An atom, when excited, will typically decay with a characteristic decay time. An ensemble of atoms, collectively coupled together with just one of the atoms excited will conspire to decay much faster than the single atom case. This enhancement of light-matter interaction is known as superradiance. Rohlsberger et al. (p. [1248][1], published online 13 May; see the cover; see the Perspective by [Scully and Svidzinsky][2] ) present the realization of an artificial superradiant system comprising resonant iron atoms embedded in a semiconductor cavity and excited by synchrotron radiation and report the signature collective Lamb shift expected from the cooperative interaction and enhanced decay rate. The availability of such a controlled system to look closer at this effect should shed light on its role in natural and complex light-harvesting systems, and possibly allow the production of more efficient solar cells.

 [1]: /lookup/doi/10.1126/science.1187770
 [2]: /lookup/doi/10.1126/science.1190737

/pdf/collective-lamb-shift-in-single-photon-superradiance-22p9edf68i.pdf

Collective Lamb shift in single-photon superradiance.

A central goal within quantum optics is to realize efficient, controlled interactions between photons and atomic media. A fundamental limit in nearly all applications based on such systems arises from spontaneous emission, in which photons are absorbed by atoms and then rescattered into undesired channels. In typical theoretical treatments of atomic ensembles, it is assumed that this rescattering occurs independently, and at a rate given by a single isolated atom, which in turn gives rise to standard limits of fidelity in applications such as quantum memories for light or photonic quantum gates. However, this assumption can in fact be dramatically violated. In particular, it has long been known that spontaneous emission of a collective atomic excitation can be significantly suppressed through strong interference in emission between atoms. While this concept of “subradiance” is not new, thus far the techniques to exploit the effect have not been well understood. In this work, we provide a comprehensive treatment of this problem. First, we show that in ordered atomic arrays in free space, subradiant states acquire an elegant interpretation in terms of optical modes that are guided by the array, which only emit due to scattering from the ends of the finite system. We also go beyond the typically studied regime of a single atomic excitation and elucidate the properties of subradiant states in the many-excitation limit. Finally, we introduce the new concept of “selective radiance.” Whereas subradiant states experience a reduced coupling to all optical modes, selectively radiant states are tailored to simultaneously radiate efficiently into a desired channel while scattering into undesired channels is suppressed, thus enabling an enhanced atom-light interface. We show that these states naturally appear in chains of atoms coupled to nanophotonic structures, and we analyze the performance of photon storage exploiting such states. We find numerically that selectively radiant states allow for a photon storage error that scales exponentially better with the number of atoms than previously known bounds.

https://link.aps.org/pdf/10.1103/PhysRevX.7.031024

Exponential Improvement in Photon Storage Fidelities Using Subradiance and “Selective Radiance” in Atomic Arrays

Since Dicke's seminal paper on coherence in spontaneous radiation by atomic ensembles, superradiance has been extensively studied. Subradiance, on the contrary, has remained elusive, mainly because subradiant states are weakly coupled to the environment and are very sensitive to nonradiative decoherence processes. Here, we report the experimental observation of subradiance in an extended and dilute cold-atom sample containing a large number of particles. We use a far detuned laser to avoid multiple scattering and observe the temporal decay after a sudden switch-off of the laser beam. After the fast decay of most of the fluorescence, we detect a very slow decay, with time constants as long as 100 times the natural lifetime of the excited state of individual atoms. This subradiant time constant scales linearly with the cooperativity parameter, corresponding to the on-resonance optical depth of the sample, and is independent of the laser detuning, as expected from a coupled-dipole model.

/pdf/subradiance-in-a-large-cloud-of-cold-atoms-20m0m15e3m.pdf

Subradiance in a Large Cloud of Cold Atoms.

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 N 2. As a result, the atoms radiate their energy N times faster than for incoherent emission. It is this anomalous radiance that Dicke dubbed “superradiance” ( 1 – 3 ).

https://science.sciencemag.org/content/sci/325/5947/1510.full.pdf

The Super of Superradiance

We review here the studies performed about interactions in an assembly of cold Rydberg atoms. We focus especially on the review of the dipole–dipole interactions and on the effect of the dipole blockade in the laser Rydberg excitation, which offers attractive possibilities for quantum engineering. We present first the various interactions between Rydberg atoms. The laser Rydberg excitation of such an assembly is then described with the introduction of the dipole blockade phenomenon. We report recent experiments performed in this subject by starting with the case of a pair of atoms allowing the entanglement of the wave-functions of the atoms and opening a fascinating way for the realization of quantum bits and quantum gates. We consider then several works on the blockade effect in a large assembly of atoms for three different configurations: blockade through electric-field induced dipole, through Forster resonance, and in van der Waals interaction. The properties of coherence and cooperativity are analyzed. Finally, we treat the role of dipole–dipole interactions between Rydberg atoms responsible for Penning ionization. The perturbation of the dipole blockade by ions and the evolution of the Rydberg towards an ultracold plasma are discussed.

