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arXiv:2411.04241 · New Journal of Physics

Non-classicality and non-adiabaticity in a single trapped ion

Claver Francisco Francisco Palomino Palomino Avalos, M. C. de Oliveira

Published Feb 1, 2025• 1 citation
arXivHTMLPDF

Abstract

Abstract Trapped ion systems present non-classical characteristics such as squeezed states that show a quantum advantage in quantum sensing, quantum information processing and quantum thermodynamics. We analyze the non-classical characteristics of a system described by a single ion trapped by a periodic potential field. Within the regime of non-adiabatic manipulation of the potential field, the dynamics of motion of the center of mass of the ion can be described by a dimensionless parameter called the non-adiabatic parameter Q ∗ . This parameter allows us to distinguish the classical and non-classical characteristics of the system. Using the equations of motion of observables in the Heisenberg picture, we propose an analysis of the unitary time evolution operator and discuss the squeezing behavior in the state of motion of the ion. The results shown can serve as a basis to discuss the presence of squeezing as a resource in quantum thermodynamics in the non-adiabatic regime in actual achievable experimental limitations.

DOI
10.1088/1367-2630/adb646

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Abstract Trapped ion systems present non-classical characteristics such as squeezed states that show a quantum advantage in quantum sensing, quantum information processing and quantum thermodynamics. We analyze the non-classical characteristics of a system described by a single ion trapped by a periodic potential field. Within the regime of non-adiabatic manipulation of the potential field, the dynamics of motion of the center of mass of the ion can be described by a dimensionless parameter called the non-adiabatic parameter Q ∗ . This parameter allows us to distinguish the classical and non-classical characteristics of the system. Using the equations of motion of observables in the Heisenberg picture, we propose an analysis of the unitary time evolution operator and discuss the squeezing behavior in the state of motion of the ion. The results shown can serve as a basis to discuss the presence of squeezing as a resource in quantum thermodynamics in the non-adiabatic regime in actual achievable experimental limitations.
Abstract Quantum thermodynamics aims at investigating both the emergence and the limits of the laws of thermodynamics from a quantum mechanical microscopic approach. In this scenario, thermodynamic processes with no heat exchange, namely, adiabatic transformations, can be implemented through quantum evolutions in closed systems, even though the notion of a closed system is always an idealization and approximation. Here, we begin by theoretically discussing thermodynamic adiabatic processes in open quantum systems, which evolve non-unitarily under decoherence due to its interaction with its surrounding environment. From a general approach for adiabatic non-unitary evolution, we establish heat and work in terms of the underlying Liouville superoperator governing the quantum dynamics. As a consequence, we derive the conditions that an adiabatic open-system quantum dynamics implies in the absence of heat exchange, providing a connection between quantum and thermal adiabaticity. Moreover, we determine families of decohering systems exhibiting the same maximal heat exchange, which imply in classes of thermodynamic adiabaticity in open systems. We then approach the problem experimentally using a hyperfine energy-level quantum bit of an Ytterbium 171Yb+ trapped ion, which provides a work substance for thermodynamic processes, allowing for the analysis of heat and internal energy throughout a controllable engineered dynamics.
We study theoretically the mechanical drive of a trapped ultracold ion by a charged nanowire through their mutual Coulomb interaction. We characterize the perturbation of the trapping potential for the ion by the nanowire and discuss the parameters determining the dynamics of the ion under the action of the nanooscillator. We explore the classical dynamics as well as motional quantum states of the ion which can be generated and manipulated with the resonant drive of the nanowire and the effects of anharmonicities of the ion-trap potential on the system. Our modelling indicates that unusual quantum states of the ion motion can be generated with this approach and that sympathetic cooling and quantum entanglement can be realised when both subsystems operate in the quantum regime. The present ion-mechanical hybrid system might prove interesting as a new quantum device, for quantum sensing experiments, for spectroscopy and for mass spectrometry.
In this article I review some results obtained during my PhD work in the group of Professor Messina, at the University of Palermo. I discuss some proposals aimed at exploring fundamental issues of quantum theory, e.g. entanglement and quantum superpositions, in the context of single trapped ions. This physical context turns out to be extremely well suited both for studying fundamental features of quantum mechanics, such as the quantum–classical border, and for technological applications such as quantum logic gates and quantum registers. I focus on some procedures for engineering nonclassical states of the vibrational motion of the centre of mass of the ion. I consider both the case in which the ion interacts with classical laser beams and the case of interaction with a quantized mode of light. In particular, I discuss the generation of Schrodinger cat-like states, Bell states and Greenberger–Horn–Zeilinger states. The schemes for generating nonclassical states stem from two different quantum processes: the parity effect and the quantum state manipulation via quantum non-demolition measurement. Finally, I consider a microscopic theory of the interaction of a quantum harmonic oscillator (the centre of mass of the ion in the trapped ion context) with a bosonic thermal environment. Using an exact approach to the dynamics, I discuss a quantum theory of heating of trapped ions able to describe both the short time non-Markovian regime and the thermalization process. I conclude showing briefly how the trapped ion systems can be used as simulators of key models of open quantum systems such as the Caldeira–Leggett model.
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The quantum dynamics of a trapped ion which acts with two standing light fields with different frequency is investigated on the condition of high detuning. Evolution of the quantum mean energy of the ion with time displays the characteristic of collapse revival which implies the vibration states of the ion have squeezing effect. The higher the value of the squeezing parameter G 3 . The higher the degree of squeezing of the vibration states of the ion can be observed. If G 3 is greater than a particular value, the degree of squeezing will become smaller.