This paper outlines our realisation of the key insulation and stabilisation stages used for the high-finesse cavity, which is used for stabilising the frequency of the spectroscopy laser used in cold ion experiments. It mainly covers the mechanical structure of the insulation, including vibration isolation, acoustic shielding and a home-made water-cooling system using the gravity effect. The resulting effective suppression of vibration in the spectral range from 0.1 Hz to 150 Hz is by a factor of 20.

The optical interference constitutes a paramount resource in modern physics. At the scale of individual atoms and photons, it is a diverse concept that causes different coherent phenomena. We present the experimental characterization of both coherent and statistical properties of light emitted from ensembles of trapped ions increasing with a number of contributing phase-incoherent independent atomic particles ranging from a single to up to several hundreds. It conclusively demonstrates how super-Poissonian quantum statistics non-trivially arises purely from the finite number of indistinguishable single-photon emitters in the limit of a single detection mode. The achieved new optical emission regime in which these independent atoms contribute coherently to the super-Poissonian statistics provides a new perspective on the emergence of optical coherence at the atomic scale and constitutes a unique toolbox for its generation and control at the most microscopic level.

Quantum non-Gaussian (QNG) mechanical states from inherently nonlinear quantum processes are already required in quantum sensing, become essential in quantum thermodynamics, and also open directions in quantum computing with continuous variables. The discrete building blocks of such states are the energy eigenstates - Fock states. Despite the progress in their experimental preparation, the remaining energy uncertainty can still invisibly cause loss of the critical quantum non-Gaussian aspects of the phonon distribution relevant for the applications.

Challenging experiments for tests in fundamental physics require highly coherent optical frequency references with suppressed phase noise from hundreds of kHz down to μHz of Fourier frequencies. It can be achieved by remote synchronization of many frequency references interconnected by stabilized optical fibre links. Here we describe the path to realize a delocalized optical frequency reference for spectroscopy of the isomeric state of the nucleus of Thorium-229 atom. This is a prerequisite for the realization of the next generation of an optical clock - the nuclear clock. We present the established 235 km long phase-coherent stabilized cross-border fibre link connecting two delocalized metrology laboratories in Brno and Vienna operating highly-coherent lasers disciplined by active Hydrogen masers through optical frequency combs. A significant part (up to tens of km) of the optical fibre is passing urban combined collectors with a non-negligible level of acoustic interference and temperature changes, which results in a power spectral density of phase noise over 105 rad2· Hz-1. Therefore, we deploy a digital signal processing technique to suppress the fibre phase noise over a wide dynamic range of phase fluctuations. To demonstrate the functionality of the link, we measured the phase noise power spectral density of a remote beat note between two independent lasers, locked to high-finesse stable resonators. Using optical frequency combs at both ends of the link, a long-term fractional frequency stability in the order of 10-15 between local active Hydrogen masers was measured as well. Thanks to this technique, we have achieved reliable operation of the phase-coherent fibre link with fractional stability of 7 × 10-18 in 103 s.

Trapped ions, as one of the pillars of progress in frequency metrology and quantum optics, require a complex experimental environment with well-defined conditions. We present that a feature called dark resonance, provided by the trapped ion itself, can be used as a versatile sensor for enhanced in-situ analysis of interacting fields. The dark resonance is formed in the lambda-type energy level scheme of a laser cooled 40Ca+ ion and corresponds to a fluorescence quenching. The method uses an analysis of the detection times of photons emitted from the upper energy level, which is excited via two optical dipole transitions. The two excitation lasers are phase locked to an optical frequency comb to reduce their linewidths and for precise control of their optical frequencies within the dark resonance. The amplitudes of interacting fields are obtained using the Fourier transform of the ion fluorescence or photon correlation measurements. This paper shows that the method can be applied for sensing of electric, magnetic and electromagnetic fields. Firstly, we present the potential for frequency analysis of the secular motion of a few-ion Coulomb crystal, which corresponds to the axial static electric field of a linear ion trap. Secondly, we demonstrate the optical frequency analysis of the employed lasers driving the two transitions. In the last case we show the analysis of an alternating magnetic field at the position of single ion.

in this paper, we present the preliminary results of a local magnetic field measurement at the position of 40 Ca + ion. We employ the simultaneous locking of the frequency of clock laser onto two transitions of Zeeman sublevels on transition 4s 2 S 1/2 (m=-1/2) − 3d 2 D 5/2 (m=-1/2 and -5/2). The frequency deviation from the spectral line center of both selected Zeeman transitions determines the magnetic field value on basis of the linear Zeeman shift thus one can estimate the clock frequency of the unperturbed 4s 2 S 1/2 − 3d 2 D 5/2 transition.