Dipole blockade in a cold Rydberg atomic sample [Invited]

We consider collective emission of a single photon from a cloud of $N$ two-level atoms (one excited, $N\ensuremath{-}1$ ground state). For a dense cloud the problem is reduced to finding eigenfunctions and eigenvalues of an integral equation. We discuss an exact analytical solution of this many-atom problem for a spherically symmetric atomic cloud. Some eigenstates decay much faster then the single atom decay rate, while the others undergo very slow decay. We show that virtual processes yield a small effect on the evolution of rapidly decaying states. However, they change the long time dynamics from exponential decay into a power-law behavior which can be observed experimentally. For trapped states virtual processes are much more important yielding additional decay channels which results in a slow decay of the otherwise trapped states. We also show that quantum mechanical treatment of spontaneous emission of weakly excited atomic ensemble is analogous to emission of $N$ classical harmonic oscillators.

Cooperative spontaneous emission of N atoms: Many-body eigenstates, the effect of virtual Lamb shift processes, and analogy with radiation of N classical oscillators

We study the correlated spontaneous emission from a dense spherical cloud of N atoms uniformly excited by absorption of a single photon. We find that the decay of such a state depends on the relation between an effective Rabi frequency Omega proportional square root N and the time of photon flight through the cloud R/c. If OmegaR/c >1, the coupled atom-radiation system oscillates between the collective Dicke state (with no photons) and the atomic ground state (with one photon) with frequency Omega while decaying at a rate c/R.

Dynamical evolution of correlated spontaneous emission of a single photon from a uniformly excited cloud of N atoms.

We study emission of a single photon from a spherically symmetric cloud of $N$ atoms (one atom is excited; $N\ensuremath{-}1$ are in the ground state) and present an exact analytical expression for eigenvalues and eigenstates of this many-body problem. We found that some states decay much faster than the single-atom decay rate, while other states are trapped and undergo very slow decay. When the size of the atomic cloud is small compared with the radiation wavelength, we found that the radiation frequency undergoes a large shift.

Cooperative spontaneous emission as a many-body eigenvalue problem

Precision measurement of small separations between two atoms or molecules has been of interest since the early days of science. Here, we discuss a scheme which yields spatial information on a system of two identical atoms placed in a standing wave laser field. The information is extracted from the collective resonance fluorescence spectrum, relying entirely on far-field imaging techniques. Both the interatomic separation and the positions of the two particles can be measured with fractional-wavelength precision over a wide range of distances from about $\ensuremath{\lambda}∕550$ to $\ensuremath{\lambda}∕2$.

/pdf/measurement-of-the-separation-between-atoms-beyond-3jt77c17lc.pdf

Measurement of the separation between atoms beyond diffraction limit

The intensity-intensity correlation function of the resonance fluorescence light of two two-level atoms driven by a resonant standing-wave laser field is examined. Our aim is to gain information on the distance between the two atoms from observables accessible in experiments. For this, we numerically solve the time-evolution equations of the system and calculate the steady-state intensity-intensity correlation by using the Laplace transform and quantum regression theory. By varying the interatomic distance from about half a wavelength down to small fractions of a wavelength, we show that the correlation function exhibits characteristic properties for different distance ranges. Based on these results, we propose a scheme to obtain interatomic distance information from the power spectrum of the correlation function, which allows us to extract the desired distance information over a wide range of distances with high accuracy.

/pdf/distilling-two-atom-distance-information-from-intensity-4z8sa7wpy6.pdf

Jun-Tao Chang

Papers

Cooperative spontaneous emission of N atoms: Many-body eigenstates, the effect of virtual Lamb shift processes, and analogy with radiation of N classical oscillators

Dynamical evolution of correlated spontaneous emission of a single photon from a uniformly excited cloud of N atoms.

Cooperative spontaneous emission as a many-body eigenvalue problem

Measurement of the separation between atoms beyond diffraction limit

Distilling two-atom distance information from intensity-intensity correlation functions