Microwave Field Amplitude Research Articles

Peculiarities in Rabi oscillations for fast-relaxing electron spins

Rabi oscillations (transient nutations) are a phenomenon that has proven itself well in EPR for identifying electron spin quantum numbers and electron-spin transitions. They are successfully applied when the Rabi frequency significantly exceeds the spin relaxation rates and therefore does not depend on these rates. However, the short transverse relaxation time, being comparable to or even shorter than the dead time of EPR spectrometers, makes it difficult to observe Rabi oscillations and their frequency depends not only on the intensity of the short microwave pulse, but also on its shape and relaxation rates. Two techniques are considered that are suitable for this case, in which Rabi oscillations are detected by monitoring the FID amplitude as a function of pulse duration or microwave field amplitude. We describe the FID-detected Rabi oscillations analytically or numerically for rectangular or shaped pulses, respectively. The description is confirmed by EPR experiments using DPPH as a model sample.

Exciting High‐Frequency Short‐Wavelength Spin Waves using High Harmonics of a Magnonic Cavity Mode

AbstractSpin waves (SWs) are promising objects for signal processing and future quantum technologies due to their high microwave frequencies with corresponding nanoscale wavelengths. However, the nano‐wavelength SWs generated so far are limited to low frequencies. In the paper, using micromagnetic simulations, it is shown that a microwave‐pumped SW mode confined to the cavity of a thin film magnonic crystal (MC) can be used to generate waves at tens of GHz and wavelengths well below 50 nm. These multi‐frequency harmonics of the fundamental cavity mode are generated when the amplitude of the pumping microwave field exceeds a threshold, and their intensities then scale linearly with the field intensity. The frequency of the cavity mode is equal to the ferromagnetic resonance frequency of the planar ferromagnetic film, which overlaps with the magnonic bandgap, providing an efficient mechanism for confinement and magnetic field tunability. The effect reaches saturation when the microstrip feed line covers the entire cavity, making the system feasible for realization.

Dynamic nuclear polarization pulse sequence engineering using single-spin vector effective Hamiltonians.

Dynamic nuclear polarization (DNP) has proven to be a powerful technique to enhance nuclear spin polarization by transferring the much higher electron spin polarization to nuclear spins prior to detection. While major attention has been devoted to high-field applications with continuous microwave irradiation, the introduction of fast arbitrary waveform generators is gradually increasing opportunities for the realization of pulsed DNP. Here, we describe how static-powder DNP pulse sequences may systematically be designed using single-spin vector effective Hamiltonian theory. Particular attention is devoted to the intricate interplay between two important parts of the effective first-order Hamiltonian, namely, linear field (single-spin) terms and Fourier coefficients determining scaling of the bilinear coupling terms mediating polarization transfer. We address two cases. The first case operates in the regime, where the microwave field amplitude is lower than the nuclear Larmor frequency. Here, we illustrate the predictive strength of a single-spin vector model by comparing analytical calculations with experimental DNP results at 9.8 GHz/15 MHz on trityl radicals at 80 K. The second case operates in the high-power regime, where we combine the underlying single-spin vector design principles with numerical non-linear optimization to optimize the balance between the linear terms and the bilinear Fourier coefficients in a figure of merit function. We demonstrate, numerically and experimentally, a broadband DNP pulse sequence PLATO (PoLarizAtion Transfer via non-linear Optimization) with a bandwidth of 80 MHz and optimized for a microwave field with a maximum (peak) amplitude of 32 MHz.

Bimetal Temperature-Compensated Ramsey Cavity for Atomic Fountain Frequency Standards

