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Physical Review A

Transient coherent phase modulation of nuclear states via a high-repetition-rate laser

Nan Xue, Haohan Shi, Kailin Zhang, Zuoye Liu

Published Feb 13, 2025• 3 citations
Publisher

Abstract

Advancements in x-ray sources extend the scope of light-matter interactions into the x-ray-nuclear regime. Precise temporal control of quantum phases provides fundamental insights into quantum systems and serves as a cornerstone for numerous quantum technologies. Nevertheless, achieving phase control of quantum systems with high temporal and spatial resolution remains a substantial challenge in the realm of hard x-ray quantum optics due to the ultrashort oscillation periods of photons. In this study, we propose to manipulate the magnetic properties of a thin $^{57}\text{Fe}$ film using near-infrared (NIR) pulses characterized by a high repetition rate. By calculating the evolution of quantum beats, we can theoretically extract the phase information of the nuclear response. Coherence within the nuclear ensemble is preserved throughout the entire process. This control scheme achieves quantum shifts with zeptosecond precision and modulates the spectral line shape within the frequency domain. Our proposal introduces a high-resolution method for rapidly manipulating nuclear states using optical laser pulses.

DOI
10.1103/physreva.111.023512

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ACS Photonics•Apr 20, 2026•1 citation
Advancements in x-ray sources extend the scope of light-matter interactions into the x-ray-nuclear regime. Precise temporal control of quantum phases provides fundamental insights into quantum systems and serves as a cornerstone for numerous quantum technologies. Nevertheless, achieving phase control of quantum systems with high temporal and spatial resolution remains a substantial challenge in the realm of hard x-ray quantum optics due to the ultrashort oscillation periods of photons. In this study, we propose to manipulate the magnetic properties of a thin 57Fe^{57}\text{Fe}57Fe film using near-infrared (NIR) pulses characterized by a high repetition rate. By calculating the evolution of quantum beats, we can theoretically extract the phase information of the nuclear response. Coherence within the nuclear ensemble is preserved throughout the entire process. This control scheme achieves quantum shifts with zeptosecond precision and modulates the spectral line shape within the frequency domain. Our proposal introduces a high-resolution method for rapidly manipulating nuclear states using optical laser pulses.
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.
Based on the laser-induced-phase model, periodic quantum phase modulation of the dipole response in atomic He is studied theoretically. The two-level system of the transition 1s2→1s2p with a delay width of 1.8 × 109 s-1 and an energy difference of 21.2 eV between the excited state and the ground state is used in the calculation. The system is excited by attosecond laser pulse from high harmonic generator, and the spectral response of the system is of single isolated symmetric Lorentzian absorption line. After the excitation, near infrared (NIR) femtosecond laser pulse train with a repetition rate of 5 GHz, central frequency 780 nm, and pulse duration of 100 fs, is utilized to periodically modify the spontaneous decay of the excited 1s2p level. The incremental phase step Δφ depends on the intensity of the NIR laser pulse, while the initial offset phase φ can be controlled independently by partially overlapping the first NIR pulse with the excitation. Simulated results show that the Lorentzian absorption line is transformed into comb-like spectral structure with equal gap depending on the repetition rate of the NIR pulse train. The line shape of each comb tooth is symmetric Lorentzian line by setting φ = Δφ/2 = π/2, while it is Fano line by setting φ = Δφ = π. The location of the comb structure is mainly dependent on the energy difference between the excited state and the ground state, while it can be slightly tuned by controlling the incremental phase step Δφ. We develop an analytic description of the comb-like spectral structure by Fourier analysis, depending on both the atomic and the phase-control properties. The analytical expressions can be readily used to estimate the exact experimental parameters. The universality of this mechanism allows the spectral modulation in arbitrary atomic system at arbitrary frequency, including the hard X-ray regime, by using reference transitions in highly charged ions. The generalization of this approach should thus not only enable relative frequency measurement and relevant applications at extremely high frequencies, but also open the way for pulse shaping at arbitrary frequencies.
