Subradiant States Research Articles

Subradiance and superradiant long-range excitation transport among quantum emitter ensembles in a waveguide

In contrast to free space, in waveguides the dispersive and dissipative dipole–dipole interactions among quantum emitters exhibit a periodic behavior over remarkably long distances. We propose a novel setup, to our knowledge, exploiting this long-range periodicity in order to create highly excited subradiant states and facilitate fast controlled collective energy transport among far-apart ensembles coupled to a waveguide. For sufficiently large ensembles, collective superradiant emission into the fiber modes dominates over its free space counterpart. We show that, for a large number of emitters, a fast transverse coherent pulse can create almost perfect subradiant states with up to 50% excitation. On the other hand, for a coherent excitation of one sub-ensemble above an overall excitation fraction of 50% we find a nearly lossless and fast energy transfer to the ground state sub-ensemble. This transport can be enhanced or suppressed by controlling the positions of the ensembles relative to each other, while it can also be realized with a random position distribution. In the optimally enhanced case this fast transfer appears as superradiant emission with subsequent superabsorption, yet, without a superradiant decay after the absorption. The highly excited subradiant states, as well as the superradiant excitation transfer, appear as suitable building blocks in applications such as active atomic clocks, quantum batteries, quantum information protocols, and quantum metrology procedures such as fiber-based Ramsey schemes.

Dissipative stabilization of maximal entanglement between nonidentical emitters via two-photon excitation

Two nonidentical quantum emitters, when placed within a cavity and coherently excited at the two-photon resonance, can reach stationary states of nearly maximal entanglement. In Vivas-Viaña, Martín-Cano, and Sánchez Muñoz [], we introduce a frequency-resolved Purcell effect stabilizing entangled W states among strongly interacting quantum emitters embedded in a cavity. Here we delve deeper into a specific configuration with a particularly rich phenomenology: two interacting quantum emitters under coherent excitation at the two-photon resonance. This scenario yields two resonant cavity frequencies where the combination of two-photon driving and Purcell-enhanced decay stabilizes the system into the subradiant and superradiant states, respectively. By considering the case of nondegenerate emitters and exploring the parameter space of the system, we show that this mechanism is merely one among a complex family of phenomena that can generate both stationary and metastable entanglement when driving the emitters at the two-photon resonance. We provide a global perspective of this landscape of mechanisms and contribute analytical characterizations and insights into these phenomena, establishing connections with previous reports in the literature and discussing how some of these effects can be optically detected. Published by the American Physical Society 2024

Collectively induced transparency and absorption in waveguide quantum electrodynamics with Bragg atom arrays

Collective quantum states, such as subradiant and superradiant states, are useful for controlling optical responses in many-body quantum systems. In this work, we study novel collective quantum phenomena in waveguide-coupled Bragg atom arrays with inhomogeneous frequencies. For atoms without free-space dissipation, collectively induced transparency is produced by destructive quantum interference between subradiant and superradiant states. In a large Bragg atom array, multi-frequency photon transparency can be obtained by considering atoms with different frequencies. Interestingly, we find collectively induced absorption (CIA) by studying the influence of free-space dissipation on photon transport. Tunable atomic frequencies nontrivially modify decay rates of subradiant states. When the decay rate of a subradiant state equals to the free-space dissipation, photon absorption can reach a limit at a certain frequency. In other words, photon absorption is enhanced with low free-space dissipation, distinct from previous photon detection schemes. We also show multi-frequency CIA by properly adjusting atomic frequencies. Our work presents a way to manipulate collective quantum states and exotic optical properties in waveguide quantum electrodynamics (QED) systems.