A typical Ramsey cavity, commonly used in atomic fountain frequency standards (AFFSs) for microwave interrogation, is sensitive to ambient temperature variation. Then, it becomes one of the main limiting factors for the AFFSs operating in a narrow operating-temperature range and a temperature-well-controlled environment up to now. In this article, a new design of bimetal temperature-compensated Ramsey cavity (BTCRC) based on the thermal expansion self-compensating mechanism is presented and experimentally demonstrated. This cavity is a typical TE011-mode cylindrical microwave resonator with a titanium tube and two oxygen-free copper (OFC) caps. The resonance frequency (RF) of the cavity can be immune to temperature variations if the dimensions of the tube and caps are properly designed. To validate this self-compensating mechanism, a BTCRC resonating at the Rb clock frequency with a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -factor of about 17000 is constructed. And its RF thermal coefficient is measured to be 0.73 kHz/°C, which is about 150 times superior to −115.9 kHz/°C of a typical OFC Rb cavity in the temperature range of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$22.48~^{\circ }\text{C}$ </tex-math></inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$37.48~^{\circ }\text{C}$ </tex-math></inline-formula> . During the operation of AFFSs, this BTCRC ensures that the microwave field amplitude inside the cavity, which dictates the transition probability and thus the contrast of the Ramsey fringes, will be stable in time. In addition, the potential temperature variation-induced frequency shifts due to cavity pulling are significantly minimized.

A multi-band atomic candle with microwave-dressed Rydberg atoms

Stabilizing important physical quantities to atom-based standards lies at the heart of modern atomic, molecular and optical physics, and is widely applied to the field of precision metrology. Of particular importance is the atom-based microwave field amplitude stabilizer, the so-called atomic candle. Previous atomic candles are realized with atoms in their ground state, and hence suffer from the lack of frequency band tunability and small stabilization bandwidth, severely limiting their development and potential applications. To tackle these limitations, we employ microwave-dressed Rydberg atoms to realize a novel atomic candle that features multi-band frequency tunability and large stabilization bandwidth. We demonstrate amplitude stabilization of microwave field from C-band to Ka-band, which could be extended to quasi-DC and terahertz fields by exploring abundant Rydberg levels. Our atomic candle achieves stabilization bandwidth of 100 Hz, outperforming previous ones by more than two orders of magnitude. Our simulation indicates the stabilization bandwidth can be further increased up to 100 kHz. Our work paves a route to develop novel electric field control and applications with a noise-resilient, miniaturized, sensitive and broadband atomic candle.

Analytical solution for the inverting pulses with constant adiabaticity

The exact solution was found for inverting pulses with constant adiabaticity for spin ½. The analytical relationship between the time-varying frequency of the microwave resonant field (or RF field in the case of NMR) and its amplitude time dependence such that the adiabaticity parameter remains constant for the single isochromat throughout the pulse is found. Comparison with EPR (hyperbolic tangent)-(hyperbolic secant) pulse method was carried out. On the basis of the analytical solution the pulses with different dependences of the microwave field amplitude conserving the constant adiabaticity have been constructed. The pulses exhibit rather sharp inversion selectivity that can be used in the field of EPR, NMR and MRI.

A giant self-Kerr nonlinearity using phase-sensitive excitation in a closed three-level atomic system

A third-order nonlinear response is investigated theoretically using a closed lambda system. In this scheme, a pair of optical fields and a microwave field connect three hyperfine levels in a cyclic fashion, rendering the atomic response sensitive to the relative phase of all three fields. Changing the relative phase, we can suppress the linear response of the probe field and enhance its third order self-Kerr nonlinear response using the underlying electromagnetically induced transparency (EIT) effect. The resultant giant self-Kerr nonlinear response is comparable to or exceeding that found in atomic systems at room temperature. Most importantly, we show that the self-Kerr nonlinear response at an optical frequency can be controlled using the phase and amplitude of a frequency-separated microwave field.

Thermal activation in microwave-assisted magnetization switching and its effect on the switching behavior of granular media

Microwave-assisted switching (MAS) has gathered fundamental interest and has been explored for magnetic recording since the switching field can be reduced by exciting magnetization with a microwave field in the GHz range. We theoretically study the effect of thermal activation in MAS and apply the developed analytical method to examine the result of MAS experiments on CoCrPt-${\mathrm{SiO}}_{2}$ granular media. The effective energy barrier height for magnetization switching under a microwave field is calculated from the Landau-Lifshitz-Gilbert equation. The calculated energy barrier shows that the thermal activation process plays a crucial role in MAS and modifies the dependences of the switching field on the microwave frequency and amplitude. The switching field decreases with increasing the microwave frequency up to the critical frequency, at which point the switching field abruptly increases. Thermal activation significantly increases the critical frequency and makes the slope of the frequency dependence of the switching field gradual. The maximum assistance effect increases with increasing the microwave field amplitude and is almost independent of the thermal activation. The analytical method quantitatively explains the gradual microwave frequency dependence and high critical frequency observed in MAS experiments on granular media. These results indicate the importance of thermal activation to optimize MAS behavior for practical use.

