We consider the interaction of a two-level atom with two counter-propagating light pulses of different carrier frequencies. To ensure adiabatic interaction, the pulse duration is much longer than both the inverse frequency difference and the maximum Rabi frequencies of the pulses. For the first time, we examine the case where the atom is initially prepared in a superposition of the ground and excited states with a momentum difference corresponding to one-photon recoil. We identify the conditions under which the atom’s final state is determined by the phase difference of the momentum components of the initial atomic wave. Given the large pulse duration, the interference effects depend critically on the rate of spontaneous emission from the excited state. We analyze the role of spontaneous emission using the Monte Carlo wave function method. The results of our calculations elucidate the influence of spontaneous radiation on both the momentum transferred to the atom and the interference outcome of the two atomic waves.

Nonclassical photon sources of high brightness are key components of quantum communication technologies. We here demonstrate the generation of narrowband, nonclassical photon pairs by employing spontaneous four-wave mixing in an optically-dense ensemble of cold atoms within a hollow-core fiber. The brightness of our source approaches the limit of achievable generated spectral brightness at which successive photon pairs start to overlap in time. For a generated spectral brightness per pump power of up to 2 × 10 9 pairs/(s MHz mW) we observe nonclassical correlations at pump powers below 100 nW and a narrow bandwidth of 2 π × 6.5 MHz. In this regime we demonstrate that our source can be used as a heralded single-photon source. By further increasing the brightness we enter the regime where successive photon pairs start to overlap in time and the cross-correlation approaches a limit corresponding to thermal statistics. Our approach of combining the advantages of atomic ensembles and waveguide environments is an important step toward photonic quantum networks of ensemble-based elements.

Розглянуто силу свiтлового тиску на наночастинки, що мiстять домiшки атомiв або центри забарвлення, якi резонан-сно взаємодiють з полем. Наявне кристалiчне оточення у загальному випадку унеможливлює формування дворiвневої схеми взаємодiї атома або центра забарвлення з полем завдяки зняттю заборони на частину переходiв зi спонтанним випромiнюванням. У результатi частина атомiв перебуває у станах, якi не взаємодiють з полем лазерного випромiнювання, але якi з часом релаксують до основного стану. Побудовано теорiю, яка дозволяє розрахувати силу свiтлового тиску на атоми чи центр забарвлення (i, вiдповiдно, на наночастинку, в якiй вони перебувають) у залежностi вiд параметрiв їхньої взаємодiї з полем та параметрiв релаксацiї збудженого стану i промiжних станiв. Для вивчення впливу рiзних факторiв на силу свiтлового тиску розрахунки проведенi для модельної сукупностi параметрiв, а також для параметрiв, якi визначають взаємодiю тризарядних iонiв ербiю у допованих ним кристалах Y2SiO5 та центрiв забарвлення, що виникають завдяки розташуванню атомiв кремнiю в дефектах кристала алмазу. Як виявилося, завдяки центрам забарвлення можна на кiлька порядкiв пiдняти силу тиску свiтла на малi, значно меншi за довжину хвилi, наночастинки.

Light pressure on nanoparticles containing impurity atoms or color centers interacting reso-nantly with the field has been considered. In the general case, the available crystalline envi-ronment of atoms prohibits the formation of a two-level interaction scheme of the atom or the color center with the field by eliminating the prohibition on some transitions with sponta-neous radiation emission. As a result, some atoms remain temporarily in the states that do not interact with the laser radiation field, but relax in time to the ground state. A theory which enables the calculation of the light-pressure force on atoms or color centers (and, accordingly, on the nanoparticle, where they are located) and its dependence on the atom-field interaction parameters, as well as the relaxation parameters of the excited and intermediate states, has been developed. To analyze the influence of various factors on the light-pressure force, calcu-lations are made for a model set of parameters and for the parameters corresponding to the interaction between triply charged erbium ions in erbium-doped Y2SiO5 crystals and color cen-ters that emerge owing to the occupation of defects in diamond crystals by silicon atoms. It turned out that the color centers make it possible to reinforce the light pressure on small, much smaller than the light wavelength, nanoparticles by several orders of magnitude.

