Coherent control of the waveforms of recoilless γ-ray photons

Nuclear quantum memory for hard x-ray photon wave packets

Optical quantum memories are key elements in modern quantum technologies to reliably store and retrieve quantum information. At present, they are conceptually limited to the optical wavelength regime. Recent advancements in x-ray quantum optics render an extension of optical quantum memory protocols to ultrashort wavelengths possible, thereby establishing quantum photonics at x-ray energies. Here, we introduce an x-ray quantum memory protocol that utilizes mechanically driven nuclear resonant 57Fe absorbers to form a comb structure in the nuclear absorption spectrum by using the Doppler effect. This room-temperature nuclear frequency comb enables us to control the waveform of x-ray photon wave packets to a high level of accuracy and fidelity using solely mechanical motions. This tunable, robust, and highly flexible system offers a versatile platform for a compact solid-state quantum memory at room temperature for hard x-rays.

Slowing down x-ray photons in a vibrating recoilless resonant absorber

Recently, an observation of acoustically induced transparency (AIT) of a stainless-steel foil for resonant 14.4-keV photons from a radioactive ⁵⁷Co Mössbauer source due to collective uniform oscillations of atomic nuclei was reported [Phys Rev Lett 124,163602, 2020]. In this paper, we propose to use the steep resonant dispersion of the absorber within the AIT spectral window to dramatically reduce a propagation velocity of γ-ray and x-ray photons. In particular, we show that a significant fraction (more than 40%) of a 97-ns γ-ray single-photon wave packet from a ⁵⁷Co radioactive source can be slowed down up to 3 m/s and delayed by 144 ns in a ⁵⁷Fe-enriched stainless-steel foil at room temperature. We also show that a similarly significant slowing down up to 24 m/s and a delay by 42 ns can be achieved for more than 70% of the 100-ns 14.4-keV x-ray single-photon pulse from a synchrotron Mössbauer source available at European Synchrotron Radiation Facility (ESRF) and Spring-8 facility. The propagation velocity can be widely controlled by changing the absorber vibration frequency. Achieving the propagation velocity on the order of 1-50 m/s would set a record in the hard x-ray range, comparable to what was obtained in the optical range.

Nonlinearity-mediated digitization and amplification in electromechanical phonon-cavity systems

Electromechanical phonon-cavity systems are man-made micro-structures, in which vibrational energy can be coherently transferred between different degrees of freedom. In such devices, the energy transfer direction and coupling strength can be parametrically controlled, offering great opportunities for both fundamental studies and practical applications such as phonon manipulation and sensing. However, to date the investigation of such systems has largely been limited to linear vibrations, while their responses in the nonlinear regime remain yet to be explored. Here, we demonstrate nonlinear operation of electromechanical phonon-cavity systems, and show that the resonant response differs drastically from that in the linear regime. We further demonstrate that by controlling the parametric pump, one can achieve nonlinearity-mediated digitization and amplification in the frequency domain, which can be exploited to build high-performance MEMS sensing devices based on phonon-cavity systems. Our findings offer intriguing opportunities for creating frequency-shift-based sensors and transducers.

High-Brilliance Ultranarrow-Band X Rays via Electron Radiation in Colliding Laser Pulses

A setup of a unique x-ray source is put forward employing a relativistic electron beam interacting with two counterpropagating laser pulses in the nonlinear few-photon regime. In contrast to Compton scattering sources, the envisaged x-ray source exhibits an extremely narrow relative bandwidth of the order of 10^{-4}, comparable with an x-ray free-electron laser. The brilliance of the x rays can be an order of magnitude higher than that of a state-of-the-art Compton source. By tuning the laser intensities and the electron energy, one can realize either a single peak or a comblike x-ray source of around keV energy. The laser intensity and the electron energy in the suggested setup are rather moderate, rendering this scheme compact and tabletop size, as opposed to x-ray free-electron laser and synchrotron infrastructures.

