Nanoscale lattices create a broadband quantum light source

Researchers at the Universidad Autónoma de Madrid and the Instituto de Química Física Blas Cabrera have demonstrated a way to manipulate light at the quantum level using nanoscale lattices of quantum emitters. The work reveals that these lattices, functioning as quantum metasurfaces with subwavelength periods, can populate excitonic Bloch states with wavevectors exceeding the limits of conventional optics.

In strong-driving regimes, the lattices produce a broadband background of photons, closely related to resonance fluorescence, and enter a bistable regime, a behavior contrasting sharply with classical systems, allowing for selective control of optical quantum nonlinearities. This bistable behavior enables the selective activation and deactivation of the optical quantum nonlinearities of the system.

Quantum Metasurface Behavior in Emitter Lattices

Subwavelength lattice periods enable the population of excitonic Bloch states with wavevectors that exceed the light cone’s limitations, a phenomenon not typically observed in conventional optics. This unusual behavior arises when a resonant plane wave interacts with the lattice, effectively altering the pathways available to excitons, quasiparticles representing excited states in the material. Researchers demonstrated this effect through theoretical investigation of two-level quantum emitters arranged in a periodic lattice and coherently driven by a laser.

The resulting excitonic Bloch states possess parallel wavevectors differing from the incident field, opening possibilities for manipulating light at the nanoscale. Unlike typical light sources that emit within a narrow band, this broadband emission suggests a fundamentally different process governing photon generation within the lattice. This characteristic is particularly notable given the lattices’ structure, where the period approaches the driving wavelength, inducing a bistable regime.

This bistability, a state where the system can exist in one of two stable conditions, contrasts sharply with the behavior of its classical counterparts. The team’s analysis reveals that the bistability originates from the renormalization of the driving rate, altering how the laser interacts with the emitters. Prior to the onset of bistability, excitonic Bloch states with zero parallel wavevector are coherently populated, with minimal incoherent contributions at other wavevectors.

The theoretical work, supported by MCIN/AEI/10. 13039/501100011033/FEDER under projects PID2021-126964OB-I00, TED2021-130552B-C21 and PID2022-137569NB-C42, builds on two decades of research into metallic nanostructure lattices and their ability to support lattice resonances. Recent advances in controlling quantum emitter ensembles have further propelled exploration of collective modes in the quantum realm. Antonio I. The research demonstrates a pathway toward harnessing quantum effects within engineered materials, potentially leading to advancements in quantum technologies. The ability to selectively control nonlinearities within these lattices offers a promising avenue for manipulating quantum states and developing novel quantum devices.

Exciton Anharmonicity Drives Broadband Emission

The far-field emission from lattices of quantum emitters, when strongly driven by a laser, is dominated by a wide spectrum of photons, a phenomenon closely linked to resonance fluorescence. Unlike typical light sources that focus on narrow bands of wavelengths, this system generates a significantly broader emission profile.

The ability to populate these unusual excitonic states stems from the unique behavior of the lattice when its period approaches the driving wavelength. The team’s analysis reveals that the exciton population in a single quantum emitter saturates at one-half under strong coherent driving, a key characteristic of this process that influences the observed phenomena, enabling the population of Bloch states with wavevectors.

The Mollow triplet, originating from two-photon transitions involving virtual states, features emission peaks at specific frequencies determined by the driving laser and the emitter’s properties. Calculations show the exciton population is influenced by both coherent and incoherent terms, with the coherent term corresponding to the population of Bloch states with the incident wavevector. The intensity of the emitted light, normalized to a reference value, varies as a function of the driving rate, further illustrating the complex interplay of these factors.

Previous studies have largely focused on the single excitation limit, simplifying the analysis by linearizing the emitters. However, this work extends beyond that approximation, revealing that the incoherent excitation of detuned Bloch states generates the broadband background of photon emission observed in both frequency and wavevector.

This emission is not limited to the zeroth-order diffraction peak, but rather extends across the entire Brillouin zone, indicating a highly dispersed and isotropic emission pattern. The emergence of bistability and hysteresis, driven by long-range interactions between emitters, further enhances the system’s potential. This allows for abrupt changes in exciton population and emission properties as the driving rate is adjusted.

These results build upon previous work in the deep subwavelength regime, generalizing findings obtained with different methods. The ability to manipulate the exciton population and emission characteristics through external control opens avenues for advanced optical devices and quantum information processing.

