We theoretically investigate the emission properties of a single-mode cavity coupled to a mesoscopic number of incoherently pumped quantum emitters. We propose an operational measure for the medium cooperativity, valid both in the bad- and in the good-cavity regimes. We show that the opposite regimes of subradiance and super-radiance correspond to negative and positive cooperativity, respectively. The lasing regime is shown to be characterized by non-negative cooperativity. In the bad-cavity regime we show that the cooperativity defines the transitions from subradiance to super-radiance. In the good-cavity regime it helps to define the lasing threshold, also providing distinguishable signatures indicating the lasing regime. Increasing the quality factor of the cavity mode induces a crossover from the solely super-radiant to the lasing regime. Furthermore, we verify that lasing is manifested in a wide range of positive cooperative behavior, showing that stimulated emission and super-radiance can coexist. The robustness of the cooperativity is studied with respect to experimental imperfections, such as inhomogeneous broadening and pure dephasing.
We theoretically investigate the emission properties of a single-mode cavity coupled to a mesoscopic number of incoherently pumped quantum emitters. We propose an operational measure for the medium cooperativity, valid both in the bad- and in the good-cavity regimes. We show that the opposite regimes of subradiance and super-radiance correspond to negative and positive cooperativity, respectively. The lasing regime is shown to be characterized by non-negative cooperativity. In the bad-cavity regime we show that the cooperativity defines the transitions from subradiance to super-radiance. In the good-cavity regime it helps to define the lasing threshold, also providing distinguishable signatures indicating the lasing regime. Increasing the quality factor of the cavity mode induces a crossover from the solely super-radiant to the lasing regime. Furthermore, we verify that lasing is manifested in a wide range of positive cooperative behavior, showing that stimulated emission and super-radiance can coexist. The robustness of the cooperativity is studied with respect to experimental imperfections, such as inhomogeneous broadening and pure dephasing.
We study the temporal correlations of the field emitted by an electromagnetic resonator coupled to a mesoscopic number of two-level emitters that are incoherently pumped by a weak external drive. We solve the master equation of the system for increasing number of emitters and as a function of the cavity quality factor, and we identify three main regimes characterized by well-distinguished statistical properties of the emitted radiation. For small cavity decay rates, the emission events are uncorrelated and the number of photons in the emitted field becomes larger than one, resembling the build-up of a laser field inside the cavity. At intermediate decay rates (as compared with the emitter–cavity coupling) and for a few emitters, the statistics of the emitted radiation is bunched and strikingly dependent on the parity of the number of emitters. The latter property is related to the cooperativity of the emitters mediated by their coupling to the cavity mode, and its connection with steady-state subradiance is discussed. Finally, in the bad cavity regime the typical situation of emission from a collection of individual emitters is recovered. We also analyze how the cooperative behavior evolves as a function of pure dephasing, which allows us to recover the case of a classical source made of an ensemble of independent emitters, similar to what is obtained for a very leaky cavity. State-of-the-art techniques of Q -switch of resonant cavities, allied with the recent capability of tuning single emitters in and out of resonance, suggest this system to be a versatile source of different quantum states of light.
Cooperative effects such as super(or sub)radiance in quantum systems arise from the interplay among quantum emitters. While bright superradiant states have been extensively studied and have yielded important insights into cooperative phenomena, subradiant states remain less explored due to their inherently dark state nature. However, subradiance holds significant potential as a valuable quantum resource exploiting long-lived and large-scale entanglement, which is a key for advancing quantum information technologies. Here, we demonstrate strong collective emission from a cavity-mediated steady-state subradiant state. In a tailored photonic environment with balanced cavity dissipation, emitter-field coupling strength, and incoherent pumping, two quantum dots coupled to a low-Q cavity exhibit a steady-state population in a subradiant state with a highly negative cooperativity parameter among the emitters. As a key signature of steady-state subradiance, the system shows strong photon bunching ( g(2)(0)>8 ) and suppressed single-photon decay (36 ns). Furthermore, we investigate that such collective interactions can be manipulated by controlling various system parameters, such as detuning and dephasing, supported by numerical simulations. Our approach to inducing cavity-mediated subradiance paves the way for generating and harnessing quantum correlations among quantum emitters via controlled dissipation. Subradiance is a cooperative effect in systems of quantum emitters, which is the opposite of superradiance, or enhanced emission, but has been less explored. Here, the authors demonstrate a steady-state subradiant state in a system of two InAs quantum dots coupled to a low-Q nanophotonic cavity.
