We study collective spontaneous emission from arbitrary distributions of N two-state atoms using quantum trajectory theory and without an a priori single-mode assumption. Assuming a fully excited initial state, we calculate the angular distribution of the average integrated intensity. We investigate the dependence of the angular distribution of emission on the geometry of the atomic distribution. The formalism is developed around an unravelling of the master equation in terms of source mode quantum jumps. A modified boson approximation is made to treat the many-atom case, where it is found that strong directional superradiance occurs for a few hundred to a few thousand atoms. In order to illustrate important differences between our model and single-mode models we consider shot-to-shot intensity fluctuations and angular correlations in the emitted intensity.We study collective spontaneous emission from arbitrary distributions of N two-state atoms using quantum trajectory theory and without an a priori single-mode assumption. Assuming a fully excited initial state, we calculate the angular distribution of the average integrated intensity. We investigate the dependence of the angular distribution of emission on the geometry of the atomic distribution. The formalism is developed around an unravelling of the master equation in terms of source mode quantum jumps. A modified boson approximation is made to treat the many-atom case, where it is found that strong directional superradiance occurs for a few hundred to a few thousand atoms. In order to illustrate important differences between our model and single-mode models we consider shot-to-shot intensity fluctuations and angular correlations in the emitted intensity.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEMay 16, 20030 citations

Quantum trajectory theory of superradiant emission from randomly distributed atomic samples

Ryan Nowak, James Clemens

We consider the directed superradiant emission from a collection of N two-state atoms with arbitrary spatial locations within the framework of quantum trajectory theory and without a single-mode assumption. The formalism is developed around an unravelling of the master equation in terms of source mode quantum jumps. A modified boson approximation is made to treat the many-atom case, where it is found that strong directional superradiance occurs for a few thousand atoms, even with randomized atomic positions.We consider the directed superradiant emission from a collection of N two-state atoms with arbitrary spatial locations within the framework of quantum trajectory theory and without a single-mode assumption. The formalism is developed around an unravelling of the master equation in terms of source mode quantum jumps. A modified boson approximation is made to treat the many-atom case, where it is found that strong directional superradiance occurs for a few thousand atoms, even with randomized atomic positions.

Journal of the Optical Society of America BMar 24, 20086 citations

Collective spontaneous emission from a line of atoms

James Clemens, Levente Horvath, Barry C. Sanders +1 more

We study collective spontaneous emission from a linear array of N two-state atoms using quantum trajectory theory and without an a priori single-mode assumption. Assuming a fully excited initial state, we calculate the angular distribution of the $k\mathrm{th}$ emitted photon, $k=1,\dots{},N.$ We investigate the evolution of the distribution from a dipole radiation pattern for the first photon emission to a distribution characteristic of directional superradiance. The formalism is developed around an unravelling of the master equation in terms of source-mode quantum jumps. Exact calculations for 11 and fewer atoms do not show directional superradiance, but are characterized by delayed (subradiant) photon emissions directed along the axis of the linear array. A modified boson approximation is made to treat the many-atom case, where it is found that strong directional superradiance occurs for a few hundred atoms; the decay of subradiant excitations is preserved in the tail of the superradiant pulse.We study collective spontaneous emission from a linear array of N two-state atoms using quantum trajectory theory and without an a priori single-mode assumption. Assuming a fully excited initial state, we calculate the angular distribution of the $k\mathrm{th}$ emitted photon, $k=1,\dots{},N.$ We investigate the evolution of the distribution from a dipole radiation pattern for the first photon emission to a distribution characteristic of directional superradiance. The formalism is developed around an unravelling of the master equation in terms of source-mode quantum jumps. Exact calculations for 11 and fewer atoms do not show directional superradiance, but are characterized by delayed (subradiant) photon emissions directed along the axis of the linear array. A modified boson approximation is made to treat the many-atom case, where it is found that strong directional superradiance occurs for a few hundred atoms; the decay of subradiant excitations is preserved in the tail of the superradiant pulse.

Physical Review AAug 25, 2003120 citations

Stochastic initiation of superradiance in a cavity: An approximation scheme within quantum trajectory theory

James Clemens, H. J. Carmichael

We investigate the stochastic initiation of superradiant emission from a collection of excited two-state atoms coupled through a low-Q cavity mode. Noncollective emission into other modes of the electromagnetic field is included, allowing us to describe the transition from predominantly noncollective to collective behavior as the number of atoms is increased. We examine the dependence of the photon statistics on the number of atoms and the ratio of collective to noncollective decay rates. Numerical results for a few to ${10}^{6}$ atoms are obtained using an approximation scheme developed within the framework of quantum trajectory theory. Results are compared with those for a pure collective emission process and an earlier treatment of noncollective effects.We investigate the stochastic initiation of superradiant emission from a collection of excited two-state atoms coupled through a low-Q cavity mode. Noncollective emission into other modes of the electromagnetic field is included, allowing us to describe the transition from predominantly noncollective to collective behavior as the number of atoms is increased. We examine the dependence of the photon statistics on the number of atoms and the ratio of collective to noncollective decay rates. Numerical results for a few to ${10}^{6}$ atoms are obtained using an approximation scheme developed within the framework of quantum trajectory theory. Results are compared with those for a pure collective emission process and an earlier treatment of noncollective effects.

