Detection of weak electromagnetic waves and hypothetical particles aided by quantum amplification is important for fundamental physics and applications. However, demonstrations of quantum amplification are still limited; in particular, the physics of quantum amplification is not fully explored in periodically driven (Floquet) systems, which are generally defined by time-periodic Hamiltonians and enable observation of many exotic quantum phenomena such as time crystals. Here we investigate the magnetic-field signal amplification by periodically driven ^{129}Xe spins and observe signal amplification at frequencies of transitions between Floquet spin states. This "Floquet amplification" allows us to simultaneously enhance and measure multiple magnetic fields with at least one order of magnitude improvement, offering the capability of femtotesla-level measurements. Our findings extend the physics of quantum amplification to Floquet spin systems and can be generalized to a wide variety of existing amplifiers, enabling a previously unexplored class of "Floquet spin amplifiers".
Detection of weak electromagnetic waves and hypothetical particles aided by quantum amplification is important for fundamental physics and applications. However, demonstrations of quantum amplification are still limited; in particular, the physics of quantum amplification is not fully explored in periodically driven (Floquet) systems, which are generally defined by time-periodic Hamiltonians and enable observation of many exotic quantum phenomena such as time crystals. Here we investigate the magnetic-field signal amplification by periodically driven ^{129}Xe spins and observe signal amplification at frequencies of transitions between Floquet spin states. This "Floquet amplification" allows us to simultaneously enhance and measure multiple magnetic fields with at least one order of magnitude improvement, offering the capability of femtotesla-level measurements. Our findings extend the physics of quantum amplification to Floquet spin systems and can be generalized to a wide variety of existing amplifiers, enabling a previously unexplored class of "Floquet spin amplifiers".
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.
Periodic driving of a quantum system can significantly alter its energy bands and even change the band topology, opening a completely new avenue for engineering novel quantum matter. Although important progress has been made recently in measuring topological properties of Floquet bands in different systems, direct experimental measurement of full Floquet band dispersions and their topology change is still demanding. Here we directly measure Floquet band dispersions in a periodically driven spin-orbit-coupled ultracold Fermi gas using spin-injection radio-frequency spectroscopy. We observe that the Dirac point originating from two-dimensional spin-orbit coupling can be manipulated to emerge at the lowest or highest two dressed bands by fast modulating Raman laser frequencies, demonstrating topological change of Floquet bands. Our work will provide a powerful tool for understanding fundamental Floquet physics as well as engineering exotic topological quantum matter.
We give a general overview of the high-frequency regime in periodically driven systems and identify three distinct classes of driving protocols in which the infinite-frequency Floquet Hamiltonian is not equal to the time-averaged Hamiltonian. These classes cover systems, such as the Kapitza pendulum, the Harper–Hofstadter model of neutral atoms in a magnetic field, the Haldane Floquet Chern insulator and others. In all setups considered, we discuss both the infinite-frequency limit and the leading finite-frequency corrections to the Floquet Hamiltonian. We provide a short overview of Floquet theory focusing on the gauge structure associated with the choice of stroboscopic frame and the differences between stroboscopic and non-stroboscopic dynamics. In the latter case, one has to work with dressed operators representing observables and a dressed density matrix. We also comment on the application of Floquet Theory to systems described by static Hamiltonians with well-separated energy scales and, in particular, discuss parallels between the inverse-frequency expansion and the Schrieffer–Wolff transformation extending the latter to driven systems.
We experimentally observe Floquet Raman transitions in the weakly driven solid-state spin system of a nitrogen-vacancy center in diamond. The periodically driven spin system simulates a two-band Wannier-Stark ladder model and allows us to observe coherent spin state transfer arising from a Raman transition mediated by Floquet synthetic levels. It also leads to the prediction of an analog photon-assisted Floquet Raman transition and dynamical localization in a driven two-level quantum system. The demonstrated rich Floquet dynamics offers new capabilities to achieve effective Floquet coherent control of a quantum system with potential applications in various types of quantum technologies based on driven quantum dynamics. In particular, the Floquet Raman system may be used as a quantum simulator for the physics of periodically driven systems.
Periodically driven systems, so-called Floquet systems, exhibit novel and exotic phases of matters inaccessible in static counterparts. The associated flexibility offered by Floquet engineering has helped gain insight into synthetic dimensions of quantum systems, non-equilibrium dynamics, and topology. Here, we apply the technique of Floquet engineering to the coherent dressing of spin states, aiming to provide a new dimension in the spin manipulation. We use an anti-relaxation coated 87 Rb vapor cell interacting with a transverse radio-frequency magnetic field, which is resonant with the Larmor precession and excites the coherence between adjacent Zeeman sublevels. The narrow linewidth of the natural resonance promises the successful observation of a radio-frequency dressed spin state via electromagnetically induced transparency spectroscopy. In this configuration, we create a Floquet system by adding a longitudinal oscillating magnetic field to periodically drive Zeeman levels. We experimentally observe the Floquet engineered coherent dressing spectroscopy, featuring a series of sidebands in frequency space with weight factor in terms of Bessel function, as expected by our theoretical model. Our method can be applied to coherent dressed states of natural and artificial atoms, offering the possibilities of quantum bit control and quantum sensing.
Simultaneous ideal quantum measurements of multiple single-photon-level signals would advance applications in quantum information processing, metrology, and astronomy but require the first amplifier to be simultaneously broadband, quantum limited, and directional.However, conventional traveling-wave parametric amplifiers support broadband amplification at the cost of increased added noise and are not genuinely directional due to non-negligible nonlinear backward-wave generation.In this work, we introduce a new class of amplifiers that encode the information in the Floquet modes of the system.Such Floquetmode amplifiers prevent information leakage and overcome the trade-off between quantum efficiency (QE) and bandwidth.Crucially, Floquet-mode amplifiers strongly suppress the nonlinear forward-backward wave coupling and are therefore genuinely directional and readily integrable with qubits, clearing another major obstacle toward broadband ideal quantum measurements.Furthermore, Floquet-mode amplifiers are insensitive to out-of-band impedance mismatch, which otherwise may lead to gain ripples, parametric oscillations, and instability in conventional traveling-wave parametric amplifiers.Finally, we show that a Floquet-mode Josephson traveling-wave parametric amplifier implementation can simultaneously achieve > 20 dB gain and a QE of η/η ideal > 99.9% of the quantum limit over more than an octave of bandwidth.The proposed Floquet scheme is also widely applicable to other platforms, such as kinetic inductance traveling-wave amplifiers and optical parametric amplifiers.