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arXiv:1803.02993 · Physical Review A

Dynamical resonances and stepped current in an attractive quantum pump

Kunal K. Das, Joshua Garner, Kevin Ruppert

Published Mar 21, 2018• 0 citations
arXivHTMLPDF

Abstract

We report on the transport properties of a single-mode quantum pump that operates by the simultaneous translation and oscillation of a potential well. We examine the dynamics comparatively using quantum, classical, and semiclassical simulations. The use of an attractive or well potential is found to present several striking features absent if a barrier potential is used instead, as usually favored. The trapping of particles by the well for variable durations and subsequent release leads to a fractal-like structure in the distribution of the classical scattering trajectories. Interference among them leads to a rich dynamical structure in the quantum current, conspicuously missing in the classical current. Specifically, we observe sharp steps, spikes, and dips in the current as a function of the incident energy of the carriers and determine that a dynamical version of Fano resonance has a role that depends on the direction of incidence and on multiple scattering by the potential.

DOI
10.1103/physreva.97.033614

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We report on the transport properties of a single-mode quantum pump that operates by the simultaneous translation and oscillation of a potential well. We examine the dynamics comparatively using quantum, classical, and semiclassical simulations. The use of an attractive or well potential is found to present several striking features absent if a barrier potential is used instead, as usually favored. The trapping of particles by the well for variable durations and subsequent release leads to a fractal-like structure in the distribution of the classical scattering trajectories. Interference among them leads to a rich dynamical structure in the quantum current, conspicuously missing in the classical current. Specifically, we observe sharp steps, spikes, and dips in the current as a function of the incident energy of the carriers and determine that a dynamical version of Fano resonance has a role that depends on the direction of incidence and on multiple scattering by the potential.
We present a detailed study of scattering by an amplitude-modulated potential barrier using three distinct physical frameworks: quantum, classical, and semiclassical. Classical physics gives bounds on the energy and momentum of the scattered particle, while also providing the foundation for semiclassical theory. We use the semiclassical approach to selectively add quantum-mechanical effects such as interference and diffraction. We find good agreement between the quantum and semiclassical momentum distributions. Our methods and results can be used to understand quantum and classical aspects of transport mechanisms involving time-varying potentials, such as quantum pumping.
We propose and study a quantum pump which emulates a traditional paddlewheel, that can be implemented with ultracold atoms in waveguides. We use wave-packet propagation to study its single-mode dynamics, which also determines its multimode current for mesoscopic setups. Energy flow with or without particle transport is possible. The spectrum reveals unusual features such as nonuniform Floquet sidebands and counterintuitive scattering. Explanations are found by examining the scattering dynamics comparatively using quantum, classical, and semiclassical pictures, indicating a rich system and experimentally accessible method to explore quantum versus classical dynamics.
Abstract We explore the dynamics of matter wave scattering in finite potential wells using analytical solutions of the Schrödinger equation within the framework of a quantum shutter model. We find that the incident wave interferes with the bound states of the quantum well, resulting in time-domain oscillations. These oscillations exhibit Rabi-type frequencies, characterised by the energy differences between the incident wave and the bound states of the quantum well. We show that in systems with double-bound states, the interference pattern is characterised by quantum beats in the time-dependent probability density. The period of these beatings depends on the energy difference between the bound states, which can be tuned by controlling the potential parameters. In the general case where bound, anti-bound, and resonant states coexist in the system spectrum, complex oscillations in the probability density arise from the interactions of the incident wave with different quantum states. We demonstrate that the bound states sector can effectively describe this complex behaviour, providing a simple and reliable analytical expression for the probability density in multilevel systems. This formula highlights the significant role of bound states, whose interaction with the incident wave dominates the transient probability density. This contrasts with conventional systems with potential barriers and wells, where resonances govern the wave dynamics.
A quantum pump is a device that transports particles through a circuit with localized time-varying potentials, and without the need for an external applied voltage or chemical potential. Quantum pumping was originally proposed in the context of electron transport in nanowires, but has proven difficult to implement. The ultracold atom approach represents a possible route around the current experimental bottleneck. We present an experiment to study 1D quantum mechanical scattering by an amplitude-modulated barrier. This experiment represents a first step toward implementing a quantum pump for ultracold atoms based on two such barriers modulated out of phase with one another. A single oscillating barrier imparts or subtracts kinetic energy in discrete amounts from the scattered atoms. In this manner, the energy spectrum of the scattered atoms resembles a comb with a tooth spacing proportional to the oscillation frequency of the barrier. This effect is analogous to the frequency modulation of a radio wave to add sidebands to a carrier frequency, where the carrier is the kinetic energy of ultracold atoms and the oscillating barrier provides the modulating signal. Numerical simulations of the scattering process confirm this basic scattering picture. We present dual chamber, dual-species a atom chip apparatus that produces quasi-pure Rubidium-87 Bose-Einstein condensates (BEC) of 10,000 atoms used to study the quantum scattering dynamics. The proposed experiment operates by releasing a BEC from a relaxed magnetic chip trap and directing it horizontally towards a tightly focused laser beam that serves as an oscillating barrier. A magnetic field gradient provided by is used to control the vertical motion of the BEC. Detection is carried out with a time of flight technique to resolve discrete atomic packet sidebands. This method can be used to study momentum sideband generation with a BEC in the presence of no or weak interactions. Dark-ground imaging can be used to detect small atom number BECs, which will have the benefit of weaker interactions.
In order to better understand the trapping and response time of resonant electron wave packets in a resonant tunneling structure, we examined the time-dependent transport of a spherically symmetric Gaussian wave packet through a model double-barrier potential. Within the effective mass picture, the wave packet is projected onto the complete eigenstates of the model potential. The wave packet is initially localized to the left of the barriers and allowed to propagate through the structure. At wave packet energies corresponding to the resonant energies, the probability transmitted to the right of the barriers exhibits a steplike behavior as a function of time. A computation is made of the quantum mechanical delay time, to~tclass, where to is the packet transit time and tclass is the transit time for a classical particle. An increase in this delay time is observed when the packet energy corresponds to the energy of the resonant levels, and a comparison is made to the decay time of a particle in the first resonant state of the well. The delay time increases with increasing barrier area and decreasing packet energy width.
Two rectangular models described by the one-dimensional Schr\"odinger equation with sharply localized potentials are suggested. The potentials have a multilayer thin structure being composed from adjacent barriers and wells. Their peculiar tunneling properties are studied in considerable detail. Particularly, in the zero-range limit when the potentials are squeezed to a single point, sharp peaks with total transmission are observed at certain (positive and negative) quantized values of the potential strength constant forming infinite discrete sets. Beyond these sets, the barrier-well structures behave as a perfectly reflecting wall. The transcendental equations with respect to potential strengths, the solutions of which determine transmission (resonance) sets, are derived. In this regard, both the models are exactly solvable. The energy dependence of an incident particle is shown to reveal a resonance behavior, being completely different from that observed in a typical double-barrier structure.