Quantum optical cavities

The main hardware types offered by physics are mentioned, namely trapped ions (or trapped atoms), quantum dots, quantum optical cavities, rf superconducting quantum interference devices (SQUIDs) and nitrogen-vacancy (NV) defects on diamond. Some are important simply as a benchmark to evaluate the quality of the implementations offered by chemistry, whereas others might be combined with lanthanide complexes to produce heterogeneous quantum information processors which combine the advantages of different hardware types. 

Photons in quantum optical cavities also constitute excellent qubit candidates [52]. Resonant coupling of atoms with a single mode of the radiation field was experimentally achieved 25 years ago [53], and eventually the coherent coupling of quantum optical cavities with atoms or (simple) molecules was suggested as a means to achieve stable quantum memories in a hybrid quantum processor [54]. There might be a role to play for molecular spin qubits in this kind of hybrid quantum devices that combine solid-state with flying qubits. 

An optical microcavity produced by the latter process has been applied to tune the emission from erbium-doped PS [Zh6], Erbium compounds like Er203 are known to exhibit a narrow emission band at 1.54 pm, which is useful for optical telecommunications. Several methods have been used to incorporate erbium in PS. A simple and economical way is cathodic electrochemical doping. External quantum efficiencies of up to 0.01% have been shown from erbium-doped PS films under electrical excitation [Lo2]. The emission band, however, is much broader than observed for Er203. This drawback can be circumvented by the use of an optical cavity formed by PS multilayers. In this case the band is narrowed and the intensity is increased because emission is only allowed into optical cavity modes [Lo3]. 

We perform concrete calculations in the complex P-representation [Drummond 1980 McNeil 1983] in the frame of both probability distribution functions and stochastic equations for the complex c-number variables. We follow the standard procedures of quantum optics to eliminate the reservoir operators and to obtain a master equation for the density operator of the modes. The master equation is then transformed into a Fokker-Planck equation for the P-quasiprobability distribution function. In particular, for an ordinary NOPO and in the case of high cavity losses for the pump mode (73 7), if in the operational regime the pump depletion effects are involved, this approach yields... 

Quantum errors. A quantum computer can never be regarded as perfectly isolated in all the experimental setups which have been considered (optical photon, optical cavity quantum electrodynamics, ion traps, NMR,... 

In this section we discuss problems that could be involved in any attempt to detect an internal entangled state of two coupled atoms in free space. Beige et al. [34] have proposed a scheme, based on the quantum Zeno effect, to observe a decoherence-free state in a system of two 3-level atoms located inside an optical cavity. Here, we discuss possible schemes to detect entangled states of two 2-level atoms in free space. 

The branch of quantum optics studying the processes of interaction of one or a few atoms with the quantized cavity modes is usually called cavity quantum electrodynamics (cavity QED). The theoretical concepts of cavity QED are based in the first place on investigation of the Jaynes-Cummings model [67] and its generalizations (for a review, see Ref. 68). The reason for this is that the model describes fairly well the physical processes under consideration and at the same time admits an exact solution. 

R.H. Johnson, Characteristics of acousto-optic cavity dumping in a mode-locked laser. IEEE J. Quantum Electron. 9, 255 (1973)... 

General Motors Research Laboratories (GMR). Molecular beam epitaxial (MBE) growth of Pbi xEuxSeyTei y lattice-matched to PbTe substrates has been used to fabricate double heterojunction diode lasers, including quantum well, large optical cavity (LOG) devices, the first such TDL structures reported for a lead-salt compound. These Mesa stripe... 

Savage, C. M., Marksteiner, S., and Zoller, P. (1993). Atomic waveguides and cavities from hollow optical fibres. In Fundamental of quantum optics (ed. F. Ehlotzky), vol. 3. pp. 60-74. Springer, Berlin. 

In this chapter we summarize basic concepts of lasers with regard to their applications in spectroscopy. A well-founded knowledge of some subjects in laser physics, such as passive and active optical cavities and their mode spectra, amplification of light and saturation phenomena, mode competition and the frequency spectrum of laser emission, will help the reader to gain a deeper understanding of many problems in laser spectroscopy and to achieve optimum performance of an experimental setup. A more detailed treatment of laser physics and an extensive discussion of various types of lasers can be found in textbooks on lasers (see, for instance, [1.1-3, 5.1-4]). For more advanced presentations based on a quantum mechanical description of lasers, the reader is referred to [1.4,5, 5.5-7]. 

The time evolution of such a system is described by a 2 °x2 °matrix This demonstrates the complexity of quantum mechanical time evolution. At the same time it becomes clear that quantum systems have - due to the fact that they describe the evolution of all possible states simultaneously - a sort of inner parallelism . Therefore, they will be an ideal medium for real parallel computations as soon as the dynamical behaviour of the quantum states can be controlled in isolation from the rest of the world (with which an interaction is only needed if one wants to read out the result). New experimental possibilities for realizing quantum computers, ranging from neutral atoms interacting with microwaves over optical cavities and nuclear spins to trapped ions, offer most promising perspectives [15]. The chapters by Tino Gramss and Thomas Pellizzari on the Theory of Quantum Computation and First Steps Towards a Realization of Quantum Computers, respectively, will introduce the reader to recent developments in this exciting field. 

In Sect. 6.6 a proposal to implementing a QC based on optical cavity quantum electrodynamics is described (Pellizzari et al. 1995). The scheme is similar to the ion trap QC in the sense that the atomic quantum bits are resting in a trap. However, quantum communication is provided by photons instead of phonons. 

Fig. 6.11 A quantum computer proposal in the context of optical cavity quantum electrodynamics. Atoms or ions are used to represent the qubits and are trapped within two mirrors so as to communicate with each other by photon exchange. The qubits have to be addressed individually by laser beams.

Fig. 6.13 Schematic representation of the experimental setup to perform quantum logic with photonic qubits. Two optical photons with different colors intersect with a beam of atoms. The interaction with the atoms is enhanced by a high-finesse optical cavity. Further downstream the photons are analyzed.

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