We present the experimental characterization of coherence of light scattered from ensembles of noninteracting trapped ions. We set up and prove an indistinguishable emission from many ions by observation of photon bunching in a single-mode Hanbury-Brown and Twiss detection scheme.

We demonstrate an optical frequency analysis method using the Fourier transform of detection times of fluorescence photons emitted from a single trapped 40Ca+ ion. The response of the detected photon rate to the relative laser frequency deviations is recorded within the slope of a dark resonance formed in the lambda-type energy level scheme corresponding to two optical dipole transitions. This approach enhances the sensitivity to the small frequency deviations and does so with reciprocal dependence on the fluorescence rate. The employed lasers are phase locked to an optical frequency comb, which allows for precise calibration of optical frequency analysis by deterministic modulation of the analyzed laser beam with respect to the reference beam. The attainable high signal-to-noise ratios of up to a MHz range of modulation deviations and up to a hundred kHz modulation frequencies promise the applicability of the presented results in a broad range of optical spectroscopic applications.

We report on the robust experimental accumulation of nonclassicallity of motion of a single trapped ion. The nonclassicality stems from deterministic incoherent modulation of thermal phonon number distribution implemented by a laser excitation of nonlinear coupling between the ion's internal - electronic levels and external - motional states. We demonstrate that the repetitive application of this nonlinear process monotonically accumulates the observable state nonclassicality. The output states converge to a phonon number distribution with high overlap with a particular Fock state and visible quantum non-Gaussian aspects including corresponding negative Wigner function. The resulting oscillator states prove deterministic transition in the hierarchy of quantum non-Gaussianity up to four phonons. This transition is very robust against experimental imperfections and produces increasing entanglement potential.

The demonstration of optical multipath interference from a large number of quantum emitters is essential for the realization of many paradigmatic experiments in quantum optics. However, such interference remains still unexplored as it crucially depends on the sub-wavelength positioning accuracy and stability of all emitters. We present the observation of controlled interference of light scattered from strings of up to 53 trapped ions. The light scattered from ions localized in a harmonic trapping potential is collected along the ion crystal symmetry axis, which guarantees the spatial indistinguishability and allows for an efficient scaling of the contributing ion number. We achieve the preservation of the coherence of scattered light observable for all the measured string sizes and nearly-optimal enhancement of phase sensitivity. The presented results will enable realization and control of directional photon emission, direct detection of enhanced quadrature squeezing of atomic resonance fluorescence, or optical generation of genuine multi-partite entanglement of atoms.

The lifetime of trapped ion ensembles corresponds to a crucial parameter determining the potential scalability of their prospective applications and is often limited by the achievable vacuum level in the apparatus. We report on the realization of a room-temperature 40Ca+ ion trapping vacuum apparatus with unprecedentedly low reaction rates of ions with a dominant vacuum contaminant: hydrogen. We present our trap assembly procedures and hydrogen pressure characterization by analysis of the CaH+ molecule formation rate.

The demonstration of coherence between a large number of quantum emitters is essential for the realization of many paradigmatic experiments in quantum optics. Here we present the observation of controlled interference of light scattered from crystal strings of up to 53,trapped ions. The scattered light is collected along the crystal symmetry axis, which guarantees spatial indistinguishability of photons scattered by different ions and allows for convenient scaling of the number of contributing particles. The interference phase is tuned by changing the mutual distance between the ions and the observed pattern corresponds qualitatively to a simple theoretical model considering point-like emitters. The observed interference visibility remains in the 0.34 to 0.53 range for all the measured string sizes, limited mostly by the spatially inhomogeneous laser intensity seen by the long ion strings. The presented results open the possibility for experimental investigation of a whole range of fundamental physical phenomena, including engineered directional photon emission, direct detection of quadrature squeezing of atomic resonance fluorescence, and optical generation of genuine multi-partite entanglement between a large number of trapped ions.

