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We present two methods for characterization of motional-mode configurations that are generally applicable to the weak and strong-binding limit of single or multiple trapped atomic ions. Our methods are essential to realize control of the…
Spectral properties of the Hamiltonian function which characterizes a trapped ion are investigated. In order to study semiclassical dynamics of trapped ions, coherent state orbits are introduced as sub-manifolds of the quantum state space,…
The state of a microscopic system encodes its complete quantum description, from which the probabilities of all measurement outcomes are inferred. Being a statistical concept, the state cannot be obtained from a single system realization.…
A non-Gaussian state being a mixture of the vacuum and single-photon states can be generated by truncating a thermal state in a quantum scissors device of Pegg et al. [Phys. Rev. Lett. 81 (1998) 1604]. In contrast to the thermal state, the…
We derive sampling functions for estimation of quantum state fidelity with Schr\"odinger cat-like states, which are defined as superpositions of two coherent states with opposite amplitudes. We also provide sampling functions for fidelity…
Laser spectroscopy of cold and trapped molecular ions is a powerful tool for fundamental physics, including the determination of fundamental constants, the laboratory test for their possible variation, and the search for a possible electric…
Determining the state of a system and measuring properties of its evolution are two of the most important tasks a physicist faces. For the first purpose one can use tomography, a method that after subjecting the system to a number of…
We propose a new scheme for supplying voltages to the electrodes of microfabricated ion traps, enabling access to a regime in which changes to the trapping potential are made on timescales much shorter than the period of the secular…
We implement the squeezing operation as a genuine quantum gate, deterministically and reversibly acting `online' upon an input state no longer restricted to the set of Gaussian states. More specifically, by applying an efficient and robust…
We have cooled a two-ion-crystal to the ground state of its collective modes of motion. Laser cooling, more specific resolved sideband cooling is performed sympathetically by illuminating only one of the two $^{40}$Ca$^+$ ions in the…
We demonstrate the simultaneous quantum state reconstruction of the spectral modes of the light field emitted by a continuous wave degenerate optical parametric amplifier. The scheme is based on broadband measurement of the quantum…
The present paper describes the experimental implementation of a measuring technique employing a slowly moving, near resonant, optical standing wave in the context of trapped ions. It is used to measure several figures of merit that are…
The measurement process is taken into account in the dynamics of trapped ions prepared in nonclassical motional states. The induced decoherence is shown to manifest itself both in the inhibition of the internal population dynamics and in a…
In a numerical study, we investigate the steady-state generation of nonclassical states of light from a coherently driven two-level atom in a one-dimensional waveguide. Specifically, we look for states with a negative Wigner function, since…
We present a protocol that permits the generation of a subtle with superposition with 2^(l+1) displaced number states on a circle in phase space as target state for the center-of-mass motion of a trapped ion. Through a sequence of 'l'…
We propose a generation method of Bell-type states involving light and the vibrational motion of a single trapped ion. The trap itself is supposed to be placed inside a high-$Q$ cavity sustaining a single mode, quantized electromagnetic…
In order to use a collection of trapped ions for experiments where a well defined preparation of vibrational states is necessary, all vibrational modes have to be cooled to ensure precise and repeatable manipulation of the ions' quantum…
Observing a physical quantity without disturbing it is a key capability for the control of individual quantum systems. Such back-action-evading or quantum-non-demolition measurements were first introduced in the 1970s in the context of…
We demonstrate imaging of neutral atoms via the light scattered during continuous Raman sideband cooling. We detect single atoms trapped in optical tweezers while maintaining a significant motional ground-state fraction. The techniques…
Why do we need quantization to describe vision? What are the quadrature operators of the electromagnetic field? Is it possible to measure them? What are the characteristic functions useful for? In this brief tutorial we provide the…