We present a unified and transparent theoretical framework for two longstanding phenomena in light-matter systems: collective emission and anomalous transport. Although both subjects have been extensively studied, we revisit them using a field-theoretical approach that solves the dressed Bloch wave functions of photons and electrons in an irradiated array of two-level atoms. This treatment reveals that the evolution of emission with irradiation frequency-from subradiance to superradiance-is directly encoded in the dressed photon momentum, which captures radiative decay and coherence. At the same time, photon-mediated interactions give rise to unconventional transport responses, including near-zero and even negative resistivity, whose microscopic origin can be consistently explained through the self-energy of the dressed electron. Framed in terms of Bloch polaritons, our results establish a direct link between radiative decay, cooperative interference, and transport anomalies, providing fresh insights into engineered light-matter platforms with tunable emission and transport properties.
We present a unified and transparent theoretical framework for two longstanding phenomena in light-matter systems: collective emission and anomalous transport. Although both subjects have been extensively studied, we revisit them using a field-theoretical approach that solves the dressed Bloch wave functions of photons and electrons in an irradiated array of two-level atoms. This treatment reveals that the evolution of emission with irradiation frequency-from subradiance to superradiance-is directly encoded in the dressed photon momentum, which captures radiative decay and coherence. At the same time, photon-mediated interactions give rise to unconventional transport responses, including near-zero and even negative resistivity, whose microscopic origin can be consistently explained through the self-energy of the dressed electron. Framed in terms of Bloch polaritons, our results establish a direct link between radiative decay, cooperative interference, and transport anomalies, providing fresh insights into engineered light-matter platforms with tunable emission and transport properties.
In a quantum system of arrayed two-level atoms interacting with light, the interacted (dressed) photon is propagating in a periodic medium and its eigenstate ought to be of Bloch type with lattice symmetry. As the energy of photon is around the spacing between the two atomic energy levels, the photon will be absorbed and is not in the propagating mode but the attenuated mode. Therefore an energy gap exists in the dispersion relation of the photonic Bloch wave of dressed photon in addition to the nonlinear behaviors due to atom-light interactions. There follows several interesting results which are distinct from those obtained through a linear dispersion relation of free photon. For example, slow light can exist, the density of state of dressed photon is non-Lorentzian and is very large around the energy gap; the Rabi oscillations become monotonically decreasing in some cases; and besides the superradiance occurs at long wavelengths, the spontaneous emission is also very strong near the energy gap because of the high density of state.
We present a framework to investigate the collective properties of atomic lattices in one, two, and three dimensions. We analyze the single-photon band structure and associated atomic decay rates, revealing a fundamental dependence on dimensionality. One- and two-dimensional arrays are shown to be inherently radiative, exhibiting band gaps and decay rates that oscillate between superradiant and subradiant regimes, as a function of lattice spacing. In contrast, three-dimensional lattices are found to be fundamentally non-radiative due to the inhibition of spontaneous emission, with decay only at discrete Bragg resonances. Furthermore, we demonstrate that this structural difference dictates the system dynamics, which crosses over from dissipative decay in lower dimensions to coherent transport in three dimensions. Our results provide insight into cooperative effects in atomic arrays at the single-photon level.
When quantum emitters couple indistinguishably to light, they can synchronize into a collective light matter system with radiative properties profoundly different from those of independent particles. To date, the resulting collective effects have largely been confined to point like or homogeneous ensembles. Here, we open access to a qualitatively new collective regime by realizing geometrically ordered, spatially extended atom arrays with subwavelength spacing. This establishes a fundamentally new platform in which collective emission is no longer confined to a single Dicke mode but instead emerges from an ordered network of photon mediated interactions. We find that 2D atom arrays undergo strong super and subradiant emission. Despite subwavelength spacing, we achieve site resolved imaging and directly observe the buildup of spatial correlations, demonstrating the transformation of cooperative decay into a strongly correlated many-body process. We observe extensive scaling of superradiance, uncover superradiant revivals, and reveal the ferromagnetic nature of superradiance and the antiferromagnetic nature of subradiance. Our results realize a novel programmable platform for exploring and utilizing dissipative many-body quantum physics, opening new possibilities for photon capture, storage, and atom photon entanglement.
In dense and ordered atomic arrays, destructive interference in photon emission leads to the emergence of subradiant states, which are protected from radiative decay and are characterized by long lifetimes. Within linear optics, subradiant states of one-dimensional chains can be interpreted as guided modes. Collective interactions in arrays have attracted a lot of interest recently, with work showing that collective emission can be used to realize improved quantum memories [1, 2] as well as almost-perfect atomic mirrors [3, 4], among other exciting applications. While tantalizing, these ideas strongly rely on one assumption: that atoms are two-level systems and only have a unique electronic ground state. However, most atoms exhibit a rich and complex internal structure. In this talk, I will discuss the properties of subradiant states of two-level and multilevel atoms. In particular, I will present a new mechanism for subradiance and atomic wave-guiding in atoms with hyperfine structure, which crucially depends on many-body correlations, a radical departure from conventional subradiant states found in classical-dipole lattices or two-level-atom arrays [5].
In this paper we attempt to unify the theoretical treatment of a variety of cooperative interaction phenomena occurring in resonantly interacting radiation-matter systems. The system consists of a multimode optical field interacting with N resonant atoms in a region of large spatial extent. The field and atoms may or may not be coupled to reservoirs. We derive a set of coupled master equations for the reduced matter and radiation density operators of the composite system in the first Born approximation, using a method due to Bogoliubov. These equations describe within a single framework phenomena involving superradiant emission and coherent propagation. In the first place, our theory generalizes existing formulations of the superradiance problem by treating the radiation field as part of the dynamical system rather than as a reservoir. Hence, our equations describe stimulated interaction effects, which are entirely absent in the usual superradiance master equations. Moreover, our equations contain terms describing the self-consistent interaction of an average field with a set of polarizable atoms, as in the coupled Bloch and Maxwell equations of the theory of coherent pulse propagation, and enable us to describe fluctuations, arising from incoherent emission, about the average behavior described by the Bloch-Maxwell theory. We solve formally the dynamical equation for the radiation density operator and obtain a displaced multivariate Gaussian distribution centered on the solution of the Maxwell wave equation, which has as parameters the first and second moments of the matter density operator. Then we derive and discuss the field and atomic-moment equations, both in the wave-number and position representations. The moment equations enable us to show the relationship between descriptions of superradiant damping based on the Bloch equations and those based on the existence of correlated atomic states, including both as special cases. We introduce reduced matter moments, which allow us to separate incoherent- and coherent-emission effects and enable us to discuss the question of the closure of the moment equations. Then we consider cases where the behavior of the atomic system is dominated by a strong coherent pump wave or where the atoms are in a symmetric correlated state and show how the slowly-varying-envelope approximation simplifies the radiation-moment equations in these two cases. In the former case, we obtain an approximate theory which consists, in lowest order, of the Bloch-Maxwell equations with radiative-damping terms, plus an equation describing the time development of the correlation function for field fluctuations. Returning to our general formalism, we relate the usual parameters of the theory of radiative decay and of resonant interactions to the more general quantities appearing in our spatial analysis. Finally, we discuss the importance of the stimulated-emission terms appearing in our theory and describe several extensions, including the introduction of inhomogeneous broadening.
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.