Supersymmetric quantum mechanics based on higher excited states

We generalize the formalism and the techniques of the supersymmetric (susy) quantum mechanics to the cases where the superpotential is generated/defined by higher excited eigenstates. The generalization is technically almost straightforward but physically quite nontrivial since it yields an infinity of new classes of susy-partner potentials, whose spectra are exactly identical except for the lowest m+1 states, if the superpotential is defined in terms of the (m+1)-st eigenfunction, with m=0 reserved for the ground state. It is shown that in case of the infinite 1-dim potential well nothing new emerges (the partner potential is still of P\"oschl-Teller type I, for all m), whilst in case of the 1-dim harmonic oscillator we get a new class of infinitely many partner potentials: for each m the partner potential is expressed as the sum of the quadratic harmonic potential plus rational function, defined as the derivative of the ratio of two consecutive Hermite polynomials. These partner potentials of course have m singularities exactly at the locations of the nodes of the generating (m+1)-st wavefunction. The susy formalism applies everywhere between the singularities. A systematic application of the formalism to other potentials with known spectra would yield an infinitely rich class of "solvable" potentials, in terms of their partner potentials. If the potentials are shape invariant they can be solved at least partially and new types of analytically obtainable spectra are expected. PACS numbers: 03.65.-w, 03.65.Ge, 03.65.SqComment: 15 pages LaTeX file, no figures, submitted to J. Phys. A: accepted for publication

Chip-based microcavities coupled to NV centers in single crystal diamond

Optical coupling of nitrogen vacancy centers in single-crystal diamond to an on-chip microcavity is demonstrated. The microcavity is fabricated from a hybrid gallium phosphide and diamond material system, and supports whispering gallery mode resonances with spectrometer resolution limited Q > 25000

Quantum Optics with Surface Plasmons

We describe a technique that enables strong, coherent coupling between individual optical emitters and guided plasmon excitations in conducting nano-structures at optical frequencies. We show that under realistic conditions, optical emission can be almost entirely directed into the plasmon modes. As an example, we describe an application of this technique involving efficient generation of single photons on demand, in which the plasmon is efficiently out-coupled to a dielectric waveguide.Comment: 11 pages, 3 figure

Adjusted indices of multiple deprivation to enable comparisons within and between constituent countries of the UK including an illustration using mortality rates

OBJECTIVES: Social determinants can have a major impact on health and as a consequence substantial inequalities are seen between and within countries. The study of inequalities between countries relies on having accurate and consistent measures of deprivation across the country borders. However, in the UK most socioeconomic deprivation measures are not comparable between countries. We give a method of adjusting the Indices of Multiple Deprivation (IMD) for use across the UK, describe the deprivation of each UK country, and show the problems introduced by naïvely using country-specific deprivation measures in a UK-wide analysis of mortality rates. SETTING/PARTICIPANTS: 42 148 geographic areas covering the population of the UK. OUTCOME MEASURES: Adjusted IMD scores based on the income and employment domains of country-specific IMD scores, adjusting for the contribution of other domains. The mortality rate among people aged under 75 years standardised to the UK age structure was compared between country-specific and UK-adjusted IMD quintiles. RESULTS: Of the constituent countries of the UK, Northern Ireland was the most deprived with 37% of the population living in areas in the most deprived fifth of the UK, followed by Wales with 22% of the population living in the most deprived fifth of the UK. England and Scotland had similar levels of deprivation. Deprivation-specific mortality rates were similar in England and Wales. Northern Ireland had lower mortality rates than England for each deprivation group, with similar differences for each group. Scotland had higher mortality rates than England for each deprivation group, with larger differences for more deprived groups. CONCLUSIONS: Analyses of between-country and within-country inequalities by socioeconomic position should use consistent measures; failing to use consistent measures may give misleading results. The published adjusted IMD scores we describe allow consistent analysis across the UK

Optical loss and lasing characteristics of high-quality-factor AlGaAs microdisk resonators with embedded quantum dots

Optical characterization of AlGaAs microdisk resonant cavities with a quantum dot active region is presented. Direct passive measurement of the optical loss within AlGaAs microdisk resonant structures embedded with InAs/InGaAs dots-in-a-well (DWELL) is performed using an optical-fiber-based probing technique at a wavelength (lambda~1400 nm) that is red-detuned from the dot emission wavelength (lambda~1200 nm). Measurements in the 1400 nm wavelength band on microdisks of diameter D = 4.5 microns show that these structures support modes with cold-cavity quality factors as high as 360,000. DWELL-containing microdisks are then studied through optical pumping at room temperature. Pulsed lasing at lambda ~ 1200 nm is seen for cavities containing a single layer of InAs dots, with threshold values of ~ 17 microWatts, approaching the estimated material transparency level. Room-temperature continuous wave operation is also observed.Comment: 4 pages, 3 figure

Properties of implanted and CVD incorporated nitrogen-vacancy centers: preferential charge state and preferential orientation

The combination of the long electron state spin coherence time and the optical coupling of the ground electronic states to an excited state manifold makes the nitrogen-vacancy (NV) center in diamond an attractive candidate for quantum information processing. To date the best spin and optical properties have been found in centers deep within the diamond crystal. For useful devices it will be necessary to engineer NVs with similar properties close to the diamond surface. We report on properties including charge state control and preferential orientation for near surface NVs formed either in CVD growth or through implantation and annealing

Observation of the dynamic Jahn-Teller effect in the excited states of nitrogen-vacancy centers in diamond

The optical transition linewidth and emission polarization of single nitrogen-vacancy (NV) centers are measured from 5 K to room temperature. Inter-excited state population relaxation is shown to broaden the zero-phonon line and both the relaxation and linewidth are found to follow a T^5 dependence for T up to 100 K. This dependence indicates that the dynamic Jahn-Teller effect is the dominant dephasing mechanism for the NV optical transitions at low temperatures

Low-temperature tapered-fiber probing of diamond NV ensembles coupled to GaP microcavities

In this work we present a platform for testing the device performance of a cavity-emitter system, using an ensemble of emitters and a tapered optical fiber. This method provides high-contrast spectra of the cavity modes, selective detection of emitters coupled to the cavity, and an estimate of the device performance in the single- emitter case. Using nitrogen-vacancy (NV) centers in diamond and a GaP optical microcavity, we are able to tune the cavity onto the NV resonance at 10 K, couple the cavity-coupled emission to a tapered fiber, and measure the fiber-coupled NV spontaneous emission decay. Theoretically we show that the fiber-coupled average Purcell factor is 2-3 times greater than that of free-space collection; although due to ensemble averaging it is still a factor of 3 less than the Purcell factor of a single, ideally placed center.Comment: 15 pages, 6 figure