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Journal of the Physical Society of Japan

Fluctuation of Polarized Light in Cooperative Spontaneous Emission

Takeshi Baba, Kensuke S. Ikeda

Published Jan 1, 1981• 5 citations
Publisher

Abstract

Macroscopic fluctuation of superradiance most sensitively appears as the fluctuation of the polarized photon number. This fluctuation is not much affected by unexpected variation of the exciting pulse area. In the superradiance limit the relative fiuctuation of the polarized photon number is equal to \(\sqrt{1/3}\), and it decreases rapidly as the atomic number density is reduced below a threshold density. Such a characteristic change is attributed to a transition from the superradiant emission to the amplified spontaneous emission.

DOI
10.1143/jpsj.50.217

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Macroscopic fluctuation of superradiance most sensitively appears as the fluctuation of the polarized photon number. This fluctuation is not much affected by unexpected variation of the exciting pulse area. In the superradiance limit the relative fiuctuation of the polarized photon number is equal to (\sqrt{1/3}), and it decreases rapidly as the atomic number density is reduced below a threshold density. Such a characteristic change is attributed to a transition from the superradiant emission to the amplified spontaneous emission.
Superradiance is an extensive cooperative spontaneous emission phenomenon, exhibited by some atomic collective-spin states. However, distinct initial states differ in their decay dynamics. Dicke states ∣j,m⟩|j,m\rangle∣j,m⟩ with distinct numbers of excitations n=m+jn=m+jn=m+j, driven by vacuum fluctuations, have their peak emission intensity shifted in time. Rotating Dicke states relative to the decay axis introduces an interesting parity structure that affects the pulse profile and photon correlations. Squeezed-bath prepared states undergo a squeezing-controlled crossover to the rotated Dicke states, making the emission character dependent on the amount of squeezing transferred from light to the atomic state. For semiclassical states with a macroscopic dipole moment, like the atomic coherent state, the emission intensity depends on their polarization. We present detailed results on the superradiant dynamics of a representative selection of states expanded in Dicke states to highlight the initial state as an independent dynamical control parameter. For large-NNN, we are able to predict fairly accurately the pulse profile in each case using the mean-field approximation, an approach based on the Fokker--Planck equation. We also present comparative results on the intensity correlation function, quantify the coherent and incoherent contributions of the emission, and contrast between small and large ensembles.
Fully-excited two-level atoms separated by less than the transition wavelength cooperatively emit light in a short burst, a phenomenon called superradiance by R. Dicke in 1954. The burst is characterized by a maximum intensity scaling with the square of the number of atoms NNN and a temporal width reduced by NNN compared to the single atom spontaneous decay time. Both effects are usually attributed to a synchronization of the electric dipole moments of the atoms occurring during the process of light emission. Contrary to this explanation, it was recently shown by use of a quantum path description that the peak intensity results from the quantum correlations among the atoms when occupying symmetric Dicke states. Here we investigate from this perspective the temporal evolution of the ensemble, starting in the small sample limit, i.e., when the atoms have mutual separations much smaller than the transition wavelength λλλ and pass down the ladder of symmetric Dicke states. In addition, we explore the temporal evolution for the case of non-interacting atoms with mutual separations much larger than λλλ. We show that in this case a similar superradiant burst of the emitted radiation is observed if the quantum correlations of the atoms are generated by conditional photon measurements retaining the atomic ensemble within or close to the symmetric subspace.
When atoms are coupled to a common electromagnetic environment, the exchange of photons through dipole-dipole interactions leads to the emergence of cooperative effects. As a particular example, superradiance arises from spontaneous emission when this exchange leads to constructive interference of the emitted photons. Here, we introduce an integrated method for studying cooperative radiation in many-body systems. This method, which allows to study extended systems with arbitrarily large number of particles, can be formulated by an effective, nonlinear, two-atom master equation that describes the dynamics using a closed form which treats single- and many-body terms on an equal footing. We apply this method to a homogeneous gas of initially inverted two-level atoms, and demonstrate the appearance of both superradiance and subradiance, identifying a many-body coherence term as the source of these cooperative effects. We describe the many-body induced broadening -- which is analytically found to scale with the optical depth of the system -- and light shifts, and distinguish spontaneous effects from induced ones. In addition, we theoretically predict the time-dependence of subradiance, and the phase change of the radiated field during the cooperative decay.
We describe a new approach to the problem of superradiant spontaneous emission, which is applicable whether the number of atoms is large or small. We use this approach to formulate intensity correlations of arbitrary order, and then explicitly evaluate the second-order normally ordered relative intensity fluctuation. Large fluctuations at the onset of emission indicate the discrete nature of the spontaneous emission process; and the very small fluctuations found later at the emission peak show that the emitting process has by then become essentially classical.
Fully excited two-level atoms separated by less than the transition wavelength cooperatively emit light in a short burst, a phenomenon called superradiance by R. Dicke in 1954 [Phys. Rev. 93, 99 (1954)]. The burst is characterized by a maximum intensity scaling with the square of the number of atoms NNN and a temporal width reduced by NNN compared to the single atom spontaneous decay time. Both effects are usually attributed to a synchronization of the electric dipole moments of the atoms occurring during the process of light emission. Contrary to this explanation, it was recently shown by use of a quantum path description that the peak intensity results from the quantum correlations among the atoms when occupying symmetric Dicke states. Here we investigate from this perspective the temporal evolution of the ensemble, starting in the small sample limit, i.e., when the atoms have mutual separations much smaller than the transition wavelength $\ensuremath{\lambda}$ and pass down the ladder of symmetric Dicke states. In addition, we explore the temporal evolution for the case of distant noninteracting atoms with mutual separations much larger than $\ensuremath{\lambda}$. We show that in this case a similar superradiant burst of the emitted radiation is observed if the quantum correlations of the atoms are generated by conditional photon measurements retaining the atomic ensemble within or close to the symmetric subspace.
The second-order photon correlation function g((2))(tau) of photons emitted by a continuously pumped ensemble of N two-level systems coupled to a single-mode optical cavity well below the lasing threshold is investigated theoretically. A giant photon bunching is found for N < 10 emitters as the microscopic counterpart of spontaneous emission noise driven quasi-periodic superradiant pulse sequences in macroscopic systems of large numbers of emitters N >> 1. The phenomenon of giant photon bunching is preserved even for N = 2 and can be explained by the cooperative evolution via dark and bright two-atom states resulting into emission of superradiant photon pairs. The sensitivity of g((2)) to microscopic dephasing processes and resonance frequency detuning opens the door for photon bunching spectroscopy.