We investigate the statistical properties of superradiant pulses emitted by a system of many atoms. By using a representation of the atomic density operator in terms of directed angular-momentum states (which are also known as atomic coherent states), we find that the statistical behavior of the atoms is formally equivalent to that of a harmonic oscillator subject to linear amplitude amplification and driven by Gaussian white noise. The emitted light pulses are then found to exhibit very large quantum fluctuations for atomic initial states corresponding to complete or nearly complete excitation. For all other atomic initial states the superradiant pulses show classical behavior.We investigate the statistical properties of superradiant pulses emitted by a system of many atoms. By using a representation of the atomic density operator in terms of directed angular-momentum states (which are also known as atomic coherent states), we find that the statistical behavior of the atoms is formally equivalent to that of a harmonic oscillator subject to linear amplitude amplification and driven by Gaussian white noise. The emitted light pulses are then found to exhibit very large quantum fluctuations for atomic initial states corresponding to complete or nearly complete excitation. For all other atomic initial states the superradiant pulses show classical behavior.

Physical Review AJan 1, 1976112 citations

Giant photon bunching, superradiant pulse emission and excitation trapping in quantum-dot nanolasers

F. Jahnke, Christopher Gies, Marc Aßmann +7 more

Light is often characterized only by its classical properties, like intensity or coherence. When looking at its quantum properties, described by photon correlations, new information about the state of the matter generating the radiation can be revealed. In particular the difference between independent and entangled emitters, which is at the heart of quantum mechanics, can be made visible in the photon statistics of the emitted light. The well-studied phenomenon of superradiance occurs when quantum-mechanical correlations between the emitters are present. Notwithstanding, superradiance was previously demonstrated only in terms of classical light properties. Here, we provide the missing link between quantum correlations of the active material and photon correlations in the emitted radiation. We use the superradiance of quantum dots in a cavity-quantum electrodynamics laser to show a direct connection between superradiant pulse emission and distinctive changes in the photon correlation function. This directly demonstrates the importance of quantum-mechanical correlations and their transfer between carriers and photons in novel optoelectronic devices.Light is often characterized only by its classical properties, like intensity or coherence. When looking at its quantum properties, described by photon correlations, new information about the state of the matter generating the radiation can be revealed. In particular the difference between independent and entangled emitters, which is at the heart of quantum mechanics, can be made visible in the photon statistics of the emitted light. The well-studied phenomenon of superradiance occurs when quantum-mechanical correlations between the emitters are present. Notwithstanding, superradiance was previously demonstrated only in terms of classical light properties. Here, we provide the missing link between quantum correlations of the active material and photon correlations in the emitted radiation. We use the superradiance of quantum dots in a cavity-quantum electrodynamics laser to show a direct connection between superradiant pulse emission and distinctive changes in the photon correlation function. This directly demonstrates the importance of quantum-mechanical correlations and their transfer between carriers and photons in novel optoelectronic devices.

Nature CommunicationsMay 10, 2016164 citations

Quantum statistics of a superradiant laser

R. Bonifacio, M. Gronchi

Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento BMar 1, 19724 citations

Quantum Statistical Theory of Superradiance. I

R. Bonifacio, P. Schwendimann, Fritz Haake

We discuss the cooperative decay of initial atomic excitation for a pencil-shaped active volume filled with two-level atoms. As long as the length of the sample is much smaller than a certain maximal cooperation length, the atom-field interaction producing the superradiant pulse can be treated in terms of the simplest possible laser model (single mode). The basic laser master equation turns out to be exactly solvable if specified for the superradiance limit which is characterized by two conditions: (i) The photons escape from the low- $Q$ cavity so fast that they cannot feed themselves back into atomic excitation to any appreciable amount (this no-feedback condition is equivalent to the above-mentioned requirement for the length of the sample). (ii) The incoherent atomic decay due to natural relaxation is so slow that the individual atomic dipoles do not dephase before engaging themselves cooperatively in the interaction with the electromagnetic field. The present paper presents the derivation and general discussion of the equations describing the statistical properties of atoms and field in a superradiant pulse. Analytical and numerical solutions will be presented in a subsequent paper.We discuss the cooperative decay of initial atomic excitation for a pencil-shaped active volume filled with two-level atoms. As long as the length of the sample is much smaller than a certain maximal cooperation length, the atom-field interaction producing the superradiant pulse can be treated in terms of the simplest possible laser model (single mode). The basic laser master equation turns out to be exactly solvable if specified for the superradiance limit which is characterized by two conditions: (i) The photons escape from the low-$Q$ cavity so fast that they cannot feed themselves back into atomic excitation to any appreciable amount (this no-feedback condition is equivalent to the above-mentioned requirement for the length of the sample). (ii) The incoherent atomic decay due to natural relaxation is so slow that the individual atomic dipoles do not dephase before engaging themselves cooperatively in the interaction with the electromagnetic field. The present paper presents the derivation and general discussion of the equations describing the statistical properties of atoms and field in a superradiant pulse. Analytical and numerical solutions will be presented in a subsequent paper.

Physical Review AJul 1, 1971522 citations

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cavity so fast that they cannot feed themselves back into atomic excitation to any appreciable amount (this no-feedback condition is equivalent to the above-mentioned requirement for the length of the sample). (ii) The incoherent atomic decay due to natural relaxation is so slow that the individual atomic dipoles do not dephase before engaging themselves cooperatively in the interaction with the electromagnetic field. The present paper presents the derivation and general discussion of the equations describing the statistical properties of atoms and field in a superradiant pulse. Analytical and numerical solutions will be presented in a subsequent paper.