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Bulletin of the American Physical Society

A QUANTUM NEWTONS CRADLE

Toshiya Kinoshita

Published Jan 1, 2006• 46 citations
OpenAlex

Abstract

Cradle to wave Newton's cradle, the popular lecture aid and executive toy, demonstrates the conservation of momentum in one dimension. Now there is a quantum equivalent, created in a one-dimensional Bose gas. In a quantum Newton's cradle, one-dimensional arrays of ultracold rubidium atoms mutually collide thousands of times, bouncing off each other or transmitting through each other, without significant damping. This system may find application in force sensing and atom interferometry.

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Cradle to wave Newton's cradle, the popular lecture aid and executive toy, demonstrates the conservation of momentum in one dimension. Now there is a quantum equivalent, created in a one-dimensional Bose gas. In a quantum Newton's cradle, one-dimensional arrays of ultracold rubidium atoms mutually collide thousands of times, bouncing off each other or transmitting through each other, without significant damping. This system may find application in force sensing and atom interferometry.
A quantum analogue of the popular "Newton's cradle" toy has been proposed by a duo of physicists in Italy. Like momentum transferred in the toy, the team argues that it should be possible to achieve the nearly perfect transmission of a quantum wavefunction along a line of ultracold atoms in a 1D Bose-Einstein condensate. According to the pair, the work could help develop quantum-information systems that achieve high-quality wave transmission. Best described as an "executive desk toy", a Newton's cradle is a device that demonstrates the conservation of energy and momentum. It consists of small, identically sized metal balls suspended from two horizontal bars. When a ball is lifted and allowed to fall, it strikes its immediate neighbour and comes to a stop. But its momentum is transferred across the rest of the spheres and propels only the sphere at the opposite end of the line into the air.
We propose a possible experimental realization of a quantum analogue of Newton's cradle using a configuration which starts from a Bose–Einstein condensate. The system consists of atoms with two internal states trapped in a one-dimensional tube with a longitudinal optical lattice and maintained in a strong Tonks–Girardeau regime at maximal filling. In each site the wave-function is a superposition of the two atomic states and a disturbance of the wave-function propagates along the chain in analogy with the propagation of momentum in the classical Newton cradle. The quantum travelling signal is generally deteriorated by dispersion, which is large for a uniform chain and is known to be zero for a suitably engineered chain, but the latter is hardly realizable in practice. Starting from these opposite situations we show how the coherent behaviour can be enhanced with minimal experimental effort.
We show that when two quantum-mechanical particles of the same mass, interacting through a hard-core repulsive potential, collide in one dimension, they exchange their wavefunctions, making them look as if they had passed through each other. We give a simple explanation of this phenomenon, and compare to its classical analog, which can be demonstrated using the “Newton's cradle” toy. We also consider briefly what happens when the masses are unequal, showing how entanglement arises in this case.
Describing and understanding the motion of quantum gases out of equilibrium is one of the most important modern challenges for theorists. In the groundbreaking Quantum Newton Cradle experiment [Kinoshita, Wenger and Weiss, Nature 440, 900 (2006)], quasi-one-dimensional cold atom gases were observed with unprecedented accuracy, providing impetus for many developments on the effects of low dimensionality in out-of-equilibrium physics. But it is only recently that the theory of generalized hydrodynamics has provided the adequate tools for a numerically efficient description. Using it, we give a complete numerical study of the time evolution of an ultracold atomic gas in this setup, in an interacting parameter regime close to that of the original experiment. We evaluate the full evolving phase-space distribution of particles. We simulate oscillations due to the harmonic trap, the collision of clouds without thermalization, and observe a small elongation of the actual oscillation period and cloud deformations due to many-body dephasing. We also analyze the effects of weak anharmonicity. In the experiment, measurements are made after release from the one-dimensional trap. We evaluate the gas density curves after such a release, characterizing the actual time necessary for reaching the asymptotic state where the integrable quasi-particle momentum distribution function emerges.
We study the nonequilibrium dynamics of the quantum Newton's cradle in a one-dimensional (1D) Bose gas in the weakly interacting quasicondensate regime. This is the opposite regime to the original quantum Newton's cradle experiment of [Kinoshita et al., Nature 440, 900 (2006)], which was realized in the strongly interacting 1D Bose gas. Using finite temperature ccc-field methods, we calculate the characteristic relaxation rates to the final equilibrium state. Hence, we identify the different dynamical regimes of the system in the parameter space that characterizes the strength of interatomic interactions, the initial temperature, and the magnitude of the Bragg momentum used to initiate the collisional oscillations of the cradle. In all parameter regimes, we find that the system relaxes to a final equilibrium state for which the momentum distribution is consistent with a thermal distribution. For sufficiently large initial Bragg momentum, the system can undergo hundreds of repeated collisional oscillations before reaching the final thermal equilibrium. The corresponding thermalization timescales can reach tens of seconds, which is an order of magnitude smaller than in the strongly interacting regime.