Anomalous Quantum Reflection of Bose-Einstein Condensates from a Silicon Surface: The Role of Dynamical Excitations

R. G. Scott, A. M. Martin, T. M. Fromhold, and F. W. Sheard

Phys. Rev. Lett. 95, 073201 – Published 11 August 2005

Abstract

We investigate the effect of interatomic interactions on the quantum-mechanical reflection of Bose-Einstein condensates from regions of rapid potential variation. The reflection process depends critically on the density and incident velocity of the condensate. For low densities and high velocities, the atom cloud has almost the same form before and after reflection. Conversely, at high densities and low velocities, the reflection process generates solitons and vortex rings that fragment the condensate. We show that this fragmentation can explain the anomalously low reflection probabilities recently measured for low-velocity condensates incident on a silicon surface.

Received 14 December 2004

DOI:https://doi.org/10.1103/PhysRevLett.95.073201

Authors & Affiliations

R. G. Scott¹, A. M. Martin², T. M. Fromhold¹, and F. W. Sheard¹

¹School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
²School of Physics, University of Melbourne, Parkville, Victoria 3010, Australia

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Vol. 95, Iss. 7 — 12 August 2005

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Images

Figure 1
Solid curves: schematic representations of $V_{I} (x)$ (a), $V_{II} (x)$ (b), and $V_{III} (x)$ (c). Dot-dashed curves: the potential energy of the harmonic trap, shown as a function of $x$ , immediately after the trap displacement. Shaded areas in (a)–(c) represent the initial atom density profile $| Ψ (x, 0, 0) |^{2}$ . Dashed line in (c) shows the imaginary potential used to model the adsorption of Na atoms on the Si surface.Reuse & Permissions
Figure 2
Gray-scale plots of atom density ( $black = high$ ) in the $x − r$ plane (axes inset) for a BEC with $n_{0} = 2.2 \times 10^{12} {cm}^{- 3}$ , $ω_{x} (ω_{r}) = 2 π \times 3.3 (2 π \times 4.5) rad s^{- 1}$ and $v_{x} \approx 1.2 mm s^{- 1}$ , reflecting from potential I, shown at $t = 0 ms$ (a), 90 ms (b), 122 ms (c), and 143 ms (d). The phase of the BEC wave function within the dashed box in (d) is shown in the gray-scale plot ( $white = 0$ , $black = 2 π$ ) to the right of the density profile. Horizontal bar shows scale.Reuse & Permissions
Figure 3
Gray-scale plots of atom density ( $black = high$ ) in the $x − r$ plane (axes inset) for a BEC with $n_{0} = 2.2 \times 10^{12} {cm}^{- 3}$ , $ω_{x} (ω_{r}) = 2 π \times 3.3 (2 π \times 4.5) rad s^{- 1}$ , and $v_{x} \approx 1.2 mm s^{- 1}$ (a), $2.1 mm s^{- 1}$ (b), reflecting from potential I, shown at $t = 150 ms$ . (c),(d) Same as (a),(b), but for potential II. (e),(f) Same as (a),(b), but for potential III. Horizontal bar shows scale. Arrows in (a),(c), and (e) indicate the direction of quantized circulation around vortex cores.Reuse & Permissions
Figure 4
Solid curves: $R (v_{x})$ for potential III, calculated from the entire reflected atom cloud with (squares) and without (crosses) interatomic interactions. Dotted curve with circles: $R (v_{x})$ calculated with interatomic interactions, but omitting regions of the atom cloud where $| Ψ |^{2} \leq 0.25$ $n_{0}$ . For the solid and dotted curves, $n_{0} = 2.2 \times 10^{12} {cm}^{- 3}$ and $ω_{x} (ω_{r}) = 2 π \times 3.3 (2 π \times 4.5) rad s^{- 1}$ . Dot-dashed curve with triangles: as dotted curve with circles, but for a BEC with $n_{0} = 3.6 \times 10^{12} {cm}^{- 3}$ . Inset: data points (squares) show $\ln (v_{p})$ vs $\ln (n_{0})$ , where $v_{p}$ is the position of the peak in $R (v_{x})$ curves calculated omitting regions where $| Ψ |^{2} \leq 0.25$ $n_{0}$ , and dashed line is least squares fit.Reuse & Permissions
Figure 5
Gray-scale plots of atom density ( $black = high$ ) in the $x − r$ plane (axes inset) for a BEC with $n_{0} = 2.2 \times 10^{12} {cm}^{- 3}$ , $ω_{x} (ω_{r}) = 2 π (2 π \times 4.5) rad s^{- 1}$ , and $v_{x} \approx 2.1 mm s^{- 1}$ , reflecting from potential III, shown at $t = 0 ms$ (a), 270 ms (b), and 460 ms (c). Horizontal bar shows scale. Arrows in (c) enclose a vortex ring.Reuse & Permissions

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