Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE Conference on Nanotechnology (IEEE NANO)

On the Global Dynamic Behavior of Trapped Ions in a Thermal Environment

Michele Bonnin, Pier Paolo Civalleri, Marco Gilli

Published Aug 1, 2008• 0 citations
Publisher

Abstract

Strings of ions confined in a radio-frequency trap represent a promising architecture for quantum computers. The ions can be considered as an ensemble of harmonic oscillators, interacting through the Coulomb repulsion, and subject to the influence of the external environment, here represented by an electromagnetic field. In this view, the system is regarded as an open quantum system. By decomposing the oscillations into normal modes, a quantum master equation can be derived, which is of paramount importance to study quantum phenomena such as decoherence and entanglement. The solution of the master equation, gives information about the thermal equilibrium state, the energy distribution and the dynamical behavior of the trapped ions.

DOI
10.1109/nano.2008.122

Related papers

Thermalization of trapped ions: A quantum perturbation approach

S. K. Lamoreaux

The rate at which external random thermal fluctuations drive transitions between, and cause decoherence of, the near ground vibrational (harmonic oscillator) quantum states of trapped cold ions is of crucial importance in relation to quantum computing. Presented here is an estimate of these rates, for a single trapped ion, based on a quantum perturbation approach where an external thermal energy reservoir is electrically coupled to the ion. The results are for a general system, and it is shown that the relevant parameter in the interpretation of experimentally observed heating rates is the correlation time of the fluctuations. The rates due to the fluctuating electric field associated with blackbody radiation are also considered and shown to be negligible.

Physical Review A•Dec 1, 1997•43 citations

Decoherence, Measurement and Quantum Computing in Ion Traps

Sara Schneider

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.

•Jan 1, 2000•0 citations

Dynamics of a trapped ion in a quantum gas: Effects of particle statistics

Lorenzo Oghittu, Melf Johannsen, Antonio Negretti +1 more

We study the quantum dynamics of an ion confined in a radio-frequency trap in interaction with either a Bose or spin-polarized Fermi gas. To this end, we derive quantum optical master equations in the limit of weak coupling and the Lamb-Dicke approximations. For the bosonic bath, we also include the so-called ``Lamb-shift'' correction to the ion trap due to the coupling to the quantum gas as well as the extended Fr\"ohlich interaction within the Bogolyubov approximation that have been not considered in previous studies. We calculate the ion kinetic energy for various atom-ion scattering lengths as well as gas temperatures by considering the intrinsic micromotion and we analyze the damping of the ion motion in the gas as a function of the gas temperature. We find that the ion's dynamics depends on the quantum statistics of the gas and that a fermionic bath enables to attain lower ionic energies.

arXiv:2109.03143•Physical Review A•Nov 17, 2021•13 citations

Computational study of vibrational qubits in anharmonic linear ion traps

Lei Wang

A string of cold ions confined in a linear trap represents a man-made quantum object with a broad range of applications in atomic and molecular spectroscopy, such as high-precision measurement of atomic properties. An efficient isolation from the environment guarantees excellent coherent properties of such systems and makes them suitable for practical realization of the quantum information processing. The pioneering theoretical [Cirac and Zoller] and experimental [Wineland and Monroe] work in 1990s resulted in the explosive expansion of this field during the last decade. In this dissertation an alternative new method for controlling the quantized motional/vibrational states of ions in a trap is explored theoretically. It is proposed to create small anharmonicity in the trapping potential which would modify the spectrum of states and allow addressing the state-to-state transitions selectively. In this approach all ions remain in the ground electronic state and their motion is controlled adiabatically and coherently by applying the optimally shaped electric fields (RF). The optimal control theory, accurate numerical calculation of the energies and wavefunctions, and numerical propagation of wave packets are employed. Two sources of vibrational anharmonicity are studied: the intrinsic Coulomb anharmonicity due to the ion-ion interactions and the external anharmonicity of the trapping potential. It is shown that the magnitude of Coulomb anharmonicity is insufficient for the control. In contrast, anharmonicity of the trapping potential allows controlling the motion of ions very accurately. It is demonstrated that one ion in a slightly anharmonic trap can be easily controlled and used to represent one qubit. A multi-qubit system can be created by employing a long progression of states of a single ion, or by trapping multiple ions and controlling several normal vibration modes of the ion string. Up to four qubits are modeled in this work and accurate pulses are optimized for a set of universal quantum gates: NOT, conditional NOT (CNOT) and Hadamard transformation. The control field for Shor's algorithm (quantum algorithm for factorization onto prime numbers) is also obtained. It is demonstrated that a careful choice of system properties allows achieving very high accuracy of qubit transformations, up to 0.999.

•Jan 1, 2012•0 citations

Quantum dynamics of single trapped ions

Dietrich G. Leibfried, R. Blatt, Christopher R. Monroe +1 more

Single trapped ions represent elementary quantum systems that are well isolated from the environment. They can be brought nearly to rest by laser cooling, and both their internal electronic states and external motion can be coupled to and manipulated by light fields. This makes them ideally suited for quantum-optical and quantum-dynamical studies under well-controlled conditions. Theoretical and experimental work on these topics is reviewed in the paper, with a focus on ions trapped in radio-frequency (Paul) traps.

