The Super of Superradiance

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Science  18 Sep 2009:
Vol. 325, Issue 5947, pp. 1510-1511
DOI: 10.1126/science.1176695

In 1954, Robert Dicke introduced the concept of superradiance in describing the cooperative, spontaneous emission of photons from a collection of atoms. The concept of superradiance can be understood by picturing each atom as a tiny antenna emitting electromagnetic waves. Thermally excited atoms emit light randomly, and the emitted intensity is a function of the number of atoms, N. However, when the atomic “antennas” are coherently radiating in phase with each other, the net electromagnetic field is proportional to N, and therefore, the emitted intensity goes as N2. As a result, the atoms radiate their energy N times faster than for incoherent emission. It is this anomalous radiance that Dicke dubbed “superradiance” (13).

An even more interesting kind of radiation speedup can occur when a single photon is stored uniformly in a cloud of N atoms (see the figure, panel A). Suppose you have one atom that decays with a rate γ. Then suppose there are N such atoms close together in an atom cloud with only one of the atoms excited (but we don't know which one). Because there is only one atom excited, you might expect the decay rate to be γ. But if the atoms are symmetrically organized within the cloud, the decay rate is actually Nγ (1). This enhanced single-photon emission rate is “the greatest radiation anomaly” inherent in superradiance. Single-photon superradiance has become a subject of current interest (412), and promises to yield new tools for storing quantum information and deeper insight into the physics of virtual processes.

Dicke's point is that the N atoms act like one big atom and decay collectively. This is intuitive when the atoms are close together compared to the wavelength of radiation λ. When the same symmetric state is formed but the atomic cloud size is larger than λ, there is no longer constructive cooperation in radiation emission. The atoms will trap the light, decreasing the emission rate.

Nevertheless, it is possible to produce a state such that the large cloud also emits radiation with an enhanced rate proportional to Nγ (4, 5). This is important because in quantum optics the sample is usually large compared to λ.

However, things are a bit trickier here. More subtle and interesting physics come into play, extending from quantum information and a new kind of cavity quantum electrodynamics (QED) (13), to new insights into quantum field theory (912).

The essential new physics is the transition from the coherent antenna array to the single-photon state in which cooperative emission is due to N entangled atoms (not N coherent emitters). This is made possible by conditioned preparation of the initial atomic states (see the figure, panel A) (4, 5).

With the large sample, however, it is not so clear why the emitted photon should go in the same direction as the exciting photon given that there is no antenna dipole associated with the atoms (see the figure, panel B). One atom is excited, but we do not know which one. The answer is associated with timing: The atoms at the front of the sample are excited first and those at the back, last (4, 5). These excitations appear as spatial phase factors. It is this timing that yields directionality in the emitted radiation. Without the timed excitation, the radiation will be substantially trapped in the gas (11).

Collective action.

(A) Conditioned excitation prepares the timed uniform state in three logical steps (4): (i) Consider a pair of short single-photon pulses produced by a down converter (which absorbs one “blue” photon and emits two lower-energy “red” photons). A count in detector D2 ensures that a photon of wave vector ∼k0 is entering the atomic cloud at some time t0. (ii) The atoms are detuned from resonance by an amount Δ so that the excitation probability is weak and every atom is equally likely to be excited but at different times, depending on its position. (iii) Most of the time the photon will pass through the gas, and a count is registered in the “perfect” detector D1; lack of a count tells us one atom is excited, but we don't know which one. Then, conditioned on a count in D2, but not in D1, the detuning Δ is switched to zero. The atoms are now resonant with k0 and emit spontaneously. (B) For a large atomic sample, the conditioned preparation depicted in (A) results in a radiation pattern that is strongly peaked in the k0 direction. To a good approximation, the timed excitation yields emission speedup, which is proportional to the number of atoms and the solid diffraction angle given by the squared ratio of the wavelength to the sample size. Evolution of the single-photon timed state in the large sample has much in common with evolution of the symmetric state for a small atomic cloud. (C) For a very large cloud, the photon is reabsorbed and reemitted many times and the atomic state oscillates with a frequency that goes as Embedded Image. This is to be compared to the cavity QED scenario (13) in which an atom is cycled between the ground and excited states with a frequency which goes as Embedded Image, where n is the number of photons in the cavity. P is the probability that the atom is excited.

In particular, in the conditioned excitation case, the decay rate continues to be proportional to the number of atoms; but it also involves the diffraction factor (λ/R)2, where R is the radius of the sample. This is the case for gas clouds that are large compared with λ but small compared with the size of the radiation pulse length Lp. However, when R > Lp, the coupled atom-radiation system shows absorption-emission oscillations (see the figure, panel C) that are similar to those observed in cavity QED (13), where the Rabi oscillation frequency is determined by the volume of the cavity and the number of photons in the cavity. In the present case, the oscillation frequency is determined by the volume of the cloud and the number of atoms (14). This surprising result is indeed a new kind of cavity QED.

Another fascinating aspect of single-photon superradiance is the collective N-atom Lamb shift, which is due to the rapid emission and reabsorption of (virtual) photons (1012). As the decay rate is enhanced by collective emission, so too is the frequency shift associated with the virtual photons. Furthermore, the virtual photons dramatically change the evolution of trapped states (11). They provide new decay channels, which ultimately result in a slow decay of the otherwise trapped state. However, for the rapidly decaying states, these virtual processes are relatively unimportant (11). In such a case, virtual photons excite other states with only a relatively small probability, depending on the size of the atomic cloud. In addition, the essentially new many-particle Lamb shift is not divergent. That is, the usual single-atom Lamb shift calculations involve infinities, high-frequency cutoffs, and so forth. However, in the many-atom version, the most interesting physics comes from this “infinity-free QED.”

A single photon stored in a large cloud of atoms provides new insights into the radiation physics of single-photon superradiance, virtual photons, and more. The single-photon states also have potential for application to quantum informatics.

References and Notes

  1. The beautiful cavity QED experiments of Haroche and co-workers and Walther and co-workers are nicely explained in (15). When atoms are placed in a cavity (e.g., a microwave cavity), the atom-photon interaction is changed.

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