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arXiv:2406.09100 · Journal of Physics A Mathematical and Theoretical

Emergence of superradiance in dissipative dipolar-coupled spin systems

Saptarshi Saha, Yeshma Ibrahim, Rangeet Bhattacharyya

Published Dec 12, 2024• 2 citations

Abstract

Abstract In the superradiance phenomenon, a collection of non-interacting atoms exhibits collective dissipation due to interaction with a common radiation field, resulting in a non-monotonic decay profile. This work shows that the dissipative dipolar-coupled systems exhibit an identical collective dissipation aided by the nonsecular part of the dipolar coupling. We consider a simplified dipolar network where the dipolar interaction between the spin-pairs is assumed to be identical. For a suitable choice of the initial condition, the resulting dynamics requires dealing with a smaller subspace that helps extend the analysis to a larger spin network. To include the nonsecular dipolar relaxation, we use a fluctuation-regulated quantum master equation. Moreover, we find that for an ensemble of N spins, the maximum intensity of the radiation exhibits a nearly quadratic scaling (N 2), and the dipolar relaxation time follows an inverse square proportionality ( 1 / N 2 ); these two observations help characterize the emergence of superradiance. Our results agree well with the standard results of pure spin superradiance observed experimentally in various systems.

DOI: 10.1088/1751-8121/ad9e54

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Abstract In the superradiance phenomenon, a collection of non-interacting atoms exhibits collective dissipation due to interaction with a common radiation field, resulting in a non-monotonic decay profile. This work shows that the dissipative dipolar-coupled systems exhibit an identical collective dissipation aided by the nonsecular part of the dipolar coupling. We consider a simplified dipolar network where the dipolar interaction between the spin-pairs is assumed to be identical. For a suitable choice of the initial condition, the resulting dynamics requires dealing with a smaller subspace that helps extend the analysis to a larger spin network. To include the nonsecular dipolar relaxation, we use a fluctuation-regulated quantum master equation. Moreover, we find that for an ensemble of N spins, the maximum intensity of the radiation exhibits a nearly quadratic scaling (N 2), and the dipolar relaxation time follows an inverse square proportionality ( 1 / N 2 ); these two observations help characterize the emergence of superradiance. Our results agree well with the standard results of pure spin superradiance observed experimentally in various systems.

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

N

and a temporal width reduced by

N

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

λ

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

λ

. 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 excited to high-lying Rydberg states they interact strongly with dipolar forces. The resulting state-dependent level shifts allow us to study many-body systems displaying intriguing nonequilibrium phenomena, such as constrained spin systems, and are at the heart of numerous technological applications, e.g., in quantum simulation and computation platforms. Here, we show that these interactions also have a significant impact on dissipative effects caused by the inevitable coupling of Rydberg atoms to the surrounding electromagnetic field. We demonstrate that their presence modifies the frequency of the photons emitted from the Rydberg atoms, making it dependent on the local neighborhood of the emitting atom. Interactions among Rydberg atoms thus turn spontaneous emission into a many-body process which manifests, in a thermodynamically consistent Markovian setting, in the emergence of collective jump operators in the quantum master equation governing the dynamics. We discuss how this collective dissipation-stemming from a mechanism different from the much studied superradiance and subradiance-accelerates decoherence and affects dissipative phase transitions in Rydberg ensembles.

We investigate the emergence of cooperative radiation phenomena in ensembles of two-level atoms coupled to a lossy resonant cavity beyond the Markovian and mean-field approximations. By deriving a complete analytical solution for the two-emitter case and employing a numerically exact method for larger ensembles, we characterize the full transition from Markovian to non-Markovian collective dynamics for systems of up to

10^3

emitters. Our results reveal three distinct regimes: a Markovian phase exhibiting the standard superradiant burst, a non-Markovian phase featuring spontaneous superabsorption of the emitted field, and a critical regime marked by pulsed collective emission. We show that the critical spectral width separating these behaviors increases monotonically with the number of emitters, demonstrating that environmental memory effects can be enhanced by cooperativity. Finally, we find that the superradiant scaling of the peak intensity progressively degrades with increasing system size, approaching a subquadratic law in the limit of a perfect cavity. In this regime, spontaneous superabsorption emerges as a distinct manifestation of non-Markovian cooperativity.

We have developed a novel method to describe superradiance and related cooperative and collective effects in a closed form. Using the method we derive a two-atom master equation in which any complexity of atomic levels, semiclassical coupling fields and quantum fluctuations in the fields can be included, at least in principle. As an example, we consider the dynamics of an initially inverted two-level system and show how even such in a simple system phenomena such as the initial radiation burst or broadening due to dipole-dipole interactions occur, but it is also possible to estimate the population of the subradiant state during the radiative decay. Finally, we find that correlation only, not entanglement is responsible for superradiance.

The question addressed here is: What originates pure spin superradiance in a polarized spin system placed inside a resonantor? The term ``pure'' means that no initial coherence is imposed on spins, and its appearance manifests a purely self-organized collective effect. An accurate solution of evolution equations for a microscopic model is given. The results show that the resonator Nyquist noise does not play any role in starting spin superradiance, but the emergence of the latter is initiated by local spin fluctuations due to nonsecular dipole interactions.