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The one-half spin free Larmor and parametrically induced Rabi precessions simulated with two coupled pendula

Valentin Leroy, J.-C. Bacri, Thierry Hocquet, Martin Devaud

Published Jul 30, 2009• 0 citations
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Abstract

It was already shown that, with a simplest classical device, namely two coupled pendula, one can simulate the movement of a free quantum two-level system, as for instance a one-half spin in a static magnetic field. We now show that, with a hardly more sophisticated device, one can simulate the latter system undergoing a sinusoidal perturbation. We present an experimental mechanical illustration of the transition of the system between its two eigenstates, known as the Rabi precession. Abstract theoretical concepts of absorption and stimulated emission of energy are thus provided with an intuitive support.

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It was already shown that, with a simplest classical device, namely two coupled pendula, one can simulate the movement of a free quantum two-level system, as for instance a one-half spin in a static magnetic field. We now show that, with a hardly more sophisticated device, one can simulate the latter system undergoing a sinusoidal perturbation. We present an experimental mechanical illustration of the transition of the system between its two eigenstates, known as the Rabi precession. Abstract theoretical concepts of absorption and stimulated emission of energy are thus provided with an intuitive support.
It has already been shown that, with the simplest classical device, namely two coupled pendula, one can simulate the movement of a free quantum two-level system, as for instance a one-half spin in a static magnetic field. We now show that, with a hardly more sophisticated device, one can simulate the latter system undergoing outer perturbation. In the case of sinusoidal excitation, we present an experimental mechanical illustration of the transition of the system between its two eigenstates, known as the Rabi precession. Abstract theoretical concepts of absorption and stimulated emission of energy are thus provided with intuitive support.
We propose a classical analogy to illustrate the up ↔ down flip of a one-half spin submitted to a static and a rotating magnetic field, in the standard magnetic resonance configuration. Surprising though it may seem, it is possible to design a rather simple device-namely a set of two coupled pendula-to simulate and visualize the Larmor and Rabi precessions of the latter spin. In this analogy, the static field is associated with the angular frequency detuning between both eigenmodes of the two-degree-of-freedom harmonic oscillator constituted by the two pendula, whereas the rotating field is simulated by means of a parametric modulation of the length of one of the pendula. Under the circumstances, the up or down spin states are represented by either eigenmodes, and consequently the spin-flip is put in concrete form by the coupled pendula being driven from one eigenmode to the other. In the present paper, we experimentally demonstrate the possibility of triggering such a flip using a mechanical analogy of the so-called rapid adiabatic passage technique.
It is shown that, with a simple two-pendulum device, one can experimentally simulate the behaviour of a one-half spin. After a quick overflight of the two-degree-of-freedom harmonic oscillator's properties, we show that, in the quasi-degeneracy limit, this system is formally equivalent to a one-half spin: its physical states can be described by state vectors belonging to a two-dimensional Hilbert space; its free motion obeys a Schrödinger equation. An -isomorphous representation space is used to illustrate this movement in terms of Larmor precession.
Abstract The behavior of a magnetic dipole in magnetic fields is of interest in many systems including magnetic resonance imaging. The explanation presented in this chapter combines quantum physics and electricity and magnetism. The chapter begins with an explanation of magnetic dipole Larmor precession in static magnetic fields. The discussion then shifts to time-dependent magnetic fields and how they lead to transitions between the dipole’s energy states. The calculations are carried out both by using the time dependence of energy eigenstates and by solving the differential equations describing the quantum state vector amplitudes. The results are expressed in terms of the Rabi frequency and the Rabi formula. For the special cases of π and π/2 pulses of the oscillating magnetic field, the results show how those pulses implement quantum gates for the dipole system.
Coupled nanomechanical resonators have recently attracted much attention for both fundamental studies in physics and broad applications in high-precession detection or sensing. By studying the Landau-Zener transitions and Rabi oscillation of two coupled resonators, it has been shown that such a two-mode system acts as a classical two-level system bearing the analog to a quantum mechanical two-level one. Here we construct a Stückelberg interferometer with two coupled cantilevers by driving the system through the avoided crossing twice. By measuring the non-adiabatic phase acquired at the Landau-Zener transition, we unveil an in-depth analog between the two-mode and quantum two-level systems. Our study opens up new opportunities for constructing interferometers with classical devices.
Stimulated emission and absorption are two fundamental processes of light–matter interaction, and the coefficients of the two processes should be equal. However, we will describe a generic method to realize the significant difference between the stimulated emission and absorption coefficients of two nondegenerate energy levels, which we refer to as a nonreciprocal transition. As a simple implementation, a cyclic three-level atom system, comprising two nondegenerate energy levels and one auxiliary energy level, is employed to show a nonreciprocal transition via a combination of synthetic magnetism and reservoir engineering. Moreover, a single-photon nonreciprocal transporter is proposed using two one-dimensional semi-infinite coupled-resonator waveguides connected by an atom with nonreciprocal transition effect. Our work opens up a route to design atom-mediated nonreciprocal devices in a wide range of physical systems.