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

An array of radiatively coupled emitters is an exciting new platform for generating, storing, and manipulating quantum light. However, the simultaneous positioning and tuning of multiple lifetime-limited emitters into resonance remains a significant challenge. Here we report the creation of superradiant and subradiant entangled states in pairs of lifetime-limited and sub-wavelength spaced organic molecules by permanently shifting them into resonance with laser-induced tuning. The molecules are embedded as defects in an organic nanocrystal. The pump light redistributes charges in the nanocrystal and dramatically increases the likelihood of resonant molecules. The frequency spectra, lifetimes, and second-order correlation agree with a simple quantum model. This scalable tuning approach with organic molecules provides a pathway for observing collective quantum phenomena in sub-wavelength arrays of quantum emitters.

At sub-wavelength spacings, quantum emitters interact collectively with the electromagnetic field.Absorption and emission from separated atoms interfere, leading to super-and subradiant emitter states [1,2].The subradiant states form a decoherence free-subspace [3,4] useful for the manipulation of quantum states [5] and the simulation of many-body states [6,7].The collective emission also creates a wide variety of quantum states of light [8][9][10], which can be useful in quantum imaging and sensing [11].In regular arrays, collective emitters can function as light-matter interfaces of unit coupling, allowing the efficient storage and manipulation of light [4,[12][13][14][15].While optical superradiance has been observed in a wide variety of atomic [16][17][18][19][20] and solid-state ensembles [21][22][23][24], the observation of individual states is hampered by three major requirements: subwavelength positioning, tuning into resonance, and minimizing dephasing from the environment.The realization of all three has only recently been demonstrated for two emitters using quantum dots coupled to a waveguide [25] and organic molecules tuned by nano-electrodes [26], but the challenge remains to scale this up to large system sizes.
In this work, we demonstrate a new scalable method for tuning lifetime-limited organic molecules in close proximity into resonance.We observe the superradiant and subradiant states for a pair of molecules as they are brought into resonance using laser-induced tuning, as shown in Fig. 1(g).Dibenzoterrylene molecules embedded as defects in an anthracene crystal [27,28] are excellent quantum emitters and lifetime-limited below 3 K [29,30].The tuning light causes migration of charges within the nanocrystal [31], locally decreasing inhomogeneous broadening.After tuning, the likelihood of pairs of molecules interacting is three orders of magnitude greater than would be expected for randomly distributed positions and frequencies.
We characterize multiple molecule pairs at large detuning and near resonance and find excellent agreement of the linewidths, lifetimes, and second-order correlations with a master equation simulation.The agreement with a simple model, ease of fabrication, and scalability of the tuning method demonstrate that organic molecules are a promising platform for creating cooperative phenomena in arrays of quantum emitters.

