One-dimensional Optical Cavity Research Articles

Bistable behavior of a two-mode Bose–Einstein condensate in an optical cavity

We consider a two-component Bose–Einstein condensate in a one-dimensional optical cavity. Specifically, the condensate atoms are taken to be in two degenerate modes due to their internal hyperfine spin degrees of freedom and they are coupled to the cavity field and an external transverse laser field in a Raman scheme. A parallel laser also excites the cavity mode. When the pump laser is far detuned from its resonance atomic transition frequency, an effective nonlinear optical model of the cavity–condensate system is developed under the discrete mode approximation (DMA), while matter–field coupling has been considered beyond the rotating wave approximation. By analytical and numerical solutions of the nonlinear dynamical equations, we examine the mean cavity field and population difference (magnetization) of the condensate modes. The stationary solutions of both the mean cavity field and normalized magnetization demonstrate bistable behavior under certain conditions for the laser pump intensity and matter–field coupling strength.

Faraday-rotation spectrum of electron spins in microcavity-embedded GaAs quantum wells

Using the time-resolved magneto-optical Faraday effect, the dynamics of electron spins is measured in a GaAs quantum well embedded in a vertical one-dimensional optical cavity. The cavity leads to an enhancement of the Faraday-rotation amplitude that varies with the detuning between the QW absorption peak and the cavity resonance. We find a transition in the Faraday rotation spectrum that is triggered by the cavity detuning. This is attributed to a modification of the phase of the cavity reflectivity at the impedance-matching condition of the cavity. If the QW absorption is too small to compensate the asymmetry of the cavity mirrors, the Faraday-rotation signal is dominated by spin-induced circular birefringence, whereas contributions from circular dichroism predominate for higher quantum-well absorption. A numerical calculation of the Faraday-rotation spectrum is in good agreement with the experimental results.

Theory of short optical cavity with dielectric multilayer film mirrors

A theory for a one-dimensional optical cavity with multi-layer dielectric film mirrors is developed by the matrix method, where normalized orthogonal mode functions with a continuous spectrum are derived both inside and outside the cavity, and the field is quantized with them. The theory provides an exact means to study the mode characteristics of, and hence the spontaneous emission in a short optical cavity with mirrors of finite thickness. On the basis of this theory, we study in detail a short optical cavity with a length of half-wavelength and mirrors of quarter-wavelength single-layer dielectric film. The result shows that the resonant frequency is slightly different from that in a cavity of the same cavity length and the same mirror reflectivity but with two δ-function like mirrors. Furthermore, with the derived mode functions the spontaneous emission from a two-level atom in such a cavity is analyzed under a perturbation approximation, and the result shows that the spontaneous emission in the cavity is enhanced by the cavity quality factor Q when the atom is at the antinode and is inhibited by the factor 1/ Q when the atom is at the node.

Quantum theory of spontaneous emission in a one-dimensional optical cavity with two-side output coupling.

A quantum theory of spontaneous emission from an initially excited two-level atom in a one-dimensional optical cavity with output coupling from both sides is developed. Orthonormal mode functions with a continuous spectrum are employed, which are derived by imposing a periodic boundary condition on the whole space with a period much larger than the cavity length. The delay differential equation of the atomic state of Cook and Milonni [Phys. Rev. A 35, 5081 (1987)] is re-derived in a strict manner, where the reflectivity of the cavity mirrors is included naturally in the mode functions. An approximate solution at a single-resonant-mode limit shows the results of ``vacuum'' Rabi oscillation in an underdamped cavity and enhanced spontaneous emission rate in an overdamped cavity. For the latter case, it is found that in the optical range the spontaneous emission rate is enhanced by a factor F (finesse of the cavity).

Optical cavity with absorptive medium and output coupling

The normal modes of a one-dimensional optical cavity having an absorptive medium plus output coupling are investigated. It is shown that these two line-broadening mechanisms lead to a set of collective modes, each one having a Lorentzian line shape whose linewidth is not simply a sum of the contributions of absorption and outcoupling. The application of these collective modes in a laser theory using this lossy cavity is mentioned.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Quantum theory of a one-dimensional optical cavity with output coupling. V. Spontaneous emission

For pt.IV see J. Phys. Soc. Japan, vol.47, p.217-224 (1982). Spontaneous emission in a lossy one-dimensional cavity is analyzed under the perturbation approximation and the Wigner-Weisskopf approximation. The cavity loss due to output coupling is treated quantum mechanically by the use of a set of continuously distributed radiation modes. The enhancement and reduction factors in the spontaneous emission probability due to the presence of the cavity structure are derived. Interesting transients in spontaneous emission during a time of the order of the cavity decay time are predicted, which leads to an interpretation of the enhancement or the reduction in spontaneous emission in terms of feedback and self-interference effects. The detection of the emitted photon by a detector atom outside the cavity is also discussed. >