Shape anisotropy effect on magnetization reversal induced by linear down chirp pulse

We investigate the shape anisotropy effect on the magnetization reversal of a nanoparticle driven by a down-chirp microwave field pulse (DCMP). Based on the Landau–Lifshitz–Gilbert equation, numerical results reveal that the microwave amplitude, initial frequency, and chirp rate of DCMP decrease with the increase of shape anisotropy. For a certain shape of the nanoparticle, the reversal time is significantly reduced. These findings can be attributed as the shape anisotropy opposes the magnetocrystalline anisotropy, and thus the energy barrier decreases. The result of damping dependence of reversal indicates that there exists an optimal damping situation at which magnetization is fastest. Moreover, the required microwave field amplitude can be lowered by applying the spin-polarized current simultaneously. The usage of an optimum combination of DCMP and current is suggested to achieve cost-effective and faster switching. So these findings might be useful to realize the fast and power-efficient data storage device.

Fast magnetization reversal of a magnetic nanoparticle induced by cosine chirp microwave field pulse

We investigate the magnetization reversal of single-domain magnetic nanoparticle driven by the circularly polarized cosine chirp microwave pulse (CCMP). The numerical findings, based on the Landau–Lifshitz–Gilbert equation, reveal that the CCMP is by itself capable of driving fast and energy-efficient magnetization reversal. The microwave field amplitude and initial frequency required by a CCMP are much smaller than that of the linear down-chirp microwave pulse. This is achieved as the frequency change of the CCMP closely matches the frequency change of the magnetization precession which leads to an efficient stimulated microwave energy absorption (emission) by (from) the magnetic particle before (after) it crosses over the energy barrier. We further find that the enhancement of easy-plane shape anisotropy significantly reduces the required microwave amplitude and the initial frequency of CCMP. We also find that there is an optimal Gilbert damping for fast magnetization reversal. These findings may provide a pathway to realize the fast and low-cost memory device.

Vortex Dynamics and Dissipation under High-Amplitude Microwave Drive

In this paper, we describe the vortex dynamics under high-amplitude microwave drive and its effect on the surface resistance of superconductors. The vortex surface resistance is calculated with a Montecarlo approach, where the vortex motion equation is solved for a collection of vortex flux lines each oscillating within a random pinning landscape. This approach is capable of providing a detailed description of the microscopic vortex dynamics and in turn important insights into the microwave field amplitude dependence of the vortex surface resistance. The numerical simulations are compared against experimental data of vortex surface resistance at high microwave amplitude measured by means of bulk niobium superconducting-radio frequency cavities operating at 1.3 GHz. The good qualitative agreement of simulations and experiments suggests that the non-linear dependence of the trapped flux surface resistance with the microwave field amplitude is generated by progressive microwave depinning and vortex jumps.

Measuring atom positions in a microwave cavity to evaluate distributed cavity phase shifts

Distributed cavity phase (DCP) frequency shifts are a leading systematic effect in atomic fountain frequency standards. They originate from the phase variations of the field in the microwave cavity combined with different positions of the atoms in the cavity on the ascent and descent. Here we demonstrate techniques to precisely determine the position of the cloud of atoms in the microwave cavity, using either the approximately linear variation of the transverse components of the microwave field or the quadratic variation of the longitudinal microwave field amplitude in the cavity. We also show that shifting the initial position of the atoms gives a significantly higher sensitivity to DCP variations than the often-used tilting of fountains. A demonstrated centring precision of order 50 μm will enable DCP frequency shift uncertainties to be reduced to less than 10–17 and thereby contribute insignificantly to the accuracy budget of a standard. These techniques to vertically align a fountain are straightforward to automate for routine operation and require a negligible fraction of the standard’s averaging time.