Methods:
Dibenzoterrylene (DBT) molecules, shown in Fig. 1(b), are embedded as defects in anthracene nanocrystals [27,28,32], with a HOMO-LUMO transition near 785 nm [33].Below 3 K, the transition is lifetime-limited with high purity of single-photon emission, measured through linewidths and autocorrelation spectra, as shown in Fig. 1(d, e).The excited state decays to the zero-phonon line of the ground vibrational state with a probability of 30%, given by the product of the Franck-Condon and Debye-Waller factors.
DBT and other polyaromatic hydrocarbons are leading candidates for solid-state quantum emitters and have demonstrated 94% indistinguishability for two photons from the same emitter [34], 70% indistinguishability for photons from different emitters [35], and a photon collection efficiency of 99% [36].
Anthracene nanocrystals doped with a few hundred DBT molecules are self-assembled by precipitation from solution in a sonicator [32] and vary from 200 nm to 1 µm in size.The DBT molecule transition frequencies can be tuned by 100 GHz through exposure to intense laser light, as demonstrated in Ref. [31].The tuning persists after the pump light is turned off and is likely due to a photoionization process, whereby an electron from DBT is mobilized into the surrounding lattice, resulting in a Stark shift through the static electric field.We pump the nanocrystals with around 1 mW of 785 nm light focused through an objective to a waist of 1.5 µm for tens of minutes.We then look for a two-photon peak with a height that depends on power squared, which indicates an interaction as described below.Out of twenty-five pumped nanocrystals, we observe ten signatures of interactions.
The molecules interact through the electric fields of their oscillating dipole moments.The dipole moments are linear and all aligned to the crystalline lattice [33].The Hamiltonian for a system of N interacting dipoles with frequencies ω i is (1) The non-Hermitian rates Γ 0 and Γ ij are the spontaneous decay and dipole-dipole stimulated decay rates [2].The coherent dipole-dipole interaction J ij generates energy exchange between molecules, and in the near-field is given by As shown in the level structure in Fig. 1(f), the singly-excited states |eg⟩ and |ge⟩ are coupled by Here, tan θ = (2J)/(∆ + ∆).
As the pumping laser shifts interacting molecules into resonance, the anti-symmetric subradiant peak becomes dark to the symmetric drive Hamiltonian H D = i Ωi 2 (σ i + σ † i ) and extinguishes when ∆ < 2J.When the molecules are fully entangled, the eigenstates are the purely symmetric and anti-symmetric states In Fig. 2(a), two coupled molecules are tuned into resonance, causing the subradiant state to narrow and decrease in intensity as it decouples from the symmetric laser probe.After the extinction of the subradiant state, one pair of molecules remained resonant for over 24 hours of continuous monitoring.Other pairs of interacting molecules remained detuned by a few GHz despite undergoing tens of GHz of accumulated frequency shifting.
When the coupled states are degenerate, the magnitude of the coupling strength J = −116 MHz is equal to half the splitting of the eigenstates.The sign of the coupling strength depends on the relative orientation of the dipoles and determines which eigenstate has higher energy.In the H-aggregate (J-aggregate) orientation, the dipoles are perpendicular (parallel) to their separation vector, J is positive (negative), and the superradiant state is higher (lower) in energy.
The Rabi frequency exhibits a more pronounced effect because it is only related to the transition frequency with which the molecules interact.The lifetime, in contrast, contains both the decay from the interacting transition and the decay to the other vibrational states and phonon sidebands.
Fig. 3(a) shows a series of fluorescence spectra of two interacting molecules with increasing excitation power.At high excitation power, the doubly-excited state |ee⟩ populates, and a twophoton peak emerges in the center of the coupled resonances.Fig. 3(b-c) compares these spectra with a master equation simulation with J = 1020 MHz, a DWFC factor α = 0.11, 1 MHz dephasing, and Γ 0 = 33 MHz.These values are extracted from the g (2) (τ ) and lifetime measurements shown in Fig. 2(c-d).To illustrate the agreement between experiment and theory, the scattering rates and linewidths of the three peaks are extracted with Lorentzian fits and plotted against the simulation values in Fig. 3(c).Above saturation, the asymmetry of the superradiant and subradiant peaks depends on J and α.In contrast, the height of the two-photon peak is sensitive to J and dephasing, and the saturated linewidths are primarily sensitive to J.Because the superradiant state is higher in energy than the subradiant, we can infer that the molecules are in the H-aggregate orientation, with dipoles roughly perpendicular to the separation vector.Fig. 3(d-e) shows a similar set of data for a pair of molecules in the J-aggregate orientation, with J = −116 MHz, α = 0.135, 1 MHz dephasing, and Γ 0 = 37 MHz, which are extracted from lifetime measurements and the extinction curve in Fig. 2(b).The FCDW factors of α = 0.135 and 0.11 are lower than the reported value of 0.3 for a single DBT molecule.This may be due to the close proximity of the molecules, differences in the synthesis, or misalignment of the dipoles.Fig. 4(a) shows many molecules in a single nanocrystal shifting during successive pump cycles.The colored lines highlight three molecules being brought into resonance from a detuning of over 25 GHz, with spectra of the three molecules before and after shown to the right.Given the large inhomogeneous broadening, three molecules randomly shifting into resonance is unlikely, and this is an indicator of the tuning methods's ability to locally decrease inhomogeneous broadening.
One likely explanation is that as the highintensity light mobilizes charge carriers in the lattice, they migrate to minimize local electric field gradients contributing to inhomogeneous broadening.This picture could explain the consistency with which this effect can generate pairs of interacting molecules, as showcased in Fig. 4(b).After laser-induced shifting, ten nanocrystals out of twenty-five had clear two-photon peaks.Interestingly, the coupled molecules commonly came into resonance with additional molecules, and some remained in resonance even while tuning.For example, the subradiant peak in the lowerright spectrum of Fig. 4(b) is broader than the corresponding superradiant peak because it is overlapped with an additional resonance, as verified by the g (2) (τ ) and saturation spectra.This result is promising for the creation of many-body interactions and will be the subject of future research.
The length scale over which inhomogeneous broadening can be reduced is likely determined by the length scale of imperfections in the lattice, which cause inhomogeneous broadening.With an increase in the purity of nanocrystal synthesis or dopant density of high-purity synthesis methods like cosublimation, the length scale of this effect could be increased, allowing for the creation of many-body collective effects in the solid state.

