Sub-Planck structures in non-Gaussian probability densities of phase space variables are pervasive in bosonic quantum systems. They are almost universally present if the bosonic system evolves via nonlinear dynamics or nonlinear measurements. So far, identification and comparison of such structures remains qualitative. Here we provide a universally applicable and experimentally friendly method to identify, quantify and compare sub-Planck structures from directly measurable or estimated probability densities of single phase space variables. We demonstrate the efficacy of this method on experimental high order Fock states of a single-atom mechanical oscillator, showing provably finer sub-Planck structures as the Fock occupation increases despite the accompanying uncertainty increase in the phonon, position, and momentum bases.

Quantum interference between interacting systems is fundamental to basic science and quantum technology, but it typically requires precise control of the interaction phases of lasers or microwave generators. Can interference be observed if those interaction phases are stable but unknown, usually prohibitive for complex state without active control? Here, we answer this question by experimentally preparing a Schrödinger-cat-like state of an internal qubit and a motional oscillator of a trapped ^40Ca^+ ion, and its robustness to such uncontrolled phase. By applying alternating red and blue sideband pulses, we enforce a strict qubit-parity correlation and interference inherently insensitive to stable but unknown phases of the driving laser. For this qubit-parity interference, we use a minimal two-pulse interferometric sequence to demonstrate characteristic visibilities of 20% and 40%, which approach the theoretical visibility limit, providing a scalable coherence witness without full state tomography for high-dimensional states.

The coherence of light from independent ensembles of elementary atomic emitters plays a paramount role in diverse areas of modern optics. We demonstrate the interference of photons scattered from independent ensembles of warm atoms in atomic vapor. It relies on the feasibility of the preservation of coherence of light scattered elastically in the forward and backward directions from Doppler-broadened atomic ensembles, such that photons with chaotic photon statistics from two opposite atomic velocity groups contribute to the same detection mode. While the random phase fluctuations of the scattered light caused by a large thermal motion prevent direct observability of the interference in the detected photon rate, the stable frequency difference between photons collected from scattering off counter-propagating laser beams provides strong periodic modulation of the photon coincidence rate with the period given by the detuning of the excitation laser from the atomic resonance. The presented interferometry represents a sensitive and robust methodology for Doppler-free optical atomic and molecular spectroscopy based on photon correlation measurements on scattered light.

The efficient detection of light from trapped ions in free space is paramount for most of their applications. We propose a scheme to enhance the photon collection from linear ion strings. It employs the constructive interference of light scattered from ions along the axial direction in linear Paul traps. The coherent enhancement of photon collection is numerically optimized for a range of feasible spatial angles and realistic ion positions in a single harmonic Coulomb potential. Despite the large mutual distance of scatterers on the order of many wavelengths of scattered light, the experimental tests presented confirm the feasibility of enhancements by a factor of 3.05 ± 0.09 with a crystal of nine 40Ca+ ions. The proposed collection geometry is intrinsic to diverse linear ion trap designs, and the methodology can be directly applied to an observation of scattering from ion crystals prepared in collective electronic excitations.

While the spontaneous emission from independent emitters provides spatially uncorrelated photons-a typical manifestation of quantum randomness, the interference of the coherent scattering leads to a well-defined intensity pattern-a feature described by linear optics. We here demonstrate experimentally how the interplay between the two mechanisms in large systems of quantum emitters leads to spatial variations of photon correlations. The implementation with trapped ion crystals in free space allows us to observe the anticorrelation between photon rates and variance of the photon number distributions in chains of up to 18 ions. For smaller crystals of four ions, the transition from antibunching to bunching and super-Poissonian statistics of the scattered light is reported. For higher numbers of scatterers, the photon statistics still display a strong deviation from the fully incoherent scattering case. Our results illustrate how the interference of coherent scattering, combined with spontaneous emission, provides a control mechanism for the light statistics.

Light is characterized by its electric field, yet quantum optics has revealed the importance of monitoring photon-photon correlations at all orders. We here present a comparative study of two experimental setups, composed of cold and warm Rubidium atoms, respectively, which allow us to probe and compare photon correlations up to the fourth order. The former operates in the quantum regime where spontaneous emission dominates, whereas the latter exhibits a temperature-limited coherence time. While both setups present almost-chaotic light statistics, we discuss how the access to different orders of photon correlations allows one to better characterize the mechanisms responsible for deviations from those statistics.

- Light is characterized by its electric field, yet quantum optics has revealed the importance of monitoring photon-photon correlations at all orders. We here present a comparative study of two experimental setups, composed of cold and warm rubidium atoms, respectively, which allow us to probe and compare photon correlations. The former operates in the quantum regime where spontaneous emission dominates, whereas the latter exhibits a temperature-limited coherence time. We demonstrate our capability to measure photon correlations up to the fourth order which could be useful to better characterize light scattered by cold atoms beyond the chaotic statistics.

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.

