The resonant heating of a harmonically trapped ion by a standing-wave light field is described as a quantum stochastic process combining a coherent Schrödinger evolution with Bohr-Einstein quantum jumps. The dependence of the center-of-mass motion on Lamb-Dicke parameter is studied. For Lamb-Dicke parameters greater than unity we demonstrate significant departures from the diffusion process that holds in the limit of small momentum “kicks”; a strong inhibition of the heating of the ion (fluorescence) occurs. Heating rates are calculated as a Monte-Carlo average from both the full quantum stochastic process and its semi-quantum approximation.The resonant heating of a harmonically trapped ion by a standing-wave light field is described as a quantum stochastic process combining a coherent Schrödinger evolution with Bohr-Einstein quantum jumps. The dependence of the center-of-mass motion on Lamb-Dicke parameter is studied. For Lamb-Dicke parameters greater than unity we demonstrate significant departures from the diffusion process that holds in the limit of small momentum “kicks”; a strong inhibition of the heating of the ion (fluorescence) occurs. Heating rates are calculated as a Monte-Carlo average from both the full quantum stochastic process and its semi-quantum approximation.

Quantum-Atom Optics Downunder (QAO)Jan 1, 20070 citations

Quantum motion of trapped ions

R. Blatt, J. I. Cirac, A. S. Parkins +1 more

A single ion trapped in a harmonic potential and laser cooled at the node of a standing wave can be described in terms of the Jaynes-Cummings Hamiltonian known in quantum optics. Similar to nonclassical states of light we propose to prepare nonclassical states of the ion motion in a harmonic trap. In particular, several schemes for the preparation of Fock states are presented, and techniques for the preparation of squeezed states and coherent states of the ion motion are indicated. For an observation of these nonclassical states we propose to measure quantum collapse and revival in the population inversion of a single trapped ion.A single ion trapped in a harmonic potential and laser cooled at the node of a standing wave can be described in terms of the Jaynes-Cummings Hamiltonian known in quantum optics. Similar to nonclassical states of light we propose to prepare nonclassical states of the ion motion in a harmonic trap. In particular, several schemes for the preparation of Fock states are presented, and techniques for the preparation of squeezed states and coherent states of the ion motion are indicated. For an observation of these nonclassical states we propose to measure quantum collapse and revival in the population inversion of a single trapped ion.

Physica ScriptaJan 1, 199510 citations

Stochastic Cooling of a Trapped Ion by Null Detection of Its Fluorescence

Jürgen Eschner, Bernd Appasamy, P. E. Toschek

When a single trapped ion is laser excited to a metastable state, its ``quantum jump'' inhibits the laser-excited light scattering on a resonance line. This event, and its inverse, modifies the distribution over the oscillator levels $(n)$ of the ion's vibration in the trap. In particular, unsuccessful attempts to deexcite on vibrational sidebands decrease $〈n〉$ to sub-Doppler values and may leave the ion in a ``trapped'' Fock state decoupled from the light.When a single trapped ion is laser excited to a metastable state, its ``quantum jump'' inhibits the laser-excited light scattering on a resonance line. This event, and its inverse, modifies the distribution over the oscillator levels $(n)$ of the ion's vibration in the trap. In particular, unsuccessful attempts to deexcite on vibrational sidebands decrease $〈n〉$ to sub-Doppler values and may leave the ion in a ``trapped'' Fock state decoupled from the light.

