Deep-Learning Approach for the Atomic Configuration Interaction Problem on Large Basis Sets.

High-precision atomic structure calculations require accurate modeling of electronic correlations typically addressed via the configuration interaction (CI) problem on a multiconfiguration wave function expansion. The latter can easily become challenging or infeasibly large even for advanced supercomputers. Here, we develop a deep-learning approach which allows us to preselect the most relevant configurations out of large CI basis sets until the targeted energy precision is achieved. The large CI computation is thereby replaced by a series of smaller ones performed on an iteratively expanding basis subset managed by a neural network. While dense architectures as used in quantum chemistry fail, we show that a convolutional neural network naturally accounts for the physical structure of the basis set and allows for robust and accurate CI calculations. The method was benchmarked on basis sets of moderate size allowing for the direct CI calculation, and further demonstrated on prohibitively large sets where the direct computation is not possible.

Dynamical Control of Nuclear Isomer Depletion via Electron Vortex Beams.

Some nuclear isomers are known to store a large amount of energy over long periods of time, with a very high energy-to-mass ratio. Here, we describe a protocol to achieve the external control of the isomeric nuclear decay by using electron vortex beams whose wave function has been especially designed and reshaped on demand. Recombination of these electrons into the isomer's atomic shell can lead to the controlled release of the stored nuclear energy. On the example of ^{93m}Mo, we show theoretically that the use of tailored electron vortex beams increases the depletion by 4 orders of magnitude compared to the spontaneous nuclear decay of the isomer. Furthermore, specific orbitals can sustain an enhancement of the recombination cross section for vortex electron beams by as much as 6 orders of magnitude, providing a handle for manipulating the capture mechanism. These findings open new prospects for controlling the interplay between atomic and nuclear degrees of freedom, with potential energy-related and high-energy radiation source applications.

Nuclear Excitation of the

When Th nuclei are doped in CaF_{2} crystals, a set of electronic defect states appear in the crystal band gap which would otherwise provide complete transparency to vacuum-ultraviolet radiation. The coupling of these defect states to the 8 eV ^{229m}Th nuclear isomer in the CaF_{2} crystal is investigated theoretically. We show that although previously viewed as a nuisance, the defect states provide a starting point for nuclear excitation via electronic bridge mechanisms involving stimulated emission or absorption using an optical laser. The rates of these processes are at least 2 orders of magnitude larger than direct photoexcitation of the isomeric state using available light sources. The nuclear isomer population can also undergo quenching when triggered by the reverse mechanism, leading to a fast and controlled decay via the electronic shell. These findings are relevant for a possible solid-state nuclear clock based on the ^{229m}Th isomeric transition.

Can Extreme Electromagnetic Fields Accelerate the α Decay of Nuclei?

The possibility to control the α decay channel of atomic nuclei with electromagnetic fields of extreme intensities envisaged for the near future at multipetawatt and exawatt laser facilities is investigated theoretically. Using both analytic arguments based on the Wentzel-Kramers-Brillouin approximation and numerical calculations for the imaginary time method applied in the framework of the α decay precluster model, we show that no experimentally detectable modification of the α decay rate can be observed with super-intense lasers at any so-far-available wavelength. Comparing our predictions with those reported in several recent publications, where a considerable or even giant laser-induced enhancement of the decay rate has been claimed, we identify there the misuse of a standard approximation.

Electronic Bridge Excitation in Highly Charged

The excitation of the 8 eV ^{229m}Th isomer through the electronic bridge mechanism in highly charged ions is investigated theoretically. By exploiting the rich level scheme of open 4f orbitals and the robustness of highly charged ions against photoionization, a pulsed high-intensity optical laser can be used to efficiently drive the nuclear transition by coupling it to the electronic shell. We show how to implement a promising electronic bridge scheme in an electron beam ion trap starting from a metastable electronic state. This setup would avoid the need for a tunable vacuum ultraviolet laser. Based on our theoretical predictions, determining the isomer energy with an uncertainty of 10^{-5} eV could be achieved in one day of measurement time using realistic laser parameters.

Energy of the 229Th nuclear clock transition.

Owing to its low excitation energy and long radiative lifetime, the first excited isomeric state of thorium-229, 229mTh, can be optically controlled by a laser1,2 and is an ideal candidate for the creation of a nuclear optical clock3, which is expected to complement and outperform current electronic-shell-based atomic clocks4. A nuclear clock will have various applications-such as in relativistic geodesy5, dark matter research6 and the observation of potential temporal variations of fundamental constants7-but its development has so far been impeded by the imprecise knowledge of the energy of 229mTh. Here we report a direct measurement of the transition energy of this isomeric state to the ground state with an uncertainty of 0.17 electronvolts (one standard deviation) using spectroscopy of the internal conversion electrons emitted in flight during the decay of neutral 229mTh atoms. The energy of the transition between the ground state and the first excited state corresponds to a wavelength of 149.7 ± 3.1 nanometres, which is accessible by laser spectroscopy through high-harmonic generation. Our method combines nuclear and atomic physics measurements to advance precision metrology, and our findings are expected to facilitate the application of high-resolution laser spectroscopy on nuclei and to enable the development of a nuclear optical clock of unprecedented accuracy.