Light pressure on nanoparticles containing impurity atoms or color centers interacting resonantly with the field has been considered. In the general case, the available crystalline environment of atoms prohibits the formation of a two-level interaction scheme of the atom or the color center with the field by eliminating the prohibition on some transitions with spontaneous radiation emission. As a result, some atoms remain temporarily in the states that do not interact with the laser radiation field, but relax in time to the ground state. A theory which enables the calculation of the light-pressure force on atoms or color centers (and, accordingly, on the nanoparticle, where they are located) and its dependence on the atom–field interaction parameters, as well as the relaxation parameters of the excited and intermediate states, has been developed. To analyze the influence of various factors on the light-pressure force, calculations are made for a model set of parameters and for the parameters corresponding to the interaction between triply charged erbium ions in erbium-doped Y2SiO5 crystals and color centers that emerge owing to the occupation of defects in diamond crystals by silicon atoms. It turned out that the color centers make it possible to reinforce the light pressure on small, much smaller than the light wavelength, nanoparticles by several orders of magnitude. K e yw o r d s: atoms, nanoparticles, laser radiation, light pressure.

Theoretical and experimental data is presented for the application of an injection-seeded frequency-shifted feedback (FSF) laser for high accuracy ranging. Previous work discussed such a ranging scheme with a phase-modulated single-frequency laser where the phase modulation is done by an electro-optical modulator driven by a single frequency Ω which is swept over a certain bandwidth depending on the given experimental situation. In the present theoretical and experimental work, the phase modulation of the injection laser is done by a frequency comb with temporally fixed frequency components at intervals Ω d spanning a bandwidth adapted to the geometry of the object to be measured. It is shown that the superposition of such FSF radiation returning from the object and a reference surface on a detector leads to a train of sinusoidal pulses with an instantaneous frequency Ω inst in the radio-frequency range. The repetition rate of these pulses is Ω d and their duration is < 2 π / Ω d . The central result of this work is the observation that the path length difference between reference and object surface can be deduced from Ω inst , e.g. by frequency counting. The benefit of this approach lies in the fact that active frequency variation is not needed; all features of the entire system (FSF laser plus phase-modulated injected radiation) are constant in time. Proof-of-concept results using an FSF-laser ranging scheme based on a semiconductor laser are presented.

Quantum emitters with a Λ-type level structure enable numerous protocols and applications in quantum science and technology. Understanding and controlling their dynamics is, therefore, one of the central research topics in quantum optics. Here, we drive two-photon Rabi oscillations between the two ground states of cesium atoms and observe the associated oscillatory Raman gain and absorption that stems from the atom-mediated coherent photon exchange between the two drive fields. The atoms are efficiently and homogeneously coupled with the probe field by means of a nanofiber-based optical interface. We study the dependence of the two-photon Rabi frequency on the system parameters and observe Autler–Townes splitting in the probe transmission spectrum. Beyond shedding light on the fundamental processes underlying two-photon Rabi oscillations, our method could also be used to investigate (quantum) correlations between the two drive fields as well as the dynamical establishment of electromagnetically induced transparency.

The original version of this book was inadvertently published without including a chapter. The chapter titled “Hybrid Hydrogels with Biologically Active Dyes and Their Antibacterial Efficacy” has been added at the end of the book.

We study numerically the evolution of the velocity distribution of atoms under the action of the bichromatic force. The comparison of the time dependencies of the distribution width and the average acceleration of atoms reveal the correlation of these quantities. We show that the estimation of the momentum diffusion coefficient on the basis of the analogy between the interaction of atoms with the counter-propagating bichromatic waves and the interaction of atoms with the counter-propagating sequences of the $\pi$-pulses roughly corresponds to the results of numerical calculations. To separate the influence of the momentum diffusion on the evolution of atomic momentum distribution from the influence of the time-dependent Doppler shift, we study the motion of a ``heavy'' atom, for which the velocity change during the interaction of an atom with the field can be neglected. Provided that the parameters of the atom-field interaction are optimal, we show that the momentum diffusion coefficient is proportional to the intensity of the laser radiation. We used the Monte Carlo wave-function method for the numerical simulation of the atomic motion.