Physical Review AJan 16, 200221 citations

Effect of atomic distribution on cooperative spontaneous emission

Wei Feng, Yong Li, Shi‐Yao Zhu

We study cooperative single-photon spontaneous emission from $N$ multilevel atoms for different atomic distributions in optical vector theory. Instead of the average approximation for interatomic distance or the continuum approximation (sums over atoms replaced by integrals) for atomic distribution, the positions of every atom are taken into account by numerical calculation. It is shown that the regularity of atomic distribution has considerable influence on cooperative spontaneous emission. For a small atomic sample (compared with radiation wavelength), obtaining strong superradiance requires not only the uniform excitation (the Dicke state) but also the uniform atomic distribution. For a large sample, the uniform atomic distribution is beneficial to subradiance of the Dicke state, while the influence of atomic distribution on the timed Dicke state is weak and its time evolution obeys exponential decay approximately. In addition, we also investigate the corresponding emission spectrum and verify the directed emission for the timed Dicke state for a large atomic sample.We study cooperative single-photon spontaneous emission from $N$ multilevel atoms for different atomic distributions in optical vector theory. Instead of the average approximation for interatomic distance or the continuum approximation (sums over atoms replaced by integrals) for atomic distribution, the positions of every atom are taken into account by numerical calculation. It is shown that the regularity of atomic distribution has considerable influence on cooperative spontaneous emission. For a small atomic sample (compared with radiation wavelength), obtaining strong superradiance requires not only the uniform excitation (the Dicke state) but also the uniform atomic distribution. For a large sample, the uniform atomic distribution is beneficial to subradiance of the Dicke state, while the influence of atomic distribution on the timed Dicke state is weak and its time evolution obeys exponential decay approximately. In addition, we also investigate the corresponding emission spectrum and verify the directed emission for the timed Dicke state for a large atomic sample.

arXiv:1310.4687Physical Review AJan 14, 201431 citations

Angular Distribution and Polarization of Superradiant Emission from Atomic Ensembles

V. L. Jacobs

A density-matrix approach is developed to provide a theoretical description of the intensity, angular distribution, and polarization of superradiative emission from an ensemble of many-electron atomic systems. The many-electron atomic systems are described as cooperatively interacting by means of forces that can be long range. Particular emphasis is given to the coherent excitation of the collective atomic-ensemble states, which may be produced by incident laser radiation. The initial excitation and spontaneous emission processes may be described as independent. Both frequency-domain and time-domain formulations of the density-matrix approach are developed. The collective atomic-ensemble states are specified in a detailed hyperfine representation, corresponding to successively coupling the individual hyperfine angular momenta F pertaining to the many-electron atoms. A less detailed fine-structure angular-momentum representation may also be used. In the density-operator approach, account can be taken of the coherent excitation of a particular subspace of the initial atomic-ensemble states. For a comprehensive and unified development of time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations, a reduced-density-matrix (quantum-open-systems) approach is introduced. The non-equilibrium atomic-ensemble-state kinetics and the homogeneous spectral-line shapes can thereby be systematically and self-consistently determined. The collective atomic-ensemble states may be obtained using a variety of different methods. These states can be determined using a dressed-state approach, in which the required states are calculated in the presence of an electromagnetic field.A density-matrix approach is developed to provide a theoretical description of the intensity, angular distribution, and polarization of superradiative emission from an ensemble of many-electron atomic systems. The many-electron atomic systems are described as cooperatively interacting by means of forces that can be long range. Particular emphasis is given to the coherent excitation of the collective atomic-ensemble states, which may be produced by incident laser radiation. The initial excitation and spontaneous emission processes may be described as independent. Both frequency-domain and time-domain formulations of the density-matrix approach are developed. The collective atomic-ensemble states are specified in a detailed hyperfine representation, corresponding to successively coupling the individual hyperfine angular momenta F pertaining to the many-electron atoms. A less detailed fine-structure angular-momentum representation may also be used. In the density-operator approach, account can be taken of the coherent excitation of a particular subspace of the initial atomic-ensemble states. For a comprehensive and unified development of time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations, a reduced-density-matrix (quantum-open-systems) approach is introduced. The non-equilibrium atomic-ensemble-state kinetics and the homogeneous spectral-line shapes can thereby be systematically and self-consistently determined. The collective atomic-ensemble states may be obtained using a variety of different methods. These states can be determined using a dressed-state approach, in which the required states are calculated in the presence of an electromagnetic field.

World Journal of Applied PhysicsJan 1, 20201 citation

k\mathrm{th}

emitted photon,

k=1,\dots{},N.

We investigate the evolution of the distribution from a dipole radiation pattern for the first photon emission to a distribution characteristic of directional superradiance. The formalism is developed around an unravelling of the master equation in terms of source-mode quantum jumps. Exact calculations for 11 and fewer atoms do not show directional superradiance, but are characterized by delayed (subradiant) photon emissions directed along the axis of the linear array. A modified boson approximation is made to treat the many-atom case, where it is found that strong directional superradiance occurs for a few hundred atoms; the decay of subradiant excitations is preserved in the tail of the superradiant pulse.

{10}^{6}

atoms are obtained using an approximation scheme developed within the framework of quantum trajectory theory. Results are compared with those for a pure collective emission process and an earlier treatment of noncollective effects.

We study cooperative single-photon spontaneous emission from

N

multilevel atoms for different atomic distributions in optical vector theory. Instead of the average approximation for interatomic distance or the continuum approximation (sums over atoms replaced by integrals) for atomic distribution, the positions of every atom are taken into account by numerical calculation. It is shown that the regularity of atomic distribution has considerable influence on cooperative spontaneous emission. For a small atomic sample (compared with radiation wavelength), obtaining strong superradiance requires not only the uniform excitation (the Dicke state) but also the uniform atomic distribution. For a large sample, the uniform atomic distribution is beneficial to subradiance of the Dicke state, while the influence of atomic distribution on the timed Dicke state is weak and its time evolution obeys exponential decay approximately. In addition, we also investigate the corresponding emission spectrum and verify the directed emission for the timed Dicke state for a large atomic sample.