Entanglement Rate for Gaussian Continuous Variable Beams

We derive a general expression that quantifies the total entanglement production rate in continuous variable systems, where a source emits two entangled Gaussian beams with arbitrary correlators.This expression is especially useful for situations where the source emits an arbitrary frequency spectrum,e.g. when cavities are involved. To exemplify its meaning and potential, we apply it to a four-mode optomechanical setup that enables the simultaneous up- and down-conversion of photons from a drive laser into entangled photon pairs. This setup is efficient in that both the drive and the optomechanical up- and down-conversion can be fully resonant.Comment: 18 pages, 6 figure

Pattern phase diagram for 2D arrays of coupled limit-cycle oscillators

Arrays of coupled limit-cycle oscillators represent a paradigmatic example for studying synchronization and pattern formation. They are also of direct relevance in the context of currently emerging experiments on nano- and optomechanical oscillator arrays. We find that the full dynamical equations for the phase dynamics of such an array go beyond previously studied Kuramoto-type equations. We analyze the evolution of the phase field in a two-dimensional array and obtain a "phase diagram" for the resulting stationary and non-stationary patterns. The possible observation in optomechanical arrays is discussed briefly

Geometric phases in astigmatic optical modes of arbitrary order

The transverse spatial structure of a paraxial beam of light is fully characterized by a set of parameters that vary only slowly under free propagation. They specify bosonic ladder operators that connect modes of different order, in analogy to the ladder operators connecting harmonic-oscillator wave functions. The parameter spaces underlying sets of higher-order modes are isomorphic to the parameter space of the ladder operators. We study the geometry of this space and the geometric phase that arises from it. This phase constitutes the ultimate generalization of the Gouy phase in paraxial wave optics. It reduces to the ordinary Gouy phase and the geometric phase of non-astigmatic optical modes with orbital angular momentum states in limiting cases. We briefly discuss the well-known analogy between geometric phases and the Aharonov-Bohm effect, which provides some complementary insights in the geometric nature and origin of the generalized Gouy phase shift. Our method also applies to the quantum-mechanical description of wave packets. It allows for obtaining complete sets of normalized solutions of the Schr\"odinger equation. Cyclic transformations of such wave packets give rise to a phase shift, which has a geometric interpretation in terms of the other degrees of freedom involved.Comment: final versio

Rotationally induced vortices in optical cavity modes

We show that vortices appear in the modes of an astigmatic optical cavity when it is put into rotation about its optical axis. We study the properties of these vortices and discuss numerical results for a specific realization of such a set-up. Our method is exact up to first order in the time-dependent paraxial approximation and involves bosonic ladder operators in the spirit of the quantum-mechanical harmonic oscillator.Comment: 8 pages, 5 figures. Accepted for publication in a special issue (singular optics 2008) of Journal of Optics A: Pure and Applied Optic

Single-photon nonlinearities in two-mode optomechanics

We present a detailed theoretical analysis of a weakly driven, multimode optomechanical system, in which two optical modes are strongly and near-resonantly coupled to a single mechanical mode via a three-wave mixing interaction. We calculate one- and two-time intensity correlations of the two optical fields and compare them to analogous correlations in atom-cavity systems. Nonclassical photon correlations arise when the optomechanical coupling g exceeds the cavity decay rate κ, and we discuss signatures of one- and two-photon resonances as well as quantum interference. We also find a long-lived correlation that decays slowly with the mechanical decay rate γ, reflecting the heralded preparation of a single-phonon state after detection of a photon. Our results provide insight into the quantum regime of multimode optomechanics, with potential applications for quantum information processing with photons and phonons.Physic

Rotational stabilization and destabilization of an optical cavity

We investigate the effects of rotation about the axis of an astigmatic two-mirror cavity on its optical properties. This simple geometry is the first example of an optical system that can be destabilized and, more surprisingly, stabilized by rotation. As such, it has some similarity with both the Paul trap and the gyroscope. We illustrate the effects of rotational (de)stabilization of a cavity in terms of the spatial structure and orbital angular momentum of its modes.Comment: 5 pages, 3 figures. Accepted for publication in Physical Review

A probabilistic deep learning model of inter-fraction anatomical variations in radiotherapy

