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Results in Physics

Controlling straight line motion up to quantum levels by quantum measurements

Yong-Yi Huang

Published Jul 31, 2018• 0 citations
Publisher

Abstract

A classical charged particle moves along a straight line and interacts with a silver atom in its ground state fixed at the origin of coordinates through Biot-Savart coupling. If the silver atom initially lies in a spin superposition state of valence electron, in the co-moving reference frame the projected measurements of the spin of silver’s valence electron along the z direction determine the moving direction of the charged particle. The projected measurements of that spin along the x or the y direction yield straight line motion versions of Schrödinger’s cat state for the charged particle. When the spin coherence state of the silver atom suffers from its environment decoherence, as long as the silver atom’s spin is entangled with the trajectories of the moving charged particle, the measurements on the silver atom’s spin also yield the partial superpositions of different trajectories of the moving charged particle. It is possible to control mechanical motion up to quantum level by the means of quantum measurements.

DOI
10.1016/j.rinp.2018.07.031

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A classical charged particle moves along a straight line and interacts with a silver atom in its ground state fixed at the origin of coordinates through Biot-Savart coupling. If the silver atom initially lies in a spin superposition state of valence electron, in the co-moving reference frame the projected measurements of the spin of silver’s valence electron along the z direction determine the moving direction of the charged particle. The projected measurements of that spin along the x or the y direction yield straight line motion versions of Schrödinger’s cat state for the charged particle. When the spin coherence state of the silver atom suffers from its environment decoherence, as long as the silver atom’s spin is entangled with the trajectories of the moving charged particle, the measurements on the silver atom’s spin also yield the partial superpositions of different trajectories of the moving charged particle. It is possible to control mechanical motion up to quantum level by the means of quantum measurements.
A classical charged particle travels along a circular orbit and interacts with a silver atom in its ground state fixed at the center of the circle through Biot-Savart coupling. We find that if the silver atom initially lies in a spin superposition state of valence electron, in the co-rotating frame of reference the projected measurements of the spin of silver’s valence electron along the z direction determine the rotational direction, and the projected measurements of that spin along the x or the y direction yield planet versions of the state of Schrödinger’s cat.
Summary form only given, as follows. The ability to create and completely characterize a variety of fundamental quantum states has long been sought after in the laboratory since it brings to the forefront issues involving the relationship between quantum and classical physics. The interaction of a trapped atom with classical laser light constitutes a simple and well-isolated quantum system that makes experiments along these lines possible. The motion of an ion trapped in a rf-trap can be described as a quantum harmonic oscillator. If the ion is driven by a classical light field, several interactions similar to and beyond the simple Jaynes-Cummings coupling can be realized. These couplings allow for precisely controlled engineering and measurement of quantum states. We create states having both classical and nonclassical character including thermal, number, coherent, squeezed, and Schrodinger cat states. The motional quantum state is fully reconstructed with use of two novel schemes that determine the density matrix in the number state basis and the Wigner function. Our techniques allow well-controlled experiments on decoherence and related phenomena on the quantum-classical borderline.
Optimal simultaneous control of position and momentum can be achieved by maximizing the probabilities of finding their experimentally observed values within two well-defined intervals. The assumption that particles move along straight lines in free space can then be tested by deriving a lower limit for the probability of finding the particle in a corresponding spatial interval at any intermediate time ttt. Here, it is shown that this lower limit can be violated by quantum superpositions of states confined within the respective position and momentum intervals. These violations of the particle propagation inequality show that quantum mechanics changes the laws of motion at a fundamental level, providing a different perspective on causality relations and time evolution in quantum mechanics.
Summary form only given. The development of methods to manipulate and measure the quantum mechanical state of a physical system represents one of the great challenges of modern science. Examples of systems in which quantum control is sought or has been accomplished include trapped atomic ions, the electromagnetic field, Rydberg electrons, nuclear spins and vibrations in molecules, and chemical reactions. For many years a paradigm for quantum coherent evolution has been the occurrence of tunneling in macroscopic and mesoscopic double-well potentials. Much theoretical work has been done on this model system, but a series of fundamental questions remain to be addressed in well-controlled experiments, notably whether coherent evolution can be enforced in the presence of a noisy environment, by suitable perturbations of the state of the tunneling particle. The challenge is to find simple physical systems, which can be made to interact with a well characterized environment in a controlled manner.
A solitary electron in free space is not a fixed particle at rest in a given inertial frame of reference. It is always oscillating in a simple harmonic motion (SHM) in its own electromagnetic inertia field, even at zero kelvin temperature. A Newtonian particle exhibits uniform motion in a straight line. A quantum particle like the electron exhibits uniform motion along a sine wave path. This explains the physical concept of the wave-particle nature of the electron. As the mass of a quantum particle increases, the wavelength of the particle decreases as per French physicist Louis de Broglie. In the limiting case the sine wave becomes a straight line. Also, a hypothetical electron without an electric charge is like the bob of a simple pendulum without a string. In an electron-spin qubit, the electron can oscillate either clockwise or anti-clockwise and cannot oscillate both clockwise and anti-clockwise at the same time. It cannot be both spin-up and spin-down at the same time.
This 1-D Schrodinger equation describes the non relativistic motion of a single charged particle (mass m = 1, = 1) with a potential V in a uniform electric field t → u(t). With v = −u, (1) represents also the dynamics of a particle in a non Galilean frame of absolute position v (see, e.g., [9]). A change of independent variables (t, q) → (t, z) and dependent variable ψ → φ, transform (1) into (2) where the control appears as a shift on the space variable. These classical transformations are as follows (see, e.g., [2]). Instead of considering u as control, take v defined by v = −u as control. Then