Theoretical Predictions for the Magnetic Dipole Moment of

A recent laser spectroscopy experiment [J. Thielking et al., Nature, (London) 556, 321 (2018)] has determined for the first time the magnetic dipole moment of the 7.8 eV isomeric state ^{229m}Th. The measured value differs by a factor of approximately 5 from previous nuclear theory predictions based on the Nilsson model, raising questions about our understanding of the underlying nuclear structure. Here, we present a new theoretical prediction based on a nuclear model with coupled collective quadrupole-octupole and single-particle motions. Our calculations yield an isomer magnetic dipole moment of µ_{IS}=-0.35µ_{N} in surprisingly good agreement with the experimentally determined value of -0.37(6)µ_{N}, while overestimating the ground state dipole moment by a factor 1.4. The model provides further information on the role and strength of the Coriolis mixing and the most probable value of the gyromagnetic ratio g_{R} and its consequences for the transition probability B(M1). The key role of the magnetic moment values as constraints in the determination of the isomer decay rates is discussed.

Nuclear excitation by electron capture in optical-laser-generated plasmas.

The process of nuclear excitation by electron capture in plasma environments generated by the interaction of ultrastrong optical lasers with solid-state samples is investigated theoretically. With the help of a plasma model, we perform a comprehensive study of the optimal parameters for the most efficient nuclear excitation and determine the corresponding laser setup requirements. We discern between the low-density plasma regime, modeled by scaling laws, and the high-density regime, for which we perform particle-in-cell calculations. As a nuclear transition case study we consider the 4.85-keV nuclear excitation starting from the long-lived ^{93m}Mo isomer. Our results show that the optimal plasma and laser parameters are sensitive to the chosen observable and that measurable rates of nuclear excitation and isomer depletion of ^{93m}Mo should be already achievable at laser facilities existing today.

Tailoring Laser-Generated Plasmas for Efficient Nuclear Excitation by Electron Capture.

The optimal parameters for nuclear excitation by electron capture in plasma environments generated by the interaction of ultrastrong optical lasers with solid matter are investigated theoretically. As a case study we consider a 4.85 keV nuclear transition starting from the long-lived ^{93m}Mo isomer that can lead to the release of the stored 2.4 MeV excitation energy. We find that due to the complex plasma dynamics, the nuclear excitation rate and the actual number of excited nuclei do not reach their maximum at the same laser parameters. The nuclear excitation achievable with a high-power optical laser is up to twelve and up to six orders of magnitude larger than the values predicted for direct resonant and secondary plasma-mediated excitation at the x-ray free electron laser, respectively. Our results show that the experimental observation of the nuclear excitation of ^{93m}Mo and the subsequent release of stored energy should be possible at laser facilities available today.

Reduced Transition Probabilities for the Gamma Decay of the 7.8 eV Isomer in

The reduced magnetic dipole and electric quadrupole transition probabilities for the radiative decay of the ^{229}Th 7.8 eV isomer to the ground state are predicted within a detailed nuclear-structure model approach. We show that the presence and decay of this isomer can only be accounted for by the Coriolis mixing emerging from a remarkably fine interplay between the coherent quadrupole-octupole motion of the nuclear core and the single-nucleon motion within a reflection-asymmetric deformed potential. We find that the magnetic dipole transition probability which determines the radiative lifetime of the isomer is considerably smaller than presently estimated. The so-far disregarded electric quadrupole component may have non-negligible contributions to the internal conversion channel. These findings support new directions in the experimental search of the ^{229}Th transition frequency for the development of a future nuclear frequency standard.

Optomechanically induced transparency of x-rays via optical control.

The search for new control methods over light-matter interactions is one of the engines that advances fundamental physics and applied science alike. A specific class of light-matter interaction interfaces are setups coupling photons of distinct frequencies via matter. Such devices, nontrivial in design, could be endowed with multifunctional tasking. Here we envisage for the first time an optomechanical system that bridges optical and robust, high-frequency x-ray photons, which are otherwise notoriously difficult to control. The x-ray-optical system comprises of an optomechanical cavity and a movable microlever interacting with an optical laser and with x-rays via resonant nuclear scattering. We show that optomechanically induced transparency of a broad range of photons (10 eV-100 keV) is achievable in this setup, allowing to tune nuclear x-ray absorption spectra via optomechanical control. This paves ways for metrology applications, e.g., the detection of the 229Thorium clock transition, and an unprecedentedly precise control of x-rays using optical photons.