In radiotherapy, the internal movement of organs between treatment sessions causes errors in the final radiation dose delivery. Motion models can be used to simulate motion patterns and assess anatomical robustness before delivery. Traditionally, such models are based on principal component analysis (PCA) and are either patient-specific (requiring several scans per patient) or population-based, applying the same deformations to all patients. We present a hybrid approach which, based on population data, allows to predict patient-specific inter-fraction variations for an individual patient. We propose a deep learning probabilistic framework that generates deformation vector fields (DVFs) warping a patient's planning computed tomography (CT) into possible patient-specific anatomies. This daily anatomy model (DAM) uses few random variables capturing groups of correlated movements. Given a new planning CT, DAM estimates the joint distribution over the variables, with each sample from the distribution corresponding to a different deformation. We train our model using dataset of 312 CT pairs from 38 prostate cancer patients. For 2 additional patients (22 CTs), we compute the contour overlap between real and generated images, and compare the sampled and ground truth distributions of volume and center of mass changes. With a DICE score of 0.86 and a distance between prostate contours of 1.09 mm, DAM matches and improves upon PCA-based models. The distribution overlap further indicates that DAM's sampled movements match the range and frequency of clinically observed daily changes on repeat CTs. Conditioned only on a planning CT and contours of a new patient without any pre-processing, DAM can accurately predict CTs seen during following treatment sessions, which can be used for anatomically robust treatment planning and robustness evaluation against inter-fraction anatomical changes

Robustness analysis of CTV and OAR dose in clinical PBS-PT of neuro-oncological tumors:prescription-dose calibration and inter-patient variation with the Dutch proton robustness evaluation protocol

Objective:The Dutch proton robustness evaluation protocol prescribes the dose of the clinical target volume (CTV) to the voxel-wise minimum (VWmin) dose of 28 scenarios. This results in a consistent but conservative near-minimum CTV dose (D98%,CTV). In this study, we analyzed (i) the correlation between VWmin/voxel-wise maximum (VWmax) metrics and actually delivered dose to the CTV and organs at risk (OARs) under the impact of treatment errors, and (ii) the performance of the protocol before and after its calibration with adequate prescription-dose levels.Approach. Twenty-one neuro-oncological patients were included. Polynomial chaos expansion was applied to perform a probabilistic robustness evaluation using 100,000 complete fractionated treatments per patient. Patient-specific scenario distributions of clinically relevant dosimetric parameters for the CTV and OARs were determined and compared to clinical VWmin and VWmax dose metrics for different scenario subsets used in the robustness evaluation protocol.Main results. The inclusion of more geometrical scenarios leads to a significant increase of the conservativism of the protocol in terms of clinical VWmin and VWmax values for the CTV and OARs. The protocol could be calibrated using VWmin dose evaluation levels of 93.0%-92.3%, depending on the scenario subset selected. Despite this calibration of the protocol, robustness recipes for proton therapy showed remaining differences and an increased sensitivity to geometrical random errors compared to photon-based margin recipes.Significance. The Dutch proton robustness evaluation protocol, combined with the photon-based margin recipe, could be calibrated with a VWmin evaluation dose level of 92.5%. However, it shows limitations in predicting robustness in dose, especially for the near-maximum dose metrics to OARs. Consistent robustness recipes could improve proton treatment planning to calibrate residual differences from photon-based assumptions.</p

Cochlear-optimized treatment planning in photon and proton radiosurgery for vestibular schwannoma patients

Objective: To investigate the potential to reduce the cochlear dose with robotic photon radiosurgery or intensity-modulated proton therapy planning for vestibular schwannomas. Materials and Methods: Clinically delivered photon radiosurgery treatment plans were compared to five cochlear-optimized plans: one photon and four proton plans (total of 120). A 1x12 Gy dose was prescribed. Photon plans were generated with Precision (Cyberknife, Accuray) with no PTV margin for set-up errors. Proton plans were generated using an in-house automated multi-criterial planning system with three or nine-beam arrangements, and applying 0 or 3 mm robustness for set-up errors during plan optimization and evaluation (and 3 % range robustness). The sample size was calculated based on a reduction of cochlear Dmean &gt; 1.5 Gy(RBE) from the clinical plans, and resulted in 24 patients. Results: Compared to the clinical photon plans, a reduction of cochlear Dmean &gt; 1.5 Gy(RBE) could be achieved in 11/24 cochlear-optimized photon plans, 4/24 and 6/24 cochlear-optimized proton plans without set-up robustness for three and nine-beam arrangement, respectively, and in 0/24 proton plans with set-up robustness. The cochlea could best be spared in cases with a distance between tumor and cochlea. Using nine proton beams resulted in a reduced dose to most organs at risk. Conclusion: Cochlear dose reduction is possible in vestibular schwannoma radiosurgery while maintaining tumor coverage, especially when the tumor is not adjacent to the cochlea. With current set-up robustness, proton therapy is capable of providing lower dose to organs at risk located distant to the tumor, but not for organs adjacent to it. Consequently, photon plans provided better cochlear sparing than proton plans.</p