Quantum theory of a one-dimensional laser with output coupling: Linear approximation

A simple model of a one-dimensional optical cavity having output coupling is used to develop a fully quantized linear laser theory. The present model and procedure, which work directly within the continuous spectrum, allow us to find a simple treatment that leads to explicit solutions for the field inside and outside the laser cavity. The threshold condition for laser light onset is obtained by assuming the field operating in a single collective mode and the usual adiabatic hypothesis. A development that removes this later restriction is also discussed and outlined.

Quantum theory of a one-dimensional optical cavity with output coupling. III. Cavity quasimodes as the field eigenvalue

The quantum theory is developed for an arbitrarily stratified one-dimensional optical cavity which transmits light at one of its end The field is expanded in terms of the modes of the universe and each universal mode is quantized separately by means of the usual method. A class of coherent states which yields oscillation wave shapes of the cavity quasimodes as the field eigenvalue is studied. A state of this class gives an eigenvalue for the annihilation operator of a universal mode which is an analytic function of the mode frequency except for a mode-dependent phase factor. The mathematical meaning of the phase factor is studied. A new scheme of field quantization is developed which absorbs the above phase factor and yields simpler forms of the eigenvalue equations for the above class of states. For a state of the class, the local intensity, its fluctuation, and the various correlations of the field decay with time. For the local field inside or outside of an optical structure which is coupled to the free space, the almost definite phase relationship among the universal modes plays a decisive role.

Quantum Theory of a One-Dimensional Optical Cavity with Output Coupling. IV. The Fluctuation-Dissipation Theorem in an Arbitrarily Stratified Structure

Chaotic fields in a general class of one-dimensional optical cavity having output coupling is considered. The fluctuation-dissipation theorem is derived assuming that the cavity materials are lossless. The cavity admittance probed by a prescribed current source for an arbitrarily stratified optical cavity is calculated and using the explicit expression for the admittance the “dissipation” is proved to be equal to the radiation loss. The form of the fluctuation-dissipation theorem for a restricted frequency region around a cavity mode is discussed with particular attention to the cavity mode degeneracy.

Quantum theory of a one-dimensional optical cavity with output coupling. II. Thermal radiation field and the fluctuation-dissipation theorem

The normally ordered correlation function and the power spectrum (cross spectral tensor) of a thermal radiation field existing inside and outside a one-dimensional optical cavity which transmits radiation at one of its end surfaces are calculated on the basis of a multimode formulation of the field developed in a previous paper. The correlation function is found to consist of a series of trigamma functions resulting from retarded correlations due to reflections at the cavity end surfaces. The power spectrum is a product of the Planck distribution and the mode functions of the universe which have a periodic factor with the period being equal to the cavity mode separation. For the purpose of obtaining a description of the cavity which allows one to deduce its thermal noise property, a form of fluctuation-dissipation theorem is derived which connects, in a one-dimensional space with arbitrary structure, the normally ordered correlation function with the admittance for the electric field probed by a current. Application of this theorem to the model cavity leads to an explicit and simultaneous description of the fluctuation and dissipation associated with all the cavity modes. The dissipation is shown to be due to radiation of electromagnetic energy into the free space. The above relation is reduced, under the assumption of high cavity quality factor and of single-cavity-mode selection, to that of a Markovian noise associated with a single decay constant. The consistency of these results with the field commutation relation is examined.

Quantum theory of a one-dimensional optical cavity with output coupling. Field quantization

The quantum theory of a one-dimensional optical cavity is developed with emphasis on the presence of output coupling. First the resonant mode is defined and calculated classically. Then the field is decomposed into a sequence of modes by introducing an imaginary boundary at a large distance. The mode functions are proved to be orthogonal with respect to an integration with the dielectric constant as a weighting factor. The Hamiltonian of the field is shown to be equivalent to that of a collection of independent harmonic oscillators, the mass of which is a function of the frequency of oscillation. This equivalent of mass appears on normalizing the mode functions and proves to carry information on the structure of the cavity. Quantization of the field is carried out, and the commutation relation for the electric fields inside and outside the cavity is derived. The commutator is composed of an infinite set of derivatives of $\ensuremath{\delta}$ functions, which discloses the effect of the presence of output coupling and that of the small size of the cavity on the radiation field. Also, the commutator is shown to have some properties common with the classical resonant mode, i.e., the property of exponential decay and its rate.