We obtain a master equation for a parametrically driven optomechanical cavity. We use a more correct dissipation model that accounts for the modification of the quasienergy spectrum caused by the driving. When the natural frequency of the mechanical object oscillates periodically around its mean value, the master equation with the improved dissipation model is expressed using Floquet operators. We apply the corresponding master equation to model the laser cooling of the mechanical object. Using an adiabatic approximation, an analytical expression for the number of excitations of the mechanical oscillator can be obtained. We find that the number of excitations can be lower than in the non-time-dependent case. Our results raise the possibility of achieving lower temperatures for the mechanical object if its natural frequency can be controlled as a function of time.

We present a closed-form analytical solution to the eigenvalue problem of the Liouville operator generating the dissipative dynamics of the standard optomechanical system.The corresponding Lindblad master equation describes the dynamics of a single-mode field inside an optical cavity coupled by radiation pressure to its moving mirror.The optical field and the mirror are in contact with separate environments, which are assumed at zero and finite temperature, respectively.The optomechanical damping basis refers to the exact set of eigenvectors of the generator that, together with the exact eigenvalues, are explicitly derived.Both the weak-and the strong-coupling regime, which includes combined decay mechanisms, are solved in this work.

Quantum networks require flying qubits that transfer information between the nodes. This may be implemented by means of single atoms (the nodes) that emit and absorb single photons (the flying qubits) and requires full control of photon absorption and emission by the individual emitters. In this paper, we theoretically characterize the wave packet of a photon emitted by a single atom undergoing a spontaneous Raman transition in a three-level scheme. We investigate several excitation schemes that are experimentally relevant and discuss control parameters that allow one to tailor the spectrum of the emitted photon wave packet.

We investigate a single laser driven atom trapped in a non-harmonic potential. We present the performance of ground-state laser cooling and Doppler cooling and the signatures of the center-of-mass motion in the power spectrum of the scattered light. In order to illustrate the results we provide two explicit examples for the confining potential: the infinite square well and the Morse potential.

We theoretically analyse the cooling dynamics of a high-Q mode of a mechanical resonator, when the structure is also an optical cavity and is coupled with a NV center. The NV center is driven by a laser and interacts with the cavity photon field and with the strain field of the mechanical oscillator, while radiation pressure couples mechanical resonator and cavity field. Starting from the full master equation we derive the rate equation for the mechanical resonator's motion, whose coefficients depend on the system parameters and on the noise sources. We then determine the cooling regime, the cooling rate, the asymptotic temperatures, and the spectrum of resonance fluorescence for experimentally relevant parameter regimes. For these parameters, we consider an electronic transition, whose linewidth allows one to perform sideband cooling, and show that the addition of an optical cavity in general does not improve the cooling efficiency. We further show that pure dephasing of the NV center's electronic transitions can lead to an improvement of the cooling efficiency.

In a hybrid optomechanical setup consisting of a two-level atom in a cavity with a pendular end mirror, the interplay between the light field's radiation pressure on the mirror and the dipole interaction with the atom can lead to an effect, which manifests itself in the suppression of Rabi oscillations of the atomic population. This effect is present when the system is in the single-photon strong-coupling regime and has an analogy in the photon blockade of optomechanics.

We theoretically study the laser cooling of cavity optomechanics when the mechanical resonance frequency and damping depend on time. In the regime of weak optomechanical coupling we extend the theory of laser cooling using an adiabatic approximation. We discuss the modifications of the cooling dynamics and compare it with numerical simulations in a wide range of modulation frequencies.

We demonstrate cooling of the motion of a single neutral atom confined by a dipole trap inside a high-finesse optical resonator. Cooling of the vibrational motion results from electromagnetically induced transparency (EIT)-like interference in an atomic Lambda-type configuration, where one transition is strongly coupled to the cavity mode and the other is driven by an external control laser. Good qualitative agreement with the theoretical predictions is found for the explored parameter ranges. Further, we demonstrate EIT cooling of atoms in the dipole trap in free space, reaching the ground state of axial motion. By means of a direct comparison with the cooling inside the resonator, the role of the cavity becomes evident by an additional cooling resonance. These results pave the way towards a controlled interaction among atomic, photonic, and mechanical degrees of freedom.

We provide an elementary description of the dynamics of defect centers in crystals in terms of a quantum optical master equation which includes spontaneous decay and a simplified vibronic interaction with lattice phonons. We present the general solution of the dynamical equation by means of the eigensystem of the Liouville operator and exemplify the usage of this damping basis to calculate the dynamics of the electronic and vibrational degrees of freedom and to provide an analysis of the spectra of scattered light. The dynamics and spectral features are discussed with respect to the applicability for color centers, especially for negatively charged nitrogen-vacancy centers in diamond.