We present a thorough experimental investigation of the loading process of laser-cooled atoms from a magneto-optical trap into an optical dipole trap located inside a hollow-core photonic bandgap fiber, followed by propagation of the atoms therein. This, e.g., serves to identify limits to the loading efficiency and thus optical depth which is a key parameter for applications in quantum information technology. Although only limited access in 1D is available to probe atoms inside such a fiber, we demonstrate that a detailed spatially-resolved characterization of the loading and trapping process along the fiber axis is possible by appropriate modification of probing techniques combined with theoretical analysis. Specifically, we demonstrate the loading of up to 2 . 1 × 10 5 atoms with a transfer efficiency of 2 . 1 % during the course of 50 ms and a peak loading rate of 4 . 7 × 10 3 atoms ms − 1 resulting in a peak atomic number density on the order of 10 12 cm − 3 . Furthermore, we determine the evolution of the spatial density (profile) and ensemble temperature as it approaches its steady-state value of T = 1400 µ K, as well as loss rates, axial velocity and acceleration. The spatial resolution along the fiber axis reaches a few millimeters, which is much smaller than the typical fiber length in experiments. We compare our results to other fiber-based as well as free-space optical dipole traps and discuss the potential for further improvements.

A possibility of the two-photon excitation of an isomeric state in a nucleus of thorium-229 has been discussed. The fluorescence intensity of the excitation is demonstrated to be identical for the irradiation of nuclei with either monochromatic light or polychromatic radiation consisting of a sequence of short lightpulses of the same intensity. The two-photon excitation of Th3+ ion in an electromagnetic trap with a focused laser beam with a wavelength of about 320 nm and power of 100 mW can lead to the absorption saturation, at which the fluorescence emission with the frequency of the transition in a nucleus is maximal. In crystals doped with Th4+ to a concentration of about 1018 cm-3 and irradiated with a laser radiation 10 W in power, the emission of several photons persecond with a wavelength of about 160 nm becomes possible.

We have shown that, by properly detuning the carrier frequencies in each of two perpendicularly intersecting bichromatic waves from the atomic transition frequency, it is possible to create a two-dimensional trap for atoms, if the wave intensities are sufficiently high. At the zero and near-zero values of the initial wave phases, as well as at the phase shift between the intersecting waves equal to п or close to п values, the dynamic spatial patterns of atoms consisting of square cells with the side length equal to л/√2 are formed. Numerical simulations were carried out for sodium atoms.

The momentum diffusion of atoms in the field of two counter-propagating stochastic waves, one of which reproduces the other one with a certain time delay, has been studied. It is shown that the parameters of atom-field interaction, at which the light pressure force is maximum, correspond to the increasing momentum diffusion coefficient. In the case of high-intensity field described by the stochastic field model, the momentum diffusion coefficient was found to be proportional to the square root of the field autocorrelation time. The wave function describing the inner state of atoms is modeled, by using the Monte-Carlo method. Numerical calculations are carried out for cesium atoms.

Absolute gravimeters on the basis of atomic interferometer with freely falling cold atoms have already demonstrated top-level performance in terms of sensitivity, long-term stability and accuracy which are comparable with the best characteristics of classical ballistic gravimeters, as confirmed in international comparisons. The accuracy of 10 nm.s(-2) is demonstrated not only by stationary laboratory absolute atomic gravimeters, but also by devices intended for field measurements [1]. Atomic gravimeters have a number of potential advantages - the absence of moving parts, a higher sampling rate and they are considered today as a promising area of modern gravimetric technology. In this paper, an overview of publications describing the physical schemes of modern atomic gravimeters is given, the main units of the atomic gravimeter, their purpose and principles of functioning are considered in details. The main attention is paid to laser systems in terms of determining the achievement of necessary conditions for cooling atoms, manipulation of their motion, preparation of quantum states, functioning of the atomic interferometer and detection of the signal. As can be seen from the overview, in modern atomic gravimeters, predominantly semiconductor lasers are used with high, and in some cases, unique technical parameters, which ensure simultaneous achievement of high values of output power, monochromaticity, stability of energy parameters and frequency of radiation, precision control of wavelengths at sufficiently wide range of their values. The creation of such laser systems requires the solution of a number of complex technical problems - the development and creation of effective laser amplification schemes, modulators for the formation of the necessary laser frequencies, and the schemes for locking laser frequencies along the absorption lines of alkaline atoms. The paper also examines the requirements for a highly vacuum system, magnetic shielding schemes, vibration and seismic protection, and discusses the prospects of development of such gravimeters in Ukraine.

