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arXiv:2011.02548 · Physical Review Letters

Superradiance and Subradiance due to Quantum Interference of Entangled Free Electrons

Aviv Karnieli, Nicholas Rivera, Ady Arie, Ido E. Kaminer

Published Aug 5, 2021• 45 citations
arXivHTMLPDF

Abstract

When multiple quantum emitters radiate, their emission rate may be enhanced or suppressed due to collective interference in a process known as super- or subradiance. Such processes are well known to occur also in light emission from free electrons, known as coherent cathodoluminescence. Unlike atomic systems, free electrons have an unbounded energy spectrum, and, thus, all their emission mechanisms rely on electron recoil, in addition to the classical properties of the dielectric medium. To date, all experimental and theoretical studies of super- and subradiance from free electrons assumed only classical correlations between particles. However, dependence on quantum correlations, such as entanglement between free electrons, has not been studied. Recent advances in coherent shaping of free-electron wave functions motivate the investigation of such quantum regimes of super- and subradiance. In this Letter, we show how a pair of coincident path-entangled electrons can demonstrate either super- or subradiant light emission, depending on the two-particle wave function. By choosing different free-electron Bell states, the spectrum and emission pattern of the light can be reshaped, in a manner that cannot be accounted for by a classical mixed state. We show these results for light emission in any optical medium and discuss their generalization to many-body quantum states. Our findings suggest that light emission can be sensitive to the explicit quantum state of the emitting matter wave and possibly serve as a nondestructive measurement scheme for measuring the quantum state of many-body systems.

DOI
10.1103/physrevlett.127.060403

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When multiple quantum emitters radiate, their emission rate may be enhanced or suppressed due to collective interference in a process known as super- or subradiance. Such processes are well known to occur also in light emission from free electrons, known as coherent cathodoluminescence. Unlike atomic systems, free electrons have an unbounded energy spectrum, and, thus, all their emission mechanisms rely on electron recoil, in addition to the classical properties of the dielectric medium. To date, all experimental and theoretical studies of super- and subradiance from free electrons assumed only classical correlations between particles. However, dependence on quantum correlations, such as entanglement between free electrons, has not been studied. Recent advances in coherent shaping of free-electron wave functions motivate the investigation of such quantum regimes of super- and subradiance. In this Letter, we show how a pair of coincident path-entangled electrons can demonstrate either super- or subradiant light emission, depending on the two-particle wave function. By choosing different free-electron Bell states, the spectrum and emission pattern of the light can be reshaped, in a manner that cannot be accounted for by a classical mixed state. We show these results for light emission in any optical medium and discuss their generalization to many-body quantum states. Our findings suggest that light emission can be sensitive to the explicit quantum state of the emitting matter wave and possibly serve as a nondestructive measurement scheme for measuring the quantum state of many-body systems.
Coherent emission of light by free charged particles is believed to be successfully captured by classical electromagnetism in all experimental settings. However, recent advances triggered fundamental questions regarding the role of the particle wave function in these processes. Here, we find that even in seemingly classical experimental regimes, light emission is fundamentally tied to the quantum coherence and correlations of the emitting particle. We use quantum electrodynamics to show how the particle's momentum uncertainty determines the optical coherence of the emitted light. We find that the temporal duration of Cherenkov radiation, envisioned for almost a century as a shock wave of light, is limited by underlying entanglement between the particle and light. Our findings enable new capabilities in electron microscopy for measuring quantum correlations of shaped electrons. Last, we propose new Cherenkov detection schemes, whereby measuring spectral photon autocorrelations can unveil the wave function structure of any charged high-energy particle.
Spontaneous light emission is central to a vast range of physical systems and is a founding pillar for the theory of light–matter interactions. In the presence of complex photonic media, the description of spontaneous light emission usually requires advanced theoretical quantum optics tools such as macroscopic quantum electrodynamics, involving quantized electromagnetic fields. Although rigorous and comprehensive, the complexity of such models can obscure the intuitive understanding of many quantum-optical phenomena. Here, we review a method for calculating spontaneous emission and other quantum-optical processes without making explicit use of quantized electromagnetic fields. Instead, we introduce the concept of transition currents, comprising charges in matter that undergo transitions between initial and final quantum states. We show how predictions that usually demand advanced methods in quantum electrodynamics or quantum optics can be reproduced by feeding these transition currents as sources to the classical Maxwell equations. One then obtains the relevant quantum observables from the resulting classical field amplitudes, without washing out quantum optical effects. We show that this procedure allows for a straightforward description of quantum phenomena, even when going beyond the dipole approximation and single emitters. As illustrative examples, we calculate emission patterns and Purcell-enhanced emission rates in both bound-electron and free-electron systems. For the latter, we derive cathodoluminescence emission and energy-loss probabilities of free electrons interacting with nanostructured samples. In addition, we calculate quantum-beat phenomena in bound-electron systems and wave function-dependent optical coherence in free-electron systems. Remarkably, the transition-current formalism captures more complex phenomena, such as many-body interference effects and super-radiance of both bound- and free-electron systems, second-order processes such as two-photon emission, and quantum recoil corrections to free-electron radiation. We review a variety of light–matter interactions in fields ranging from electron microscopy to nanophotonics and quantum optics, for which the transition-current theoretical formalism facilitates practical simulations and a deeper understanding of novel applications.
Dicke superradiance, i.e., the enhanced spontaneous emission of coherent radiation, is often attributed to radiation emitted by synchronized dipoles coherently oscillating in phase. At the same time, Dicke derived superradiance assuming atoms in entangled Dicke states which do not display any dipole moment. To shed light on this apparent paradox, we study the intensity distribution arising from two identical two-level atoms prepared either in an entangled Dicke state or in a separable atomic state with a nonvanishing dipole moment. We find that the two configurations produce similar far-field intensity patterns, although they stem from fundamentally distinct types of coherence: while in the second case the atoms display coherence among the individual particles, leading to Young-type interference like that known from classical dipoles, atoms in Dicke states possess collective quantum coherence stemming from entanglement and quantum correlations of the state, leading to an interference pattern resulting from enhanced spontaneous emission. This demonstrates that the radiation generated by synchronized dipoles and Dicke superradiance---even if they do produce the same interference pattern---are fundamentally distinct phenomena and have to be interpreted in different ways.
There exist two families of superradiance phenomena: relying on free electrons or on correlated emission by ensembles of atoms. Here we investigate emission from ensembles of atoms driven by coherently shaped free electrons. This interaction creates superradiance emerging from both the atoms' and the electrons' coherence---with emission intensity that scales quadratically in both the number of atoms and number of electrons. This phenomenon enables electrons to become probes of quantum correlations in matter, with high temporal and spatial resolution.
We investigate collective radiant properties of two separated atoms in X-type quantum states. We show that quantum correlations measured by quantum discord (QD) can induce and enhance superradiance and subradiance in the two-atom system even though in the absence of interatomic quantum entanglement. We also explore quantum statistical properties of photons in the superradiance and subradiance by addressing the second-order correlation function. In particular, when the initial state of the two separated atoms is the Werner state with non-zero QD, we find that radiation photons in the superradiant region exhibit the nonclassical sub-Poissonian statistics and the degree of the sub-Poissonian statistics increases with increasing of the QD amount, while radiation photons in the subradiant region have either the sub-Poissonian or super-Poissonian statistics depending on the amount of QD and the directional angle. In the subradiant regime we predict the QD-induced photon statistics transition from the super-Poissonian to sub-Poissonian statistics. These results shed a new light on applications of QD as a quantum resource.