Breakdown of the few-level approximation in collective systems

The validity of the few-level approximation in dipole-dipole interacting collective systems is discussed. As example system, we study the archetype case of two dipole-dipole interacting atoms, each modelled by two complete sets of angular momentum multiplets. We establish the breakdown of the few-level approximation by first proving the intuitive result that the dipole-dipole induced energy shifts between collective two-atom states depend on the length of the vector connecting the atoms, but not on its orientation, if complete and degenerate multiplets are considered. A careful analysis of our findings reveals that the simplification of the atomic level scheme by artificially omitting Zeeman sublevels in a few-level approximation generally leads to incorrect predictions. We find that this breakdown can be traced back to the dipole-dipole coupling of transitions with orthogonal dipole moments. Our interpretation enables us to identify special geometries in which partial few-level approximations to two- or three-level systems are valid

Lifetimes of Confined Acoustic Phonons in Ultra-Thin Silicon Membranes

We study the relaxation of coherent acoustic phonon modes with frequencies up to 500 GHz in ultra-thin free-standing silicon membranes. Using an ultrafast pump-probe technique of asynchronous optical sampling, we observe that the decay time of the first-order dilatational mode decreases significantly from \sim 4.7 ns to 5 ps with decreasing membrane thickness from \sim 194 to 8 nm. The experimental results are compared with theories considering both intrinsic phonon-phonon interactions and extrinsic surface roughness scattering including a wavelength-dependent specularity. Our results provide insight to understand some of the limits of nanomechanical resonators and thermal transport in nanostructures

Electronic interactions in fullerene spheres

The electron-phonon and Coulomb interactions inC$_{60}$, and larger fullerene spheres are analyzed. The coupling between electrons and intramolecular vibrations give corrections $\sim 1 - 10$ meV to the electronic energies for C$_{60}$, and scales as $R^{-4}$ in larger molecules. The energies associated with electrostatic interactions are of order $\sim 1 - 4$ eV, in C$_{60}$ and scale as $R^{-1}$. Charged fullerenes show enhanced electron-phonon coupling, $\sim 10$ meV, which scales as $R^{-2}$. Finally, it is argued that non only C$_{60}^{-}$, but also C$_{60}^{--}$ are highly polarizable molecules. The polarizabilities scale as $R^3$ and $R^4$, respectively. The role of this large polarizability in mediating intermolecular interactions is also discussed.Comment: 12 pages. No figure

Spectral structure and decompositions of optical states, and their applications

We discuss the spectral structure and decomposition of multi-photon states. Ordinarily `multi-photon states' and `Fock states' are regarded as synonymous. However, when the spectral degrees of freedom are included this is not the case, and the class of `multi-photon' states is much broader than the class of `Fock' states. We discuss the criteria for a state to be considered a Fock state. We then address the decomposition of general multi-photon states into bases of orthogonal eigenmodes, building on existing multi-mode theory, and introduce an occupation number representation that provides an elegant description of such states that in many situations simplifies calculations. Finally we apply this technique to several example situations, which are highly relevant for state of the art experiments. These include Hong-Ou-Mandel interference, spectral filtering, finite bandwidth photo-detection, homodyne detection and the conditional preparation of Schr\"odinger Kitten and Fock states. Our techniques allow for very simple descriptions of each of these examples.Comment: 12 page

Reflective Journaling: A Theoretical Model and Digital Prototype for Developing Resilience and Creativity

Reflection is commonly discussed as a tool for personal and professional development that is becoming increasingly important in today’s global and digital world. In this paper, we propose a model that suggests ways in which reflection, in the form of Reflective Journaling, can support the development of creativity and resilience, which are needed to enable individuals to function effectively in a fast-changing environment. In addition, the model proposes ways in which external support and progress monitoring can be used in conjunction with skills in adaptive resilience and structured creativity, to support the maintenance of reflective journaling as a habit, in the longer term, thus creating virtuous cycles of skills and behaviours that can reinforce each other. Based on our model, and additional user research, we describe the design of a first digital prototype that aims to support the use of Reflective Journaling and to develop creativity and resilience through suggested mechanisms. Initial evaluations of our prototype are positive. It has been well-received by early test users, and has the potential to address all the connections defined. We therefore suggest that the theoretical model can be used to develop digital tools, such as the one included, to help those who wish to develop the habit of reflective journaling, and through that a range of other skills associated with resilience and creative thinking. We see this as a starting point for investigating this potential in more depth

Signatures of exciton coupling in paired nanoemitters

An exciton formed by the delocalized electronic excitation of paired nanoemitters is interpreted in terms of the electromagnetic emission of the pair and their mutual coupling with a photodetector. A formulation directly tailored for fluorescence detection is identified, giving results which are strongly dependent on geometry and selection rules. Signature symmetric and antisymmetric combinations are analyzed and their distinctive features identified

Quantum control of proximal spins using nanoscale magnetic resonance imaging

Quantum control of individual spins in condensed matter systems is an emerging field with wide-ranging applications in spintronics, quantum computation, and sensitive magnetometry. Recent experiments have demonstrated the ability to address and manipulate single electron spins through either optical or electrical techniques. However, it is a challenge to extend individual spin control to nanoscale multi-electron systems, as individual spins are often irresolvable with existing methods. Here we demonstrate that coherent individual spin control can be achieved with few-nm resolution for proximal electron spins by performing single-spin magnetic resonance imaging (MRI), which is realized via a scanning magnetic field gradient that is both strong enough to achieve nanometric spatial resolution and sufficiently stable for coherent spin manipulations. We apply this scanning field-gradient MRI technique to electronic spins in nitrogen-vacancy (NV) centers in diamond and achieve nanometric resolution in imaging, characterization, and manipulation of individual spins. For NV centers, our results in individual spin control demonstrate an improvement of nearly two orders of magnitude in spatial resolution compared to conventional optical diffraction-limited techniques. This scanning-field-gradient microscope enables a wide range of applications including materials characterization, spin entanglement, and nanoscale magnetometry.Comment: 7 pages, 4 figure

Photon Statistics; Nonlinear Spectroscopy of Single Quantum Systems

A unified description of multitime correlation functions, nonlinear response functions, and quantum measurements is developed using a common generating function which allows a direct comparison of their information content. A general formal expression for photon counting statistics from single quantum objects is derived in terms of Liouville space correlation functions of the material system by making a single assumption that spontaneous emission is described by a master equation