Conclusion:
This work marks the first demonstration of permanently tuning lifetimelimited solid-state emitters into resonance and preparing the superradiant and subradiant states.Laser-induced tuning increases the likelihood of obtaining resonant molecules within a nanocrystal by three orders of magnitude, and two-photon peaks from interacting molecules are observed in 30% of nanocrystals.We characterized interacting molecules in different orientations, extracted the interaction strengths and branching ratios, and showed good agreement with a simple theory.
The light-based tuning method can be scaled to larger arrays of emitters.Molecules separated by more than 200 nm could also be addressed individually with light [31].The molecules could be positioned with sub-wavelength accuracy using techniques like nanoprinting [37].Organic molecules have also been shown to be compatible with nanophotonic devices [38], which would enhance the Franck-Condon/Debye-Waller factor, create long-range interactions, and increase the photon collection efficiency.
Entangled states in collections of organic molecules could be used to generate, manipulate, and detect quantum light, measure electric fields with enhanced sensitivity, or elucidate the role of dephasing and vibrational states in collective states [39,40].

Fig. 1
Fig. 1 Overview of DBT interactions (a) Two DBT molecules in an anthracene crystal interact through their dipole moments with rate J.(b) The DBT molecule is embedded as a defect into an anthracene crystal and has a HOMO-LUMO transition near 785 nm with a linear dipole moment.(c) Level structure of DBT.The excited state decays with rate αΓ 0 to the electronic and vibrational ground state, where α is the combined Debye-Waller/Franck-Condon factor.The excited state also decays with rate (1 − α)Γ 0 to higher vibrational states and their phonon sidebands.The decay into the ground vibrational state is filtered out, and the decay to the vibrational levels is used for all fluorescence measurements.(d) Lifetimelimited linewidth scan of a single DBT molecule at 2.7 K. (e) The g (2) (τ ) for a single molecule with g (2) (0) = 0.065(9).(f ) This interaction leads to collective superradiant |+⟩ and subradiant |−⟩ states.(g) Spectra of two molecules as they are tuned into resonance with intense illumination.The subradiant peak extinguishes as the detuning becomes smaller than the interaction J.

Fig. 2
Fig.2Spectroscopy of two molecules tuned into resonance.(a) Spectra of the superradiant (|+⟩) and subradiant (|−⟩) states of two coupled molecules as the molecules are tuned into resonance.The tuning in (a) was done with 170 cycles of 100-second exposure to 4 kW/cm 2 of 785 nm laser light.(b) Ratio of the heights of the subradiant and superradiant peak as a function of detuning, fitted to a master equation simulation to obtain J = −116 MHz.Spectra were obtained at an excitation intensity of I = 0.43 W/cm 2 (c) Second-order correlation functions g(2) (τ ) and (d) lifetimes of a different pair of superradiant and subradiant peaks at ∆ = 2600 MHz detuning.The superradiant (subradiant) state has an increased (decreased) Rabi-frequency, which results in faster (slower) oscillation of g(2) (τ ) for a given excitation power.The g(2) (τ ) functions are fitted to a master equation simulation to give J = 1020 MHz, I/Isat = 27, and dephasing of 1 MHz.The lifetimes are fitted to give Γ 0 = 33 MHz and α = 0.11.

Fig. 3
Fig.3Simulation of saturation spectra (a-c) Saturation spectra for molecules in the H-aggregate orientation, where the dipoles are oriented perpendicular to the separation vector and the superradiant state is higher in energy than the subradiant.The spectra are aligned by the average of their superradiant and subradiant frequencies.As excitation power increases, the two-photon peak appears between the two dressed states.The heights and widths are extracted with Lorentzian fits and plotted in (c).The simulation parameters are Γ 0 = 33 MHz, J = 1020 MHz, α = 0.11, dephasing = 1 MHz, fitted through g(2) (τ ) and lifetime simulations.(d-e) The same simulation was performed for molecules in the J-aggregate orientation, with dipoles parallel to the separation vector and the superradiant state lower in energy than the subradiant state.The fit parameters are Γ 0 = 37 MHz, J = −116 MHz, α = 0.135, dephasing = 1 MHz.

Fig. 4
Fig. 4 Laser-induced tuning (a) Many molecules tuning in a single nanocrystal.The nanocrystal is pumped with 16 kW/cm 2 for 10 seconds between probes.Panels (1) and (2) show three resonances being tuned within a single linewidth.The right two panels A and B are spectra showing the three molecules in and out of resonance.(b) Nine two-photon peaks from separate nanocrystals, each pumped with 10 mW of light for 30 minutes.The coupled molecules exhibit both H-aggregate and J-aggregate orientations, as well as weak and strong interaction strength regimes.Several spectra indicate more than two interacting molecules.