In this thesis thin-film cavities with embedded Mössbauer nuclei probed by near-resonant x-ray light are studied from a quantum optical perspective. A theoretical framework is developed and compact expressions for the observables are derived for the linear excitation regime, which is encountered in current experiments. Even advanced cavity layouts can be modeled in excellent agreement with the results of previous experiments and semi-classical approaches. In the absence of magnetic hyperfine splitting, the spectral response of the system is found to be formed by tunable Fano profiles. An experimental implementation of this line shape control allows to extract spectroscopic signatures with high precision and to reconstruct the phase of the nuclear transition in good agreement with the theoretical predictions. The alignment of medium magnetization and polarization control of the x-rays enable to engineer advanced quantum optical level schemes, in which vacuum induced coherence effects are predicted and successfully demonstrated in an experiment. Furthermore, it is shown that group velocity control for x-ray pulses can be achieved in the cavity. A scheme for its observation is proposed and then employed to experimentally confirm sub-luminal x-ray propagation. Finally, non-linear effects, which could become accessible with future light sources, are explored and a non-linear line shape control mechanism is discussed.
Creating and controlling well-defined single-photon states is important for many quantum enhanced technologies. Information can be encoded in any degree of freedom associated with a single-photon field excitation, for example in the polarization or transverse spatial mode structure. The ability to encode multiple qubits in these states is desirable for high data transmission rates and increased information processing capacity. The spectral-temporal domain offers a large Hilbert space for encoding information, well suited to integrated optical architectures owing to the low cross-talk between channels. Indeed, time-frequency encoding is an integral component of existing information technologies infrastructure. Thus, complete, coherent control of the spectral-temporal mode structure of light is essential to advancing optical quantum technologies. Arbitrary control of single-photon states has been demonstrated in the polarization and spatial-momentum degrees of freedom however, is yet to be established in the spectral-temporal domain. Recently it was shown that spectral-temporal pulse shaping is experimentally feasible using nonlinear optical methods. However, such techniques can introduce noise photons, are challenging to implement deterministically and require specially prepared auxiliary pump pulses. Furthermore, they are typically only possible at relatively low repetition rates to avoid damage of nonlinear optical materials. Here, we demonstrate deterministic pulse shaping of single-photon wave packets by introducing a time-varying phase. Applying linear or quadratic phase to the wave packet introduces a spectral shift or spectral broadening, respectively. Achieving significant spectral manipulation requires temporal-phase modulation on the order of π. The phase must also vary on the same time scale as the optical pulses, approximately 1 ps in duration here. This relatively rapid phase variation is achieved using a fast electro-optic phase modulator. The modulator is driven by a time-varying voltage that is synchronized with a pulse train of single-photon wave packets for accurate temporal phase control. In this thesis, we experimentally demonstrate control of the spectral-temporal state of single-photon wave packets using this method. Heralded single-photon wave packets are generated by spontaneous parametric down conversion pumped by a frequency-doubled Titanium-Sapphire laser oscillator with 80 MHz repetition rate. To achieve significant modulation of single-photon pulses a 10 V peak-to-peak radio-frequency signal of 40 GHz drives the phase modulator, which requires approximately 3.6 V to achieve a π phase shift. The signal is synchronized with the oscillator pulse train using custom designed electronics. Details of these electronics are presented, resulting in a robust phase and amplitude controllable 40 GHz voltage source, phase locked to the single-photon pulse train. To demonstrate the utility of this pulse-shaping method we experimentally show spectral shearing of almost 1 nm for single-photon wave packets with 830 nm central wavelength and 1 nm bandwidth. Measurement of the second-order intensity correlation before and after the wave-packet manipulation remains constant within uncertainty of the measurement, showing that the quantum nature of the single-photon source is not deteriorated by the modulator. Preservation of the wave-packet coherence is verified by two-photon interference between spectrally sheared and non-modulated single-photons.
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.
The attosecond pump-femtosecond probe technique is widely used in electron dynamics research, with temporal resolution reaching tens of attoseconds. Here, we propose a scheme for controlling the Fano line shapes of helium doubly excited states by replacing the pump source with a pair of time-delayed attosecond pulses. We show that the interference induced by this delay provides an additional, highly effective means of controlling electron dynamics, enabling temporal resolution on the zeptosecond scale. We demonstrate that the corresponding line shapes in transient absorption spectra can shift dramatically within a time-delay variation of just a few hundred zeptoseconds. This extreme spectral modulation occurs under two key conditions: (i) when the time delay aligns with the spectral minimum of the coherently combined attosecond pulses in the frequency domain, and (ii) when the delay between the infrared probe pulse and the first attosecond pulse is held constant. This approach opens a new pathway to zeptosecond-scale control in quantum systems and demonstrates the powerful synergy between phase manipulation in both light and electron waves for achieving ultrafast spectral transformations.