Measurement of the Effect of Thermal Noise on the Amplitude of Oscillation of a Maser Oscillator

Experimental verification of the effect of thermal noise on the oscillation amplitude of a maser is described. Two different masers are considered, the H maser with an homogeneous atomic line and the Rb maser with an inhomogeneous line. The effect is characterized by the spectral density of the relative amplitude fluctuations and this parameter is measured with a conventional superheterodyne AM receiver for various maser saturation factors. Experimental results show good agreement with theoretical predicted values. At high saturation factors, a peak appears with a maximum at a frequency close to the Rabi frequency. Observed values at high Fourier frequencies allow a measurement of the atomic power by the knowledge of the absolute temperature of the cavity and the prediction of the oscillator short-term frequency stability. Furthermore, the effect on amplitude and on frequency noise of an external feedback loop used to increase the cavity quality factor is discussed.     

Spatial variations of field polarization and phase in microwavecavities: application to the cesium fountain cavity

Wall losses in microwave cavities will generate a phase difference between the components of the field, and give rise to spatial phase variations which are related to the geometry of complicated shaped metal boundaries. Such effects are important to the design of the cavities used in the field of atomic frequency standards. Past attempts at calculating spatial phase variations in microwave cavities have been either limited to 1-D models or based upon an idealized model of the cavity, which simplifies its boundary shapes and neglects the effect of the source. In this paper, a numerical implementation of an electromagnetic field approach is used to overcome these limitations. The finite element method (FEM) is used to solve the driven form of the electromagnetic wave equation. The results show good agreement with transmission line predictions for a structure having simply shaped metal walls. The spatial phase distribution is then calculated for a 2-D approximation of the fountain cavity operating in the cylindrical TE₀₁₁ mode, which has been recommended for use in a Cs fountain frequency standard. A physical interpretation of the gradient of the phase in the cavity is presented, which shows it to be proportional to power flow     

Double-boson stimulated terahertz emission in a polariton cascade laser

A system of equidistant polariton states interacting with a terahertz electromagnetic field are considered that are localized in a cavity for terahertz radiation. Accumulation of terahertz photons in the cavity, together with boson stimulation of the transitions between polariton levels, leads to intense radiative transitions between terahertz levels. A concept of double-boson stimulated transitions between polariton levels in the boson cascade laser is proposed. We study a possibility of using the boson cascade laser in generation of terahertz radiation. The system exhibits threshold dependence of the intensity of terahertz radiation on pumping. The quantum effectiveness of the boson cascade laser can exceed unity when pumping is performed above the threshold. The interaction of polaritons with the cavity leads to an increase in the threshold of pumping and a decrease in quantum effectiveness.     

The phase evolution of a micromaser field without the rotating-wave approximation

Abstract

In a one-atom micromaser, the expression for the density matrix of the cavity field without the rotating-wave approximation (RWA) is derived using a perturbation method. The phase evolution of the cavity field is investigated without the RWA, and the results are compared with those within the RWA. It is shown that the virtual-photon processes make the symmetric phase distribution in the RWA asymmetric and cause additional quantum oscillation, which indicate the field's phase fluctuation and frequency shift. Virtual photons also cause an extra phase distribution to the field which is initially in a vacuum state. The unique characteristic of the phase properties in the course of forming a photon-number state is investigated. Other new phenomena such as the undamped oscillation of the phase variance against the injected atomic number are found.     

A moving three-level atom interacting with a two-mode field: some atom–field aspects

In this paper, the interaction of a moving three-level atom and a two-mode quantized electromagnetic cavity field is extended to involve the effects of the atomic motion. Detuning parameters, Kerr nonlinearity, Stark shift contributions and arbitrary forms of intensity-dependent atom–field coupling have been taken into account. The constants of motion and the wave function, when the atom is initially prepared in superposition states and the field is initially prepared in squeezed coherent states, have been obtained. We calculate some statistical aspects such as atomic inversion, purity, Mandel Q-parameter, cross-correlation, momentum increment, momentum diffusion and Husimi Q-function.     

