Rabi Oscillation Frequency Research Articles

Multiband Rabi antenna using nest microstrip add-drop filter (NMADF) for relativistic sensing applications

A microstrip circuit is designed, constructed, and tested based on the nest microstrip add-drop filters (NMADF). The multi-level system oscillation is generated by the wave-particle behaviors of AC driven along the microstrip ring circular path. The continuous successive filtering is applied via the device input port. The higher-order harmonic oscillations can be filtered, from which the two-level system known as a Rabi oscillation is achieved. The outside microstrip ring energy is coupled to the inside rings, from which the multiband Rabi oscillations can be formed within the inner rings. The resonant Rabi frequencies can be applied for multi-sensing probes. The relationship between electron density and Rabi oscillation frequency of each microstrip ring output can be obtained and used for multi-sensing probe applications. The relativistic sensing probe can be obtained by the warp speed electron distribution at the resonant Rabi frequency respecting the resonant ring radii. These are available for relativistic sensing probe usage. The obtained experimental results have shown that there are 3-center Rabi frequencies obtained, which can be used for 3-sensing probes simultaneously. The sensing probe speeds of 1.1c, 1.4c, and 1.5c are obtained using the microstrip ring radii of 14.20, 20.12, and 34.49 mm, respectively. The best sensor sensitivity of 1.30 ms is achieved. The relativistic sensing platform can be used for many applications.

Self-Stopping of Light.

Here, we show that light can bring itself to a complete standstill (self-stop) via self-interaction mediated by the resonant nonlinearity in a fully homogeneous medium. An intense few-cycle pulse, entering the medium, may reshape to form a strongly coupled light-matter bundle, in which the energy is transferred from light to the medium and back periodically on the single-cycle scale. Such oscillating structure can decelerate, alter its propagation direction, and even completely stop, depending on the state of its internal degrees of freedom. This phenomenon is expected to occur in the few-cycle strong-field regime when the Rabi oscillation frequency becomes comparable with the frequency of the incoming light.

Fragility of classical Hamiltonian period doubling to quantum fluctuations

We add quantum fluctuations to a classical period-doubling Hamiltonian time crystal, replacing the $N$ classical interacting angular momenta with quantum spins of size $l$. The full permutation symmetry of the Hamiltonian allows a mapping to a bosonic model and the application of exact diagonalization for a quite large system size. In the thermodynamic limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$ the model is described by a system of Gross-Pitaevskii equations whose classical-chaos properties closely mirror the finite-$N$ quantum chaos. For $N\ensuremath{\rightarrow}\ensuremath{\infty}$, and $l$ finite, Rabi oscillations mark the absence of persistent period doubling, which is recovered for $l\ensuremath{\rightarrow}\ensuremath{\infty}$ with Rabi-oscillation frequency tending exponentially to 0. For the chosen initial conditions, we can represent this model in terms of Pauli matrices and apply the discrete truncated Wigner approximation. For finite $l$ this approximation reproduces no Rabi oscillations but correctly predicts the absence of period doubling. Our results show the instability of time-translation symmetry breaking in this classical system even to the smallest quantum fluctuations, because of tunneling effects.

Electrical control of coherent spin rotation of a single-spin qubit

Nitrogen vacancy (NV) centers, optically active atomic defects in diamond, have attracted tremendous interest for quantum sensing, network, and computing applications due to their excellent quantum coherence and remarkable versatility in a real, ambient environment. One of the critical challenges to develop NV-based quantum operation platforms results from the difficulty in locally addressing the quantum spin states of individual NV spins in a scalable, energy-efficient manner. Here, we report electrical control of the coherent spin rotation rate of a single-spin qubit in NV-magnet based hybrid quantum systems. By utilizing electrically generated spin currents, we are able to achieve efficient tuning of magnetic damping and the amplitude of the dipole fields generated by a micrometer-sized resonant magnet, enabling electrical control of the Rabi oscillation frequency of NV spins. Our results highlight the potential of NV centers in designing functional hybrid solid-state systems for next-generation quantum-information technologies. The demonstrated coupling between the NV centers and the propagating spin waves harbored by a magnetic insulator further points to the possibility to establish macroscale entanglement between distant spin qubits.

Circularly polarized microwave antenna for nitrogen vacancy centers in diamond.

