Bent waveguides for matter-waves: supersymmetric potentials and reflectionless geometries

Non-zero curvature in a waveguide leads to the appearance of an attractive quantum potential which crucially affects the dynamics in matter-wave circuits. Using methods of supersymmetric quantum mechanics, pairs of bent waveguides are found whose geometry-induced potentials share the same scattering properties. As a result, reflectionless waveguides, dual to the straight waveguide, are identified. Strictly isospectral waveguides are also found by modulating the depth of the trapping potential. Numerical simulations are used to demonstrate the efficiency of these approaches in tailoring and controlling curvature-induced quantum-mechanical effects.

[1]  W. Talbot.  Facts relating to optical science , 1836 .

[2]  J. Pritchard,et al.  Demonstration of an inductively coupled ring trap for cold atoms , 2012, 1207.4225.

[3]  Jakob Reichel,et al.  Atom chips. , 2005, Scientific American.

[4]  Exact propagators for SUSY partners , 2007, math-ph/0702088.

[5]  L. Gendenshtein.  Derivation of Exact Spectra of the Schrodinger Equation by Means of Supersymmetry , 1984 .

[6]  Interference of a Bose-Einstein condensate in a hard-wall trap: from nonlinear Talbot effect to formation of vorticity , 1999, cond-mat/9908095.

[7]  Stefan Nolte,et al.  Supersymmetric mode converters , 2014, Nature Communications.

[8]  Maier,et al.  Controlling cold atoms using nanofabricated surfaces: atom chips , 1999, Physical review letters.

[9]  Eric J. Heller.  Guided Gaussian Wave Packets , 2006 .

[10]  Mark Bashkansky,et al.  Cold-atom confinement in an all-optical dark ring trap , 2007, 0802.1213.

[11]  W. Phillips,et al.  Driving phase slips in a superfluid atom circuit with a rotating weak link. , 2012, Physical review letters.

[12]  W. Schleich,et al.  Bound states in sharply bent waveguides: analytical and experimental approach. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  A. Khare,et al.  Supersymmetry, Shape Invariance and Exactly Solvable Potentials , 1988 .

[14]  E. Switkes,et al.  Kinetic energy and path curvature in bound state systems , 1977 .

[15]  A. Tünnermann,et al.  Geometric potential and transport in photonic topological crystals. , 2010, Physical review letters.

[16]  H. Friedrich,et al.  Working with WKB waves far from the semiclassical limit , 2004 .

[17]  C. MacCormick,et al.  Experimental demonstration of painting arbitrary and dynamic potentials for Bose–Einstein condensates , 2009, 0902.2171.

[18]  A. Shabat.  The infinite-dimensional dressing dynamical system , 1992 .

[19]  B. M. Fulk.  MATH , 1992 .

[20]  J. Danzl,et al.  Demonstration of the temporal matter-wave Talbot effect for trapped matter waves , 2011, 1105.0295.

[21]  Matthias Heinrich,et al.  Supersymmetric optical structures. , 2013, Physical review letters.

[22]  Petr Šeba,et al.  Bound states in curved quantum waveguides , 1989 .

[23]  Conductance of the elliptically shaped quantum wire , 2001, cond-mat/0512110.

[24]  P. Leboeuf,et al.  Bose-Einstein beams: Coherent propagation through a guide , 2001 .

[25]  C. Sukumar.  Supersymmetry, potentials with bound states at arbitrary energies and multi-soliton configurations , 1986 .

[26]  C. Foot,et al.  A ring trap for ultracold atoms in an RF-dressed state , 2008 .

[27]  D. Guéry-Odelin,et al.  A quasi-monomode guided atom laser from an all-optical Bose-Einstein condensate , 2008, 0802.2601.

[28]  Edward Witten,et al.  Dynamical Breaking of Supersymmetry , 1981 .

[29]  Horst Conrad,et al.  Trapping Molecules on a Chip , 2009, Science.

[30]  D. R. Scherer,et al.  Vortex formation by merging of multiple trapped Bose-Einstein condensates. , 2007, Physical review letters.

[31]  A. Aspect,et al.  Quantum reflection: atomic matter-wave optics in an attractive exponential potential , 1996 .

[32]  C. Monroe,et al.  Architecture for a large-scale ion-trap quantum computer , 2002, Nature.

[33]  Irene Marzoli,et al.  Quantum carpets, carpets of light , 2001 .

[34]  R. C. T. da Costa,et al.  Quantum mechanics of a constrained particle , 1981 .

[35]  J. Goldstone,et al.  Bound states in twisting tubes. , 1992, Physical review. B, Condensed matter.

[36]  C. Ryu,et al.  Experimental realization of Josephson junctions for an atom SQUID. , 2013, Physical review letters.

[37]  Hammond,et al.  Near-field imaging of atom diffraction gratings: The atomic Talbot effect. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[38]  Irene Marzoli,et al.  Quantum carpets woven by Wigner functions , 2000 .

[39]  M. Kasevich,et al.  Microwave guiding of electrons on a chip. , 2010, Physical review letters.

[40]  M. Berry.  Quantum fractals in boxes , 1996 .

[41]  V. Vuletić,et al.  Atom Chips: REICHEL:ATOM CHIPS O-BK , 2011 .

[42]  Alexander L. Gaunt,et al.  Robust Digital Holography For Ultracold Atom Trapping , 2011, Scientific Reports.

[43]  S. Schwartz,et al.  One-dimensional description of a Bose–Einstein condensate in a rotating closed-loop waveguide , 2006, cond-mat/0606262.

[44]  A. Aspect,et al.  Guided quasicontinuous atom laser. , 2006, Physical review letters.

[45]  Stefan Nolte,et al.  Realization of reflectionless potentials in photonic lattices. , 2011, Physical review letters.

[46]  Robert P. Smith,et al.  Quantized supercurrent decay in an annular Bose-Einstein condensate , 2011, 1112.0334.

[47]  D. Picca.  Constraints in quantum mechanics , 1982 .

[48]  S Gupta,et al.  Bose-Einstein condensation in a circular waveguide. , 2005, Physical review letters.

[49]  Daniel J Heinzen,et al.  1.5% root-mean-square flat-intensity laser beam formed using a binary-amplitude spatial light modulator. , 2009, Applied optics.

[50]  On the number of particles that a curved quantum waveguide can bind , 1998, math/9801021.

[51]  D. Struik.  Lectures on classical differential geometry , 1951 .

[52]  A. Bracken,et al.  Effective potentials of quantum strip waveguides and their dependence upon torsion , 1996 .

[53]  Avinash Khare,et al.  Supersymmetry and quantum mechanics , 1995 .