Super-radiance is a striking phenomenon resulting from the collective interaction of emitters with light, and it is fundamentally related to the appearance of long-range correlations between the dipole moments of the emitters. As such, it represents a distinct phase of dissipative many-body systems compared to the case of independent emitters, similarly to how ferromagnetism stands out in magnetic materials in contrast to paramagnetism. In this work we address the conditions under which the transition to super-radiance can occur in ensembles of emitters subject to dephasing and individual decay -- a situation which is particularly relevant to the case of emitters in the solid state. The simplifying assumption of an ensemble of permutationally invariant emitters allows for the efficient solution of both the dissipative dynamics after a pulsed excitation, as well as of the steady state under incoherent pumping. This exact solution allows us to benchmark a truncated cumulant expansion approach, which can give predictions for arbitrarily big system sizes. We show that super-radiance is fundamentally robust to sizable dephasing and non-radiative decay rates, both under a pulsed excitation, as well as under continuous pumping. This robustness is the result of the collective acceleration effect of super-radiant emission with respect to the individual coupling to a local environment. We establish the universal critical scaling laws at the transition between normal radiance and super-radiance; and we show that, in the super-radiant phase, significant finite-size crossovers can be observed before reaching the asymptotic scaling regime. Our results pave the way for future experiments to provide a quantitative characterization of the scaling properties of super-radiance, seen as a distinct non-equilibrium many-body phase in ensembles of incoherently pumped emitters.
Cooperative phenomena, such as super(sub)radiance in quantum systems, arise from interactions among quantum emitters. Superradiance has been intensively studied from various platforms. While superradiance provides a good insight into the collective effect in quantum systems, exploiting the entangled state is not easy because of its strong radiative nature. In contrast, subradiance remains largely unexplored due to its inherent dark nature, despite its long lifetime and robustness against dephasing. Here, we experimentally demonstrate a long-lived subradiance among multiple quantum dots coupled to a low-Q cavity. The directional cavity mode provides a constant momentum condition, similar to a waveguide, and facilitates a shared radiative field among the quantum dots. By balancing cavity dissipation, incoherent pumping, and coupling strength, we realize steady-state subradiance rather than superradiance. As a key signature of subradiance, we observe a stark change in the photon statistics, with photon bunching exceeding the classical limit of 2. Additionally, we engineer the coupled system by changing detuning and incoherent pumping. Furthermore, modifying the pumping mechanism allows us to manipulate the dephasing of quantum dots involved in the cooperative process. Our experimental study on cavity-mediated cooperative phenomena among multiple quantum dots introduces a novel approach to generating quantum correlations with long-lived entanglement, offering potential applications in quantum storage and metrology.
We present a study of the quantum statistical properties of light emitted by two coherently driven atoms coupled to a single-mode cavity, an ideal setup to precisely investigate various aspects of collective behavior over a wide range of couplings to cavity and external drive. At high pumping and coupling, we predict the possibility of steady-state hyperradiance accompanied by (super-)bunching for an out of phase radiation. The mean photon number can be up to 2 orders of magnitude higher than in the single atom case. The highest nonclassicality in the sense of the smallest Mandel Q parameter is found when spontaneous emission, cavity decay, coherent pumping, and atom-cavity coupling are comparable. A quantum version of the negative binomial distribution with parameters directly related to Q characterizes the photon distribution in the cavity and its quantum features.
Cavity-embedded quantum emitters show strong modifications of free space radiation properties such as an enhanced decay known as the Purcell effect. The central parameter is the cooperativity C, the ratio of the square of the coherent cavity coupling strength over the product of cavity and emitter decay rates. For a single emitter, C is independent of the transition dipole moment and dictated by geometric cavity properties such as finesse and mode waist. In a recent work [Phys. Rev. Lett. 119, 093601 (2017)], we have shown that collective excitations in ensembles of dipole-dipole coupled quantum emitters show a disentanglement between the coherent coupling to the cavity mode and spontaneous free space decay. This leads to a strong enhancement of the cavity cooperativity around certain collective subradiant antiresonances. Here, we present a quantum Langevin equations approach aimed at providing results beyond the classical coupled dipoles model. We show that the subradiantly enhanced cooperativity imprints its effects onto the cavity output field quantum correlations while also strongly increasing the cavity-emitter system's collective Kerr nonlinear effect.