Atomic Resonance Frequency Research Articles

Experimental determination of the shift of the Zeeman resonance frequency of cesium atoms induced by spin-exchange collisions with rubidium atoms

s 2 -polarized pump light. The difference of the resonance frequencies measured in this manner was equal to double the magnitude (2d f 0) of the spin-exchange shift. We call attention to some procedural features of the experiment. First, because of its smallness, the observed shift 2d f 0 was measured by means of synchronous detection of the spin-exchange signal of cesium atoms with amplitude modulation of the constant magnetic field with frequency 10 Hz. For the s 2 -polarized rubidium pump light the frequency of the rf oscillator ~producing the alternating magnetic field which excited Zeeman transitions in the ground state of the Cs atoms! was tuned to the center of the magnetic resonance signal ~the minimum of the output voltage of the synchronous detector during differential passage through resonance! and the output voltage of the synchronous detector was recorded. Constant resonance conditions were maintained by stabilizing the magnetic field with a quantum magnetometer

Anharmonicity of the vacuum Rabi peaks in a many-atom system.

The interaction of a single mode of the electromagnetic field with a collection of atoms has been extensively studied in cavity quantum electrodynamics. Since the seminal work of Sanchez Mondragon et al. @1#, where the term vacuum field Rabi splitting was coined and Agarwal's calculations of the microwave absorption by Rydberg atoms in a cavity @2# were introduced, there have been extensive investigations of the transmitted spectrum of the atoms-cavity system @3-6#. The experiments have been carried out in a regime in which the excitation is extremely weak. This means that the number of energy quanta in the system is very small, much less than 1, so it cannot sustain an appreciable population in the ex- cited state. The weak excitation regime is characterized by the appearance of two peaks in the transmitted spectrum of the composite atoms-cavity system. This doublet is a mani- festation of the degeneracy in the frequency of two oscilla- tors being lifted once they are coupled. The rate for the ex- change of energy between the two oscillators is precisely the frequency splitting. One oscillator is the single mode of the electromagnetic field, while the other is the collective polar- ization of the N atoms. Not surprisingly, quantum- mechanical and classical calculations predict exactly the same spectrum. Even when dissipation is taken into account, the doublet is clearly resolved as long as the two oscillators fulfill the following condition: Their decay rates should be approximately equal and smaller than the rate of energy ex- change. The purpose of this Rapid Communication is to report an experimental study of the behavior of an atom-cavity system as the excitation increases, from low to high intensities, away from the linear regime so far explored. We follow the changes in the transmitted spectrum starting with the vacuum Rabi doublet at low intensities. The presence of more energy in the system, and the possibility of coherent exchange of that energy between the atoms and the cavity, modifies the simple harmonic-oscillator structure. The transmitted spec- trum presents hysteresis followed by the merging of the dis- torted peaks into a single peak. This work is an exploration in frequency space of the underlying structure for the dynam- ics of the atoms-cavity system with arbitrary excitation. For an elementary theory we may start with the Maxwell- Bloch equations for the atom-cavity system, following the literature in optical bistability @7#. To simplify the discus- sion, for the present we do not take into account the trans- verse character of the mode in the cavity, nor the standing waves of the Fabry-Perot interferometer. We derive the transmitted spectra for arbitrary input intensity from the steady-state solution to the Maxwell-Bloch equations when the frequency of the driving field changes by an amount V from the resonance condition. The purely radiative decay rate of the atoms is characterized by g' , while the cavity field decays with a rate k. The dipole coupling between N two-level atoms and the cavity mode is gAN, where g5(m 2 v/2\e 0 V) 1/2 ; m is the transition-dipole moment of the atom, v the resonance frequency of both atoms and cav- ity, and V the cavity mode volume. The input field amplitude y and the output field amplitude x are normalized to the square root of the saturation intensity for the atomic transi- tion. They represent the intracavity field in the absence and presence of atoms, respectively. Guided by the behavior of the system in the low-intensity regime, where there are clearly two normal modes, we write the transmission as consisting of two parts:

Polariton-atom bound state in a dispersive medium

The quantum electrodynamics of a single two-level atom placed within a frequency dispersive medium whose polariton spectrum has a gap due to photon coupling to a medium excitation (exciton, optical phonon, etc.) is studied. If the atomic resonance frequency lies near the gap, the spectrum of the system is shown to contain a novel polariton-atom bound state with an eigenfrequency lying within the gap. The radiation and medium polarization of the bound state are localized in the vicinity of the atom. A significant suppression of spontaneous emission due to the bound state is predicted.

