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arXiv:1107.5080

Superradiance of Harmonic Oscillators

Michael Delanty, S. Rebić, Jason Twamley

Published Jul 25, 2011• 0 citations
arXivHTMLPDF

Abstract

Superradiance, the enhanced collective emission of light from a coherent ensemble of quantum systems, has been typically studied in atomic ensembles. In this work we study the enhanced emission of energy from coherent ensembles of harmonic oscillators. We show that it should be possible to observe harmonic oscillator superradiance in a variety of physical platforms such as waveguide arrays in integrated photonics and resonator arrays in circuit QED. We find general conditions specifying when emission is superradiant and subradiant and find that superradiant, subradiant and dark states take the form of multimode squeezed coherent states and highly entangled multimode Fock states. The intensity, two-mode correlations and fraction of quanta trapped in the system after decay are calculated for a range of initial states including multimode Fock, squeezed, coherent and thermal states. In order to explore these effects, the Law and Eberly protocol [C. K. Law and J. H. Eberly, Phys. Rev. Lett. 76, 1055 (1996)] is generalized to prepare highly entangled multimode Fock states in circuit QED.

DOI
10.48550/arxiv.1107.5080

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Superradiance, the enhanced collective emission of light from a coherent ensemble of quantum systems, has been typically studied in atomic ensembles. In this work we study the enhanced emission of energy from coherent ensembles of harmonic oscillators. We show that it should be possible to observe harmonic oscillator superradiance in a variety of physical platforms such as waveguide arrays in integrated photonics and resonator arrays in circuit QED. We find general conditions specifying when emission is superradiant and subradiant and find that superradiant, subradiant and dark states take the form of multimode squeezed coherent states and highly entangled multimode Fock states. The intensity, two-mode correlations and fraction of quanta trapped in the system after decay are calculated for a range of initial states including multimode Fock, squeezed, coherent and thermal states. In order to explore these effects, the Law and Eberly protocol [C. K. Law and J. H. Eberly, Phys. Rev. Lett. 76, 1055 (1996)] is generalized to prepare highly entangled multimode Fock states in circuit QED.
We study the collective decay of an initially inverted ensemble of two-level emitters in two distinct scenarios: when coupled to a squeezed photonic reservoir and when interacting with a one-dimensional waveguide. Using a quantum-state diffusion approach to unravel the emission process, we investigate entanglement and classical correlations along individual quantum trajectories over time. This numerical analysis shows that despite an initial buildup of entanglement and a significant amount of entanglement due to either spin squeezing or dark states at late times, the essential features of the superradiant burst are well described by averages over fully factorizable states. We explain this observation in terms of an almost complete factorization of all 2-local observables, which we identify as a generic property of superradiant decay. Based on this insight, we provide a purely classical theory for the burst in squeezed superradiance, which is both intuitive and exact for a large number of emitters. Moreover, we find that our numerical approach also performs well in the presence of subradiant states, which dominate the slow residual decay of nonuniform ensembles at late times.
Recent works have shown that collective single photon spontaneous emission from an ensemble of N resonant two-level atoms is a rich field of study. Superradiance describes emission from a completely symmetric state of N atoms, with a single excited atom prepared with a given phase, for instance imprinted by an external laser. Instead, subradiance is associated with the emission from the remaining N−1 asymmetric states, with a collective decay rate less than the single-atom value. Here, we discuss the properties of the orthonormal basis of symmetric and asymmetric states and the entanglement properties of superradiant and subradiant states.
Superradiance in an ensemble of atoms leads to the collective enhancement of radiation in a particular mode shared by the atoms in their spontaneous decay from an excited state. The quantum aspects of this phenomenon are highlighted when such collective enhancement is observed in the emission of a single quantum of light. Here we report a further step in exploring experimentally the nonclassical features of superradiance by implementing the process not only with single excitations, but also in a two-excitation state. Particularly, we measure and theoretically model the wave packets corresponding to superradiance in both the single-photon and two-photon regimes. Such progress opens the way to the study and future control of the interaction of nonclassical light modes with collective quantum memories at higher photon numbers.