Efficient Interaction of Heralded X-Ray Photons with a Beam Splitter

We report the experimental demonstration of efficient interaction of multi-kilo-electron-volt heralded x-ray photons with a beam splitter. The measured heralded photon rate at the outputs of the beam splitter is about 0.01  counts/s which is comparable to the rate in the absence of the beam splitter. We use this beam splitter together with photon number and photon energy resolving detectors to show directly that when a single x-ray photon interacts with a beam splitter it can only be detected at either of the ports of the beam splitter but not at both simultaneously, leading to a strong anticorrelation between the detection events at the two output ports. Our experiment demonstrates the major advantage of x rays for quantum optics-the possibility to observe experimental results with high fidelity and with negligible background.

Acoustically induced transparency for synchrotron hard x-ray photons

The induced transparency of opaque medium for resonant electromagnetic radiation is a powerful tool for manipulating the field-matter interaction. Various techniques to make different physical systems transparent for radiation from microwaves to x-rays were implemented. Most of them are based on the modification of the quantum-optical properties of the medium under the action of an external coherent electromagnetic field. Recently, an observation of acoustically induced transparency (AIT) of the 57Fe absorber for resonant 14.4-keV photons from the radioactive 57Co source was reported. About 150-fold suppression of the resonant absorption of photons due to collective acoustic oscillations of the nuclei was demonstrated. In this paper, we extend the AIT phenomenon to a novel phase-locked regime, when the transmitted photons are synchronized with the absorber vibration. We show that the advantages of synchrotron Mössbauer sources such as the deterministic periodic emission of radiation and controlled spectral-temporal characteristics of the emitted photons along with high-intensity photon flux in a tightly focused beam, make it possible to efficiently implement this regime, paving the way for the development of the acoustically controlled interface between hard x-ray photons and nuclear ensembles.

Coherent X-ray-optical control of nuclear excitons

Coherent control of quantum dynamics is key to a multitude of fundamental studies and applications1. In the visible or longer-wavelength domains, near-resonant light fields have become the primary tool with which to control electron dynamics2. Recently, coherent control in the extreme-ultraviolet range was demonstrated3, with a few-attosecond temporal resolution of the phase control. At hard-X-ray energies (above 5-10 kiloelectronvolts), Mössbauer nuclei feature narrow nuclear resonances due to their recoilless absorption and emission of light, and spectroscopy of these resonances is widely used to study the magnetic, structural and dynamical properties of matter4,5. It has been shown that the power and scope of Mössbauer spectroscopy can be greatly improved using various control techniques6-16. However, coherent control of atomic nuclei using suitably shaped near-resonant X-ray fields remains an open challenge. Here we demonstrate such control, and use the tunable phase between two X-ray pulses to switch the nuclear exciton dynamics between coherent enhanced excitation and coherent enhanced emission. We present a method of shaping single pulses delivered by state-of-the-art X-ray facilities into tunable double pulses, and demonstrate a temporal stability of the phase control on the few-zeptosecond timescale. Our results unlock coherent optical control for nuclei, and pave the way for nuclear Ramsey spectroscopy17 and spin-echo-like techniques, which should not only advance nuclear quantum optics18, but also help to realize X-ray clocks and frequency standards19. In the long term, we envision time-resolved studies of nuclear out-of-equilibrium dynamics, which is a long-standing challenge in Mössbauer science20.

Coherent control of collective nuclear quantum states via transient magnons

Ultrafast and precise control of quantum systems at x-ray energies involves photons with oscillation periods below 1 as. Coherent dynamic control of quantum systems at these energies is one of the major challenges in hard x-ray quantum optics. Here, we demonstrate that the phase of a quantum system embedded in a solid can be coherently controlled via a quasi-particle with subattosecond accuracy. In particular, we tune the quantum phase of a collectively excited nuclear state via transient magnons with a precision of 1 zs and a timing stability below 50 ys. These small temporal shifts are monitored interferometrically via quantum beats between different hyperfine-split levels. The experiment demonstrates zeptosecond interferometry and shows that transient quasi-particles enable accurate control of quantum systems embedded in condensed matter environments.