Quantum non-Gaussianity (QNG) corresponds to an essential resource in many prospective applications of quantum technologies. QNG states of light have been demonstrated in a broad range of experimental platforms with various complementary advantages [1]. However, in order to allow for their direct and efficient utilization for interaction with the target quantum system, their degrees of freedom have to be well-defined and controllable. This imposes a requirement on the generation of QNG light in a single optical mode. While the intrinsic single-photon sources including trapped ions, atoms, or molecules, naturally offer a close-to a single mode emission, their technologically more accessible counterparts including majority of the solid-state emitters and sources based on heralded generation of nonclassical states in various parametric nonlinear processes typically provide a multi-mode output. Although several demonstrations of a single-mode operation of nonclassical light sources based on these platforms have been recently demonstrated, an unambiguous observation of a single-mode QNG light has never been presented.

SummaryWe present our arrangement of new apparatus for trapping Ca + and Al + ions. The apparatus consists of a compact vacuum chamber, linear quadrupole trap, one pair of Helmholtz coils, two pairs of saddle coils, and a magnetic shield. The new design respects the requirement of the large optical access for laser beam integration, a homogeneous magnetic field in the position of the ion in the trapping area, and an ultra-high vacuum regime to avoid interactions between residual gas and ions. The new apparatus is designed in a way so that all important subparts can be changed easily and allow us to minimize the time when the inner parts are exposed to the air during a component exchange. All parts of the arrangement, including the quadrupole trap, have been designed and developed by the Institute of Scientific Instruments in Brno, Czech Republic.

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.

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.

The motion of trapped atoms plays an essential role in quantum mechanical sensing, simulations and computing. Small disturbances of atomic vibrations are still challenging to be sensitively detected. It requires a reliable coupling between individual phonons and internal electronic levels that light can readout. As available information in a few electronic levels about the phonons is limited, the coupling needs to be sequentially repeated to further harvest the remaining information. We analyze such phonon measurements on the simplest example of the force and heating sensing using motional Fock states. We prove that two sequential measurements are sufficient to reach sensitivity to force and heating for realistic Fock states and saturate the quantum Fisher information for a small amount of force or heating. It is achieved by the conventionally available Jaynes–Cummings coupling. The achieved sensitivities are found to be better than those obtained from classical states. Further enhancements are expectable when the higher Fock state generation is improved. The result opens additional applications of sequential phonon measurements of atomic motion. This measurement scheme can also be directly applied to other bosonic systems including cavity QED and circuit QED.

National time and frequency dissemination networks are being developed in many countries; also international connections are being established. In the contribution we present Czech Infrastructure for Time and Frequency as a non-commercial, open activity focused on the transfer of accurate time and very stable frequency using optical networks. The national optical infrastructure for time and frequency transfer is operated on top of the CESNET network infrastructure, to have operational cost under control. We also address actually running and planned upgrades and future development plans regarding wavelength bands and considered geographic extensions. We will also focus on creation of bidirectional dark channels on different wavebands within shared fibers together with bidirectional compensation of fiber losses. Single path bidirectional amplification utilizing lumped optical amplifiers is sensitive to feedback from fiber line like back scattering and reflections and in case of increased feedback can produce unwanted oscillations, which potentially interfere with parallel data transmissions. We will also briefly mention the CLONETS-DS project working on design study for coherent Pan-European time and frequency dissemination network, which would connect national networks and provide different services based on time and frequency for a wide range of users.

We present a design of a new compact vacuum chamber with an electrical trap for trapping and laser cooling of 40Ca+ and 27Al+ ions. The custom chamber was designed to a minimum dimension to achieve ultra-high vacuum environment and good optical access to trapped ions. Combining the shape of the electrical trap with intrinsic geometrical symmetry and the size of the viewports will allow maximum efficiency of fluorescence collection from ions. The setup is ready for ablation and loading of 40Ca+ and 27Al+ ions to deal with quantum logic experiments for optical clock operation. In combination with magnetic saddle coils, Helmholtz coil and external magnetic shielding made of mu-metal, we achieve a very homogeneous magnetic field in the ion trapping area. The main part of a chamber equipped with viewports is made of titanium to maintain this homogeneous magnetic field and suppress residual fields. The presented setup will allow quantum experiments with single ions and Coulomb crystals in a stable and homogeneous magnetic field, which is necessary for many-ions optical clock systems.

The distributed quantum information processing and hybridization of quantum platforms raises increasing demands on the quality of light-matter interaction and realization of efficient quantum interfaces. This becomes particularly challenging for needed states possessing fundamental quantum non-Gaussian (QNG) aspects. They correspond to paramount resources in most potent applications of quantum technologies. We demonstrate the generation of light with provably QNG features from a warm atomic ensemble in a single-mode regime. The light is generated in a spontaneous four-wave mixing process in the presence of decoherence effects caused by a large atomic thermal motion. Despite its high sensitivity to any excess noise, direct observability of heralded QNG light could be achieved due to a combination of a fast resonant excitation, large spectral bandwidth, and a low absorption loss of resonant photons guaranteed by the source geometry.

We present an optical scheme to detect the oscillations of a two-ion string confined in a linear Paul trap. The motion is detected by analyzing the intensity correlations in the fluorescence light emitted by one or two ions in the string. We present measurements performed under continuous Doppler cooling and under pulsed illumination. We foresee several direct applications of this detection method, including motional analysis of multi-ion species or coupled mechanical oscillators, and sensing of mechanical correlations.