Superradiance of an ensemble of nuclei excited by a free electron laser

20-11-2017

A prediction about the quantum-mechanical behaviour of resonant systems has been verified in experiments at SACLA, Japan, and at the ESRF.  After nuclei in a crystal were multiply excited by a flash from the SACLA X-ray laser, the emission of X-rays was followed, one X-ray photon at a time, for up to 68 X-ray photons. A dramatic reduction in the time to emit the first X-ray photon was observed as the number of X-rays increased.  This behaviour is in good agreement with one limit of a superradiant system, as was predicted by Dicke in 1954.

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One of the broad challenges of science is to understand the behaviour of groups of atoms based on the response of a single atom in isolation, which isusually much simpler.  A facet of this is understanding the behaviour of a group of identical oscillators.  An analogy is a collection of bells that all have the same tone: one can easily imagine the sound of a single bell struck once - a clear tone ringing out with a volume that decays away over time.  

But what happens if one gently taps all the bells in a large collection?  Will the tone be the same as a single one?  What about the volume?  What about the direction - does it matter where you are standing when you listen to the sound?  Does it matter if you tap them all at the same time? 

The preceding questions can be answered using some straightforward mathematics.  But the analogous questions become more complex when one enters the quantum world of collections of atoms that emit light.  In that world, light comes in packets, photons, and the light intensity, analogous to the volume of the bells, is measured in discrete packets of photons.   Similar questions arise, but now one also has to ask how the response changes depending on the number of photons, the number of quanta of light, in the system.

A pioneering approach to these issues was developed by Robert Dicke and published in 1954 [1].  He predicted a "superradiant" state, where, when large numbers of photons or quanta are put into a system with many atoms, the decay becomes much faster than for a single atom in isolation.  In the context of the above analogy, his suggestion would mean that if you have a large number of bells that you excite together, they can ring loudly, but the sound dies out much more quickly than the gentle fading of a single bell.  His approach included quantum effects, predicting that the fastest decay occurred when the number of quanta was half the number of atoms.  The concept of superradiance has since been verified, and, indeed, is a touchstone in the field of quantum optics.  However, Dicke also predicted that a very strong change in decay rate would occur even when the number of quanta in the system is much less than the number of atoms in the system.  This is what was investigated in recent experiments at the SACLA free electron laser and at the ESRF.

Measuring the multi-photon emission after a single pulse of the XFEL

Figure 1. Measuring the multi-photon emission after a single pulse of the XFEL. a) Scope traces from the avalanche photo diode (APD) detectors after one pulse of 44 photons and the fits used to analyse the distribution. b) The distribution of multi-photon events measured in the APD detectors, as compared with a model incorporating a coherent source with few modes (M = 2.2) and an incoherent source (large M limit).

The new work replaced the low-energy quanta envisioned by Dicke with high-energy X-rays, allowing the decay of the system to be followed one quantum of X-ray light at a time.  However, getting strong pulses of X-rays is much harder than for low energy light, and required use of an X-ray free-electron laser.  Such sources have only become available recently, and of the few operating in the world, only SACLA, at the RIKEN SPring-8 Center in Japan, achieves the required high energy. Using this source, it was possible to precisely follow the decay for up to 68 X-ray photons (Figure 1). The accelerated emission of the first photon (Figure 2) was observed to be in excellent agreement with Dicke's prediction [1].  The single-photon decay under the same experimental conditions was studied at the ESRF (ID18).  From these experiments, an alternative picture of the decay properties was produced based on a statistical approach, which will be valuable for the understanding of future work.   

Acceleration of the Initial decay rate

Figure 2. Acceleration of the Initial decay rate.  The increase of the initial decay rate for the transitions from N to N-1 excited states revealed (a) by the accelerated decay of the first out of N detected photon, PN1(t) (b) by the ratios PN1(t)/P11(t) of these data to the single-photon decay P11(t) (shown in (c)), and (d) by the estimated acceleration rates (PN1/ P11)|t→0. The solid lines in (a, b) are the calculations based on the statistical approach.  The solid line in (d) is the power fit.

 

Principal publication and authors
Superradiance of an ensemble of nuclei excited by a free electron laser, A.I. Chumakov (a), A.Q.R. Baron (b), I. Sergueev (c), C. Strohm (c), O. Leupold (c), Yu. Shvyd’ko (d), G.V. Smirnov (e), R. Rüffer (a), Y. Inubushi (f), M. Yabashi (f), K. Tono (f), T. Kudo (b), T. Ishikawa (b), Nature Physics, (2017); doi: 10.1038/s41567-017-0001-z.
(a) ESRF
(b) RIKEN SPring-8 Center, Hyogo (Japan)
(c) DESY, Hamburg (Germany)
(d) Advanced Photon Source, Argonne National Laboratory, Argonne, IL (USA) 
(e) National Research Centre “Kurchatov Institute”, Moscow (Russia)
(f) Japan Synchrotron Radiation Research Institute, Hyogo (Japan)

 

References
[1] R.H. Dicke, Coherence in spontaneous radiation processes, Phys. Rev. 93, 99 (1954).