Stability theory of class-C (far-infrared) lasers with an injected signal

The behavior of a single-mode class-C laser in the presence of an injected signal is investigated theoretically in detail. We have determined the ranges of input signal strength and the frequency detuning for which the oscillations of the cavity electric field and the atomic induced dipole moment are simultaneously stable and have only one oscillation component with the frequency equal to that of the input signal (injection-locked state). One can reproduce all the previous results corresponding to class-A and class-B lasers from our results by using their relevant conditions. Finally, the energy conservation law is demonstrated for both the below-threshold and the injection-locked states of class-C laser amplifiers.     

Radiation of terahertz electromagnetic waves from build-in nano Josephson junctions of cuprate high-T(c) superconductors

The nano-scale intrinsic Josephson junctions in highly anisotropic cuprate superconductors have potential for generation of terahertz electromagnetic waves. When the thickness of a superconductor sample is much smaller than the wavelength of electromagnetic waves in vacuum, the superconductor renders itself as a cavity. Unlike conventional lasers, the presence of the cavity does not guarantee a coherent emission because of the internal degree of freedom of the superconductivity phase in long junctions. We study the excitation of terahertz wave by solitons in a stack of intrinsic Josephson junctions, especially for relatively short junctions. Coherent emission requires a rectangular configuration of solitons. However such a configuration is unstable against weak fluctuations, contrarily solitons favor a triangular lattice corresponding to an out-phase oscillation of electromagnetic waves. To utilize the cavity, we propose to use an array of stacks of short intrinsic Josephson junctions to generate powerful terahertz electromagnetic waves. The cavity synchronizes the plasma oscillation in different stacks and the emission intensity is predicted to be proportional to the number of stacks squared.     

Field quantization,photons and non-Hermitean modes

Field quantization in unstable optical systems is treated by expanding the vector potential in terms of non-Hermitean (Fox-Li) modes. We define non-Hermitean modes and their adjoints in both the cavity and external regions and make use of the important bi-orthogonality relationships that exist within each mode set. We employ a standard canonical quantization procedure involving the introduction of generalized coordinates and momenta for the electromagnetic (EM) field. Three-dimensional systems are treated, making use of the paraxial and monochromaticity approximations for the cavity non-Hermitean modes. We show that the quantum EM field is equivalent to a set of quantum harmonic oscillators (QHOs), associated with either the cavity or the external region non-Hermitean modes, and thus confirming the validity of the photon model in unstable optical systems. Unlike in the conventional (Hermitean mode) case, the annihilation and creation operators we define for each QHO are not Hermitean adjoints. It is shown that the quantum Hamiltonian for the EM field is the sum of non-commuting cavity and external region contributions, each of which can be expressed as a sum of independent QHO Hamiltonians for each non-Hermitean mode, except that the external field Hamiltonian also includes a coupling term responsible for external non-Hermitean mode photon exchange processes. The non-commutativity of certain cavity and external region annihilation and creation operators is associated with cavity energy gain and loss processes, and may be described in terms of surface integrals involving cavity and external region non-Hermitean mode functions on the cavity-external region boundary. Using the essential states approach and the rotating wave approximation, our results are applied to the spontaneous decay of a two-level atom inside an unstable cavity. We find that atomic transitions leading to cavity non-Hermitean mode photon absorption are associated with a different coupling constant to that for transitions leading to photon emission, a feature consequent on the use of non-Hermitean mode functions. We show that under certain conditions the spontaneous decay rate is enhanced by the Petermann factor.     

Scheme to measure squeezing and phase properties of a harmonic oscillator

We propose a simple scheme to measure squeezing and phase properties of a harmonic oscillator. We treat in particular the case of an electromagnetic field, but the scheme may be easily realized in ion traps. It is based on integral transforms of measured atomic properties as atoms exit a cavity. We show that by measuring atomic polarizations it is possible, after a given integration, to measure several properties of the field.     

Effects of a Moving Mass Centre on Atomic Dynamics in Locally Inhomogeneous Quantized Cavity Field

Abstract

By invoking an exactly solvable model as the generalization of the Jaynes-Cummings model, the influence of spatial motion of atomic centre on the dynamics of a single-mode cavity-two-level atom system are studied for various initial conditions. These investigations show that the Doppler effect exercised by the motion of atom in a locally inhomogeneous cavity field can lead to the phenomenon of oscillation collapse and revival in the transition probability and the atomic population inversion.     

