Spin masers with optical detection and artificial feedback are widely used in fundamental and practical applications. However, a full picture of the maser dynamics is still absent. By solving the feedback-driven Bloch equations, we simulated the dynamics of an ideal spin maser in a broad parameter space. Rich nonlinear dynamics including high-order-harmonic generation, nonperiodic spin oscillations, and frequency comb were revealed when the artificial feedback interaction exceeds the normal spin-field interaction. We also propose a pulse feedback spin maser protocol, which constructs an ultralow field magnetic frequency comb and could be useful in precision atomic magnetometers in searching for spin-dependent exotic interactions.
Spin masers with optical detection and artificial feedback are widely used in fundamental and practical applications. However, a full picture of the maser dynamics is still absent. By solving the feedback-driven Bloch equations, we simulated the dynamics of an ideal spin maser in a broad parameter space. Rich nonlinear dynamics including high-order-harmonic generation, nonperiodic spin oscillations, and frequency comb were revealed when the artificial feedback interaction exceeds the normal spin-field interaction. We also propose a pulse feedback spin maser protocol, which constructs an ultralow field magnetic frequency comb and could be useful in precision atomic magnetometers in searching for spin-dependent exotic interactions.
Nonlinear spin systems exhibit rich and exotic dynamical phenomena, offering promising applications ranging from spin masers and time crystals to precision measurement. Recent theoretical work [T. Wang et al., Commun. Phys. 8, 41 (2025)] predicted intriguing nonlinear dynamical phases arising from inhomogeneous magnetic fields and feedback interactions. However, experimental exploration of these predictions remains lacking. Here, we report the observation of nonlinear spin dynamics in dual-bias magnetic fields with dual-cell alkali-metal atomic gases and present three representative stable dynamical behaviors of limit cycles, quasi-periodic orbits, and chaos. Additionally, we probe the nonlinear phase transitions between these phases by varying the feedback gain and the difference of dual-bias magnetic fields. Furthermore, we demonstrate the robustness of the limit cycle and quasi-periodic orbit against the noise of magnetic fields. Our findings establish a versatile platform for exploring complex spin dynamics and open new avenues for the realization of multimode spin masers, time crystals and quasi-crystals, and high-precision magnetometers.
Nonlinear spin dynamics are essential in exploring nonequilibrium quantum phenomena and have broad applications in precision measurement. Among these systems, the combination of a bias magnetic field and feedback mechanisms can induce self-sustained oscillations at the base Larmor frequency due to nonlinearity. These features have driven the development of single-species and multiple-species spin masers. The latter, with multiple discrete Larmor frequencies, provides significant advantages for precision measurement by mitigating uncertainties in precession frequencies due to long-term drifts in experimental conditions. The self-sustained oscillations of single-species and multiple-species spin masers correspond to limit cycles and quasi-periodic orbits of the stable nonlinear dynamics of the systems, respectively; the correspondence is elucidated in a recent study on a related spin system featuring two discrete intrinsic Larmor frequencies under dual bias magnetic fields [T. Wang et al., Commun. Phys. 8, 41 (2025)]. Here, we extend the study to the case where the intrinsic Larmor frequencies of individual spins of the system, given rise to by an inhomogeneous bias magnetic field, form a continuum. We show that generically the stable dynamics of the system includes limit cycles, quasi-periodic orbits, and chaos. We establish the relation between the synchronization frequency of limit cycles and the field inhomogeneity and derive an equation determining the stability of limit cycles. Furthermore, detailed characteristics of different dynamical phases, especially the robustness of limit cycles and quasi-periodic orbits against experimental fluctuations, are discussed. Our findings not only encompass the case of discrete Larmor frequencies, but also provide crucial insights for precision measurement and the exploration of continuous time crystals and quasi-crystals.
Optically pumped room temperature masers are a promising platform for driven dissipative spin photon physics beyond steady state emission. Here we observe a sequence of dynamical thresholds in a room temperature nitrogen vacancy diamond maser as the optical pump is increased above the conventional masing threshold. The first threshold yields narrow-line continuous wave emission, while a second threshold produces a periodic train of microwave pulses whose repetition rate generates a frequency comb spectrum. At higher pump power, a third threshold gives rise to pulses with an oscillatory, frequency chirped decay. Time-resolved measurements link the comb directly to self-pulsing dynamics and Fourier analysis of individual bursts reveals a broad distribution of frequencies consistent with collective spin-resonator dynamics in an inhomogeneously broadened ensemble. These results establish the diamond maser as a room temperature platform for nonlinear nonequilibrium light matter dynamics and microwave comb generation.
Non-Markovian dynamics offer a new route towards engineering non-equilibrium matter, where memory and feedback act as programmable resources for controlling order in time. Here we report the realization of a non-Markovian spin oscillator in a hot vapour 129Xe-Cs co-magnetometer with programmable feedback delay and gain. By tuning these parameters, we observe a hierarchy of dynamical phases, including time-crystalline response, nonlinear bifurcations, and frequency-comb formation. The measured spectra and phase boundaries are captured by linear stability analysis of delayed Bloch equations, revealing these phenomena as different manifestations of the same memory-induced instability structure. These results establish time-delayed feedback as a powerful strategy for controlling non-equilibrium phases, enabling quantum sensing, frequency referencing, and synchronization within a single spin-based platform.
The invention of the maser stimulated many revolutionary technologies such as lasers and atomic clocks. Despite enormous progress, the realizations of masers are still confined to a limited variety of systems, in particular, the physics of masers remains unexplored in periodically driven (Floquet) systems, which are generally defined by time-periodic Hamiltonians and enable to observe many exotic phenomena such as time crystals. Here we investigate the Floquet system of periodically driven 129Xe gas under damping feedback, and surprisingly observe a multi-mode maser that oscillates at frequencies of transitions between Floquet states. Our findings extend maser techniques to Floquet systems, and open a new avenue to probe Floquet phenomena unaffected by decoherence, enabling a new class of maser sensors. As a first application, our maser offers a unique capability of measuring low-frequency (1-100 mHz) magnetic fields with femtotesla-level sensitivity, which is significantly better than state-of-the-art magnetometers, and can be immediately applied to, for example, ultralight dark matter searches.
Self-oscillating atomic magnetometers, in which the precession of atomic spins in a magnetic field is driven by resonant modulation, offer high sensitivity and dynamic range. Phase-coherent feedback from the detected signal to the applied modulation creates a resonant spin maser system, highly responsive to changes in the background magnetic field. Here we show a system in which the phase condition for resonant precession is met by digital signal processing integrated into the maser feedback loop. This system uses a modest chip-scale laser and mass-produced dual-pass caesium vapour cell and operates in a 50 [Formula: see text]T field, making it a suitable technology for portable measurements of the geophysical magnetic field. We demonstrate a Cramér-Rao lower bound-limited resolution of 50 fT at 1 s sampling cadence, and a sensor bandwidth of 10 kHz. This device also represents an important class of atomic system in which low-latency digital processing forms an integral part of a coherently-driven quantum system.