A Laser Excitation Scheme for

Direct laser excitation of the lowest known nuclear excited state in ^{229}Th has been a long-standing objective. It is generally assumed that reaching this goal would require a considerably reduced uncertainty of the isomer's excitation energy compared to the presently adopted value of (7.8±0.5) eV. Here we present a direct laser excitation scheme for ^{229m}Th, which circumvents this requirement. The proposed excitation scheme makes use of already existing laser technology and therefore paves the way for nuclear laser spectroscopy. In this concept, the recently experimentally observed internal-conversion decay channel of the isomeric state is used for probing the isomeric population. A signal-to-background ratio of better than 10^{4} and a total measurement time of less than three days for laser scanning appear to be achievable.

X-ray-generated heralded macroscopical quantum entanglement of two nuclear ensembles.

Heralded entanglement between macroscopical samples is an important resource for present quantum technology protocols, allowing quantum communication over large distances. In such protocols, optical photons are typically used as information and entanglement carriers between macroscopic quantum memories placed in remote locations. Here we investigate theoretically a new implementation which employs more robust x-ray quanta to generate heralded entanglement between two crystal-hosted macroscopical nuclear ensembles. Mössbauer nuclei in the two crystals interact collectively with an x-ray spontaneous parametric down conversion photon that generates heralded macroscopical entanglement with coherence times of approximately 100 ns at room temperature. The quantum phase between the entangled crystals can be conveniently manipulated by magnetic field rotations at the samples. The inherent long nuclear coherence times allow also for mechanical manipulations of the samples, for instance to check the stability of entanglement in the x-ray setup. Our results pave the way for first quantum communication protocols that use x-ray qubits.

Stopping Narrow-Band X-Ray Pulses in Nuclear Media.

A control mechanism for stopping x-ray pulses in resonant nuclear media is investigated theoretically. We show that narrow-band x-ray pulses can be mapped and stored as nuclear coherence in a thin-film planar x-ray cavity with an embedded ^{57}Fe nuclear layer. The pulse is nearly resonant to the 14.4 keV Mössbauer transition in the ^{57}Fe nuclei. The role of the control field is played here by a hyperfine magnetic field which induces interference effects reminiscent of electromagnetically induced transparency. We show that, by switching off the control magnetic field, a narrow-band x-ray pulse can be completely stored in the cavity for approximately 100 ns. Additional manipulation of the external magnetic field can lead to both group velocity and phase control of the pulse in the x-ray cavity sample.

Logical operations with single x-ray photons via dynamically-controlled nuclear resonances.

Photonic qubits lie at the heart of quantum information technology, often encoding information in their polarization state. So far, only low-frequency optical and infrared photons have been employed as flying qubits, as the resources that are at present easiest to control. With their essentially different way of interacting with matter, x-ray qubits would bear however relevant advantages: they are extremely robust, penetrate deep through materials, and can be focused down to few-nm waveguides, allowing unprecedented miniaturization. Also, x-rays are resonant to nuclear transitions, which are very well isolated from the environment and present long coherence times. Here, we show theoretically that x-ray polarization qubits can be dynamically controlled by nuclear Mössbauer resonances. The control knob is played by nuclear hyperfine magnetic fields, that allow via fast rotations precise processing of single x-ray quanta polarization. With such rotations, single-qubit and binary logical operations such as a destructive C-NOT gate can be implemented.

All-electromagnetic control of broadband quantum excitations using gradient photon echoes.

A broadband photon echo effect in a three level Λ-type system interacting with two laser fields is investigated theoretically. Inspired by the emerging field of nuclear quantum optics which typically deals with very narrow resonances, we consider broadband probe pulses that couple to the system in the presence of an inhomogeneous control field. We show that such a setup provides an all-electromagnetic-field solution to implement high bandwidth photon echoes, which are easy to control, store and shape on a short time scale and, therefore, may speed up future photonic information processing. The time compression of the echo signal and possible applications for quantum memories are discussed.

Proposed entanglement of X-ray nuclear polaritons as a potential method for probing matter at the subatomic scale.

A setup for generating the special superposition of a simultaneously forward- and backward-propagating collective excitation in a nuclear sample is studied. We show that by actively manipulating the scattering channels of single x-ray quanta with the help of a normal incidence x-ray mirror, a nuclear polariton which propagates in two opposite directions can be generated. The two counterpropagating polariton branches are entangled by a single x-ray photon. The quantum nature of the nuclear excitation entanglement gives rise to a subangstrom-wavelength standing wave excitation pattern that can be used as a flexible tool to probe matter dynamically on the subatomic scale.

Coherent storage and phase modulation of single hard-x-ray photons using nuclear excitons.

The coherent storage and phase modulation of x-ray single-photon wave packets in the resonant scattering of light off nuclei is theoretically investigated. We show that by switching off and on again the magnetic field in the nuclear sample, phase-sensitive storage of photons in the keV regime can be achieved. Corresponding π phase modulation of the stored photon can be accomplished if the retrieving magnetic field is rotated by 180°. The development of such x-ray single-photon control techniques is a first step towards forwarding quantum optics and quantum information to shorter wavelengths and more compact photonic devices.