0π pulse propagation in the extreme sharp-line limit

We observe the propagation and the reshaping of low-intensity (zero area) 60-fs pulses through high-density atomic Cs vapor. The breakup of the pulses is measured both for resonant excitation of the Cs atoms and for laser detunings such that the atomic resonance frequency is in the wings of the pulse spectrum. The theory of 0π pulse propagation in the extreme sharp-line limit is extended to include both resonant and off-resonant excitation. Good agreement is demonstrated between the observations and the theoretical predictions.

0π PULSE SHAPE IN THE SHARP LINE LIMIT CASE

We observe the propagation and the reshaping of low intensity (zero area) 60 fs pulses through high density atomic Cs vapor. The breakup of the pulses is measured for both resonant excitation of the Cs atoms and for laser detunings such that the atomic resonance frequency is in the wings of the pulse spectrum. The theory of 0π pulse propagation, in the extreme sharp-line limit, is extended to include both resonant and off resonant excitation. Good agreement is demonstrated between the observations and the theoretical predictions.

Atomic magnetic resonance based current source

A current of 1 A has been stabilized by locking the magnetic resonance frequency of Cs atoms placed at the center of a solenoid. Two auxiliary windings are used to obtain at the center of the solenoid a field uniformity better than 0.5 ppm in a 2 cm radius sphere, in agreement with the calculations. The variations of the external field and the effect of temperature changes are compensated for by two auxiliary feedback systems using a flux gate magnetometer and an adjustment of the locking frequency, respectively. The current fluctuation, including the noise of the current measuring system is 0.1 ppm and the current drift for 6 h is less than 0.2 ppm.

Population accumulation in dark states and subrecoil laser cooling.

The \ensuremath{\Lambda} system resulting from the interaction of counterpropagating orthogonally polarized beams of light with a ${\mathit{J}}_{\mathit{g}}$=1\ensuremath{\rightarrow}${\mathit{J}}_{\mathit{e}}$=1 transition is known to exhibit laser cooling without the presence of a damping force, through velocity selective coherent population trapping. This occurs independent of the sign of the laser's detuning from the atomic resonance frequency. We present measurements and calculations that show a detuning-dependent transient peak or dip in the ground-state momentum distribution centered at ${\mathit{p}}_{\mathit{g}}$=0, however, which is reminiscent of laser cooling by a damping force. We explain this in terms of the character of the quantum-mechanical eigenstates of the total ground-state Hamiltonian of the system, using both analytic expressions and numerical calculations.

Longitudinal–transverse mode interplay and conical emission in microchip lasers

Field confinement in a microchip laser with transversely varying gain and plane–plane cavity mirrors is theoretically discussed with a semiclassical treatment. We show that the common notion of a transverse cavity mode becomes closely linked to that of a longitudinal cavity mode owing to the key role that detuning of the longitudinal cavity frequency from the atomic resonance plays in the formation of the transverse field profile. In particular, we show that as the pump size decreases the laser emission is pulled toward the atomic resonance frequency on the negative detuning side. Strong mode pulling is interpreted as being due to the index-antiguiding effect induced by the pump and manifests itself as a ring pattern in the far-field spatial intensity.

Switching Between Rayleigh-like and Lorentzian Lineshapes of the Dispersion in Driven Two-level Atoms

Abstract We investigate the structure of the dispersion and absorption lineshapes for driven two-level systems against a weak probing laser field. It is shown that the shape of both curves depends critically on the detuning of the driving laser to the atomic resonance frequency and can be transformed continuously and oppositely between Rayleigh (or ‘dispersion-like’) and Lorentzian (or ‘absorption-like’) lineshapes. An analysis in the dressed state basis explains these features via the different influences of coherences and populations of the corresponding dressed states.

Localization of Superradiance near a Photonic Band Gap.

We describe collective spontaneous emission of $N$ two-level atoms placed within a photonic band-gap material. When the atomic resonance frequency lies at the band edge, superradiant emission remains localized in the vicinity of the atoms. This leads to a steady state with spontaneously broken symmetry in which the atomic system acquires a macroscopic polarization. The superradiant decay rate is proportional to ${N}^{2/3}$ and ${N}^{2}$ for isotropic and anisotropic 3D band gaps, respectively. The corresponding peak intensity of superradiance is proportional to ${N}^{5/3}$ and ${N}^{3}$, respectively.

