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Physical Review Letters

Collective Lamb Shift in Single Photon Dicke Superradiance

Marlan O. Scully

Published Apr 6, 2009• 303 citations
Publisher

Abstract

The collective Lamb shift and associated radiative decay of a large cloud of radius R containing N atoms uniformly excited by one photon of wavelength lambda is analyzed. It is shown that the time evolution of the symmetric state prepared by single photon absorption in the limit R>>lambda is similar to that encountered in the Dicke limit of small sample (R<<lambda) superradiance. The theory includes virtual (counterrotating) terms naturally and thus provides a simple calculation of the collective Lamb shift of a single Dicke state.

DOI
10.1103/physrevlett.102.143601

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The collective Lamb shift and associated radiative decay of a large cloud of radius R containing N atoms uniformly excited by one photon of wavelength lambda is analyzed. It is shown that the time evolution of the symmetric state prepared by single photon absorption in the limit R>>lambda is similar to that encountered in the Dicke limit of small sample (R<<lambda) superradiance. The theory includes virtual (counterrotating) terms naturally and thus provides a simple calculation of the collective Lamb shift of a single Dicke state.
We present analytical solutions for the evolution of collective states of N atoms. On the one hand is a (timed) Dicke state prepared by absorption of a single photon and exhibiting superradiant decay. This is in strong contrast to evolution of a symmetric Dicke state which is trapped for large atomic clouds. We show that virtual processes yield a small effect on the evolution of the rapidly decaying timed Dicke state. 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 and provide new decay channels resulting in a slow decay of the otherwise trapped state.
We consider collective spontaneous emission from an ensemble of N identical two-level atoms prepared by absorption of a single photon–a.k.a. single photon Dicke superradiance. We discuss dynamical properties of superradiance for small (R ≪ λ) and large (R ≫ λ) atomic cloud. Moreover, we address the effects of virtual processes on collective decay rate and Lamb shift. It turns out that virtual processes lead to relatively small yet interesting effects on the time evolution of a rapidly decaying state. However, such processes substantially modify the dynamics of trapped states by bringing in new channels of decay.
Superradiance, the cooperative spontaneous emission of photons from an ensemble of identical atoms, provides valuable insights into the many-body physics of photons and atoms. We show that an ensemble of resonant atoms embedded in the center of a planar cavity can be collectively excited by synchrotron radiation into a purely superradiant state. The collective coupling of the atoms via the radiation field leads to a substantial radiative shift of the transition energy, the collective Lamb shift. We simultaneously measured the temporal evolution of the superradiant decay and the collective Lamb shift of resonant 57Fe nuclei excited with 14.4-kilo-electron volt synchrotron radiation. Our experimental technique provides a simple method for spectroscopic analysis of the superradiant emission.
Superradiance is one of the many fascinating phenomena predicted by quantum electrodynamics that have first been experimentally demonstrated in atomic systems and more recently in condensed matter systems like quantum dots, superconducting q-bits, cyclotron transitions and plasma oscillations in quantum wells (QWs). It occurs when a dense collection of N identical two-level emitters are phased via the exchange of photons, giving rise to enhanced light-matter interaction, hence to a faster emission rate. Of great interest is the regime where the ensemble interacts with one photon only and therefore all of the atoms, but one, are in the ground state. In this case the quantum superposition of all possible configurations produces a symmetric state that decays radiatively with a rate N times larger than that of the individual oscillators. This phenomenon, called single photon superradiance, results from the exchange of real photons among the N emitters. Yet, to single photon superradiance is also associated another collective effect that renormalizes the emission frequency, known as cooperative Lamb shift. In this work, we show that single photon superradiance and cooperative Lamb shift can be engineered in a semiconductor device by coupling spatially separated plasma resonances arising from the collective motion of confined electrons in QWs. These resonances hold a giant dipole along the growth direction z and have no mutual Coulomb coupling. They thus behave as a collection of macro-atoms on different positions along the z axis. Our device is therefore a test bench to simulate the low excitation regime of quantum electrodynamics.
The collective nature of light emission by atomic ensembles yields fascinating effects such as superradiance and radiation trapping even at the single-photon level. Light emission is influenced by virtual transitions and the collective Lamb shift which yields peculiar features in temporal evolution of the atomic system. We study how two-dimensional atomic structures collectively emit a single photon. Namely, we consider spherical, cylindrical, and spheroidal shells with two-level atoms continuously distributed on the shell surface and find exact analytical solutions for eigenstates of such systems and their collective decay rates and frequency shifts. We identify states which undergo superradiant decay and states which are trapped and investigate how size and shape of the shell affects collective light emission. Our findings could be useful for quantum information storage and the design of optical switches.