Radio Frequency Mixer Based on Magnetic Skyrmion

A radio frequency (RF) mixer constructed by skyrmion‐based spin transfer nano‐oscillator (STNO) is proposed. The skyrmion oscillator is treated as an information carrier and one of the input signals, and a perpendicular microwave field acts as another input signal. It is demonstrated that skyrmion‐based RF mixer can transmit two input signals to an output signal with multiple new frequencies, which are equal to the sum and difference of input frequencies. Through micromagnetic simulations, it is found that the frequency of output signals is modulated by the amplitude of input microwave field as well as the current density applied in skyrmion oscillator and by other magnetic parameters of oscillator (such as magnetic anisotropy). Compared with conventional RF mixer with nonlinear element, such as diode, the skyrmion‐based RF mixer integrates both input signals and output signal functionality with nanometer size, which is more efficient and shows significant potential application in the RF multiplication devices, integrated electronics, and microwave generators.

Microwave-assisted switching in CoCrPt granular medium under continuous microwave fields

We have fabricated a device for microwave-assisted switching (MAS) experiments with perpendicularly magnetized CoCrPt-SiO2 granular film with anisotropy field Hk = 18.8 kOe. The device was carefully designed to be able to apply a microwave field of 0.95 kOe in amplitude continuously, allowing direct evaluation of microwave-assisted switching properties of the medium without any assumptions about time-dependent switching behavior. The coercivity of CoCrPt-SiO2 medium linearly decreases with increasing microwave frequency, and the maximum coercivity reduction ratio reaches 80% for hrf = 0.95 kOe at frf = 25 GHz after subtracting the effect of temperature rise due to microwave field application. The linear slope of coercivity against the frequency becomes steeper with increasing microwave field amplitude, which is a unique frequency and amplitude dependencies in granular media. Correlation length obtained by X-ray magnetic circular dichroism microscopy measurement decreases by applying a microwave field with higher frequency, suggesting that the magnetic clustering dimensions of the medium possibly depend on microwave frequency during microwave-assisted switching.

Reducing Cavity-Pulling Shift in Ramsey-Operated Compact Clocks.

We describe a method to stabilize the amplitude of the interrogating microwave field in compact atomic clocks working in a Ramsey approach. In this technique, we take advantage of the pulsed regime to use the atoms themselves as microwave amplitude discriminators. Specifically, in addition to the dependence on the microwave detuning, the atomic signal after the Ramsey interrogation acquires a dependence on the microwave pulse area (amplitude times duration) that can be exploited to implement an active stabilization of the microwave field amplitude, in a similar way in which the Ramsey clock signal is used to lock the local oscillator frequency to the atomic reference. The stabilization allows us to reduce the microwave field-amplitude fluctuations, which in turn impact the clock frequency through cavity pulling. The proposed technique has shown to be effective to improve our clock frequency stability on medium and long term. We demonstrate the method for a vapor-cell clock working with a hot sample of atoms, but it can be extended to cold-atom compact clocks.

Subnanosecond magnetization reversal of a magnetic nanoparticle driven by a chirp microwave field pulse

We investigate the magnetization reversal of single-domain magnetic nanoparticle driven by linear down-chirp microwave magnetic field pulse. Numerical simulations based on the Landau-Lifshitz-Gilbert equation reveal that solely down-chirp pulse is capable of inducing subnanosecond magnetization reversal. With a certain range of initial frequency and chirp rate, the required field amplitude is much smaller than that of constant-frequency microwave field. The fast reversal is because the down-chirp microwave field acts as an energy source and sink for the magnetic particle before and after crossing over the energy barrier, respectively. Applying a spin-polarized current additively to the system further reduces the microwave field amplitude. Our findings provide a new way to realize low-cost and fast magnetization reversal.

Suppression of electron spin decoherence in Rabi oscillations induced by an inhomogeneous microwave field

The decay of Rabi oscillations provides direct information about coherence of electron spins. When observed in EPR experiments, it is often shortened by spatial inhomogeneity of the microwave field amplitude in a bulk sample. In order to suppress this undesired loss of coherence, we propose an additional dressing of spin states by a weak longitudinal continuous radiofrequency field. The Gaussian, cosine and linear distributions of the microwave amplitude is analyzed. Our calculations of the Rabi oscillations between the doubly dressed spin states show that for all these distributions the maximum suppression of the inhomogeneity-induced decoherence is achieved at the so-called Rabi resonance when the radio-field frequency is in resonance with the Rabi frequency of spins in the microwave field. The manifestations of such suppression in the published EPR experiments with the bichromatic driving are discussed. The realization of the Rabi resonance using the radiofrequency field could open new possibilities for separating the contributions of relaxation mechanisms from those due to the inhomogeneous driving in spin decoherence.