We theoretically develop and experimentally demonstrate a coherence population mapping (CPM) protocol to store atomic coherences in long-lived populations, enabling storage times far beyond the typically very short decoherence times of quantum systems. The amplitude and phase of an atomic coherence is written onto the populations of a three-state system by specifically designed sequences of radiation pulses from two coupling fields. As an important feature, the CPM sequences enable a retrieval efficiency, which is insensitive to the phase of the initial coherence. The information is preserved in every individual atom of the medium, enabling applications in purely homogeneously or inhomogeneously broadened ensembles even when stochastic phase jumps are the main source of decoherence. We experimentally confirm the theoretical predictions by applying CPM for storage of atomic coherences in a doped solid, reaching storage times in the regime of 1 min.

We report results on ranging based on frequency-shifted feedback (FSF) lasers with two different implementations: (1) An Ytterbium-fiber system for measurements in an industrial environment with accuracy of the order of 1 \(\upmu \hbox {m}\), achievable over a distance of the order of meters with potential to reach an accuracy of better than 100 nm; (2) A semiconductor laser system for a high rate of measurements with an accuracy of 2 mm @ 1 MHz or 75 \(\upmu \hbox {m}\) @ 1 kHz and a limit of the accuracy of \(\ge\)10 \(\upmu \hbox {m}\). In both implementations, the distances information is derived from a frequency measurement. The method is therefore insensitive to detrimental influence of ambient light. For the Ytterbium-fiber system, a key feature is the injection of a single-frequency laser, phase modulated at variable frequency \(\varOmega\), into the FSF-laser cavity. The frequency \(\varOmega _\mathrm{{max}}\) at which the detector signal is maximal yields the distance. The semiconductor FSF-laser system operates without external injection seeding. In this case, the key feature is frequency counting that allows convenient choice of either accuracy or speed of measurements simply by changing the duration of the interval during which the frequency is measured by counting .

We calculate the temperature of the atoms in the field of counter-propagating stochastic light waves (the chaotic-field model). We show that the temperature of the atomic ensemble depends on the autocorrelation time of the waves, their intensity and the detuning of the carrier frequency of the waves from the atomic transition frequency. The field can form a one-dimensional trap for atoms, as is readily seen from our previous investigation of light-pressure force on an atom in counter-propagating stochastic light waves [V. I. Romanenko, B. W. Shore, L. P. Yatsenko, Opt. Commun. 268 (2006) 121–132]. We carry out numerical simulation of the atomic ensemble using parameters appropriate for sodium atoms. Analyzing the known investigation of the light-pressure force on atoms and their motion in the counter-propagating polychromatic waves, we suggest an hypothesis that any polychromatic counter-propagating waves that have a discrete spectrum, or waves described by a stationary stochastic process, one of which repeats the other, can form a trap for atoms.

We apply Monte Carlo wave function method and classical mechanics to description of the atomic motion in the field of laser radiation. Simultaneous use of quantum and classical mechanics for description of inner and translational motion avoids quantization of the translational degrees of freedom. The calculation are carried out for the example of atomic motion in the field of counter-propagating laser waves, one of which repeats the other. It is shown that such scheme of the atom-field interaction leads to confinement of atoms and their cooling by the same laser beams for proper the atom-field interaction parameters. The cases of laser pulses, bichromatic waves and stochastic field (the model of coloured noise) are analyzed.