Field oscillations in a micromaser with injected atomic coherence

Abstract

The electric field in a lossless, regularly-pumped micromaser with injected atomic coherence can undergo a period-two oscillation in the steady state. The field changes its value after a single atom passes through the micromaser cavity, but returns to its original value after a second atom travels through. We give a simple explanation for this phenomenon in terms of tangent and cotangent states. We also examine the effect of cavity damping on this steady state.     

N-level Atom Interacting with Single-mode Radiation Field: An Exactly Solvable Model with Multiphoton Transitions and Intensity-dependent Coupling

Abstract

We study the dynamics of an N-level atom coupled in a lossless cavity to a single-mode near-resonant quantized field. The atomic levels are coupled by the multiphoton transitions and the coupling constants between the field and the atomic levels are supposed to be intensity dependent. We find the exact solution for the state vector describing the dynamics of the atom-plus-field system. As an illustration we use the model for studying (i) the time evolution of the atomic occupation probability with the initially coherent field and (ii) the light squeezing, when the cavity field is initially in the vacuum state and the atom is prepared in the atomic ‘coherent state’ (a superposition of atomic states).     

Analysis tools for the accurate evaluation of a small frequency standard

The short, optically pumped cesium beam tube developed at Laboratoire de l'Horloge Atomique has been carefully evaluated. For that purpose, we have developed a digital servo system that controls three parameters: the frequency of the ultra stable oscillator (USO), the microwave power of the signal experienced by the cesium atoms, and the static magnetic field applied to the atoms. The frequency standard shows a very satisfactory level of short- and medium-term frequency stabilities. A relative frequency offset, measured to be 4.10(-12 ), results mainly from the residual phase difference between the oscillatory fields in the two interaction regions, which is due to imperfection in cavity symmetry. We present two different means of analyzing the causes of this spurious frequency offset using theoretical and experimental considerations. First, a numerical simulation of the beam tube response is performed as a function of the microwave field amplitude for different values of the residual phase difference DeltaPhi. Results include the cavity-pulling effect. Compared with the measured frequency offset, the numerical simulation leads to a second-order Doppler shift of -3.3 mHz and a residual phase difference, DeltaPhi, between the fields interacting with the atoms in the second and first regions of the Ramsey cavity, amounting to +150 murad. Second, an experimental method of measurement of DeltaPhi without beam reversal is implemented. The latter yields DeltaPhi=155+/-17 murad. Finally, the clock accuracy is determined. It is equal to +/-14.10(-13).     

Energy flow lines for the radiation emitted by a dipole

An oscillating electric dipole emits radiation, and the flow of energy in the electromagnetic field is represented by the field lines of the Poynting vector. In the most general state of oscillation the dipole moment vector traces out an ellipse. We have evaluated analytically the field lines of the Poynting vector for the emitted light, and it appears that each field line lies on a cone, which has its axis perpendicular to the plane of the ellipse. The field lines exhibit a vortex structure near the location of the dipole, and they approach a straight line in the far field. It is shown that due to the spiraling of the field lines near the source, the asymptotic limit of a field line is displaced as compared to a ray which would come directly out of the source. Both the spatial extent of the vortex in the near field and the magnitude of the displacement of the image in the far field are of nanoscale dimension.     

Equivalence of interaction hamiltonians in the electric dipole approximation

Abstract

The interaction of an atomic system with an externally applied electromagnetic field can be treated in the electric dipole approximation by means of either the minimal coupling (p · A) or direct coupling (d · E) Hamiltonian. It is shown that both methods lead to identical and unambiguous predictions for observable quantities as long as the atomic wavefunctions are transformed when used in the minimal-coupling formulation. The physical meaning of kinetic momentum is used to show that the atomic states must be described by wavefunctions calculated in the absence of an electromagnetic field when using the d · E (but not the p · A) form of the interaction Hamiltonian. When, however, observables are calculated using the common approximations of resonance atomic physics – the two-level approximation and the rotatingwave approximation – the two formulations can lead to measurably different results. This point is illustrated by calculating the induced polarization (and hence the refractive index) of an atomic system for the two exactly soluble cases of the harmonic oscillator and the hydrogen atom.     