The sensing applications of nitrogen-vacancy color centers in a diamond require an efficient manipulation of the color center ground state over the whole volume of an ensemble. Thus, it is necessary to produce strong uniform magnetic fields of a well-defined circular polarization at microwave frequencies. In this paper, we develop a circularly polarized microwave antenna based on the excitation of hybrid electromagnetic modes in a high-permittivity dielectric resonator. The influence of the geometrical parameters of the antenna on the reflection coefficient and magnetic field magnitude is studied numerically and discussed. The Rabi frequencies and their inhomogeneity over the volume of a commercially available diamond sample are calculated. With respect to the numerical predictions, a Rabi frequency as high as 34 MHz with an inhomogeneity of 4% over a 1.2 mm × ∅2.5 mm (5.9 mm3 in volume) diamond sample can be achieved for 10 W of input power at room temperature. The antenna prototype is fabricated, and experimental investigations of its characteristics are performed in microwave and optical frequency domains. The circular polarization of the microwave magnetic field with an ellipticity of 0.94 is demonstrated experimentally. The Rabi oscillation frequency and its inhomogeneity are measured, and the results demonstrate a good agreement with the numerically predicted results.

High Resolution Microwave B-Field Imaging Using a Micrometer-Sized Diamond Sensor**Support by the Jiangsu Distinguished Professor Program under Grant No RK002STP15001, and the NJUPT Principal Distinguished Professor Program under Grant No NY214136.

We propose a diamond-based micron-scale sensor and perform high-resolution B-field imaging of the near-field distribution of coplanar waveguides. The sensor consists of diamond crystals attached to the tip of a tapered fiber with a physical size on the order of submicron. The amplitude of the B-field component B is obtained by measuring the Rabi oscillation frequency. The result of Rabi sequence is fitted with a decayed sinusoidal. We apply the modulation-locking technique that demonstrates the vector-resolved field mapping of the micromachine coplanar waveguide structure (CPW). B-field line scan was performed on the CPW with a scan step size of 1.25 μm. To demonstrate vector resolved rf field sensing, a full field line scan acts (was performed) along four NV axes at a height of 50 μm above the device surface. The simulations are compared with the experimental results by vector-resolved measurement. This technique allows the measurement of weak microwave signals with a minimum resolvable modulation depth of 20 ppm. The sensor will have great interest in micron-scale resolved microwave B-field measurements, such as electromagnetic compatibility testing of microwave integrated circuits and characterization of integrated microwave components.

Transient response of the cavity magnon-polariton

The Rabi oscillations of a coupled spin-photon system are experimentally studied using time domain microwave transmission measurements. An external magnetic bias field is applied to control the amplitude and frequency of Rabi oscillations, which are a measure of the coherent spin-photon energy exchange and coupling strength respectively. The amplitude and frequency control is described in the time domain as the transient response of a two-level spin-photon system. This approach reveals the link between steady state and transient behaviour of the cavity-magnon-polariton, which is necessary to interpret time domain cavity-spintronic experiments. This transient model also allows us to understand and quantify the polariton mode composition, which can be controlled by the bias field.

Single-Crystal Study of a Low Spin Co(II) Molecular Qubit: Observation of Anisotropic Rabi Cycles.

A mononuclear low spin ( S = 1/2) Co(II) molecule crystallized in a 4-fold symmetry is fully investigated by CW and pulsed EPR on a single crystal sample. The quantum phase memory time of the molecule around 1 μs at 5 K is direction-independent, while the Rabi oscillation frequency is anisotropic. The spin Hamiltonian analyses reveal that the anisotropic Landé factor and hyperfine tensor do not influence the anisotropy apparently when the microwave magnetic field is applied along a certain direction. It is considered that the possibly involved nuclear spin forbidden transitions may be responsible for the small distinction of Rabi frequencies in two directions.

Survival of the fittest in the coherent evolution of quantum ensembles

We report two novel effects in an inhomogeneous ensemble of two-level systems driven by an external field. First, we observe a rigidity of the oscillation frequency: the dominant Rabi oscillation frequency does not change with the frequency of the driving field, in contrast to the well-known law of Rabi frequency increase with growing detuning of the driving field. Second, we observe a time-dependent frequency shift of the ensemble-averaged oscillation. We show that these effects follow from the inhomogeneity of the two-level splitting across the ensemble, allowing for a distribution of local oscillations in which those with high frequencies interfere destructively and decay faster than those with a low frequency, which are the only to survive in the output signal. Hence, coherence emerges from long-lived oscillations in an inhomogeneous ensemble. We analyze the Fourier spectrum of the time-dependent oscillation signal and find a non-trivial spectral structure that is double peaked for certain parameters. We show that the effects observed in alkali vapor are universal and expected in any system with a moderate inhomogeneity driven by an external field.

