We study the tunneling through an arbitrary number of finite rectangular opaque barriers and generalize earlier results by showing that the total tunneling phase time depends neither on the barrier thickness nor on the inter-barrier separation. We also predict two novel peculiar features of the system considered, namely the independence of the transit time (for non resonant tunneling) and the resonant frequency on the number of barriers crossed, which can be directly tested in photonic experiments. A thorough analysis of the role played by inter-barrier multiple reflections and a physical interpretation of the results obtained is reported, showing that multibarrier tunneling is a highly non-local phenomenon.
Quantum tunneling across multiple barriers as yet is an unsolved problem for barrier numbers greater than five. The complexity of the mathematical analysis even for small number of barriers pushed it into the realms of Numerical Analysis. This work is aimed at providing a rigorously correct solution to the general N barrier problem, where N can be any positive integer. An exact algebraic solution has been presented, which overcomes the complexity of the WKB integrals that are traditionally employed, and matches the earlier results reported for small number of barriers. The solution has been ex…
Following our work [Phys. Rev. Lett. 125, 020401 (2020)], we discuss a semiclassical description of one-dimensional quantum tunneling through multibarrier potentials in terms of complex time. We start by defining a complex-extended continuum level density of unbound systems and show its relation to a complex time shift of the transmitted wave. While the real part of the level density and time shift describes the passage of the particle through classically allowed coordinate regions, the imaginary part is connected with an instanton-like picture of the tunneling through forbidden regions. We de…
We demonstrate Resonant Tunneling Diodes, embedded in double metal cavities, strongly coupled to the cavity field, while maintaining their electronic properties. We measure the polariton dispersion and find a relative vacuum Rabi splitting of 16%, which explicitly qualifies for the strong-coupling regime. Additionally we show that electronic transport has a significant influence on the polaritons by modulating the coupling strength. The merge between electronic transport and polaritonic physics in our devices opens up a new aspect of cavity quantum electro-dynamics and integrated photonics.
Tunneling of electrons through a barrier with complex potential is investigated. We focus on two cases, symmetric double rectangular barrier and double delta potential barrier, and give expressions for resonant transmission probability for both cases. Expressions for reflection amplitude and absorption are also obtained in the case of delta potential. It will be shown that for given dimensions of the potential barrier and the real part of the potential, resonant transmission probability approaches infinity for only one positive value of the imaginary part of the potential.
By using an exact analytical non-Hermitian formalism involving the full set of resonance (quasinormal) states and complex energy eigenvalues for quantum tunneling decay, we show that unitarity holds at any instant of time for the nonstationary decaying probability density in the whole space, thus providing a fundamental description of the quantum mechanical decay process.
We propose an electromechanical transducer based on a resonant-tunneling configuration that, with respect to the standard tunneling transducers, allows larger tunneling currents while using the same bias voltage. The increased current leads to an increase of the shot noise and an increase of the momentum noise which determine the quantum limit in the system under monitoring. Experiments with micromachined masses at 4.2 K could show dominance of the momentum noise over the Brownian noise, allowing observation of the quantum-mechanical noise at the mesoscopic scale.
The fastest tunneling response in double barrier resonant structures is investigated by considering explicit analytic solutions of the time dependent Schrödinger equation. For cutoff initial plane waves, we find that the earliest tunneling events consist on the emission of a series of propagating pulses of the probability density governed by the buildup oscillations in the quantum well. We show that the fastest tunneling response comes from the contribution of incident carriers at energies different from resonance, and that its relevant time scale is given by $τ_r=π\hbar /| E-ε| $, where $ε$ i…
We study the tunneling decay of a Bose-Einstein condensate out of tilted optical lattices within the mean-field approximation. We introduce a novel method to calculate also excited resonance eigenstates of the Gross-Pitaevskii equation, based on a grid relaxation procedure with complex absorbing potentials. This algorithm works efficiently in a wide range of parameters where established methods fail. It allows us to study the effects of the nonlinearity in detail in the regime of resonant tunneling, where the decay rate is enhanced by resonant coupling to excited unstable states.
In this paper, the interaction and transmission time of quantum density solitons waves representing particles passing through finite barrier potentials is investigated. Using the conservation of energy and of quantum density, it is first demonstrated that these waves have finite de Broglie wavelength and represent particles in quantum theory. The passage of the quantum density solitons (particles) through barriers of finite energies is then shown to lead to the phenomena of resonant tunneling and, in Josephson-like configurations, to the quantization of magnetic flux. A precise general measure…
We investigate the effects of high-Q_c resonant cavity on macroscopic quantum tunneling (MQT) of fluxon both from a metastable state to continuum and from one degenerate ground-state of a double-well potential to the other. By using a set of two coupled perturbed sine-Gordon equations, we describe the tunneling processes in linear long Josephson junctions (LJJs) and find that MQT in the resonant cavity increases due to potential renomalization, induced by the interaction between the fluxon and cavity.Enhancement of the MQT rate in the weak-coupling regime is estimated by using the experimantal…
We show that discrete-time quantum walks on the line, $\mathbb{Z}$, behave as "the quantum tunneling". In particular, quantum walkers can tunnel through a double-well with the transmission probability $1$ under a mild condition. This is a property of quantum walks which cannot be seen on classical random walks, and is different from both linear spreadings and localizations.
The high internal quantum efficiency observed in higher plants remains an outstanding problem in understanding photosynthesis. Several approaches such as quantum entanglement and quantum coherence have been explored. However, none has yet drawn an analogy between superlattices and the geometrical structure of granal thylakoids in leaves. In this paper, we calculate the transmission coefficients and perform numerical simulations using the parameters relevant to a stack of thylakoid discs. We then show that quantum resonant tunneling can occur at low effective mass of particles for 680 nm and 70…
We report on measurements of flux and charge noise in an rf-SQUID flux qubit using macroscopic resonant tunneling (MRT). We measure rates of incoherent tunneling from the lowest energy state in the initial well to the ground and first excited states in the target well. The result of the measurement consists of two peaks. The first peak corresponds to tunneling to the ground state of the target well, and is dominated by flux noise. The second peak is due to tunneling to the excited state and is wider due to an intrawell relaxation process dominated by charge noise. We develop a theoretical mode…
