Atomic doughnuts from single photons

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by James K. Thompson from Nature 519, 420–422 (26 March 2015), doi:10.1038/519420b


Analysis of the interaction between a photon and an ensemble of some 3,000 atoms trapped between two mirrors has revealed a form of multi-atom quantum entanglement that has no counterpart in classical mechanics.


Read also: Entanglement with negative Wigner function of almost 3,000 atoms heralded by one photon


What is the most that could happen when you analyse a single particle of light after sending it through a few thousand atoms? McConnell et al.(1) demonstrate that the single photon creates a special quantum link between nearly all of the atoms, a link known as entanglement. The authors show that the particular ‘flavour’ of entanglement observed has no classical analogue — a first for such a large collection of atoms. Extending our ability to create entanglement in large systems may one day allow highly precise measurements of time, fields and accelerations, lead to new materials, and enhance our understanding of the transition from the quantum to the classical world.
In the quantum world, the act of measurement can profoundly change the state of the object being measured. McConnell and colleagues exploited this fundamental principle to create entanglement between almost 3,000 atoms that are laser-cooled to only a few ten-millionths of a degree above absolute zero. The atoms were levitated between two highly reflecting, weakly transmitting mirrors. Each of the atoms can be thought of as possessing an arrow, which corresponds to the orientation of the atom’s total quantum spin. All the arrows add up to make one big arrow that initially points in some direction, call it x, which lies on the equator of a sphere.
A weak pulse of light is injected through one of the mirrors and then detected after it leaks back out of the other mirror. The light also has an arrow attached to it, denoting its polarization (the direction of the light’s electric field). As the light bounces back and forth between the mirrors, it passes roughly 5,000 times through the atoms, each time being partially absorbed and then re-emitted back into the original pulse of photons (Fig. 1a).

a, Vertically polarized photons (red) pass many times through atoms (blue) as the photons bounce back and forth between highly reflecting, weakly transmitting mirrors. The polarization of a photon is only very occasionally rotated to horizontal owing to quantum noise (uncertainty) in the quantum-spin orientation of the atomic arrows. Only horizontally polarized photons generate a click on a detector. b, The quantum probability distribution of the orientation of the total atomic arrow is represented by a region (purple disk) at the tip of an arrow on the equator of a sphere. McConnell et al.1 show that detecting just one horizontal photon (click!) changes this distribution to a 'two-dimensional doughnut', which has a positive outer region (purple) and a negative inner region (yellow) — a hallmark of quantum entanglement between the atoms. The negative-probability filling means that, no matter how the doughnut is rotated about its axis, the probability of measuring the arrow on the equator is zero.

a, Vertically polarized photons (red) pass many times through atoms (blue) as the photons bounce back and forth between highly reflecting, weakly transmitting mirrors. The polarization of a photon is only very occasionally rotated to horizontal owing to quantum noise (uncertainty) in the quantum-spin orientation of the atomic arrows. Only horizontally polarized photons generate a click on a detector. b, The quantum probability distribution of the orientation of the total atomic arrow is represented by a region (purple disk) at the tip of an arrow on the equator of a sphere. McConnell et al.(1) show that detecting just one horizontal photon (click!) changes this distribution to a ‘two-dimensional doughnut’, which has a positive outer region (purple) and a negative inner region (yellow) — a hallmark of quantum entanglement between the atoms. The negative-probability filling means that, no matter how the doughnut is rotated about its axis, the probability of measuring the arrow on the equator is zero.

If the total atomic arrow were pointing slightly north or slightly south of the x direction, because of quantum Heisenberg uncertainty in its orientation (Fig 1b.), then the polarization of the light would be slightly rotated clockwise or anticlockwise, respectively, when it was re-emitted. For each pulse of light sent through the mirrors, McConnell et al. checked to see whether they detected any rotated light. On most trials, they did not detect even one rotated photon.
Failing was no problem. They just tried again until they finally detected that a single photon had been rotated. This told the experimenters that, on that particular trial, the total atomic arrow was not quite on the equator, but must have been pointing slightly north or south of x. The researchers verified that the arrow was no longer at the equator by making a second and much more precise measurement of the total atomic arrow’s north–south orientation.
The measurement apparatus fundamentally could not tell whether the polarization rotation of the single detected photon was clockwise or anticlockwise. With no further information, one would expect the measurement of a single photon to collapse the total atomic arrow into a quantum superposition state in which the arrow was simultaneously both north and south of the equator.
But confirming with the precise measurement that the total atomic arrow does not lie on the equator was not sufficient to establish the superposition nature of the quantum state(2). To do this, the authors also performed experiments in which, after detecting the rotated photon, they then rotated the total atomic arrow about the x direction by various amounts. They then made the precise north–south measurement. As predicted for a simultaneous north and south state, they observed a much lower probability that the arrow would be found on the equator than is possible for a classical arrow that is either just north or just south of the equator.
By measuring at different rotation angles, McConnell et al. determined the Wigner function — a quantum probability distribution of the direction in which the total atomic arrow points. The Wigner function looked like a two-dimensional doughnut centred on the x axis (Fig. 1b), but rather than simply having an empty hole of zero probability at its centre, the centre of this doughnut had negative probability. This negative probability was a clear sign that the measurement of a single rotated photon collapsed the atoms into an entangled state. This is the first time that a negative Wigner function has been observed for such a large collection of atoms.
Several experiments have created entanglement between atoms using many photons to measure the north–south orientation of the total atomic arrow(3), producing large amounts of ‘quantum squeezing’(4) — enhancement in the sharpness of the atomic arrow needed for realizing better quantum sensors. McConnell et al. observed no improvement in the total sharpness of their atomic arrow.
However, the squeezing experiments carried out so far can be viewed semi-classically: quantum mechanics produces a certain magnitude of ‘noise’, after which the noise can be treated as arising from a fictitious classical source. In McConnell and colleagues’ work, the observation of a negative Wigner function demonstrates that any semi-classical description fails to capture their flavour of entanglement.
The authors also demonstrate that nearly all of the roughly 3,000 atoms must be involved in the generated entanglement, by using a multipartite entanglement measure known as the entanglement depth, which has been applied in related work(5). It is unclear exactly how to interpret this particular measure because it does not provide information about the magnitude of the shared entanglement(6, 7). However, showing that entanglement can be simultaneously shared among so many atoms continues to push the progression of the observation of quantum mechanics from the microscopic to the mesoscopic regime. It may one day help us to understand the transition from the quantum to the classical world of our everyday experience, in which we would never see arrows pointing both slightly north and slightly south at the same time.
In future work, the detection of two or more rotated photons(8) may open the door to even larger amounts of entanglement, and to states that might be useful for quantum sensors such as atomic clocks, magnetometers or accelerometers.


(1) McConnell, R., Zhang, H., Hu, J., Ćuk, S. & Vuletić, V. Nature 519, 439–442 (2015).
(2) Christensen, S. L. et al. Phys. Rev. A 89, 033801 (2014).
(3) Appel, J. et al. Proc. Natl Acad. Sci. USA 106, 10960–10965 (2009).
(4) Bohnet, J. G. et al. Nature Photon. 8, 731–736 (2014).
(5) Haas, F., Volz, J., Gehr, R., Reichel, J. & Estève, J. Science 344, 180–183 (2014).
(6) Lücke, B. et al. Phys. Rev. Lett. 112, 155304 (2014).
(7) Sørensen, A. S. & Mølmer, K. Phys. Rev. Lett. 86, 4431 (2001).
(8) McConnell, R. et al. Phys. Rev. A 88, 063802 (2013).

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