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Journal of Optics B Quantum and Semiclassical Optics

Single trapped cold ions: a testing ground for quantum mechanics

Sabrina Maniscalco

Published Nov 13, 2004• 5 citations
Publisher

Abstract

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.

DOI
10.1088/1464-4266/7/1/r01

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Quantum Electronics and Laser Science Conference•Jan 1, 1997•0 citations
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.
The fundamental laws of quantum mechanics are far from our everyday life experiences. However, they have been extremely successful in explaining observations in microscopic physical systems and are, already, harnessed for several applications. Moreover, in combination with relativistic considerations, basic phenomena from quantum mechanics are accredited a central role in the (macroscopic) evolution of our universe. In this thesis, we employ a trapped ion quantum simulator to experimentally investigate two fundamental quantum mechanical effects that have been extensively studied for many decades. In the first investigation, we implement non-adiabatic changes of the ions’ trapping potential in order to amplify quantum vacuum fluctuations. Following theoretical works by others, this mechanism can be interpreted as an analog to the creation of particles during cosmic inflation in the early universe. Such cosmological particles are considered as the seeds for the formation of the large-scale structures in our universe that we observe nowadays. In our analog quantum simulation, the creation of particles is evidenced by the detection of a squeezed state in the motion of the ions. A remarkable feature of this mechanism is the accompanying creation of quantum entanglement. In case of the cosmological particles, this entanglement spreads over large, cosmic distances. In the second investigation, we benchmark a theoretical concept in the framework of open quantum systems in a most basic system and under near-ideal conditions. In nature, any quantum system inevitably interacts with its environment and, thereby, needs ultimately to be considered an open system that can build up correlations and, even, entanglement with its environment. We implement a spin-1/2 system in the electronic degree of freedom of a single trapped ion, which we couple to a bosonic environment, formed by a motional degree of freedom of the ion. Further, we implement a tunable interaction between system and environment that, in turn, can lead to entanglement. By performing measurements on the open system only, we observe quantum non-Markovian behavior, which we quantify using a rigorously defined measure. Thereby, we reveal that the quantification of such quantum memory effects is fundamentally limited by fundamental quantum mechanical measurement uncertainties. The investigations presented in this thesis significantly expand the capabilities of our trapped ion platform to perform analog quantum simulations of fundamental quantum mechanical problems under near-ideal conditions, and enable future studies of increased complexity and under more realistic conditions.
This thesis is concerned with various aspects of ion traps and their use as a quantum simulation and computation device. In its first part we investigate various sources of noise and decoherence in ion traps. As quantum information is very fragile, a detailed knowledge of noise and decoherence sources in a quantum computation device is essential. In the special case of an ion trap quantum computer we investigate the effects of intensity and phase noise in the laser, which is used to perform the gate operations. We then look at other sources of noise which are present without a laser being switched on. These are fluctuations in the trapping frequency caused by noise in the electric potentials applied to the trap and fluctuating electrical fields which will cause heating of the centre-of-mass vibrational state of the ions in the trap. For the case of fluctuating electrical fields we estimate the effect on a quantum gate operation. We then propose a scheme for performing quantum gates without having the ions cooled down to their motional ground state. The second part deals with various aspects of the use of ion traps as a device for quantum computation. We start with the use of ionic qubits as a measurement device for the centre-of-mass vibrational mode and investigate in detail the effect these measurements will have on the vibrational mode. If one wants to use quantum computation devices as systems to simulate quantum mechanics, it is of interest to know how to simulate say a k-level system with N qubits. We investigate the easiest case of this wider problem and look at how to simulate a three-level system (a so called trit) with two qubits in an ion trap quantum computer. We show how to get and measure a SU (3) geometric phase with this toy model. Finally we investigate how to simulate collective angular momentum models with a string of qubits in an ion trap. We assume that the ionic qubits are coupled to a thermal reservoir and derive a master equation for this case. We investigate the semiclassical limit of this master equation and, in the case for two qubits in the trap, determine the entanglement of the steady state. We also outline a way to find the steady state for the master equation using coherence vectors.
Experiments with individual trapped ions are ideally suited to investigate fundamental issues of quantum mechanics such as the measurement process. At the same time electrodynamically trapped ions have been used with great success to demonstrate quantum logic operations and are a candidate for scalable quantum computing. In this article a brief introduction is given to the basic steps that constitute a quantum measurement; in particular, measurements on single quantum systems are considered. Then experiments with single Yb+ are reviewed demonstrating the quantum Zeno paradox, as well as an experiment where an adaptive algorithm for quantum state estimation of qubits was implemented. In the last section of this article -- devoted to experiments and new ideas related to quantum information processing (QIP) with trapped ions -- the realization of various quantum channels using a hyperfine qubit of Yb+ is briefly discussed. Then a concept for QIP with trapped ions is reviewed where rf or microwave radiation is used instead of laser light for coherent manipulation of a collection of ions. In a suitably modified trap the ions form an artificial ion "molecule" to which the techniques developed in nuclear magnetic resonance and electron spin resonance experiments can be directly applied. Finally, coherent excitation of optical electric quadrupole transitions in Yb+ and Ba+ is reported. In addition, robust Raman cooling of a pair of Ba+ ions is reviewed.
: A single laser-cooled and trapped Be ion is used to investigate methods of coherent 9 + quantum-state synthesis and quantum logic. We create and characterize nonclassical states of motion including "Schrödinger-cat" states. A fundamental quantum logic gate is realized which uses two states of the quantized ion motion and two ion internal states as qubits. We explore some of the applications for, and problems in realizing, quantum computation based on multiple trapped ions. V w V o 2 cos(6 T t) 1 # x 2 # y 2 R 2 , 2 (1) 1. INTRODUCTION Currently, a major theme in atomic, molecular, and optical physics is coherent control of quantum states. This theme is manifested in a number of topics such as atom interferometry, Bose-Einstein condensation and the atom laser, cavity QED, quantum computation, quantumstate engineering, wavepacket dynamics, and coherent control of chemical reactions. Here, we report related trapped-ion research at NIST which is devoted primarily to a...
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.