Ramsey Resonance Research Articles

Side-Looking Radar and Optical Ramsey Resonance

Side-Looking Radar and Optical Ramsey Resonance

Theory of optical ramsey resonance in three separated fields produced by a corner reflector

In this paper we study the optical Ramsey resonance signal of two-level molecules in three separated fields consisting of one standing wave and two traveling waves of opposite directions with each other. Their separations and phase differences are given by a corner reflector. The transition probability of a molecule that traverses the three interaction regions is calculated by using an optical Bloch vector formalism. It is then integrated over distributions of molecular velocities and positions to evaluate the signal observed with a gas cell. The result is applied to compute the optical Ramsey resonance signal in the absorption line of CH4 at 3.39 μm. Variations of the Ramsey resonance lineshape and the intensity with the gas pressure and the field intensity are obtained.

Theory of optical ramsey resonance in three separated fields produced by a corner reflector

In this paper we study the optical Ramsey resonance signal of two-level molecules in three separated fields consisting of one standing wave and two traveling waves of opposite directions with each other. Their separations and phase differences are given by a corner reflector. The transition probability of a molecule that traverses the three interaction regions is calculated by using an optical Bloch vector formalism. It is then integrated over distributions of molecular velocities and positions to evaluate the signal observed with a gas cell. The result is applied to compute the optical Ramsey resonance signal in the absorption line of CH4 at 3.39 μm. Variations of the Ramsey resonance lineshape and the intensity with the gas pressure and the field intensity are obtained.

Nonlinear Ramsey resonance of the number of excited particles

An analysis is made of the interaction of three spatially separate standing Gaussian waves with an atomic beam. The case of a Doppler-broadened transition is considered. An expression is obtained for the correction to the resonance in the number of excited particles, the width of the correction being inversely proportional to the transit time between the waves. The analysis is carried out for a weak field. Numerical calculations of the amplitude and profile of the resonance are reported. The optimal (in respect of the field intensity) conditions for the observation of this resonance are determined.

Performance of the Primary Cs-Standard of the Physikalisch-Technische Bundesanstalt

First the main characteristics of the caesium beam time and frequency standard CS1 of the PTB are summarized. Then current research work on the improvement of CSI is reported: (1) Reduction of the mean beam velocity and the velocity range in the beam; (2) detection of small asymmetries of the Ramsey resonance, e.g., due to a shifted Rabi resonance; (3) development of improved analyser deflection systems. The efficiencies of beam polarizers using quadrupole magnets or hexapole magnets, or combinations of both, have been studied for CS1 achieving the reduction of the mean beam velocity to about 100 m/s and the half-width velocity range in the beam to about 16%. For the analyser a shaped quadrupole magnet or a combination of hexapole and quadrupole magnets should be advantageous. The square root of the sum of squares of the uncertainty contributions of CS1 amounts to 0.26 · 10-13, the official relative uncertainty of CS1 being 1 · 10-13.

Beam maser double resonance measurements on HDO

High resolution measurements of hyperfine structure on the 220–221 transition of HDO were made with a two-cavity beam maser using the Ramsey method and using a new double resonance technique. Resonances for magnetic dipole transitions between hyperfine sublevels of the rotational states were detected by observing intensity changes in the two-cavity interference pattern for microwave rotational transitions. The linewidth (fwhm) for the magnetic dipole transitions was 1 kHz. This linewidth allows better effective resolution than the two-cavity Ramsey resonance when nozzle beams are used. Deuterium quadrupole coupling and spin–rotation interaction strengths were obtained. This double resonance technique should be useful for other small molecules, particularly for those cases where the data cannot be obtained from the microwave transitions.

Ramsey resonance in high field; a novel method for the measurement of hyperfine Zeeman frequencies of muonium

A novel method for measuring hyperfine Zeeman transitions in muonium,i.e. « Ramsey resonance » in high field, is described both theoretically and practically. Various potential sources of systematic errors are exhaustively discussed. Data taken at 30 atm krypton buffer gas pressure are presented. They agree with the most accurate previous high-field results, and provide evidence for the so-calledgj shift in muonium.

Theory of the nonlinear Ramsey resonance in the optical part of the spectrum

It is shown that the interaction of three standing-wave light beams with a low-pressure gas gives rise to a narrow absorption power resonance. The width of this resonance is related to the transit time of gas atoms between the beams. The weak-field case is analyzed. A formula for a Held of arbitrary intensity is obtained for the situation when the dimensions of the beams are much smaller than the distances between them. Numerical calculations are reported of the resonance amplitude and profile. Optimal (in respect of the field intensity) conditions for the observation of the effect are determined. If the distances between the beams are sufficiently large, it should be possible to observe resonances of width equal to the homogeneous width of atomic radiation lines in spite of the considerable field and transit broadening. The possibility of using this power resonance in stabilization of the emission frequency of gas lasers is considered.

Non-linear ramsey resonance in the optical region

The interaction of gas particles with three separated light fields has been considered. It has been shown that a resonance with the width equal to the reciprocal transit time appears in such a system. The resonance is due to coherence conservation and change of distribution of a number of particles by nonlinear interaction with the fields. Its properties are close to the Ramsey resonance in the microwave range. This new type of resonance may have a relative width of 10−11 to 10−12.

