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Physical Review Letters

Spin Gases: Quantum Entanglement Driven by Classical Kinematics

John Calsamiglia, Ludwig Hartmann, Wolfgang Dür, Hans J. Briegel

Published Oct 26, 2005• 47 citations
Publisher

Abstract

A spin gas is a natural extension of a classical gas. It consists of a large number of particles whose (random) motion is described classically, but, in addition, have internal (quantum mechanical) degrees of freedom that interact during collisions. For specific types of quantum interactions we determine the entanglement that occurs naturally in such systems. We analyze how the evolution of the quantum state is determined by the underlying classical kinematics of the gas. For the Boltzmann gas, we calculate the rate at which entanglement is produced and characterize the entanglement properties of the equilibrium state.

DOI
10.1103/physrevlett.95.180502

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A spin gas is a natural extension of a classical gas. It consists of a large number of particles whose (random) motion is described classically, but, in addition, have internal (quantum mechanical) degrees of freedom that interact during collisions. For specific types of quantum interactions we determine the entanglement that occurs naturally in such systems. We analyze how the evolution of the quantum state is determined by the underlying classical kinematics of the gas. For the Boltzmann gas, we calculate the rate at which entanglement is produced and characterize the entanglement properties of the equilibrium state.
We study the dynamics of entanglement in spin gases. A spin gas consists of a (large) number of interacting particles whose random motion is described classically while their internal degrees of freedom are described quantum-mechanically. We determine the entanglement that occurs naturally in such systems for specific types of quantum interactions. At the same time, these systems provide microscopic models for non–Markovian decoherence: the interaction of a group of particles with other particles belonging to a background gas are treated exactly, and differences between collective and non–collective decoherence processes are studied. We give quantitative results for the Boltzmann gas and also for a lattice gas, which could be realized by neutral atoms hopping in an optical lattice. These models can be simulated efficiently for systems of mesoscopic sizes (N ~ 105).
We analyze a microscopic decoherence model in which the total system is described as a spin gas. A spin gas consists of NNN classically moving particles with additional, interacting quantum degrees of freedom (e.g., spins). For various multipartite entangled probe states, we analyze the decoherence induced by interactions between the probe and environmental spins in such spin gases. We can treat mesoscopic environments ($\ensuremath{\approx}{10}^{5}$ particles). We present results for a lattice gas, which could be realized by neutral atoms hopping in an optical lattice, and show the effects of non-Markovian and correlated noise, as well as finite-size effects.
Abstract Quantum degeneracy is the central many-body feature of ideal quantum gases stemming from quantum mechanics. In this work we address its relationship to the most fundamental form of non-classicality in many-body system, i.e. many-body entanglement. We aim at establishing a quantitative link between quantum degeneracy and entanglement in spinful ideal gases, using entanglement witness criteria based on the variance of the collective spin of the spin ensemble. We show that spin-1/2 ideal Bose gases do not possess entanglement which can be revealed from such entanglement criteria. On the contrary, ideal spin-1/2 Fermi gases exhibit spin entanglement revealed by the collective-spin variances upon entering quantum degeneracy, due to the formation of highly non-local spin singlets. We map out the regime of detectable spin entanglement for Fermi gases in free space as well as in a parabolic trap, and probe the robustness of spin entanglement to thermal effects and spin imbalance. Spin entanglement in degenerate Fermi gases is amenable to experimental observation using state-of-the-art spin detection techniques in ultracold atoms.
Dynamics play an important role in physics. From classical mechanics, astrophysics, hydrodynamics to quantum physics, the dynamics of physical systems have crucial impact on our understanding of nature. For simple configurations such as in the two-body problem the dynamics can be calculated analytically. However, things get more complicated once the number of contributors in a system increases such as in few- or many-body systems. One way to study such an ensemble is to use a model system where decisive parameters can be controlled. In this thesis I make use of an ultracold cloud of fermionic Lithium-6 atoms close to zero temperature to study dynamics of few- and many-body systems. Two experimental studies to this topic are presented. In the first study, I produced a gas of di-atomic molecules (dimers), consisting of two Lithium-6 atoms in different states, to study the reaction kinetics of the four-body process of a dimer-dimer collision. At temperatures close to absolute zero the internal and external degrees of freedom of the dimers can be well controlled. This allowed us to investigate the kinetics of a single-channel reaction. To resolve the dynamics of the process we heated a gas of molecules and tracked the state of the system as a function of time. We determined the reaction-rate constant of the process for various thermal energies which allowed us to verify the Arrhenius law for molecule-molecule reactions in the ultracold regime. Additionally, we provided first insight into the dependence of this four-body process on the particle interaction. In the second experimental work, I focused on the thermodynamical properties of the ultracold gas. Cooling the gas of Lithium-6 atoms close to zero temperature the gas undergoes a phase transition and superfluidity is established. To study the dynamics in such a gas, we used a local perturbation to produce sound waves. Depending on the excitation scheme we either excited first sound, i.e. a pressure wave, known from classical mechanics, or second sound, i.e. an entropy wave. In the study we focused on second sound and determined the second sound speed as a function of the particle interaction. We found agreement of our results with both - a numerical and an analytical description of the interaction strength dependence of the second sound speed. Besides the experimental work, a theoretical proposal for a novel imaging technique for a 2D ultracold gas in an optical lattice is presented. The scheme is based on a holographic approach and enables the detection of individual particles with only a few hundred scattered photons per atom.
The spin of an electron is an intrinsic quantum property that cannot be explained using classical mechanics. Nevertheless, it is possible to conceive semiclassical systems with internal degrees of freedom that exhibit spin-like properties. Building on the analysis of phase modulation by elliptical gears and kinematically equivalent antiparallelogram linkages, we present a novel semiclassical model of Zitterbewegung, a rapid oscillatory motion closely connected with spin. The kinematical analog is based on including the internal rotation of the linkage represented in spacetime. The system’s dynamics is related to two-center electron models, which describe the constant momentum of the center of mass and the lightlike oscillation of the center of charge at twice the Compton frequency for a particle at rest. A two-dimensional extension provides an intuitive illustration of topological spin properties and can be used to calculate the spin and magnetic moment of an electron.
From its seemingly non-intuitive and puzzling nature, most evident in numerous EPR-like gedanken experiments to its almost ubiquitous presence in quantum technologies, entanglement is at the heart of modern quantum physics. First introduced by Erwin Schrödinger nearly a century ago, entanglement has remained one of the most fascinating ideas that came out of quantum mechanics. Here, we attempt to explain what makes entanglement fundamentally different from any classical phenomenon. To this end, we start with a historical overview of entanglement and discuss several hidden variables models that were conceived to provide a classical explanation and demystify quantum entanglement. We discuss some inequalities and bounds that are violated by quantum states thereby falsifying the existence of some of the classical hidden variables theories. We also discuss some exciting manifestations of entanglement, such as N00N states and the non-separable single particle states. We conclude by discussing some contemporary results regarding quantum correlations and present a future outlook for the research of quantum entanglement.