Bound states of guided matter waves: An atom and a charged wire

Hau, Lene Vestergaard; Burns, Michael M.; Golovchenko, Jene Andrew

doi:10.1103/physreva.45.6468

Cited by 48 publications

(37 citation statements)

References 11 publications

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“…Attractive inverse square potentials occur physically as effective radial potentials between a charged wire and a polarizable neutral atom [30], the strength factor being proportional to the square of the linear charge density of the wire and thus controllable [30,31,32]. Combined with a repulsive centrifugal term, an arbitrary α/r 2 potential may be implemented.…”

Section: Discussionmentioning

confidence: 99%

“…Combined with a repulsive centrifugal term, an arbitrary α/r 2 potential may be implemented. In addition, it is possible to modify the inner region and implement a potential minimum by a time varying sinusoidal voltage in the high frequency limit [32], or by replacing the wire by a charged optical fiber with blue detuned light propagating along the fiber and the cladding removed [31]. Decay experiments with cold atoms showing exponential laws have been performed [30], and the ability to modify the potential parameters makes the observation and study of the long-time power-law in these systems a realistic prospect.…”

Section: Discussionmentioning

confidence: 99%

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Long-time deviations from exponential decay for inverse-square potentials

2008

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Quantal systems are predicted to show a change-over from exponential decay to power law decay at very long times. Although most theoretical studies predict integer power-law exponents, recent measurements by Rothe et al. of decay luminescence of organic molecules in solution {Phys. Rev. Lett. 96 (2006) 163601} found non-integer exponents in most cases. We propose a physical mechanism, within the realm of scattering from potentials with long tails, which produces a continuous range of power law exponents. In the tractable case of the repulsive inverse square potential, we demonstrate a simple relation between the strength of the long range tail and the power law exponent. This system is amenable to experimental scrutiny.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Long-time deviations from exponential decay for inverse-square potentials

2008

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“…Experimentally, the system should be immediately realizable for 25 p, K sodium atoms around a wire with a diameter of 0.5 p, m and a current of 400 p, A. can exist around a sinusoidally driven charged wire [2].…”

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confidence: 99%

Supersymmetry and the Binding of a Magnetic Atom to a Filamentary Current

Hau¹,

Golovchenko²,

Burns³

1995

Phys. Rev. Lett.

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“…Ge, 31.10.+z, Research activities in atomic and molecular physics [1, 2] is speeding up due to the advancement of laser cooling technique [3,4,5,6]. Substantial amount of people are engaged in devising suitable confining mechanism [7,8,9,10] for cold atoms and molecules so that it can be stored at a temperature down to nano-Kelvin. Among different schemes for trapping and storing cold atoms; magnetic trap, dipole trap, optical trap etc are important.…”

mentioning

confidence: 99%

“…Substantial amount of people are engaged in devising suitable confining mechanism [7,8,9,10] for cold atoms and molecules so that it can be stored at a temperature down to nano-Kelvin. Among different schemes for trapping and storing cold atoms; magnetic trap, dipole trap, optical trap etc are important.…”

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confidence: 99%

Atom Capture by Nanotube and Scaling Anomaly

Giri

2007

Int J Theor Phys

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The existence of bound state of the polarizable neutral atom in the inverse square potential created by the electric field of a single walled charged carbon nanotube (SWNT) is shown to be theoretically possible. The consideration of inequivalent boundary conditions due to self-adjoint extensions lead to this nontrivial bound state solution. It is also shown that the scaling anomaly is responsible for the existence of such bound state. Binding of the polarizable atoms in the coupling constant interval η 2 ∈ [0, 1) may be responsible for the smearing of the edge of steps in quantized conductance, which has not been considered so far in the literature.PACS numbers: 03.65. Ge, 31.10.+z, Research activities in atomic and molecular physics [1, 2] is speeding up due to the advancement of laser cooling technique [3,4,5,6]. Substantial amount of people are engaged in devising suitable confining mechanism [7,8,9,10] for cold atoms and molecules so that it can be stored at a temperature down to nano-Kelvin. Among different schemes for trapping and storing cold atoms; magnetic trap, dipole trap, optical trap etc are important. Present day technology is well equipped to handle atoms and molecules at nano-Kelvin temperature. Study of different properties of these super cold neutral atoms or molecules in electric or magnetic fields, created by charged wire [11,12], current carrying conductor or by some other mechanism is now feasible.Quantized conductance(QC) [1] is one such important property, which is usually seen when atoms are moving in the neighborhood of a charged nanotube. QC is basically discrete quantum steps in the cross section for atom capture versus voltage of the thin wire. Since the steps result from the angular momentum quantization in the attractive inverse square potential experienced by the atom, it is also called "angular momentum quantum ladder". The edge of the steps are not infinitely sharp but a little bit smeared out [1]. This exotic behavior is usually attributed to the tunneling of the neutral atoms through the inverse square potential (η 2 − 1/4)/r 2 and happens near the value η = 0 of the coupling constant. This conclusion is based on the usual boundary condition that the wave-function is zero at the singularity. But we need further quantum mechanical investigation, because the peculiar nature of the inverse square potential in the interval η ∈ [0, 1) may give rise to bound state due to a nontrivial boundary condition which is known for a long time in mathematical physics.Quantum mechanical behavior of the inverse square potential is subtle [13] in the sense that it lies between 1/r n>2 and 1/r n<2 . It should be noted that for n > 2 usually there can not be any bound states and for n < 2 the potential is capable of forming bound states. Usually * Electronic address: pulakranjan.giri@saha.ac.in a particle moving in inverse square potential does not form bound state or more specifically the system has negative infinite ground state in the region η 2 < 0 [14, 15]. It is however possible to form a sin...

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Bound states of guided matter waves: An atom and a charged wire

Cited by 48 publications

References 11 publications

Long-time deviations from exponential decay for inverse-square potentials

Long-time deviations from exponential decay for inverse-square potentials

Supersymmetry and the Binding of a Magnetic Atom to a Filamentary Current

Atom Capture by Nanotube and Scaling Anomaly

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