Determination of Velocity Distributions in Molecular Beam Frequency Standards from Measured Resonance Curves

It is shown that the Ramsey resonance curves for most atomic beam machines can be conceived as depending on two distributions of velocity, ρ(V) and ξ(V), the second being a correction for beam width.An analysis and computer program are described which permit one to obtain ρ, ξ and the nominal microwave power parameter from three or more measured Ramsey resonance curves at properly spaced power levels whose ratios are known. The determination from the functions (ρ, ξ) of bias errors due to second order Doppler shift, cavity phase difference, and cavity pulling is described.The method may also be used to improve an experimentally obtained velocity distribution (i.e., one obtained through the pulse technique); to provide the proper function ξ; and to provide diagnostic checks of the measurement technique and the validity of the model chosen for the transition probability.The method is applied to the NBS frequency standard. Error estimates indicate that it is feasible by microwave power shift measurements to evaluate the total bias error due to the above sources to within one part in 1013.

Precision Measurement of the Hyperfine Interval of Muonium by a Novel Technique: Ramsey Resonance in Zero Field

A novel method for measuring the hyperfine interval $\ensuremath{\Delta}\ensuremath{\nu}$ of muonium in "zero" magnetic field is described. It consists in applying two successive coherent microwave pulses (lengths $\ensuremath{\tau}$, separation $T$) to muonium, and observing the change in muon polarization at $t>T+2\ensuremath{\tau}$. By extrapolating two low-pressure runs in Kr we obtain $\ensuremath{\Delta}\ensuremath{\nu}(0)=4463.3013(40)$ MHz, while a joint fit with earlier Chicago Kr data gives $\ensuremath{\Delta}\ensuremath{\nu}(0)=4463.3012(23)$ (0.5 ppm). With $\frac{{f}_{\ensuremath{\mu}}}{{f}_{p}}=3.183338(13)$ this implies (a) ${\ensuremath{\alpha}}^{\ensuremath{-}1}\ensuremath{-}137=0.03619(30)$ (2.2 ppm) and (b) a proton polarizability ${{\ensuremath{\delta}}_{N}}^{(2)}=\ensuremath{-}(4\ifmmode\pm\else\textpm\fi{}4)$ ppm.

The Second Order Doppler Shift in Cesium Beam Atomic Frequency Standards

The frequency shift in cesium beam atomic frequency standards resulting from the second order doppler shift is described in terms of a truncated Maxwellian velocity distribution in the atomic beam. A means of establishing the upper and lower limits of the atomic velocities accepted by the standard, based on fitting of experimental and calculated Ramsey resonance patterns, is outlined. A detailed analysis of the influence of both the velocity distribution and the exciting power level is given, and it is shown that an asymmetric resonance results, with asymmetry greatest for a full Maxwellian distribution. Results are given for the NRC 2.1 m cesium standard, Cs III. An increase of the second order doppler shift correction for Cs III from 0.003 Hz to 0.0072 Hz is required, and the effect of this on the NRC UTA time scale is discussed.

Cesium Beam Frequency Standard Cavity Design

A new technique of constructing resonant cavities for exciting the Ramsey resonance in cesium beam frequency standards is discussed. A centrally located E-plane tee is used as the feed system in a symmetric even-order mode cavity. The location of the tee is determined initially from measurements made on the cavity when operated in a symmetric odd-order mode. Both the theoretical conditions and construction methods required to obtain very small phase differences between the oscillating magnetic fields at the ends of the cavity are described. Experimental results indicate agreement with theory and that the method is effective and simple to apply.

Analysis of Modulation Method for Measuring Atomic Resonant Frequency

In microwave spectroscopy and in atomic frequency standards, the atomic resonant frequency is often determied by the use of harmonic frequency modulation of a microwave signal. The effects of line asymmetry and modulating-signal nonlinear distortions are investigated by the use of an analytic approximation of the resonance line by means of an algebraic polynomial. The coefficients of the polynomial are determined experimentally and also derived theoretically. Detailed numerical results for a Ramsey resonance line in a cesium clock are given.

Square-Wave Phase Modulation in Ramsey-Type Molecular Beam Resonance Experiments

Square-wave phase modulation of the microwave signal which induces transitions allows one to measure velocity-dependent frequency shifts in Ramsey resonance experiments. The output signal from the molecular beam apparatus is demodulated by a synchronous detector operating in phase with the modulation. This output is proportional to the derivative of the transition probability and provides the usual resonance signal which is used in a servo loop to keep a harmonic of a voltage tunable crystal oscillator on the central peak of the resonance. A quadrature synchronous detector operating 90° out of phase with the modulating signal provides a measure of any velocity-dependent frequency shifts. Such shifts arise when there is a phase difference between the oscillating fields or when an electric field applied to a magnetic system produces a v×ε shift. We have theoretically and experimentally demonstrated that this quadrature signal is proportional to the phase difference between the microwave cavities of a Ramsey apparatus with the in-phase signal constrained at zero. We have also shown that the sensitivity of the quadrature system depends on the width of the available velocity distribution.

Observation of the field-dependent ramsey resonance without extremely homogeneous magnetic fields

The necessary condition for observation of a Ramsey resonance is given for atoms traversing a quite inhomogeneous magnetic field. The application to a field-dependent transition is demonstrated for 39K atoms in a magnetic field with variations > 0.1 G. Several applications of the technique are suggested.