Tailoring the statistics of light emitted from two interacting quantum emitters

The interaction between quantum emitters leads to the formation of superradiant and subradiant states with possible applications in quantum technologies. To improve the characterization of light emission from these systems, we present here a systematic theoretical analysis of the intensity correlation from two strongly interacting quantum emitters at cryogenic temperatures as a function of the frequency and intensity of the excitation laser. This analysis effectively accounts for the effect of vibrational modes of the emitters and of phonons of the environment through the combined Debye-Waller/Franck-Condon factor. First, we analyze the color-blind intensity correlation and show that it can be tailored from strong antibunching to strong bunching by tuning the laser from the two-photon resonance to the transition frequency of the superradiant state. We also find a particularly complex behavior of the intensity correlation when the laser frequency is tuned to that of the transition of the subradiant state, giving raise to the possibility of emitting bunched and antibunched light depending on the laser intensity and the detuning between the two emitters. The numerical results are supported by analytical equations that can be used for the experimental characterization of the interacting emitters. Additionally, by selecting photons of particular frequencies, we analyze the rich landscape of frequency-resolved intensity correlations, which also depend on the laser detuning and intensity. The analysis of the frequency-resolved correlations provides further information about the different relaxation processes underlying the photon emission, unveiling one-photon and two-photon emission processes that cannot be resolved neither in the emission spectrum nor in the color-blind intensity correlation. These results show that two interacting emitters are a versatile and practical source of quantum light and highlight the usefulness of the intensity correlation to unveil complex dynamics in this system. Published by the American Physical Society 2024

Breakdown of steady-state superradiance in extended driven atomic arrays

Recent advances in generating well controlled dense arrangements of individual atoms in free space have generated interest in understanding how the extended nature of these systems influences superradiance phenomena. Here, we provide an in-depth analysis on how space-dependent light shifts and decay rates induced by dipole-dipole interactions modify the steady-state properties of coherently driven arrays of quantum emitters. We characterize the steady-state phase diagram, with particular focus on the radiative properties in the steady state. Interestingly, we find that diverging from the well-established Dicke paradigm of equal all-to-all interactions significantly modifies the emission properties. In particular, the prominent quadratic scaling of the radiated light intensity with particle number in the steady state—a hallmark of steady-state Dicke superradiance—is entirely suppressed, resulting in only linear scaling with particle number. We show that this breakdown of steady-state superradiance occurs due to the emergence of additional dissipation channels that populate not only superradiant states but also subradiant ones. The additional contribution of subradiant dark states in the dynamics leads to a divergence in the time scales needed to achieve steady states. Building on this, we further show that measurements taken at finite times for extended atom ensembles reveal properties closely mirroring the idealized Dicke scenario. Published by the American Physical Society 2024

Scaling Law for Kasha's Rule in Photoexcited Molecular Aggregates.

We study the photophysics of molecular aggregates from a quantum optics perspective, with emphasis on deriving scaling laws for the fast nonradiative relaxation of collective electronic excitations, referred to as Kasha's rule. Aggregates exhibit an energetically broad manifold of collective states with delocalized electronic excitations originating from near-field dipole-dipole exchanges between neighboring monomers. Photoexcitation at optical wavelengths, much larger than the monomer-monomer average separation, addresses almost exclusively symmetric collective states, which for an arrangement known as H-aggregate show an upward hypsochromic shift. The extremely fast subsequent nonradiative relaxation via intramolecular vibrational modes populates lower energy, subradiant states, resulting in effective inhibition of fluorescence. Our analytical treatment allows for the derivation of an approximate scaling law of this relaxation process, linear in the number of available low-energy vibrational modes and directly proportional to the dipole-dipole interaction strength between neighboring monomers.

