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This paper

Exploring the unification of quantum theory and general relativity with a Bose-Einstein condensate

proposes using a BEC in a superposition of two locations to test gravitationally-induced quantum state reduction (read about that here and here). Section 3.1.5 discusses proposed experimental parameters: 4-40 billion Cesium atoms in each blob separated by 1-100 um to cause a collapse in 2 seconds.

How close are we to achieving these types BEC states?

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Nagerl's group at Innsbruck work with cesium BECs, and they reported condensates of approximately $10^5$ atoms in 2004, see https://link.springer.com/article/10.1007/s00340-004-1657-5. More recent work from Cornish's group at Durham give similar numbers. So it seems we are about 4 orders of magnitude away.

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  • $\begingroup$ That's a single collection of atoms too, not a spatially separated state, right? $\endgroup$ – psitae Jan 27 at 9:59
  • $\begingroup$ It's a single condensate, in a parabolic trap. So splitting the cloud in half, separating the halves, and making them spherical in shape, will be additional challenges! $\endgroup$ – Clara Diaz Sanchez Jan 27 at 10:13
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I had the pleasure of working with this group whilst conducting my masters dissertation over at Nottingham, really great people and I would definitely suggest getting in touch with Richard if you have questions.

As Clara's answer said, there have been some fantastic advancements in producing macroscopic BEC states with many atoms, but the proposal of Penrose [1] will require, as you said in your comments, something spatially separated and of the order of many atoms. What Richard and Ivette deduced in accordance with Penrose's ideas is that something more akin to macroscopic Schrodinger cat states [2] or N00N states [3] or the two-mode squeeze state [4] would be more appropriate, as these states are argued to have the quantum superposition that is important for Penrose's reduction interpretation. However, these kinds of states are proving very difficult to produce, even though there are suggestions as to how they can be produced [5]. As far as I am aware, there have been no reports of a N00N state with even a few atoms produced, never mind the ~$10^9$ required to test these ideas. I think we are some way away to be able to test QG in this sense; although just how double-well BEC's [6] will play into this may be interesting.

Ref: [1] Roger Penrose. "On the Gravitization of Quantum Mechanics 1: Quantum State Reduction". Foundations of Physics, Volume 44, Issue 5, pp 557–575 (2014).

[2] Diego A. R. Dalvit, Jacek Dziarmaga, and Wojciech H. Zurek. "Decoherence in Bose-Einstein condensates: Towards bigger and better Schrödinger cats". Phys. Rev. A 62, 013607 (2000).

[3] A. A. Bychek, D. N. Maksimov, and A. R.Kolovsky. “NOON state of Bose atoms in the double-wellpotential via an excited-state quantum phase transition”.Phys. Rev. A 97, 063624 (2017).

[4] V V Dodonov. “Nonclassical states in quantumoptics: a squeezed review of the first 75 years”. J. Opt.B: Quantum Semiclass. Opt. 4 R1R33 (2002).

[5] Seth T Merkel and Frank K Wilhelm. “Genera-tion and detection of NOON states in superconductingcircuits”. New J. Phys. 12 093036 (2010).

[6]Y. P. Huang and M. G. Moore. “Creation, detec-tion, and decoherence of macroscopic quantum superpo-sition states in double-well Bose-Einstein condensates”.Phys. Rev. A 73, 023606 (2006).

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  • $\begingroup$ Well, the paper suggests Cs and a certain number of atoms. We are positive that there are no better candidates? $\endgroup$ – user2679290 Jan 28 at 1:14

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