Gain-modulated plasmonic Rabi oscillations of coupled nanocomplex

Strong coupling in nanostructures can bring intriguing optical phenomena such as ultrafast Rabi oscillation—periodical energy exchange phenomenon between two modes. Rabi splitting appears in the frequency-domain spectra for strong coupling system. However, in metallic nanosystems the time-domain Rabi oscillations are hard to be observed because the plasmon lifetime is limited by the heavy ohmic losses. Here we report a theoretical investigation of surface plasmon coupling behaviour of two gold nanorods with one being a core-shell rod filled with a gain material and find the periodic energy exchange phenomenon which recalls the concept of Rabi oscillation. The gain material-cored gold-shell structure dipolar mode hybridizes with the solid gold rod quadrupolar mode to form the Fano resonances. Energy exchange between the two rods happens through the near field coupling. Two approaches, to prolong plasmon lifetime by increasing the gain efficiency and to increase Rabi oscillation frequency by increasing the coupling strength, are suggested to increase the Rabi oscillation cycles. Our results offer a way to achieve unique control of light at the nanoscale and further to explore plasmonic Rabi oscillation phenomena in plasmonic nanosystems.

Strong driving of a single coherent spin by a proximal chiral ferromagnet

We experimentally investigate the influence of a driven, dynamic vortex magnetization state on an individual nitrogen-vacancy (NV) spin in diamond. The vortex core can be translated within the ferromagnet using an applied magnetic field, allowing us to map out the spatial dependence of the interaction. The vortex displacement is determined using magneto-optical microscopy, while the vortex's influence on the spin is probed using optically detected magnetic resonance to measure the Rabi oscillation frequency between spin levels. We find that the close proximity of the vortex core to the NV (within about 200 nm) leads to more than an order of magnitude enhancement of the Rabi frequency. The NV/vortex interaction differs significantly for transitions to the ${m}_{s}=+1$ and ${m}_{s}=\ensuremath{-}1$ spin states, which we attribute to the chiral nature of the vortex state dynamics. We compare the results with micromagnetic simulations and a simple analytical model to shed light on the mechanisms behind the observed effects.

SPECIFICATIONS OF RABI OSCILLATIONS IN THE QUANTUM EMITTERS SYSTEMS COUPLED TO THE LOCALIZED PLASMON POLARITONS

In this work phenomenon of resonant transfer of the excited energy between quantum dipole emitters (QDE) by the localized plasmon polaritons (LPP) is investigated. In system the molecules or semiconductor quantum dots act as QDEs and the nanometer size metal particles (MNP) care LPPs. The dependence of the frequency of Rabi oscillations on system parameters (the distance between MNP and QDE, the radius of MNP and dielectric permittivity of the surrounding medium) was determined. Conditions when the period of Rabi oscillations is considerably shorter than system relaxation time were defined.

Microwave Magnetic Field Coupling with Nitrogen-Vacancy Center Ensembles in Diamond with High Homogeneity

Electron spin resonance measurements with nitrogen-vacancy (NV) center ensembles in diamond are strongly dependent on a uniform microwave magnetic field. Three different types of microwave resonators are used and are well coupled with the spin ensembles at 2.87 GHz for zero-field splitting of the NV centers. The magnitude and the uniformity of both the horizontal and vertical magnetic fields are extracted and analyzed within a $$1\times 1\times 0.5$$ mm3 volume on a diamond sample surface, and the results indicate that the field homogeneity is up to 200 times better than that of the traditional copper wire microwave delivery model. The horizontal magnetic field magnitude homogeneity is better than 5 % over an area of 1 mm2 on the thin film diamond sample with NV ensembles. The average Rabi oscillation frequency is estimated to be 2.3 MHz per 1 W of microwave input power upon strong coherent coupling between the resonators and the spin ensembles. The effect of the nonuniform microwave magnetic field on the spin signal is also discussed. The approach used here will find widespread application in microwave coupling with spin ensembles in thin films.

Magnetic-Field Dependence of Raman Coupling Strength in Ultracold 40K Atomic Fermi Gas**Supported by the National Basic Research Program of China under Grant No 2011CB921601, the National Natural Science Foundation of China under Grant Nos 11234008, 11361161002 and 11222430, and the Program for Sanjin Scholars of Shanxi Province.

We experimentally demonstrate the relation of Raman coupling strength with the external bias magnetic field in degenerate Fermi gas of 40K atoms. Two Raman lasers couple two Zeeman energy levels, whose energy splitting depends on the external bias magnetic field. The Raman coupling strength is determined by measuring the Rabi oscillation frequency. The characteristics of the Rabi oscillation is to be damped after several periods due to Fermi atoms in different momentum states oscillating with different Rabi frequencies. The experimental results show that the Raman coupling strength will decrease as the external bias magnetic field increases, which is in good agreement with the theoretical prediction.

Dynamical Fano-Like Interference between Rabi Oscillations and Coherent Phonons in a Semiconductor Microcavity System.