Subradiant plasmonic cavities make bright polariton states dark

Abstract Nanostructured plasmonic surfaces allow for precise tailoring of electromagnetic modes within sub-diffraction mode volumes, boosting light–matter interactions. This study explores vibrational strong coupling (VSC) between molecular ensembles and subradiant “dark” cavities that support infrared quadrupolar plasmonic resonances (QPLs). The QPL mode exhibits a dispersion characteristic of bound states in the continuum (BIC). That is, the mode is subradiant or evanescent at normal incidence and acquires increasing “bright” dipole character with larger in-plane wavevectors. We deposited polymethyl methacrylate (PMMA) thin films on QPL substrates to induce VSC with the carbonyl stretch in PMMA and measured the resulting infrared (IR) spectra. Our computational analysis predicts the presence of “dark” subradiant polariton states within the near-field of the QPL mode, and “bright” collective molecular states. This finding is consistent with classical and quantum mechanical descriptions of VSC that predict hybrid polariton states with cavity-like modal character and N−1 collective molecular states with minimal cavity character. However, the behaviour is opposite of what is standardly observed in VSC experiments that use “bright” cavities, which results in “bright” polariton states that can be spectrally resolved as well as N−1 collective molecular states that are spectrally absent. Our experiments confirm a reduction of molecular absorption and other spectral signatures of VSC with the QPL mode. In comparison, our experiments promoting VSC with dipolar plasmonic resonances (DPLs) reproduce the conventional behavior. Our results highlight the significance of cavity mode symmetry in modifying the properties of the resultant states from VSC, while offering prospects for direct experimental probing of the N−1 molecule-like states that are usually spectrally “dark”.

Extreme single-excitation subradiance from two-band Bloch oscillations in atomic arrays

Atomic arrays provide an important quantum optical platform with photon-mediated dipole–dipole interactions that can be engineered to realize key applications in quantum information processing. A major obstacle for such applications is the fast decay of the excited states. By controlling two-band Bloch oscillations of single excitation in an atomic array under an external magnetic field, here we show that exotic subradiance can be realized and maintained with orders of magnitude longer than the spontaneous decay time in atomic arrays with the finite size. The key finding is to show a way for preventing the wavepacket of excited states scattering into the dissipative zone inside the free space light cone, which therefore leads to the excitation staying at a subradiant state for an extremely long decay time. We show that such operation can be achieved by introducing a spatially linear potential from the external magnetic field in the atomic arrays and then manipulating interconnected two-band Bloch oscillations along opposite directions. Our results also point out the possibility of controllable switching between superradiant and subradiant states, which leads to potential applications in quantum storage.

A photonic engine fueled by entangled two atoms

Entangled states are an important resource for quantum information processing and for the fundamental understanding of quantum physics. An intriguing open question would be whether entanglement can improve the performance of quantum heat engines in particular. One of the promising platforms to address this question is to use entangled atoms as a non-thermal bath for cavity photons, where the cavity mirror serves as a piston of the engine. Here we theoretically investigate a photonic quantum engine operating under an effective reservoir consisting of quantum-correlated pairs of atoms. We find that maximally entangled Bell states alone do not help extract useful work from the reservoir unless some extra populations in the excited states or ground states are taken into account. Furthermore, high efficiency and work output are shown for the non-maximally entangled superradiant state, while negligible for the subradiant state due to lack of emitted photons inside the cavity. Our results provide insights in the role of quantum-correlated atoms in a photonic engine and present new opportunities in designing a better quantum heat engine.

Superradiant and subradiant states in lifetime-limited organic molecules through laser-induced tuning

Superradiant and subradiant states in lifetime-limited organic molecules through laser-induced tuning

Collectively enhanced Ramsey readout by cavity sub- to superradiant transition

When an inverted ensemble of atoms is tightly packed on the scale of its emission wavelength or when the atoms are collectively strongly coupled to a single cavity mode, their dipoles will align and decay rapidly via a superradiant burst. However, a spread-out dipole phase distribution theory predicts a required minimum threshold of atomic excitation for superradiance to occur. Here we experimentally confirm this predicted threshold for superradiant emission on a narrow optical transition when exciting the atoms transversely and show how to take advantage of the resulting sub- to superradiant transition. A π/2-pulse places the atoms in a subradiant state, protected from collective cavity decay, which we exploit during the free evolution period in a corresponding Ramsey pulse sequence. The final excited state population is read out via superradiant emission from the inverted atomic ensemble after a second π/2-pulse, and with minimal heating this allows for multiple Ramsey sequences within one experimental cycle. Our scheme is an innovative approach to atomic state readout characterized by its speed, simplicity, and highly directional emission of signal photons. It demonstrates the potential of sensors using collective effects in cavity-coupled quantum emitters.