Narrow-band hard-x-ray lasing with highly charged ions

A scheme is put forward to generate fully coherent x-ray lasers based on population inversion in highly charged ions, created by fast inner-shell photoionization using broadband x-ray free-electron-laser (XFEL) pulses in a laser-produced plasma. Numerical simulations based on the Maxwell–Bloch theory show that one can obtain high-intensity, femtosecond x-ray pulses of relative bandwidths Δω/ω = 10⁻⁵–10⁻⁷, by orders of magnitude narrower than in x-ray free-electron-laser pulses for discrete wavelengths down to the sub-ångström regime. Such x-ray lasers can be applicable in the study of x-ray quantum optics and metrology, investigating nonlinear interactions between x-rays and matter, or in high-precision spectroscopy studies in laboratory astrophysics.

Subattosecond x-ray Hong-Ou-Mandel metrology

We show that subattosecond delays and subangstrom optical path differences can be measured by using Hong-Ou-Mandel interference measurements with x-rays. Our scheme relies on the subattosecond correlation time of photon pairs that are generated by x-ray spontaneous parametric down-conversion, which leads to a dip in correlation measurements with a comparable width. Therefore, the precision of the measurements is expected to be better than 0.1 attosecond. We anticipate that the scheme we describe in this work will lead to the development of various techniques of quantum measurements with ultra-high precision at x-ray wavelengths.

Observation of Acoustically Induced Transparency for γ-Ray Photons

We report an observation of a 148-fold suppression of resonant absorption of 14.4 keV photons from exp(-5.2) to exp(-0.2) with preservation of their spectral and temporal characteristics in an ensemble of the resonant two-level ^{57}Fe nuclei at room temperature. The transparency was induced via collective acoustic oscillations of nuclei. The proposed technique allows extending the concept of induced optical transparency to a hard x-ray or γ-ray range and paves the way for acoustically controllable interface between x-ray or γ-ray photons and nuclear ensembles, advancing the field of x-ray or γ-ray quantum optics.

Nuclear Quantum Memory and Time Sequencing of a Single γ Photon

We propose a technique for γ photon quantum memory through a Doppler frequency comb, produced by a set of resonantly absorbing nuclear targets that move with different velocities. It provides a reliable storage, an on-demand generation, and a time sequencing of a single γ photon. This scheme presents the first γ-photon-nuclear-ensemble interface opening a new direction of research in quantum information science.

Time-Resolved sub-Ångström Metrology by Temporal Phase Interferometry near X-Ray Resonances of Nuclei

We introduce an analytical phase-reconstruction principle that retrieves atomic scale motion via time-domain interferometry. The approach is based on a resonant interaction with high-frequency light and does not require temporal resolution on the time scale of the resonance period. It is thus applicable to hard x rays and γ rays for measurements of extremely small spatial displacements or relative-frequency changes. Here, it is applied to retrieve the temporal phase of a 14.4 keV emission line of an ^{57}Fe sample, which corresponds to a spatial translation of this sample. The small wavelength of this transition (λ=0.86  Å) allows for determining the motion of the emitter on sub-Ångström length and nanosecond timescales.

Spectral Control of an X-Ray L-Edge Transition via a Thin-Film Cavity

By embedding a thin layer of tantalum in an x-ray cavity, we observe a change in the spectral characteristics of an inner-shell transition of the metal. The interaction between the cavity mode vacuum and the L_{III}-edge transition is enhanced, permitting the observation of the collective Lamb shift, superradiance, and a Fano-like cavity-resonance interference effect. This experiment demonstrates the feasibility of cavity quantum electrodynamics with electronic resonances in the x-ray range with applications to manipulating and probing the electronic structure of condensed matter with high-resolution x-ray spectroscopy in an x-ray cavity setting.

Probing Quantum Dynamical Couple Correlations with Time-Domain Interferometry

Time-domain interferometry (TDI) is a promising method to characterize spatial and temporal correlations at x-ray energies, via the so-called intermediate scattering function and the related dynamical couple correlations. However, so far, it has only been analyzed for classical target systems. Here, we provide a quantum analysis, and suggest a scheme that allows us to access quantum dynamical correlations. We further show how TDI can be used to exclude classical models for the target dynamics, and illustrate our results using a single particle in a double well potential.