Microwave electromagnetically induced transparency and Aulter-Townes spectrum of cesium Rydberg atom

We present an electromagnetically induced transparency and Aulter-Townes (EIT-AT) spectrum of a Rydberg three-level atom that is dressed with a microwave field in a room-temperature cesium cell. The EIT is a quantum coherent effect produced by the interaction of atoms with electromagnetic waves, which leads to the decrease of the absorption for a weak resonant probe laser. AT splitting refers to the phenomenon, that the absorption line splits when an electromagnetic field that is in resonance or near resonance acts on the transition of atoms. Rydberg atoms are extremely sensitive to an external electric field due to their large polarizabilities and microwave transition dipole moments, which can be used to measure the external field. In this work, a Rydberg three-level EIT is used to detect Rydberg atom and AT splitting induced by the microwave field. Cesium levels 6S1/2, 6P3/2 and 50S1/2 constitute a Rydberg three-level system, in which a weak probe laser locking to the transition from 6S1/2 to 6P3/2 couples ground-state transition and the strong coupling laser resonates on the Rydberg transition from 6P2/3 to 50S1/2. The two Rydberg levels 50S1/2 and 50P1/2 are coupled with the microwave field at a frequency of 30.852 GHz, leading to the AT splitting of EIT line and forming an EIT-AT spectrum, which is used to measure the electric field amplitude of microwave. In order to further study the EIT-AT splitting characteristics of the Rydberg levels, we carry out a series of measurements by changing the microwave field. The experimental results show a broadened EIT-AT signal for the weak field range and the four-peak spectrum for the strong field, which is attributed to the inhomogeneity of the microwave field. The microwave in cesium cell, emitted by a function generator, shows inhomogeneous behavior such that the atoms interacting with the laser field experience the different fields, leading to the line broadened and multi-peak EIT-AT spectra. For the microwave transition of nS1/2-nP1/2 in this paper, a pair of EIT-AT lines should be obtained for an electric field value. The broadening of the EIT-AT spectrum and the multi-peak structure here are due to the inhomogeneity of the microwave field measurement. We propose a method to increase the spatial resolution by reducing the length of cesium cell. The result in this work provides a method of measuring the field amplitude and monitoring the distribution of microwave electric field, meanwhile the spatial resolution of the measurements can be improved by reducing the size of the cell.

Understanding Quality Factor Degradation in Superconducting Niobium Cavities at Low Microwave Field Amplitudes.

In niobium superconducting radio frequency (SRF) cavities for particle acceleration, a decrease of the quality factor at lower fields-a so-called low field Q slope or LFQS-has been a long-standing unexplained effect. By extending the high Q measurement techniques to ultralow fields, we discover two previously unknown features of the effect: (i)saturation at rf fields lower than E_{acc}∼0.1 MV/m; (ii)strong degradation enhancement by growing thicker niobium pentoxide. Our findings suggest that the LFQS may be caused by the two level systems in the natural niobium oxide on the inner cavity surface, thereby identifying a new source of residual resistance and providing guidance for potential nonaccelerator low-field applications of SRF cavities.

Subnanosecond microwave-assisted magnetization switching in a circularly polarized microwave magnetic field

We study microwave-assisted magnetization switching (MAS) of a perpendicularly magnetized nanomagnet with a diameter of 50 nm in a circularly polarized microwave magnetic field. The MAS effect appears when the rotation direction of the microwave field matches that of the ferromagnetic resonance excitation, and a large switching field decrease from 7.1 kOe to 1.5 kOe is demonstrated. In comparison with a linearly polarized microwave magnetic field, the circularly polarized microwave field induces the same MAS effect at half the microwave field amplitude, thereby showing its efficiency. We also examine MAS in the subnanosecond region and show that the magnetization switching can be induced by a microwave field with the duration of 0.2 ns.