Physical Review LettersMar 27, 199533 citations

Quantum optics of a single trapped ion

Bernd Appasamy, Jürgen Eschner, Yves Stalgies +2 more

A single trapped and cooled ion interacting with light is the realization of a fundamental system of quantum optics. Relevant viewpoints include the light scattering and its relation to the preparation of the ion, the dynamics of the ion's internal motion, and the dynamics of its vibrational motion. As cases in point, recent results are reviewed that illustrate those viewpoints: (i) The preparation of the ion, by spontaneous emission, in a superposition of energy eigenstates of quasi-permanent lifetime. (ii) The dispersive effect of quantum jumps of the ion, to and from a metastable state, that gives rise to internally self-locking the ion in either the light-scattering bright or the non-scattering dark state. (iii) The stochastic cooling of the ion by repeated null detection of its resonance scattering. These counter-intuitive phenomena characterize a physical system, where quantum mechanics models ensembles of observations.A single trapped and cooled ion interacting with light is the realization of a fundamental system of quantum optics. Relevant viewpoints include the light scattering and its relation to the preparation of the ion, the dynamics of the ion's internal motion, and the dynamics of its vibrational motion. As cases in point, recent results are reviewed that illustrate those viewpoints: (i) The preparation of the ion, by spontaneous emission, in a superposition of energy eigenstates of quasi-permanent lifetime. (ii) The dispersive effect of quantum jumps of the ion, to and from a metastable state, that gives rise to internally self-locking the ion in either the light-scattering bright or the non-scattering dark state. (iii) The stochastic cooling of the ion by repeated null detection of its resonance scattering. These counter-intuitive phenomena characterize a physical system, where quantum mechanics models ensembles of observations.

Physica ScriptaJan 1, 19955 citations

Preparation of Fock states and squeezed states of motion in ion traps

J. I. Cirac, R. Blatt, A. S. Parkins +1 more

(1) A technique for the preparation of Fock states of a harmonic oscillator strongly coupled to a single two-level atomic transition is proposed due to the observation of quantum jumps. Examples are taken from the fields of ion trapping and cavity QED, where number states of he quantized atomic motion and photon number states may be prepared respectively. (2) We discuss a scheme for preparing coherent squeezed states of motion in an ion trap based on the multichromatic excitation of a trapped ion by standing- and traveling-wave light fields. The squeezed state is produced when the beat frequency between two standing-wave light fields is equal to twice the trap frequency, and is indicated by a {open_quotes}dark resonance{close_quotes} in the fluorescence emitted by the ion.(1) A technique for the preparation of Fock states of a harmonic oscillator strongly coupled to a single two-level atomic transition is proposed due to the observation of quantum jumps. Examples are taken from the fields of ion trapping and cavity QED, where number states of he quantized atomic motion and photon number states may be prepared respectively. (2) We discuss a scheme for preparing coherent squeezed states of motion in an ion trap based on the multichromatic excitation of a trapped ion by standing- and traveling-wave light fields. The squeezed state is produced when the beat frequency between two standing-wave light fields is equal to twice the trap frequency, and is indicated by a {open_quotes}dark resonance{close_quotes} in the fluorescence emitted by the ion.

Bulletin of the American Physical SocietyMay 1, 19930 citations

Quantum theory of heating of a single trapped ion

F. Intravaia, Maniscalco, S, Piilo, J +1 more

The heating of trapped ions due to the interaction with a quantized environment is studied without performing the Born-Markov approximation. A generalized master equation local in time is derived and a novel theoretical approach to solve it analytically is proposed. Our master equation is in the Lindblad form with time dependent coefficients, thus allowing the simulation of the dynamics by means of the Monte Carlo Wave Function (MCWF) method. For such a system, this is the first demonstration of the applicability of the quantum jump MCWF method in the non-Markovian regime.The heating of trapped ions due to the interaction with a quantized environment is studied without performing the Born-Markov approximation. A generalized master equation local in time is derived and a novel theoretical approach to solve it analytically is proposed. Our master equation is in the Lindblad form with time dependent coefficients, thus allowing the simulation of the dynamics by means of the Monte Carlo Wave Function (MCWF) method. For such a system, this is the first demonstration of the applicability of the quantum jump MCWF method in the non-Markovian regime.

Jun 21, 20029 citations

(n)

of the ion's vibration in the trap. In particular, unsuccessful attempts to deexcite on vibrational sidebands decrease

〈n〉

to sub-Doppler values and may leave the ion in a ``trapped'' Fock state decoupled from the light.