Spontaneous and Induced Atomic Decay in Photonic Band Structures

Abstract We present a comprehensive quantum electrodynamical analysis of the interaction between a continuum with photonic band gaps (PBGs) or frequency cut-off and an excited two-level atom, which can be either ‘bare’ or ‘dressed’ by coupling to a near-resonant field mode. A diversity of novel features in the atom and field dynamics is shown to arise from the non-Markovian character of radiative decay into such a continuum of modes. Firstly the excited atom is shown to evolve, by spontaneous decay, into a superposition of non-decaying single-photon dressed states, each having an energy in a different PBG, and a decaying component. This superposition is determined by the atomic resonance shift, induced by the spontaneously emitted photon, into or out of a PBG. The main novel feature exhibited by the decaying excited-state component is the occurrence of beats between the shifted atomic resonance frequency and the PBG cut-off frequencies, corresponding to a non-Lorentzian emission spectrum. Secondly the ind...

Laser second threshold: Its exact analytical dependence on detuning and relaxation rates.

An exact analysis has been carried out for general analytical expressions for the second threshold of a single-mode homogeneously broadened laser and for the initial pulsation frequency at the second threshold, for arbitary physical values of the relaxation rates, and at an arbitrary detuning between the cavity frequency and the atomic resonance frequency. These expressions also give correspondingly exact forms for asymptotic cases that have been previously studied with some approximations. Earlier approximate results are partly confirmed and partly improved by these more general expressions. The physical status of various expressions and approximations is reconsidered and specified more clearly, including an analysis of what reasonably can be attained in lasers or masers. A general analytical proof is given of the fact that, for a larger detuning of the laser cavity from resonance, a higher value of the laser excitation is required to destabilize the steady-state solution (the second threshold). We also present results for the minimum value of the second threshold at fixed detuning as a function of the other parameters of the system and for the dependence of the ratio of the second threshold to the first threshold as a function of detuning. Minima of the second threshold and of the threshold ratio occur only if the population relaxation rate is equal to zero. The minima of the threshold ratio are shown to be bounded from above as well as from below (as functions of the relaxation rates, so long as the second threshold exists). The upper bound on the minima ratio is equal to 17. The variation of the second threshold in the semi-infinite parameter space of the decay rates is shown at various detunings in plots with a finite domain by normalizing the material relaxation rates to the cavity decay rate.

Frequency Stabilization of an Internal-Mirror He-Ne Laser by Means of a Microprocessor Controller (II).

Simultaneous stabilization of the amplitude and frequency of a two-mode internal-mirror He-Ne laser (λ=633 nm) using a microprocessor controller is reported. The intensity difference between two orthgonally-polarized axial modes normalized by the total intensity is caluculated as a controlled signal. The cavity length is controlled by manipulating the current of a heater wound around the laser tube according to digital PID or I-PD algorithms so that the controlled signal coincides with a reference signal. By adjusting the reference signal, stabilized laser frequency can be tuned within ±300 MHz around the mean frequency of the atomic resonance frequencies of 20Ne and 22Ne. Frequency stability estimated by the error between the controlled and reference signals is better than 3×10-8 over a period of 30 minutes. Beat frequency fluctuations between two stabiliezed lasers over a 8 minutes are in the range 1×10-8 to 2×10-8 depending on the selected direction of polarization.

81Br and 127I NQR and Phase Transitions in CH3NH3 HgBr3 and CH3NH3 HgI3

Abstract The 81Br and 127I NQR spectra were recorded in CH3NH3 HgBr3 and CH3NH HgI3 , respectively. In addition to a phase transition at 338 K, successive phase transitions take place at 127 ± 1, 184±1 and 243±5 K in CH3NH3 HgBr3. On heating, the resonance lines of CH3NH3HgI3 disappear near a phase transition at 328 K and one line appears above this temperature. The temperature variations of the resonance frequencies of the terminal halogen atoms in both crystals are extraordinarily steep. This indicates the large amplitude molecular motions expected for the CH3NH3 cations which are linked to the terminal halogen atoms through N-H ··· X type H-bonding.

Alignment effects in Ca–He(5 1P1–5 3P J) energy transfer collisions by far wing laser scattering

The far wing absorption profiles for excitation on the Ca(4s2 1S0–4s5p 1P01) atomic transition, broadened in collisions with He are measured. We observe strong absorption in both wings and a blue wing satellite near Δ∼125 cm−1. We tentatively identify this satellite as due to a maximum in the CaHe(4s2 1∑+–4s5p 1∑+) difference potential. These line-broadening techniques are used to study electronic energy transfer in the spin-changing collisions of Ca with He: Ca(5p 1P01) +He→Ca(5p 3P0J)+He+ΔE. Measurements of the ‘‘single collision’’ triplet–singlet branching ratio as a function of laser detuning from the atomic resonance frequency indicate a clear red wing/blue wing asymmetry. We interpret this asymmetry in terms of a preferential orbital alignment effect in the energy transfer process [Phys. Rev. Lett. 53, 2296 (1984)]. No clear structure is observed in the range of detunings probed that might indicate the curve crossing responsible for the energy transfer.

