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arXiv:1301.0494 · Journal of Plasma Physics

Toward quantum gravity measurement by cold atoms

MARCILIO M. DOS SANTOS, TEODORA ONIGA, ANDREW S. MCLEMAN, MARTIN CALDWELL, CHARLES H.-T. WANG

Published Feb 22, 2013• 17 citations
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Abstract

Abstract We propose an experiment for the measurement of gravitational effect on cold atoms by applying a one-dimensional vertically sinusoidal oscillation to the magneto-optical trap, and observe the signature of low quantum energy shift of quantum-bound states as a consequence of gravitational fluctuation. To this end, we present brief details of the experiment on a Bose–Einstein condensate (BEC), and a simplistic calculation of the Gross–Pitaevskii solution using the Thomas–Fermi approximation with focus on the density of the BEC for the time-dependent perturbation. Moreover, we calculate the power induced by quantum gravity on a generic atomic ensemble. We also address the possible challenges for the measurement of the expected results. Finally, we discuss the prospect of further developing this experiment toward measuring the effect of quantum spacetime fluctuations on cold atoms.

DOI
10.1017/s0022377813000202

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Abstract We propose an experiment for the measurement of gravitational effect on cold atoms by applying a one-dimensional vertically sinusoidal oscillation to the magneto-optical trap, and observe the signature of low quantum energy shift of quantum-bound states as a consequence of gravitational fluctuation. To this end, we present brief details of the experiment on a Bose–Einstein condensate (BEC), and a simplistic calculation of the Gross–Pitaevskii solution using the Thomas–Fermi approximation with focus on the density of the BEC for the time-dependent perturbation. Moreover, we calculate the power induced by quantum gravity on a generic atomic ensemble. We also address the possible challenges for the measurement of the expected results. Finally, we discuss the prospect of further developing this experiment toward measuring the effect of quantum spacetime fluctuations on cold atoms.
A description of the dynamical response of uniformly trapped Bose–Einstein condensates (BECs) to oscillating external gravitational fields is developed, with the inclusion of damping. Two different effects that can lead to the creation of phonons in the BEC are identified; direct driving and parametric driving. Additionally, the oscillating gravitational field couples phonon modes, which can lead to the transition of excitations between modes. The special case of the gravitational field of a small, oscillating sphere located closely to the BEC is considered. It is shown that measurement of the effects may be possible for oscillating source masses down to the milligram scale, with a signal to noise ratio of the order of 10. To this end, noise terms and variations of experimental parameters are discussed and generic experimental parameters are given for specific atom species. The results of this article suggest the utility of BECs as sensors for the gravitational field of very small oscillating objects which may help pave the way towards gravity experiments with masses in the quantum regime.
We have studied the ground state energy of one-dimensional macroscopic quantum oscillator by adding gravity term as a time-independent external potential. The macroscopic quantum oscillator itself is based on discussion about Gross-Pitaevskii equation (GPE) describing Bose-Einstein condensate in anisotropic parabolic trap. That gravitational potential displaces the symmetry axis of Bose-Einstein condensation (BEC) with respect to symmetry axis of magnetic field that creates trapping potential of the Bose-Einstein condensate (BECs) in research on atomic lasers. Since the Gross-Pitaevskii equation can be treated as macroscopic quantum oscillator, we use time-independent perturbation theory as in ordinary quantum mechanics to find the ground state energy correction by assuming that other terms are very small. We also formulate the appropriate coefficients of expansion in the solution of one-dimensional GPE by considering the characteristics of harmonic oscillator eigenfunctions and find that the existence of the gravity can only be included if the higher coefficients are considered. Keywords: Gravitational potential, Gross-Pitaevskii, Quantum Oscillator.
We explore the effect of mutual gravitational interaction between ultra-cold gas atoms on the dynamics of Bose-Einstein condensates (BEC). Small amplitude oscillation of BEC is studied by applying variational technique to reduce the Gross-Pitaevskii equation, with gravity included, to the equation of motion of a particle moving in a potential. According to our analysis, if the s-wave scattering length can be tuned to zero using Feshbach resonance for future BEC with occupation numbers as high as ≈1020\approx 10^{20}≈1020, there exists a critical ground state occupation number above which the BEC is unstable, provided that its constituents interact with a $1/r^3 $ gravity at short scales.
We explore the effect of mutual gravitational interaction between ultra-cold gas atoms on the dynamics of Bose-Einstein condensates (BEC). Small amplitude oscillation of BEC is studied by applying variational technique to reduce the Gross-Pitaevskii equation, with gravity included, to the equation of motion of a particle moving in a potential. According to our analysis, if the s-wave scattering length can be tuned to zero using Feshbach resonance for future BEC with occupation numbers as high as ≈1020\approx 10^{20}≈1020, there exists a critical ground state occupation number above which the BEC is unstable, provided that its constituents interact with a $1/r^3 $ gravity at short scales.
We explore the effect of mutual gravitational interaction between ultra-cold gas atoms on the dynamics of Bose-Einstein condensates (BEC). Small-amplitude oscillation of BEC is studied by applying variational technique to reduce the Gross-Pitaevskii equation, with gravity included, to the equation of motion of a particle moving in a potential. According to our analysis, if the s-wave scattering length can be tuned to zero using Feshbach resonance for future BEC with occupation numbers as high as ≈10 20 , there exists a critical ground state occupation number above which the BEC is unstable, provided that its constituents interact with a 1/r 3 gravity at short scales.
Abstract We study both static and dynamic properties of a weakly interacting Bose–Einstein condensate (BEC) in a quasi one-dimensional gravito-optical surface trap, where the downward pull of gravity is compensated by the exponentially decaying potential of an evanescent wave. First, we work out approximate solutions of the Gross–Pitaevskii equation for both a small number of atoms using a Gaussian ansatz and a larger number of atoms using the Thomas–Fermi limit. Then we confirm the accuracy of these analytical solutions by comparing them to numerical results. From there, we numerically analyze how the BEC cloud expands non-ballistically, when the confining evanescent laser beam is shut off, showing agreement between our theoretical and previous experimental results. Furthermore, we analyze how the BEC cloud expands non-ballistically due to gravity after switching off the evanescent laser field in the presence of a hard-wall mirror which we model by using a blue-detuned far-off-resonant sheet of light. There we find that the BEC shows significant self-interference patterns for a large number of atoms, whereas for a small number of atoms, a revival of the BEC wave packet with few matter-wave interference patterns is observed.