Field redistribution inside an X-ray cavity-QED setup

The field redistribution inside an X-ray cavity-QED setup with an embedded ⁵⁷Fe layer is calculated and studied in detail. The destructive interference between two transitions from the ground state to the two upper dressed states causes that the cavity mode can not be driven. So the field intensity is very weak when the nuclear ensemble is resonant. Moreover, It is found that the resonant nuclear layer can play a role of reflective layer like a mirror and cut the size of the cavity, which will destroy the guided mode. To support this idea, we employ the ⁵⁷Fe film as the bottom mirror layer of the cavity where a guided mode can only be formed at the resonant energy. Following this perspective, the electromagnetically induced transparency structure based on X-ray cavity-QED setup with nuclear ensemble is reviewed and a phenomenologically self-consistent analysis for the field redistribution is presented.

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.

Controllable vacuum-induced diffraction of matter-wave superradiance using an all-optical dispersive cavity

Cavity quantum electrodynamics (CQED) has played a central role in demonstrating the fundamental principles of the quantum world, and in particular those of atom-light interactions. Developing fast, dynamical and non-mechanical control over a CQED system is particularly desirable for controlling atomic dynamics and building future quantum networks at high speed. However conventional mirrors do not allow for such flexible and fast controls over their coupling to intracavity atoms mediated by photons. Here we theoretically investigate a novel all-optical CQED system composed of a binary Bose-Einstein condensate (BEC) sandwiched by two atomic ensembles. The highly tunable atomic dispersion of the CQED system enables the medium to act as a versatile, all-optically controlled atomic mirror that can be employed to manipulate the vacuum-induced diffraction of matter-wave superradiance. Our study illustrates a innovative all-optical element of atomtroics and sheds new light on controlling light-matter interactions.

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.

Tailoring superradiance to design artificial quantum systems

Cooperative phenomena arising due to the coupling of individual atoms via the radiation field are a cornerstone of modern quantum and optical physics. Recent experiments on x-ray quantum optics added a new twist to this line of research by exploiting superradiance in order to construct artificial quantum systems. However, so far, systematic approaches to deliberately design superradiance properties are lacking, impeding the desired implementation of more advanced quantum optical schemes. Here, we develop an analytical framework for the engineering of single-photon superradiance in extended media applicable across the entire electromagnetic spectrum, and show how it can be used to tailor the properties of an artificial quantum system. This “reverse engineering” of superradiance not only provides an avenue towards non-linear and quantum mechanical phenomena at x-ray energies, but also leads to a unified view on and a better understanding of superradiance across different physical systems.

Interferometric phase detection at x-ray energies via Fano resonance control

Modern x-ray light sources promise access to structure and dynamics of matter in largely unexplored spectral regions. However, the desired information is encoded in the light intensity and phase, whereas detectors register only the intensity. This phase problem is ubiquitous in crystallography and imaging and impedes the exploration of quantum effects at x-ray energies. Here, we demonstrate phase-sensitive measurements characterizing the quantum state of a nuclear two-level system at hard x-ray energies. The nuclei are initially prepared in a superposition state. Subsequently, the relative phase of this superposition is interferometrically reconstructed from the emitted x rays. Our results form a first step towards x-ray quantum state tomography and provide new avenues for structure determination and precision metrology via x-ray Fano interference.

Tunable Subluminal Propagation of Narrow-band X-Ray Pulses

Group velocity control is demonstrated for x-ray photons of 14.4 keV energy via a direct measurement of the temporal delay imposed on spectrally narrow x-ray pulses. Subluminal light propagation is achieved by inducing a steep positive linear dispersion in the optical response of 57Fe Mössbauer nuclei embedded in a thin film planar x-ray cavity. The direct detection of the temporal pulse delay is enabled by generating frequency-tunable spectrally narrow x-ray pulses from broadband pulsed synchrotron radiation. Our theoretical model is in good agreement with the experimental data.

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.