We report on the working scheme of the experimental infrastructure for 40 Ca+ ion trapping and laser cooling. The important effort is to put on the excitation lasers control and their referencing to an optical frequency comb disciplined by an active H-maser. The principle of other instruments control necessary for the trapping and laser cooling setup is presented as well. The work also reports the records of the spectroscopic measurements of the ion multi-level electronic structure i.e. the occurrence of the dark resonances in the fluorescence signal on the dipole transition and the forbidden transition spectrum of the trapped single 40 Ca+ ion.

The vast majority of physical objects we are dealing with are almost exclusively made of atoms. Because of their discrete level structure, single atoms have proved to be emitters of light, which is incompatible with the classical description of electromagnetic waves. We demonstrate this incompatibility for atomic fluorescence when scaling up the size of the source ensemble, which consists of trapped atomic ions, by several orders of magnitude. The presented measurements of nonclassical statistics on light unconditionally emitted from ensembles containing up to more than a thousand ions promise further scalability to much larger emitter numbers. The methodology can be applied to a broad range of experimental platforms focusing on the bare nonclassical character of single isolated emitters.

We demonstrated that an iodine stabilized Distributed Bragg Reflector (DBR) diode based laser system lasing at a wavelength in close proximity to λ = 633 nm could be used as an alternative laser source to the He-Ne lasers in both scientific and industrial metrology.This yields additional advantages besides the optical frequency stability and coherence: inherent traceability, wider optical frequency tuning range, higher output power and high frequency modulation capability.We experimentally investigated the characteristics of the laser source in two major steps: first using a wavelength meter referenced to a frequency comb controlled with a hydrogen maser and then on a interferometric optical bench testbed where we compared the performance of the laser system with that of a traditional frequency stabilized He-Ne laser.The results indicate that DBR diode laser system provides a good laser source for applications in dimensional (nano)metrology, especially in conjunction with novel interferometric detection methods exploiting high frequency modulation or multiaxis measurement systems.

This article deals with the evaluation of the chemical purity of iodine-filled absorption cells and the optical frequency references used for the frequency locking of laser standards. We summarize the recent trends and progress in absorption cell technology and we focus on methods for iodine cell purity testing. We compare two independent experimental systems based on the laser-induced fluorescence method, showing an improvement of measurement uncertainty by introducing a compensation system reducing unwanted influences. We show the advantages of this technique, which is relatively simple and does not require extensive hardware equipment. As an alternative to the traditionally used methods we propose an approach of hyperfine transitions' spectral linewidth measurement. The key characteristic of this method is demonstrated on a set of testing iodine cells. The relationship between laser-induced fluorescence and transition linewidth methods will be presented as well as a summary of the advantages and disadvantages of the proposed technique (in comparison with traditional measurement approaches).

We report on the frequency noise investigation of a linewidth-suppressed Extended Cavity Diode Laser (ECDL), working at 729 nm. Since the ECDL is intended as an excitation laser for the forbidden transition in a trapped and laser cooled Ca-40(+) ion, an Hz-level linewidth is required. We present the experimental design that comprises a two-stage linewidth narrowing and a facility for frequency and noise analysis. The linewidth is first narrowed with a phase lock loop of the ECDL onto a selected component of an optical frequency comb where the frequency noise was suppressed with a fast electronic servo-loop controller that drives the laser injection current with a high bandwidth. The second stage comprises locking the laser onto a selected mode of a high-finesse passive optical cavity. The frequency analysis used an unbalanced Mach-Zehnder interferometer with a fiber spool inserted in the reference arm in order to give a general insight into the signal properties by mixing two separated beams, one of them delayed by the spool, and processing it with a spectral analyzer. Such a frequency noise analysis reveals what are the most significant noises contributions to the laser linewidth, which is a crucial information in field of ion trapping and cooling. The presented experimental results show the effect of the linewidth narrowing with the first stage, where the linewidth of ECDL was narrowed down to a kHz level.