We report on dynamical interference between short-lived Rabi oscillations and long-lived coherent phonons in CuCl semiconductor microcavities resulting from the coupling between the two oscillations. The Fourier-transformed spectra of the time-domain signals obtained from semiconductor microcavities by using a pump-probe technique show that the intensity of the coherent longitudinal optical phonon of CuCl is enhanced by increasing that of the Rabi oscillation, which indicates that the coherent phonon is driven by the Rabi oscillation through the Fröhlich interaction. Moreover, as the Rabi oscillation frequency decreases upon crossing the phonon frequency, the spectral profile of the coherent phonon changes from a peak to a dip with an asymmetric structure. The continuous wavelet transformation reveals that these peak and dip structures originate from constructive and destructive interference between Rabi oscillations and coherent phonons, respectively. We demonstrate that the asymmetric spectral structures in relation to the frequency detuning are well reproduced by using a classical coupled oscillator model on the basis of dynamical Fano-like interference.

Rabi oscillation generation in the microring resonator system with double-series ring resonators

In this paper, a microring resonator (MRR) system using double-series ring resonators is proposed to generate and investigate the Rabi oscillations. The system is made up of silicon-on-insulator and attached to bus waveguide which is used as propagation and oscillation medium. The scattering matrix method is employed to determine the output signal intensity which acts as the input source between two-level Rabi oscillation states, where the increase of Rabi oscillation frequency with time is obtained at the resonant state. The population probability of the excited state is higher and unstable at the optical resonant state due to the nonlinear spontaneous emission process. The enhanced spontaneous emission can be managed by the atom (photon) excitation, which can be useful for atomic related sensors and single-photon source applications.

Jaynes-Cummings dynamics in mesoscopic ensembles of Rydberg-blockaded atoms

We show that Jaynes-Cummings dynamics can be observed in mesoscopic atomic ensembles interacting with a classical electromagnetic field in the regime of a Rydberg blockade where the time dynamics of the average number of Rydberg excitations in mesoscopic ensembles displays collapses and revivals typical of this model. As the frequency of Rabi oscillations between collective states of Rydberg-blockaded ensembles depends on the number of interacting atoms, for randomly loaded optical dipole traps, we predict collapses and revivals of Rabi oscillations. We have studied the effects of finite interaction strengths and a finite laser linewidth on the visibility of the revivals. We have shown that observation of collapses and revivals of Rabi oscillations can be used as a signature of the Rydberg blockade without the need to measure the exact number of Rydberg atoms.

Mixed states in Rabi waves and quantum nanoantennas

The mixed states of Rabi waves in a one-dimensional chain of two-level quantum dots (QDs) with tunnel coupling between neighbor QDs are theoretically considered. The propagation of Rabi waves is described by a $2\ifmmode\times\else\texttimes\fi{}2$ statistical operator depending on two spatial and one temporal variables. For a statistical operator the generalized Bloch equations are derived. The eigenmodes of the statistical operator are considered, the general solution of the initial problem is obtained, and the frequency spectrum of the induced current is investigated. The high-frequency part of the spectrum corresponds to a Mollow triplet, but is distinct from the last one as it is the continuous spectral band located on both sides of the transition frequency. The low-frequency part is caused by tunnel current and includes a dc-component and continuous ac-band in the vicinity of the Rabi oscillation frequency. The application of Rabi waves to the electrically controlled quantum nanoantennas of terahertz range is considered.

Local-field correction in the strong-coupling regime

The influence of the local-field correction on the strong atom-field coupling regime are investigated using the real-cavity model. The atom is positioned at the center of a multilayer sphere. Three types of mirrors are considered: perfectly reflecting, Lorentz band gap, and Bragg-distributed ones, with special emphasis on experimental practicability. In particular, the influence of the local field on the spectral resonance lines, the Rabi oscillation frequency and decay rate, and the condition indicating the occurrence of the strong-coupling regime are studied in detail. It is shown that the local-field correction gives rise to a structureless plateau in the density of states of the electromagnetic field. The level of the plateau rises with increasing material density and/or absorption, which may eventually destroy the strong-coupling regime. The effect of the local field is especially pronounced at high-material densities due to direct energy transfer from the guest atom to the medium. At lower material density and/or absorption, variation of the material density does not seem to affect much the strong-coupling regime, except for a small shift in the resonance frequency.

Rf-SQUID-Mediated Coherent Tunable Coupling between a Superconducting Phase Qubit and a Lumped-Element Resonator

We demonstrate coherent tunable coupling between a superconducting phase qubit and a lumped-element resonator. The coupling strength is mediated by a flux-biased rf SQUID operated in the nonhysteretic regime. By tuning the applied flux bias to the rf SQUID we change the effective mutual inductance, and thus the coupling energy, between the phase qubit and resonator. We verify the modulation of coupling strength from 0 to 100 MHz by observing modulation in the size of the splitting in the phase qubit's spectroscopy, as well as coherently by observing modulation in the vacuum Rabi oscillation frequency when on resonance. The measured spectroscopic splittings and vacuum Rabi oscillations agree well with theoretical predictions.