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arXiv:1612.04477

Collective induced superradiant lineshifts

Gray Putnam, Guin-Dar Lin, Susanne F. Yelin

Published Dec 14, 2016• 1 citation
arXivHTMLPDF

Abstract

Superradiant decay is accompanied by two kinds of collective lineshifts, an induced shift and the spontaneous "collective Lamb shift." Both form as sum of dipole-dipole interaction-induced level shifts between atoms in the system. We have developed a procedure to obtain numerical results on this model that self-consistently incorporates the shifts. The induced shift displays large non-zero values early in the system evolution. In addition, its effect on the superradiant system is studied: there is only a very small dephasing effect on the decay rate. While the induced shift is largely absent in not-too strongly driven systems, this parameter region might provide a good experimental regime for measuring the collective Lamb shift. These results can have important consequences for highly sensitive systems, such as quantum information science or atomic clocks.

DOI
10.48550/arxiv.1612.04477

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Superradiant decay is accompanied by two kinds of collective lineshifts, an induced shift and the spontaneous "collective Lamb shift." Both form as sum of dipole-dipole interaction-induced level shifts between atoms in the system. We have developed a procedure to obtain numerical results on this model that self-consistently incorporates the shifts. The induced shift displays large non-zero values early in the system evolution. In addition, its effect on the superradiant system is studied: there is only a very small dephasing effect on the decay rate. While the induced shift is largely absent in not-too strongly driven systems, this parameter region might provide a good experimental regime for measuring the collective Lamb shift. These results can have important consequences for highly sensitive systems, such as quantum information science or atomic clocks.
In an ensemble of identical atoms, cooperative effects like sub- and superradiance may alter the decay rates and the energies of specific transitions may be shifted from the single-atom value by the so-called collective Lamb shift. While such effects in ensembles of two-level systems are by now well understood, realistic multilevel systems are more difficult to handle. In this work we show that in a system of atoms under the action of an external magnetic field, the collective contribution to the level shifts can amount to sizable quantitative and qualitative deviations from the single-atom Zeeman splitting picture. We develop a formalism to describe single-photon superradiance in multilevel systems and identify three-parameter regimes, two of which present measurable deviations in the radiation spectrum compared to the case of single-atom magnetic-field-induced splitting.
The electromagnetic transitions of Mössbauer nuclei provide ideal two-level systems to study the cooperative effects of X-rays with matter. Recently, we have observed the collective Lamb shift (CLS) in nuclear γ-ray superradiance [Röhlsberger, R.; Schlage, K.; Sahoo, B.; Couet, S.; Rüffer, R. Science 2010, 328, 1248–1251]. An ensemble of resonant 57Fe nuclei was embedded in the center of a planar cavity and was collectively excited by synchrotron radiation into a purely superradiant state. The decay of the superradiant state can be almost two orders of magnitude faster than the single-atom nuclear decay and can be accompanied by a CLS of more than 10 times the natural linewidth. Here we review the basic features of cooperative effects that occur in nuclear γ-ray superradiance in comparison with similar effects observed in the optical regime of the electromagnetic spectrum. We show that nuclear resonant scattering of synchrotron radiation opens new ways for systematic studies of cooperative effects in the interaction of X-rays with matter.
Finding a comprehensive and general description of the collective Lamb shift and cooperative broadening in a radiatively interacting system is a long-standing open question. Both energy levels and linewidth of individual atoms are modified by the exchange of real and virtual photons making up the dipole-dipole interaction. We introduce a method to theoretically study weakly-driven, low-excited ensembles of two-level atoms, and obtain an analytic description of the collective Lamb shift and linewidth via a self-consistent formalism including infinite order of correlations which stem from only two-body interactions. We predict the dependency of these quantities, as measurables, on system parameters: the number density of the ensemble, the detuning of an external probe field, and the geometry of the sample.
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.
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.
When a single excitation is shared between a large number of two-level systems, a strong enhancement of the spontaneous emission appears. This phenomenon is known as superradiance. This enhanced rate can be accompanied by a shift of the emission frequency, the cooperative Lamb shift, issued from the exchange of virtual photons between the emitters. In this work we present a semiconductor optoelectronic device allowing the observation of these two phenomena at room temperature. We demonstrate experimentally and theoretically that plasma oscillations in spatially separated quantum wells interact through real and virtual photon exchange. This gives rise to a superradiant mode displaying a large cooperative Lamb shift.