomena of electromagnetically induced transparency (EIT) of a weak probe field and tunable Fano resonances in hybrid optomechanics. The system of study consists of a two-level atom coupled to a single-mode field of an optomechanical resonator with a moving mirror. We show that a single EIT window exists in the presence of optomechanical coupling or Jaynes-Cummings coupling, whereas two distinct double EIT windows occur when both the couplings are simultaneously present. Furthermore, based on our analytic and numerical work, we prove the existence of tunable fano resonances in…
We study the effect of PT-symmetric complex potentials on the transport properties of non-Hermitian systems, which consist of an infinite linear chain and two side-coupled defect points with PT-symmetric complex on-site potentials. By analytically solving the scattering problem of two typical models, which display standard Fano resonances in the absence of non-Hermitian terms, we find that the PT-symmetric imaginary potentials can lead to some pronounced effects on transport properties of our systems, including changes from the perfect reflection to perfect transmission, and rich behaviors for…
Asymmetric spectral line shapes are a hallmark of interference of a quasi-bound state with a continuum of states. Such line shapes are well known for multichannel systems, for example, in photoionization or Feshbach resonances in molecular scattering. On the other hand, in resonant single channel scattering, the signature of such interference may disappear due to the orthogonality of partial waves. Here, we show that probing the angular dependence of the cross section allows us to unveil asymmetric Fano profiles also in a single channel shape resonance. We observe a shift in the peak of the re…
Observation of the Fano line shapes is essential to understand properties of the Fano resonance in different physical systems. We explore a tunable Fano resonance by tuning the phase shift in a Mach-Zehnder interferometer (MZI) based on a single-mode nano-optomechanical cavity. The Fano resonance is resulted from the optomechanically induced transparency caused by a nano-mechanical resonator and can be tuned by applying an optomechanical MZI. By tuning the phase shift in one arm of the MZI, we can observe the periodically varying line shapes of the Fano resonance, which represents an elaborate…
The Fano line profiles, originally discovered in the context of photoionization, have been found to occur in a large class of systems like resonators, metamaterials, plasmonics. We demonstrate the existence of such resonances in cavity optomechanics by identifying the interfering contributions to the fields generated at antiStokes and Stokes frequencies. Unlike the atomic systems, the optomechanical systems provide great flexibility as the width of the resonance is controlled by the coupling field. We further show how the double cavities coupled by a single optomechanical mirror can lead to th…
The Fano Resonance, involving the mixing between a quasi-bound `discrete' state of an inelastic channel lying in the continuum of scattering states belonging to the elastic channel, has several subtle features. The underlying ideas have recently attracted attention in connection with interference effects in quantum wires and mesoscopic transport phenomena. Simple toy models are provided in the present study to illustrate the basics of the Fano resonance in a simple and tractable setting.
Asymmetric resonances in elastic n+$^{19}$C scattering are attributed to Efimov states of such neutron-rich nuclei, that is, three-body bound states of the n+n+$^{18}$C system when none of the pairs is bound or some of them only weakly bound. By fitting to the general resonance shape described by Fano, we extract resonance position, width, and the "Fano profile index". While Efimov states have been discussed extensively in many areas of physics, there is only one very recent experimental observation in trimers of cesium atoms. The conjunction that we present of the Efimov and Fano phenomena ma…
We demonstrate coherent control of optomechanically induced transparency and Fano resonances in a four mirror macroscopic optomechanical cavity, with two movable mirrors, each driven by an external mechanical pump. The variable control of the amplitude and phase of the coherent mechanical pumps provides a means of tuning the shape and nature of the Fano profiles. Further, our scheme shows the occurrence of tunable optomechanical features, even at very low mechanical driving field amplitudes, in macroscopic optomechanical cavities.
In a previous paper it has been shown that the interference of the first and second order pole of the Green's function at an exceptional point, as well as the interference of the first order poles in the vicinity of the exceptional point, gives rise to asymmetric scattering cross section profiles. In the present paper we demonstrate that these line profiles are indeed well described by the Beutler-Fano formula, and thus are genuine Fano resonances. Also further away from the exceptional points excellent agreement can be found by introducing energy dependent Fano parameters.