The interaction between light and matter has captivated physicists for centuries, from early studies of vision and refraction in ancient Greece to the development of quantum mechanics and quantum electrodynamics in the past century. While the response of a single quantum emitter to light is well understood, the radiative properties of an ensemble of closely spaced emitters are far more intricate. Coupling to a shared electromagnetic environment induces coherent and dissipative interactions between emitters, giving rise to a collective response that cannot be captured by treating them independently. In the regime of few excitations, the system hosts delocalized subradiant states, that is, coherent superpositions that are largely decoupled from the electromagnetic field and thus decay at suppressed rates. While this weak coupling makes subradiant states attractive for quantum technologies, it also renders them difficult to manipulate. At higher excitation densities, the intrinsic nonlinearity of emitters and the exponential growth of the Hilbert space make theoretical and numerical descriptions of the system and its dynamics increasingly challenging. This thesis explores two fundamental questions: How can subradiant and dark states be selectively accessed and harnessed for practical applications in quantum technologies? And how can interacting ensembles of quantum emitters be efficiently simulated to uncover their many-body physics? The first part of the thesis develops protocols for controlling and addressing dark states in free-space and waveguide-coupled atomic arrays, demonstrating their utility in quantum storage and the deterministic generation of entangled photonic states. Incorporating atomic motion, we further show that collective subradiant states can enhance cooling in dense atomic arrays, offering new avenues for controlling motional dynamics. In the second part, we introduce cumulant expansions of the equations of motion as a powerful tool to analytically and numerically investigate collective decay in the many-body regime. We first examine the collective decay of fully excited atomic arrays in free space, characterizing the onset and scaling of the superradiant burst across different geometries. In collaboration with experiments on ultracold erbium atoms in optical lattices, we provide the first direct observations of many-body collective effects in free-space ordered arrays, including early-time superradiant bursts, late-time subradiant tails, and the emergence of atomic correlations throughout the dynamics. Finally, we theoretically and numerically explore the transient formation of multi-excitation subradiant states, and demonstrate how the existence of multiple dissipation channels suppresses steady-state superradiance in extended arrays.
Superradiance, i.e., spontaneous emission of coherent radiation by an ensemble of two-level atoms in collective states introduced by Dicke in 1954, is one of the enigmatic problems of quantum optics. The startling gist is that even though the atoms have no dipole moment they radiate with increased intensity in particular directions. Following the advances in our understanding of superradiant emission by atoms in entangled W-states we examine the quantum statistical properties of superradiance. Such investigations require the system to have at least two excitations in order to explore the photon-photon correlations of the radiation emitted by such states. We present specifically results for the spatially resolved photon-photon correlations of systems prepared in doubly excited W-states and give conditions when the atomic system emits nonclassial light. Equally, we derive the conditions for the occurrence of bunching and even of superbunching, a rare phenomenon otherwise known only from nonclassical states of light like the squeezed vacuum. We finally investigate the photon-photon cross correlations of the spontaneously scattered light and highlight the nonclassicalty of such correlations. The theoretical findings can be implemented with current technology, e.g., using ions in a linear rf-trap, atoms in an optical lattice or quantum dots in a cavity.
In a previous investigation, a general theory for spontaneous emission from a system of NNN identical atoms or molecules was developed. This theory was based on the master equation recently derived in another paper. In that paper, the master equation relating to spontaneous emission from a system of harmonic oscillators was also derived. In the present investigation, the normally ordered correlation functions for the oscillator system are calculated and these are then used to calculate the radiation-field correlation functions in the far zone. These correlation functions are compared for two different modes of excitation, viz., (i) when each of the oscillators is excited initially to a Fock state, and (ii) when each of the oscillators is excited to some coherent state. It is found that the even-order (2n2n2n) correlation functions for the second mode of excitation (superradiant excitation) are of order N2n{N}^{2n}N2n higher than those for the first mode of excitation. It is also shown that the photoelectron counting distribution for the superradiant excitation is Poissonian. Finally, the non-Markoffian effects in the spontaneous emission are studied in detail and their connection with exact results is described.