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arXiv:1201.2491 · Physical Review A

Positive- P phase-space-method simulation of superradiant emission from a cascade atomic ensemble

H. H. Jen

Published Jan 24, 2012• 24 citations
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Abstract

The superradiant emission properties from an atomic ensemble with cascade level configuration is numerically simulated. The correlated spontaneous emissions (signal then idler fields) are purely stochastic processes which are initiated by quantum fluctuations. We utilize the positive-$P$ phase-space method to investigate the dynamics of the atoms and counterpropagating emissions. The light field intensities are calculated, and the signal-idler correlation function is studied for different optical depths of the atomic ensemble. A shorter correlation time scale for a denser atomic ensemble implies a broader spectral window needed to store or retrieve the idler pulse.

DOI
10.1103/physreva.85.013835

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The superradiant emission properties from an atomic ensemble with cascade level configuration is numerically simulated. The correlated spontaneous emissions (signal then idler fields) are purely stochastic processes which are initiated by quantum fluctuations. We utilize the positive-PPP phase-space method to investigate the dynamics of the atoms and counterpropagating emissions. The light field intensities are calculated, and the signal-idler correlation function is studied for different optical depths of the atomic ensemble. A shorter correlation time scale for a denser atomic ensemble implies a broader spectral window needed to store or retrieve the idler pulse.
Superradiant biphoton emission from atomic ensembles provides a powerful route to generating highly correlated quantum light, yet its microscopic physical origin has remained incompletely understood. In particular, it is often unclear how collective enhancement, spontaneous emission, and vacuum fluctuations jointly give rise to both paired biphoton generation and unavoidable unpaired background within a single, self-consistent framework. Here we present a fully quantum microscopic theory within a unified Heisenberg--Langevin--Maxwell framework that explicitly incorporates dissipation and quantum noise, thereby revealing the microscopic origin of superradiant biphoton emission in atomic ensembles. The theory provides a consistent description of parametric gain and unpaired noise within the same open-quantum-system framework and applies to both Doppler-free cold atomic ensembles and Doppler-broadened warm vapors. In the high-optical-depth regime, the coupled propagation equations admit analytical solutions, under which the biphoton dynamics rigorously reduce to an effective collective two-level emission process. Within this limit, the biphoton correlation time and spectral properties are shown to obey closed-form scaling relations governed by optical depth and excited-state decoherence. Our results establish a unified microscopic picture of superradiant biphoton generation and clarify the fundamental role of vacuum fluctuations and dissipation in setting the brightness, pairing efficiency, and temporal structure of atomic biphoton sources, with direct relevance to quantum networking and atomic quantum interfaces.
In this thesis, we investigate the quantum mechanical interaction of light with matter in the form of a gas of ultracold atoms: the atomic ensemble. We present a theoretical analysis of two problems, which involve the interaction of quantized electromagnetic fields (called signal and idler) with the atomic ensemble (i) cascade two-photon emission in an atomic ladder configuration, and (ii) photon frequency conversion in an atomic diamond configuration. The motivation of these studies comes from potential applications in long-distance quantum communication where it is desirable to generate quantum correlations between telecommunication wavelength light fields and ground level atomic coherences. We develop a theory of correlated signal-idler pair correlation. The analysis is complicated by the possible generation of multiple excitations in the atomic ensemble. An analytical treatment is given in the limit of a single excitation assuming adiabatic laser excitations. The analysis predicts superradiant timescales in the idler emission in agreement with experimental observation. To relax the restriction of a single excitation, we develop a different theory of cascade emission, which is solved by numerical simulation of classical stochastic differential equation using the theory of open quantum systems. The simulations are in good qualitative agreement with the analytical theory of superradiant timescales. We provide a quantum theory of near-infrared to telecom wavelength conversion in the diamond configuration. The system provides a crucial part of a quantum-repeater memory element, which enables a "stored" near-infrared photon to be converted to a telecom wavelength for transmission without the destruction of light-atom quantum correlation.
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.
A theory of phase-matched cascade correlated emission is developed based on a source field approach. An ensemble of three-level atoms is prepared in a phased state for which the probability to have two excitations is negligibly small. The field intensity radiated on each of the transitions is calculated. The radiation on the upper transition is isotropic and unpolarized, but the phase-matched component on the lower transition can be directional and polarized. Moreover, for sufficiently high optical densities, the emission on the lower transition can be superradiant. In addition to the field intensities, the joint probability for emission on both transitions is calculated, exhibiting correlations in both the directions of emission and polarization of the fields.