Spatially oriented correlated emission based on selective drive of diatomic superradiance states

<sec>In recent years, the radiative properties of atomic systems have been a hot topic in the research fields of quantum optics and quantum information. With the continuous development of nanophotonics, quantum antennas have become an important model for studying atomic radiation. In order to investigate these phenomena in depth, we investigate a system composed of two two-level atoms, and study the two-photon emission phenomenon of diatomic system under conditions of driving directional tunable laser field, interatomic dipole-dipole interaction, and spontaneous emission coherence.</sec><sec>In this study, we diagonalize the atomic Hamiltonian to obtain the eigenvalues and entangled states of the system (symmetric and asymmetric states of two atoms), and use the rotating wave approximation to rotate the system into the laser frame. The evolution of the system is characterized mainly by the evolution of symmetric and asymmetric state, as well as the evolution of coherent terms. In our studies it is found that for identical atoms, certain laser directions and geometric configurations can exclusively drive the superradiant and subradiant states of atoms, which can enhance the first-order interference effect of the atoms and markedly increase the probability of two-photon emission in a specific detection direction. When the superradiant state of the atom is solely driven, there will be no coupling between the superradiant state and subradiant state, resulting in a correlation function angular distribution that is symmetric along the direction perpendicular to atomic axis. Further adjusting the laser direction causes the atomic interference patterns to shift, and the system will exhibit two-photon emission characteristics on one side or both sides.</sec><sec>For nonidentical atomic systems, due to detuning between the two atoms, the laser cannot drive the superradiant state or subradiant state individually, and the influence of changing the laser direction on the coupling strength diminishes with the increase of detuning between the atoms. When the laser is in resonance with one of the atoms, due to the atomic interactions, the other atom can achieve the strongest coherent effect without resonating with the laser. This research reveals that atomic detuning is crucial for the correlation values and angular distribution of the correlation function. By adjusting the atomic detuning and laser direction, the system can display highly directed one-sided two-photon emission characteristics. However, different dissipation rates will lead the probability of two-photon emission to decrease. Our studies can achieve highly directional two-photon emission on one side or both sides, which provides a theoretical basis for studying the two-photon emission of nanoantennas.</sec>

Dynamic population of multiexcitation subradiant states in incoherently excited atomic arrays

The authors theoretically investigate the creation of subradiant states with multiple excitations in dense arrays of quantum emitters, which is a long-lasting challenge due to the complexity of the system and the experimental limitations in state-of-the-art platforms. The authors analyze the effects of trapping geometry and correlations on the subradiant-state formation and provide insights for controlling and utilizing subradiant states in quantum technologies.

Effect of Motion of Atoms on the Character of Subradiance of Cold Dilute Ensembles Excited by Resonant Pulsed Radiation

The dynamics of the fluorescence of dilute atomic ensembles excited by resonant pulsed radiation has been analyzed. It has been found that the motion of atoms in ensembles cooled to sub-Doppler temperatures in certain time intervals noticeably enhances subradiance rather than suppressing it. It has also been shown that the time dependence of the spontaneous decay rate can be nonmonotonic. The revealed features occur because the character of the slow decay of the atomic excitation is determined after a certain time mainly by the dynamics of subradiant two-atom quantum states, which are due to the resonant dipole–dipole interaction between atoms.

On the Dynamics of the Tavis–Cummings Model

The purpose of this paper is to present a comprehensive study of the Tavis-Cummings model from a system-theoretic perspective. A typical form of the Tavis-Cummings model is composed of an ensemble of non-interacting two-level systems (TLSs) that are collectively coupled to a common cavity resonator. The associated quantum linear passive system is proposed, whose canonical form reveals typical features of the Tavis-Cummings model, including $\sqrt{N}$- scaling, dark states, bright states, single-excitation superradiant and subradiant states. The passivity of this linear system is related to the vacuum Rabi mode splitting phenomenon in Tavis-Cummings systems. On the basis of the linear model, an analytic form is presented for the steady-state output state of the Tavis-Cummings model driven by a single-photon state. Master equations are used to study the excitation properties of the Tavis-Cummings model in the multi-excitation scenario. Finally, in terms of the transition matrix for a linear time-varying system, a computational framework is proposed for calculating the state of the Tavis-Cummings model, which is applicable to the multi-excitation case.