Bistability Emerges with Near-Wavelength Lattice Periods

For lattice periods nearing the wavelength of the driving laser, a quantum emitter array exhibits bistability, a phenomenon where the system can exist in two stable states depending on the input driving rate. Analysis reveals that this bistability is not merely a theoretical prediction but is evidenced by the emergence of three possible solutions for the effective driving rate at periods approaching the natural wavelength, with two stable and one metastable.

The origin of this bistability lies in a combination of exciton anharmonicity within individual quantum emitters and the divergence of the lattice sum as the period approaches the driving wavelength. This divergence signifies the strengthening of collective, long-range interactions between the emitters, fundamentally altering the system’s response to external stimuli.

The researchers demonstrated that as the lattice period nears the wavelength, hysteresis appears, manifesting as abrupt transitions in the emission spectrum from a single peak to a characteristic Mollow triplet structure. Figures from the study show how the exciton population shifts dramatically, coherently populating Bloch states with specific wavevectors before the onset of bistability. The study demonstrates the emission of an incoherent background of photons spanning all frequencies and wavevectors, which dominates over the classical Rayleigh contribution under strong driving conditions.

This broadband emission, closely related to resonance fluorescence, is a hallmark of the quantum nature of the system and is enhanced by the long-range interactions within the lattice. The work builds upon previous investigations into subwavelength regimes, generalizing findings obtained with different emitter configurations.

Theoretical Framework: Lindblad Master Equation & QE Description

The calculations, based on a Lindblad master equation, describe how the lattice’s structure allows for the creation of these states, differing in parallel wavevector from the incident field. The theoretical framework employed centers on describing the quantum emitters as distinguishable two-level systems, each possessing a lower quantum operator and a natural frequency. These emitters, treated as point-dipoles, interact through coherent and dissipative coupling strengths dictated by the electromagnetic dyadic Green tensor in free space.

The system’s dynamics are governed by the evolution of its density matrix, calculated using the Lindblad master equation, a method for tracking the open quantum system’s interaction with its environment. This equation accounts for both the coherent evolution driven by the laser and the dissipative effects of spontaneous emission and interactions between emitters.

The steady-state of the system under external driving is the focus of the calculations, setting the time derivative of the density matrix to zero. The lattice amplifies this effect, creating a similar spectral signature but with unique characteristics due to the collective interactions between emitters. The analysis reveals that the lattice supports Bloch states, created by Bloch operators that do not adhere to standard bosonic or fermionic commutation rules.

Instead, these operators exhibit unique relationships reflecting the collective nature of the emitters and their quantum anharmonicity. This anharmonicity, a deviation from the harmonic oscillator model, is essential for the observed phenomena, enabling the population of Bloch states with wavevectors outside the light cone. The calculations demonstrate that this effect is not a result of direct emitter-emitter interactions but arises solely from the algebraic properties of the Bloch operators.

To quantify the excitation of these Bloch states, researchers calculated the population distribution within the first Brillouin zone of the lattice. This distribution, obtained by integrating the expectation value of the Bloch operators, provides a map of the exciton population across different wavevectors. The results show that the lattice can be driven into a bistable regime when the lattice period approaches the driving wavelength.

“We have shown that, for periods approaching the driving wavelength, the emitter lattice enters in a bistable regime due to the renormalization of the driving rate,” the authors write, highlighting the key distinction from classical analogs. This bistable behavior, they explain, enables the selective control of the lattice’s nonlinear optical properties.

Quantum Nonlinearities Enable Selective Activation of Emission

This unexpected behavior arises when the lattice structure is scaled to dimensions smaller than the wavelength of light, effectively creating a quantum metasurface. The resulting emission differs markedly from classical light sources, exhibiting wavevectors diverging from the incident field’s direction. Researchers found this broadband emission surpasses the classical Rayleigh contribution, which arises from radiative diffraction orders, demonstrating the dominance of quantum effects.

The team analyzed the total intensity radiated by the lattice, normalizing it to a reference value, as a function of driving field strength to characterize this phenomenon. The ability to selectively activate these nonlinearities is achieved through the abrupt suppression and restoration of the effective driving force, enabling precise control over the exciton population and emission properties of the lattice.

Researchers examined the spectrum emerging in this bistable regime, demonstrating how the nonlinear response can be switched on and off. The work, supported by MCIN/AEI/10. The team’s analysis of the emission spectrum reveals that the nonlinearities govern the response of the quantum emitters to the coherent driving, effectively modifying the laser amplitude.

This manipulation of the driving force is key to inducing the observed bistable phase, where the lattice’s response dramatically changes with even slight variations in the input signal. The findings demonstrate a pathway toward harnessing inherent quantum nonlinearities for advanced technological applications, particularly in areas demanding precise control over single photons and quantum states.

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