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

Quasi-classical path integral approach to supersymmetric quantum mechanics

{}From Feynman's path integral, we derive quasi-classical quantization rules in supersymmetric quantum mechanics (SUSY-QM). First, we derive a SUSY counterpart of Gutzwiller's formula, from which we obtain the quantization rule of Comtet, Bandrauk and Campbell when SUSY is good. When SUSY is broken, we arrive at a new quantization formula, which is found as good as and even sometime better than the WKB formula in evaluating energy spectra for certain one-dimensional bound state problems. The wave functions in the stationary phase approximation are also derived for SUSY and broken SUSY cases. Insofar as a broken SUSY case is concerned, there are strong indications that the new quasi-classical approximation formula always overestimates the energy eigenvalues while WKB always underestimates.Comment: 13 pages + 5 figures, complete paper submitted as postscript file, to appear in Phys. Rev.

Single microwave-photon detector using an artificial Λ\Lambda-type three-level system

Single photon detection is a requisite technique in quantum-optics experiments in both the optical and the microwave domains. However, the energy of microwave quanta are four to five orders of magnitude less than their optical counterpart, making the efficient detection of single microwave photons extremely challenging. Here, we demonstrate the detection of a single microwave photon propagating through a waveguide. The detector is implemented with an "impedance-matched" artificial $\Lambda$ system comprising the dressed states of a driven superconducting qubit coupled to a microwave resonator. We attain a single-photon detection efficiency of $0.66 \pm 0.06$ with a reset time of $\sim 400$~ns. This detector can be exploited for various applications in quantum sensing, quantum communication and quantum information processing.Comment: 5 pages (4 figures) + 4 pages (5 figures

Power-dependent internal loss in Josephson bifurcation amplifiers

We have studied nonlinear superconducting resonators: lambda/2 coplanar-waveguide (CPW) resonators with Josephson junctions (JJs) placed in the middle and lambda/4 CPW resonators terminated by JJs, which can be used for the qubit readout as "bifurcation amplifiers." The nonlinearity of the resonators arises from the Josephson junctions, and because of the nonlinearity, the resonators with appropriate parameters are expected to show a hysteretic response to the frequency sweep, or "bifurcation," when they are driven with a sufficiently large power. We designed and fabricated resonators whose resonant frequencies were around 10 GHz. We characterized the resonators at low temperatures, T<0.05 K, and confirmed that they indeed exhibited hysteresis. The sizes of the hysteresis, however, are sometimes considerably smaller than the predictions based on the loaded quality factor in the weak drive regime. When the discrepancy appears, it is mostly explained by taking into account the internal loss, which often increases in our resonators with increasing drive power in the relevant power range. As a possible origin of the power-dependent loss, the quasiparticle channel of conductance of the JJs is discussed.Comment: 8 pages, 9 figure

On the Path Integral in Imaginary Lobachevsky Space

The path integral on the single-sheeted hyperboloid, i.e.\ in $D$-dimensional imaginary Lobachevsky space, is evaluated. A potential problem which we call ``Kepler-problem'', and the case of a constant magnetic field are also discussed.Comment: 16 pages, LATEX, DESY 93-14

Equation of Motion for a Spin Vortex and Geometric Force

The Hamiltonian equation of motion is studied for a vortex occuring in 2-dimensional Heisenberg ferromagnet of anisotropic type by starting with the effective action for the spin field formulated by the Bloch (or spin) coherent state. The resultant equation shows the existence of a geometric force that is analogous to the so-called Magnus force in superfluid. This specific force plays a significant role for a quantum dynamics for a single vortex, e.g, the determination of the bound state of the vortex trapped by a pinning force arising from the interaction of the vortex with an impurity.Comment: 13 pages, plain te

Path integral for a relativistic Aharonov-Bohm-Coulomb system

The path integral for the relativistic spinless Aharonov-Bohm-Coulomb system is solved, and the energy spectra are extracted from the resulting amplitude.Comment: 6 pages, Revte

Green's function for the Relativistic Coulomb System via Sum Over Perturbation Series

We evaluate the Green's function of the D-dimensional relativistic Coulomb system via sum over perturbation series which is obtained by expanding the exponential containing the potential term $V({\bf x)}$ in the path integral into a power series. The energy spectra and wave functions are extracted from the resulting amplitude.Comment: 13 pages, ReVTeX, no figure