Reviews of Modern Physics•Mar 10, 2003•2,736 citations

Thermally induced entanglement of atomic oscillators

Pradip Laha, L. Slodička, Darren W. Moore +1 more

Laser cooled ions trapped in a linear Paul trap are long-standing ideal candidates for realizing quantum simulation, especially of many-body systems. The properties that contribute to this also provide the opportunity to demonstrate unexpected quantum phenomena in few-body systems. A pair of ions interacting in such traps exchange vibrational quanta through the Coulomb interaction. This linear interaction can be anharmonically modulated by an elementary coupling to the internal two-level structure of one of the ions. Driven by thermal energy in the passively coupled oscillators, which are themselves coupled to the internal ground states of the ions, the nonlinear interaction autonomously and unconditionally generates entanglement between the mechanical modes of the ions. We examine this counter-intuitive thermally induced entanglement for several experimentally feasible model systems and propose parameter regimes where state-of-the-art trapped ion systems can produce such phenomena. In addition, we demonstrate a multiqubit enhancement of such thermally induced entanglements.

arXiv:2107.01939•Optics Express•Feb 15, 2022•10 citations
Strings of ions confined in a radio-frequency trap represent a promising architecture for quantum computers. The ions can be considered as an ensemble of harmonic oscillators, interacting through the Coulomb repulsion, and subject to the influence of the external environment, here represented by an electromagnetic field. In this view, the system is regarded as an open quantum system. By decomposing the oscillations into normal modes, a quantum master equation can be derived, which is of paramount importance to study quantum phenomena such as decoherence and entanglement. The solution of the master equation, gives information about the thermal equilibrium state, the energy distribution and the dynamical behavior of the trapped ions.
The rate at which external random thermal fluctuations drive transitions between, and cause decoherence of, the near ground vibrational (harmonic oscillator) quantum states of trapped cold ions is of crucial importance in relation to quantum computing. Presented here is an estimate of these rates, for a single trapped ion, based on a quantum perturbation approach where an external thermal energy reservoir is electrically coupled to the ion. The results are for a general system, and it is shown that the relevant parameter in the interpretation of experimentally observed heating rates is the correlation time of the fluctuations. The rates due to the fluctuating electric field associated with blackbody radiation are also considered and shown to be negligible.
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.
We study the quantum dynamics of an ion confined in a radio-frequency trap in interaction with either a Bose or spin-polarized Fermi gas. To this end, we derive quantum optical master equations in the limit of weak coupling and the Lamb-Dicke approximations. For the bosonic bath, we also include the so-called ``Lamb-shift'' correction to the ion trap due to the coupling to the quantum gas as well as the extended Fr\"ohlich interaction within the Bogolyubov approximation that have been not considered in previous studies. We calculate the ion kinetic energy for various atom-ion scattering lengths as well as gas temperatures by considering the intrinsic micromotion and we analyze the damping of the ion motion in the gas as a function of the gas temperature. We find that the ion's dynamics depends on the quantum statistics of the gas and that a fermionic bath enables to attain lower ionic energies.
A string of cold ions confined in a linear trap represents a man-made quantum object with a broad range of applications in atomic and molecular spectroscopy, such as high-precision measurement of atomic properties. An efficient isolation from the environment guarantees excellent coherent properties of such systems and makes them suitable for practical realization of the quantum information processing. The pioneering theoretical [Cirac and Zoller] and experimental [Wineland and Monroe] work in 1990s resulted in the explosive expansion of this field during the last decade. In this dissertation an alternative new method for controlling the quantized motional/vibrational states of ions in a trap is explored theoretically. It is proposed to create small anharmonicity in the trapping potential which would modify the spectrum of states and allow addressing the state-to-state transitions selectively. In this approach all ions remain in the ground electronic state and their motion is controlled adiabatically and coherently by applying the optimally shaped electric fields (RF). The optimal control theory, accurate numerical calculation of the energies and wavefunctions, and numerical propagation of wave packets are employed. Two sources of vibrational anharmonicity are studied: the intrinsic Coulomb anharmonicity due to the ion-ion interactions and the external anharmonicity of the trapping potential. It is shown that the magnitude of Coulomb anharmonicity is insufficient for the control. In contrast, anharmonicity of the trapping potential allows controlling the motion of ions very accurately. It is demonstrated that one ion in a slightly anharmonic trap can be easily controlled and used to represent one qubit. A multi-qubit system can be created by employing a long progression of states of a single ion, or by trapping multiple ions and controlling several normal vibration modes of the ion string. Up to four qubits are modeled in this work and accurate pulses are optimized for a set of universal quantum gates: NOT, conditional NOT (CNOT) and Hadamard transformation. The control field for Shor's algorithm (quantum algorithm for factorization onto prime numbers) is also obtained. It is demonstrated that a careful choice of system properties allows achieving very high accuracy of qubit transformations, up to 0.999.
Single trapped ions represent elementary quantum systems that are well isolated from the environment. They can be brought nearly to rest by laser cooling, and both their internal electronic states and external motion can be coupled to and manipulated by light fields. This makes them ideally suited for quantum-optical and quantum-dynamical studies under well-controlled conditions. Theoretical and experimental work on these topics is reviewed in the paper, with a focus on ions trapped in radio-frequency (Paul) traps.
Laser cooled ions trapped in a linear Paul trap are long-standing ideal candidates for realizing quantum simulation, especially of many-body systems. The properties that contribute to this also provide the opportunity to demonstrate unexpected quantum phenomena in few-body systems. A pair of ions interacting in such traps exchange vibrational quanta through the Coulomb interaction. This linear interaction can be anharmonically modulated by an elementary coupling to the internal two-level structure of one of the ions. Driven by thermal energy in the passively coupled oscillators, which are themselves coupled to the internal ground states of the ions, the nonlinear interaction autonomously and unconditionally generates entanglement between the mechanical modes of the ions. We examine this counter-intuitive thermally induced entanglement for several experimentally feasible model systems and propose parameter regimes where state-of-the-art trapped ion systems can produce such phenomena. In addition, we demonstrate a multiqubit enhancement of such thermally induced entanglements.