We theoretically analyze the cooling dynamics of an atom which is tightly trapped inside a high-finesse optical resonator. Cooling is achieved by suitably tailored scattering processes, in which the atomic dipole transition either scatters a cavity photon into the electromagnetic field external to the resonator, or performs a stimulated emission into the cavity mode, which then dissipates via the cavity mirrors. We identify the parameter regimes in which the atom center-of-mass motion can be cooled into the ground state of the external trap. We predict, in particular, that for high cooperativities interference effects mediated by the atomic transition may lead to higher efficiencies. The dynamics is compared with the cooling dynamics of a trapped atom inside a resonator studied in [Phys. Rev. Lett. 95, 143001, (2005)] where the atom, instead of the cavity, is driven by a laser field.

We demonstrate cooling of the motion of a single atom confined by a dipole trap inside a high-finesse optical resonator. Cooling of the vibrational motion results from EIT-like interference in an atomic Λ-type configuration, where one transition is strongly coupled to the cavity mode and the other is driven by an external control laser. Good qualitative agreement with the theoretical predictions is found for the explored parameter ranges. The role of the cavity in the cooling dynamics is confirmed by means of a direct comparison with EIT-cooling performed in the dipole trap in free space. These results set the basis to the realization of an efficient photonic interface based on single atoms.

A cooling scheme for trapped atoms is proposed, which combines cavity-enhanced scattering and electromagnetically induced transparency. The cooling dynamics exploits a three-photon resonance, which combines laser and cavity excitations. It is shown that relatively fast ground-state cooling can be achieved in the Lamb-Dicke regime and for large cooperativity. Efficient ground-state cooling is found for parameters of ongoing experiments.

We theoretically analyze the light scattering of an optomechanical cavity which strongly interacts with a single two-level system and couples simultaneously to a mechanical oscillator by radiation forces. The analysis is based on the assumptions that the system is driven at low intensity, and that the mechanical interaction is sufficiently weak, permitting a perturbative treatment. We find quantum interference in the scattering paths, which allows to suppress the Stokes-component of the scattered light. This effect can be exploited to reduce the motional energy of the mechanical oscillator.

We theoretically study the occurrence of quantum jumps in the resonance fluorescence of a trapped atom. Here, the atom is laser cooled in a configuration of level such that the occurrence of a quantum jump is associated to a change of the vibrational center-of-mass motion by one phonon. The statistics of the occurrence of the dark fluorescence period is studied as a function of the physical parameters and the corresponding features in the spectrum of resonance fluorescence are identified. We discuss the information which can be extracted on the atomic motion from the observation of a quantum jump in the considered setup.

We theoretically study the occurrence of quantum jumps in the resonance fluorescence of a trapped atom. Here, the atom is laser cooled in a configuration of level such that the occurrence of a quantum jump is associated to a change of the vibrational center-of-mass motion by one phonon. The statistics of the occurrence of the dark fluorescence period is studied as a function of the physical parameters and the corresponding features in the spectrum of resonance fluorescence are identified. We discuss the information which can be extracted on the atomic motion from the observation of a quantum jump in the considered setup.

We derive an imaging budget from the performance of EUV optics with NA = 0.32, and demonstrate that the 22nm node requirements are met. Based on aerial image simulations, we analyze the impact of all relevant contributors, ranging from conventional quantities, like straylight or aberrations, to EUV-specific topics, namely influence of 3D mask effects and facetted illumination pupils. As test structures we consider dense to isolated lines, contact holes, and 2D elbows. We classify the contributions in a hierarchical order according to their weight in the CDU budget and identify the main drivers. The underlying physical mechanisms causing different contributions to be critical or less significant are clarified. Finally, we give an outlook for the 16nm and 11nm nodes. Future developments in optics manufacturing will keep the budgets controlled, thereby paving the way to enable printing of these upcoming nodes.

We derive an imaging budget from the performance of extreme ultraviolet (EUV) optics with NA = 0.32, and demonstrate that the requirements for 22-nm applications are met. Based on aerial image simulations, we analyze the impact of all relevant contributors, ranging from conventional quantities like straylight or aberrations, to EUV-specific topics, namely the influence of 3-D mask effects and faceted illumination pupils. As test structures we consider dense to isolated lines, contact holes, and 2-D elbows. We classify the contributions in a hierarchical order according to their weight in the critical dimension uniformity (CDU) budget and identify the main drivers. The underlying physical mechanisms causing different contributions to be critical or less significant are clarified. Finally, we give an outlook for the 16- and 11-nm nodes. Future developments in optics manufacturing will keep the budgets controlled, thereby paving the way to enable printing of these up-coming nodes. (C) 2009 Society of Photo-Optical Instrumentation Engineers. [DOI: 10.1117/1.3238543]

We study the spectra of emission of a system composed by an atom, tightly confined inside a high-finesse resonator, when the atom is driven by a laser and is at steady state of the cooling dynamics induced by laser and cavity fields. In general, the spectrum of resonance fluorescence and the spectrum at the cavity output contain complementary information about the dynamics undergone by the system. In certain parameter regimes, quantum interference effects between the scattering processes induced by cavity and laser fields lead to the selective suppression of features of the resonance fluorescence spectrum, which are otherwise visible in the spectrum of laser-cooled atoms in free space.