A route toward lineshape engineering of Fano resonances in photonic structures is theoretically proposed, which uses dynamic modulation of the refractive index of a microcavity. The method is exemplified by considering coupled-resonator optical waveguide systems. An exact Floquet analysis, based on coupled-mode theory, is presented. Two distinct kinds of resonances can be dynamically created, depending on whether the static structure sustains a localized mode or not. In the former case a single Fano resonance arises, which can be tuned in both frequency and line width by varying the refractive…
We investigate the effect of decoherence on Fano resonances in wave transmission through resonant scattering structures. We show that the Fano asymmetry parameter q follows, as a function of the strength of decoherence, trajectories in the complex plane that reveal detailed information on the underlying decoherence process. Dissipation and unitary dephasing give rise to manifestly different trajectories. Our predictions are successfully tested against microwave experiments using metal cavities with different absorption coefficients and against previously published data on transport through qua…
Fano resonance is a unique feature of interacting quantum systems, exhibiting resonance shapes distinctively different from conventional symmetric resonance curves. Recently, Fano resonances have been found in plasmonic nanoparticles, photonic crystals, and electromagnetic metamaterials. Here we report Fano-like photoluminiscence curves in nanodiamond solutions as a result of incoherent combination of two or more scattering and fluorescence processes. We argue that, analogously to Fano resonances, the steep asymmetric dispersion of the photoluminiscence profile in nanodiamond solutions, in com…
We investigate the controllability of electromagnetically induced transparency (EIT) and Fano resonances in hybrid optomechanical system which is composed of cigar-shaped Bose-Einstein condensate (BEC) trapped inside high-finesse Fabry-Pérot cavity driven by a single mode optical field along the cavity axis and a transverse pump field. Here, transverse optical field is used to control the phenomenon of EIT in the output probe laser field. The output probe laser field can efficiently be amplified or attenuated depending on the strength of transverse optical field. Furthermore, we demonstrate th…
Spectroscopic signatures associated with symmetric Lorentzian and asymmetric Fano line shapes are ubiquitous. Distinct features of Fano resonances in contrast with conventional symmetric resonances have found several applications in photonics such as optical switching, sensing, lasing, and nonlinear and slow-light devices. Therefore, it is important to have control over the generation of these resonances. In this work, we show through ab initio simulations of coupled light-matter systems that Fano interference phenomena can be realized in a multimode photonic environment by strong coupling to …
We revisit the basic properties of Fano-Feshbach resonances in two-body systems with van der Waals tail interactions, such as ultracold neutral atoms. Using a two-channel model and two different methods, we investigate the relationship between the width and shift of the resonances and their dependence on the low-energy parameters of the system. Unlike what was previously believed [Rev. Mod. Phys. 82, 1225 (2010)] for magnetic resonances, we find that the ratio between the width and the shift of a resonance does not depend only on the background scattering length, but also on a closed-channel s…
We study a resonator coupled to a generic detector and calculate the noise spectra of the two sub-systems. We describe the coupled system by a closed, linear, set of Langevin equations and derive a general form for the finite frequency noise of both the resonator and the detector. The resonator spectrum is the well-known thermal form with an effective damping, frequency shift and diffusion term. In contrast, the detector noise shows a rather striking Fano-like resonance, i.e. there is a resonance at the renormalized frequency, and an anti-resonance at the bare resonator frequency. As examples …
In this study, a standing wave in an optical nanocavity with Bose-Einstein condensate (BEC) constitutes a one-dimensional optical lattice potential in the presence of a finite two bodies atomic interaction. We report that the interaction of a BEC with a standing field in an optical cavity coherently evolves to exhibit Fano resonances in the output field at the probe frequency. The behavior of the reported resonance shows an excellent compatibility with the original formulation of asymmetric resonance as discovered by Fano [U. Fano, Phys. Rev. 124, 1866 (1961)]. Based on our analytical and nume…
We demonstrate theoretically the Fano resonance and the conversion from fast to slow light in a hybrid quantum dot-semiconductor/superconductor ring device, where the QD is coupled to a pair of MFs appearing in the hybrid S/S ring device. The absorption spectra of the weak probe field can exhibit a series of asymmetric Fano line shapes and their related propagation properties such as fast and slow light effects are investigated based on the hybrid system for suitable parametric regimes. The positions of the Fano resonances can be determined by the parameters, such as different detuning regimes…
We report the observation of resonance-like loss in the trap population of ultracold dysprosium as a function of magnetic field, which we attribute to anisotropy-induced Fano-Feshbach resonances arising from Dy's large magnetic dipole moment and nonzero electronic orbital angular momentum. We recorded these resonances for four different isotopes, three bosonic and one fermionic, over a field range of 0-6 G and show that the number of resonances changes significantly as a function of temperature, even in the nK regime. Most of the observed resonances are of very narrow width. The fermionic isot…
We demonstrate a classical analogy to the Fano anti-resonance in levitated optomechanics by applying a DC electric field. Specifically, we experimentally tune the Fano parameter by applying a DC voltage from 0~kV to 10~kV on a nearby charged needle tip. We find consistent results across negative and positive needle voltages, with the Fano line-shape feature able to exist at both higher and lower frequencies than the fundamental oscillator frequency. We can use the Fano parameter to characterize our system to be sensitive to static interactions which are ever-present. Currently, we can distingu…
A critical aspect of quantum mechanics is the nonlocal nature of the wavefunction, a characteristic that may yield unexpected coupling of nominally-isolated systems. The capacity to detect this coupling can be vital in many situations, especially those in which its strength is weak. In this work we address this problem in the context of mesoscopic physics, by implementing an electron-wave realization of a Fano interferometer using pairs of coupled quantum point contacts (QPCs). Within this scheme, the discrete level required for a Fano resonance is provided by pinching off one of the QPCs, the…