Waveguide quantum electrodynamics: Collective radiance and photon-photon correlations

Quantum emitters coupled to waveguides experience long-range interactions mediated by photons. This leads to superradiant and subradiant states, photon bound states, and various mechanisms for the preparation of entangled states of the emitters. This article reviews experiments on a wide range of systems and their description by theoretical methods and insights from different fields of physics.

Temperature-modulated superradiance near phase transition material

We study the interaction between two quantum emitters connected through vanadium dioxide (VO2) which exhibits a first-order metal–insulator transition (MIT). The experimental data describing the dielectric function of VO2 in this study are collected from previously published works. The radiative states denoted as decay factor of two quantum emitters in the reflection and transmission configurations are investigated in detail. We find that the interconversion of the superradiant and subradiant states can easily be achieved in both configurations by controlling the temperature of VO2. The transition of decay factors from insulator to metal (heating process) and metal to insulator (cooling process) follows different paths. These factors exhibit hysteresis phenomenon and form a hysteresis loop. We also find that the decay factor in either the heating or cooling process increases sharply and reaches a maximum value at the phase transition temperature. The temperature-modulated superradiance obtained in this work offers a new efficient method to control the interaction between quantum emitters.

Quantum Electrodynamics of Dicke States: Resonant One-Photon Exchange Energy and Entangled Decay Rate

We calculate the fully retarded one-photon exchange interaction potential between electrically neutral, identical atoms, one of which is assumed to be in an excited state, by matching the scattering matrix (S matrix) element with the effective Hamiltonian. Based on the Feynman prescription, we obtain the imaginary part of the interaction energy. Our results lead to precise formulas for the distance-dependent enhancement and suppression of the decay rates of entangled superradiant and subradiant Dicke states (Bell states), as a function of the interatomic distance. The formulas include a long-range tail due to entanglement. We apply the result to an example calculation involving two hydrogen atoms, one of which is in an excited P state.

Control of Localized Single- and Many-Body Dark States in Waveguide QED.

Subradiant states in a finite chain of two-level quantum emitters coupled to a one-dimensional reservoir are a resource for superior photon storage and their controlled release. As one can maximally store one energy quantum per emitter, storing multiple excitations requires delocalized states, which typically exhibit fermionic correlations and antisymmetric wave functions, thus making them hard to access experimentally. Here we identify a new class of quasilocalized dark states with up to half of the qubits excited, which only appear for lattice constants of an integer multiple of the wavelength. These states allow for a high-fidelity preparation and minimally invasive readout in state-of-the-art setups. In particular, we suggest an experimental implementation using a coplanar waveguide coupled to superconducting transmon qubits on a chip. With minimal free space and intrinsic losses, virtually perfect dark states can be achieved for a low number of qubits featuring fast preparation and precise manipulation.

Subradiant states for two imperfect quantum emitters coupled by a nanophotonic waveguide

Coherent interactions between quantum emitters in tailored photonic structures is a fundamental building block for future quantum technologies, but remains challenging to observe in complex solid-state environments, where the role of decoherence must be considered. Here, we investigate the optical interaction between two quantum emitters mediated by one-dimensional waveguides in a realistic solid-state environment, focusing on the creation, population and detection of a sub-radiant state, in the presence of dephasing. We show that as dephasing increases, the signatures of sub-radiance quickly vanish in intensity measurements yet remain pronounced in photon correlation measurements, particularly when the two emitters are pumped separately so as to populate the sub-radiant state efficiently. The applied Green's tensor approach is used to model a photonic crystal waveguide, including the dependence on the spatial position of the integrated emitter. The work lays out a route to the experimental realization of sub-radiant states in nanophotonic waveguides containing solid-state emitters.