Temperature dependence of nqr spectra in MSbBrF3 (M=Na, Cs, NH4) and Cs3Sb2Br9

We have studied the temperature dependence of the NQR parameters of123Sb and81Br in the range 77–360 K for the complexes of MSbBrF3 (M=Na, Cs, NH4) and Cs3Sb2Br9. We have established the temperature regions for which piezoelectric properties appear in the crystal hydrate NaSbBrF3.H2O, and in the compounds MSbBrF3 (M=Na, NH4) and Cs3Sb2Br9 anomalous changes appear in the dependences of the quadrupole coupling constant, the asymmetry parameter of the electric field gradient for the antimony atoms and the resonance frequency of the bromine atoms.

Laser stabilisation for velocity-selective atomic absorption

A relatively simple method is described for stabilising a dye laser at a frequency nu = nu 0+ nu c in the vicinity of an atomic resonance frequency nu 0. The Doppler effect is exploited by looking for atomic fluorescence when a laser beam is crossed with an atomic beam at certain angles alpha i. Absolute preselection of nu c (the deviation from resonance) up to approximately 120 MHz is possible by the choice of alpha i, and a laser stabilisation to better than 1 MHz is obtained. The authors apply this stabilisation to collision experiments with velocity-selected excited Na atoms.

Waveguide effects in superfluorescence and stimulated Raman scattering.

A quantum theory of formation and propagation of superfluorescence and Stokes pulses in samples of small Fresnel numbers is presented. Linearized Maxwell-Heisenberg equations for the system of two-level atoms and a quantized electromagnetic field are solved analytically in the second-order Debye approximation. Under this approximation paths of rays which undergo one reflection from the sides of the sample and those which propagate without reflections are studied. We point out that due to guiding effects, if the Fresnel number is smaller than unity, the contribution from totally reflected rays is not negligible with respect to that from nonreflected rays. This leads to the interference between reflected and nonreflected rays which affects spatial properties of superfluorescence and Stokes pulses. Moreover, as a consequence of guiding effects, the spectral density of light becomes asymmetric and shifted from the atomic resonance frequency.

Validity conditions for the optical Bloch equations

In a recent experiment [ DevoeR. G.BrewerR. G., Phys. Rev. Lett.50, 1269 ( 1983)], it was found that the optical Bloch equations could not satisfactorily explain the signal that was observed for free-induction decay in the impurity ion cyrstal Pr3+:LaF3. Several theories have been proposed to explain this failure of the Bloch equations. In this paper, the general validity conditions for the optical Bloch equations are examined within the limits of a Markovian relaxation model. The specific problem to be considered is the interaction of an optical field with two-level atoms. The atoms undergo relaxation as a result of coupling to a perturber bath that, itself, is negligibly affected by the relaxation process. First, a simple decay-parameter model is assumed for the relaxation of atomic density-matrix elements. Such a model is found to lead to a set of generalized Bloch equations of which the conventional Bloch equations form a subset. Subsequently, more-realistic models for relaxation in both vapors and solids are considered within the limits of the impact approximation (i.e., the duration of a fluctuation can be viewed as instantaneous with respect to all relevant time scales in the problem). It is found that, even in the impact (Markovian) approximation, the generalized Bloch equations cannot be expected to provide an adequate description of relaxation, owing to effects in which a fluctuation-induced change in the atomic transition frequency persists between fluctuations. In vapors this frequency shift is produced by velocity-changing collisions that change the atomic resonance frequency (as seen in the laboratory frame), whereas in solids it is produced by local-field fluctuations. The limiting conditions under which one can expect both the generalized and the conventional Bloch equations to retain their validity are explored.

Ultrahigh-resolution two-photon optical Ramsey spectroscopy of an atomic fountain.

We present a semiclassical analysis of ultrahigh-resolution two-photon optical Ramsey spectroscopy of cold neutral atoms falling freely in a fountain. Considering atoms which interact with the same standing-wave laser field twice on their parabolic trajectories and averaging over a broad atomic velocity distribution, we predict a nearly Lorentzian line shape whose width is just the natural linewidth. We have investigated a number of systematic corrections to the atomic resonance frequency, including first-order and second-order Doppler shifts, gravitational red shifts, and ac Stark shifts. First-order Doppler shifts due to vertical motion cancel even if the counterpropagating beams are slightly misaligned, and resolutions below 1 Hz appear feasible with a fountain of modest dimensions.