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arXiv:1112.1975 · Physical Review A

Superradiance in spin- j particles: Effects of multiple levels

Guin-Dar Lin, Susanne F. Yelin

Published Mar 26, 2012• 26 citations
arXivHTMLPDF

Abstract

We study the superradiance dynamics in a dense system of atoms each of which can be generally a spin-$j$ particle, with $j$ an arbitrary half-integer. We generalize Dicke's superradiance point of view to multiple-level systems and compare the results based on a novel approach we developed previously [Lin and Yelin, Adv. Atom. Mol. Opt. Phys. 61, in press (2012)]. Using this formalism we derive an effective two-body description that shows cooperative and collective effects for spin-$j$ particles, taking into account the coherence of transitions between different atomic levels. We find that superradiance, which is well known as a many-body phenomenon, can also be modified by multiple-level effects. We also discuss the feasibility and propose that our approach can be applied to polar molecules, for their vibrational states have a multilevel structure which is partially harmonic.

DOI
10.1103/physreva.85.033831

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We study the superradiance dynamics in a dense system of atoms each of which can be generally a spin-jjj particle, with jjj an arbitrary half-integer. We generalize Dicke's superradiance point of view to multiple-level systems and compare the results based on a novel approach we developed previously [Lin and Yelin, Adv. Atom. Mol. Opt. Phys. 61, in press (2012)]. Using this formalism we derive an effective two-body description that shows cooperative and collective effects for spin-jjj particles, taking into account the coherence of transitions between different atomic levels. We find that superradiance, which is well known as a many-body phenomenon, can also be modified by multiple-level effects. We also discuss the feasibility and propose that our approach can be applied to polar molecules, for their vibrational states have a multilevel structure which is partially harmonic.
Up to now, the problem of the influence of level degeneracy on superradiance has been neglected. We describe here a first approach to this problem, in the frame of "small system" quantum model, generalized to the case of a collection of atoms with two degenerate levels of angular momenta jjj and ${j}^{\ensuremath{'}}$ connected by an electric or magnetic dipole transition. The differences between this case and the well-known case of two (nondegenerate) level atoms are of two types. The first type is due to the competition between different transitions sharing a common state: superradiant emission on a transition inhibits or initiates superradiance on transitions with smaller transition probability, depending upon which state, upper or lower, is the common one. This effect does not come from the equality of the different wavelengths and would also appear with the same states even if the degeneracy were removed; its qualitative influence on the features of the superradiant pulse can be easily estimated. The second type of differences is quite specific to level degeneracy and consists in interferences between the transitions of the collective system having the same frequency and polarization. In analogy with the description of collections of two-level atoms as spin-\textonehalf{} systems, a group-theoretical description of the considered collection of atoms is found suitable; the problem of the determination of a basis of collective states and its group-theoretical implications are discussed; in particular, it is found that the isotropic character of spontaneous emission allows us to use tensorial formalism and simplifies the formal description of the problem.
We investigate cooperative phenomena and superradiance for vibrational transitions in polar molecule spectroscopy of high optical-depth samples. Such cooperativity comes from the build-up of inter-particle coherence through dipole–dipole interactions and leads to speed-up of decay processes. We compare our calculation to recent work and find very good agreement, suggesting that superradiant effects need to be taken into account in a wide variety of ultracold molecule experiments, including vibrational and rotational states.
Dicke's superradiance from a gas system of atoms and molecules was described in terms of two-level atoms, i.e., as an assembly of half-spin operators. In this system the magnitude of the total spin, which is called a cooperation number, is conserved at the maximum for the whole radiative process. We will answer in this paper how this superradiance is modified in the crystal in which an excitation can propagate from atom to atom through dipolar interactions. As a prototype of a crystal, we choose a linear chain of two-level atoms. The superradiance master equation of this system can be solved in terms of the exact solution of Lieb, Shultz, and Mattis for the spin system. The first effect is that the emitted frequency shows opposite shifts red and blue, respectively, for the first and second halves of the superradiance pulse, or vice versa, depending upon the sign of the transfer-matrix element of the excitation. The second effect is the appearance of a slow component in the emission tail, which originates from mixture of the states with smaller cooperation numbers or smaller oscillator strength under the transfer of the excitations. These results are demonstrated for a mesoscopic system of linear chains.
Exploring operational regimes of many-body cavity QED with multilevel atoms remains an exciting research frontier for their enhanced storage capabilities of intralevel quantum correlations. In this work, we consider an experimentally feasible many-body cavity QED model describing a four-level system, where each of those levels is formed from a combination of different spin and momentum states of ultracold atoms in a cavity. The resulting model comprises a pair of Dicke Hamiltonians constructed from pseudospin operators, effectively capturing two intertwined superradiant phase transitions. The phase diagram reveals regions featuring weak and strong entangled states of spin and momentum atomic degrees of freedom. These states exhibit different dynamical responses, ranging from slow to fast relaxation, with the added option of persistent entanglement temporal oscillations. We discuss the role of cavity losses in steering the system's dynamics into such entangled states and propose a readout scheme that leverages different light polarizations within the cavity. Our work paves the way to connect the rich variety of non-equilibrium phase transitions that occur in many-body cavity QED to the buildup of quantum correlations in systems with multilevel atom descriptions. Published by the American Physical Society 2024
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.
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.