Influence of external cavity length on multimode hopping in microchip Nd:YAG lasers

The influence of external cavity length on multimode hopping in microchip Nd:YAG lasers is investigated experimentally. With an optical feedback loop, the threshold gain of different longitudinal modes are all modulated by changing the external cavity length; a lambda/2 change in the external cavity length causes a one-period oscillation. The longitudinal modes can be divided into groups according to different initial threshold gain variations and modulation trends corresponding to different external cavity phases. Because of the initial gain difference, only one mode in each group is the dominant potential lasing mode, while others are suppressed. During the 2 pi change of the external cavity phase, mode hopping occurs among these potential lasing modes from different groups. Both the intensity waveforms and the number of hopping modes strongly depend on the external cavity length. Experimental results agree well with the theoretical analysis of the phenomenon of multimode hopping subjected to optical feedback in microchip Nd:YAG lasers.     

Atomic interference in the micromaser and statistical properties of the micromaser field

Abstract

In this paper we report on atomic interferometry in the micromaser. The atomic inversion is recorded while scanning the cavity frequency across the atomic resonance. For high pump rates, interference patterns are observed on the low-frequency wing of the maser line. The interferences are due to the non-adiabatic mixing of dressed states of the atoms at the entrance and exit holes of the maser cavity, leading to a Ramsey-type two-field interaction. Furthermore, statistical properties of the maser field are investigated via a measurement of the statistics of the pump atoms that leave the maser cavity. Theoretical expressions for the time dependence of the Fano–Mandel parameter Q _A(t) are compared with the experimental data. We demonstrate, that metastability of the maser field and atomic interference strongly influence the approach to a steady-state value of Q _A(t).     

Optical bistability and multistability in an open ladder-type atomic system

A novel scheme is proposed for controlling the optical bistability and multistability in an atomic system. In an open ladder-type three-level atomic system, it is shown that, by adjusting the ratio between atomic injections and exit rates from the cavity, the intensity threshold of optical bistability can be controlled. The effect of incoherent pumping field and spontaneously generated coherence (SGC) on optical bistability for different values of exit rates is also discussed. It is found that SGC makes the medium phase dependent, so the optical bistability and multistability threshold can be controlled via relative phase between applied fields. Moreover, it is shown that the optical bistability can be switched to optical multistability, which is favorable for the next generation of all-optical systems and quantum networks.     

Population trapping in the Jaynes-Cummings model with a Kerr nonlinearity in the cavity

Abstract

An electromagnetic field state is found which maintains the population inversion of the atom stationary during the interaction with the field through a Jaynes-Cummings model (JCM) with a Kerr type nonlinearity in the cavity. The condition of stationarity of the population inversion includes the phase coupling of atomic dipole with the field. We have shown that the Kerr nonlinearity in the cavity field significantly modifies the photon statistics of the trapped field state through an intensity dependent detuning in the field compared to the normal JCM trapping state. We have also demonstrated the novel features of sub-Poissonian character and the squeezing of the trapped field state. The dynamics of the initial trapped field is studied in terms of squeezing and the Q-function.     

Observation of sub-kilohertz resonance in Rf-optical double resonance experiment in rare earth ions in solids

Abstract

We have observed kilohertz and sub-kilohertz resonance structures in RF-optical double resonance experiments of rare-earth-doped solids, when the frequency of the RF field is scanned across the hyperfine transitions while monitoring the resonant optical absorption of a CW laser. The effect is observed only when the laser spectral width is broad compared to the hyperfine structure. The observed line widths are apparently free of the inhomogeneous widths of hyperfine levels and the line shape has peculiar double peak structure. The effect is modelled with a resonance involving three atomic levels interacting with three electromagnetic fields, two optical and one RF, in a triangular or “delta’ configuration. While the ordinary optical-RF two-field resonance is limited by spin inhomogeneous width, the simultaneous excitation of three coupled transitions leads to narrow and highly nonlinear resonance structures that are not averaged by the inhomogeneous distribution of hyperfine transition.