Polaritons Reveal New Control over Quantum Interactions

Scientists are increasingly investigating polaritonic systems as promising platforms for quantum simulation and information processing. Nabaneet Sharma, Anushree Dey, and Bimalendu Deb, all from the School of Physical Sciences at the Indian Association for the Cultivation of Science, demonstrate precise control over the correlations within a polaritonic Luttinger liquid through the implementation of engineered cross-Kerr nonlinearity. Their work details a multi-connected Jaynes, Cummings lattice designed on a circuit quantum electrodynamics platform, allowing for the mimicry of attractive nearest-neighbour interactions. This research is significant because it establishes a pathway to manipulate fundamental properties like compressibility and correlation decay in these systems, potentially paving the way for advanced quantum devices and a deeper understanding of many-body physics in condensed matter systems.

A multiconnected Jaynes, Cummings (MCJC) lattice, constructed from alternating qubits and resonators with differing couplings, underpins this work. By manipulating interactions between light and matter, researchers have engineered a pathway to slower decay of quantum correlations within a polaritonic system, potentially enhancing the coherence of quantum information. This unique architecture allows manipulation of light-matter interactions at a microscopic level, enabling exploration of complex quantum phenomena, focusing on polaritons, hybrid light-matter quasiparticles formed when light and matter strongly interact. Introducing an attractive nearest-neighbour interaction via engineered cross-Kerr nonlinearity, a type of interaction linking photons in adjacent resonators, reduces the compressibility of a specific polariton mode.

This reduction enhances the Luttinger parameter, slowing the algebraic decay of single-particle correlations, signifying that information can be preserved for a longer duration, a vital characteristic for quantum technologies. This achievement relies on a sophisticated theoretical framework combining a Bose, Hubbard-like model, describing interacting particles on a lattice, with a continuum bosonization approach. This allows expression of the system’s behaviour in terms of collective modes, simplifying analysis and revealing the underlying physics. Careful control of system parameters tunes the interactions between polaritons, enhancing coherence. Once the system reached a regime where one sector of the collective modes developed a finite energy gap, the research team reduced the complexity of the model to a single-component Luttinger liquid. This simplification provides a clear pathway to understand how the engineered nonlinearity influences the long-distance behaviour of the polaritonic system, suggesting a route toward designing quantum systems with enhanced stability and prolonged coherence times, potentially benefiting quantum computation and communication.

Engineered qutrit coupling induces nearest-neighbour interactions within a polariton lattice

A multiconnected Jaynes, Cummings (MCJC) lattice, constructed from alternating qubits and resonators with differing couplings, underpins this work. This lattice architecture allows for the study of polariton correlations at zero temperature, facilitated by engineered cross-Kerr nonlinearity which mimics attractive nearest-neighbour interactions. The MCJC lattice comprises cavity modes locally coupled to qubits and indirectly connected via asymmetric qubit-mediated hopping processes, ensuring translational invariance and a polaritonic band structure at low energies.

Qubits are labelled with odd integers, while resonators receive even integer designations, assuming periodic boundary conditions throughout the system. To introduce interactions beyond on-site terms, auxiliary three-level qutrits were integrated to couple neighbouring cavities, generating effective nearest-neighbour cross-Kerr terms. These qutrits alternate between adjacent links, creating a bipartite lattice with two inequivalent sublattices, A and B.

The Hamiltonian describing the MCJC lattice is formulated as H MCJC = H 0 + H l + H r, where H 0 defines the qubit and resonator energies, and H l and H r represent the left and right qubit-resonator couplings. Working within the dispersive regime, the qutrit degrees of freedom were eliminated using successive Schrieffer, Wolff transformations. This perturbative approach yielded an effective resonator-only interaction, specifically an induced cross-Kerr interaction. This allows the research team to map the low-energy Hamiltonian to a bipartite extended Bose, Hubbard model, enabling detailed analysis of the system’s collective behaviour.

Cross-Kerr interactions induce slowed correlation decay and enhanced coherence in a polariton lattice

Researchers detail a compelling picture of polariton behaviour within a specially engineered circuit quantum electrodynamics lattice. Initial measurements reveal a cross-Kerr interaction strength of χ = λ2 ∆c, where λ is determined by the coupling strengths and detunings of the constituent components. This interaction, arising from dispersively coupled qutrit couplers, fundamentally alters the system’s properties.

The study demonstrates a reduction in the compressibility of the symmetric collective mode, alongside an enhanced Luttinger parameter. The most striking result is the observed slowing of single-particle correlation decay, now exhibiting a power law, indicating diminished particle scattering and more coherent excitation propagation. This slower decay is a direct consequence of the attractive nearest-neighbour interaction induced by the cross-Kerr term.

By projecting onto the lower-polaritonic manifold, the work derives an extended Bose, Hubbard-like model, effectively describing the system as interacting bosons on a lattice. At zero qubit-resonator detuning, polariton operators were defined, and a Hamiltonian was constructed encompassing on-site terms, intercell transfer, and the crucial cross-Kerr interaction.

Further analysis, truncating the local occupation to the two-excitation manifold, yielded a bipartite extended Bose, Hubbard Hamiltonian. This model incorporates hopping amplitudes, on-site repulsion, and the attractive cross-Kerr interaction, providing a framework for a low-energy continuum description. Since the system exhibits tinter = tintra = gl/4, the hopping terms are equal, simplifying the analysis.

Applying a harmonic-fluid approach, the research identified symmetric and antisymmetric collective modes, φ± and θ±, which diagonalize the Gaussian sector at long wavelengths. The (+) fields represent in-phase fluctuations, while the (-) fields describe relative fluctuations between sublattices. These findings provide a detailed understanding of the collective behaviour and correlation properties within this multiconnected Jaynes, Cummings lattice, opening avenues for exploring novel quantum phenomena.

Engineered polariton lattices enable control of collective quantum behaviour

Scientists are beginning to exert finer control over the behaviour of light and matter at the quantum level, as demonstrated by recent advances in manipulating polaritons within specifically designed circuits. Achieving predictable and scalable interactions between quantum particles has presented a substantial hurdle, largely due to the difficulty of isolating systems from environmental noise.

This work bypasses some of those limitations by embedding polaritons, hybrid light-matter quasiparticles, within a carefully constructed lattice, allowing researchers to observe and influence their collective behaviour. The ability to engineer these interactions opens doors to exploring complex quantum phenomena previously confined to theoretical models.

The significance extends beyond simply observing these effects. Understanding how these polariton systems correlate could inform the development of new types of quantum simulators, devices capable of modelling complex physical systems beyond the reach of classical computers, promising breakthroughs in materials science, drug discovery, and fundamental physics.

Current implementations remain small-scale and operate under extremely controlled conditions, limiting immediate practical applications. However, the observed slowing of correlation decay, a key indicator of enhanced control, represents a measurable step towards more stable and manipulable quantum systems. Building larger, more complex lattices will undoubtedly introduce new challenges in maintaining coherence and minimising errors.

Researchers must explore how to integrate these polariton lattices with other quantum technologies, such as superconducting qubits, to create hybrid systems with expanded capabilities. This system’s reliance on collective modes offers a potential pathway to mitigating some of the inherent limitations of individual quantum components. This work isn’t just about refining existing techniques; it’s about charting a course towards a future where quantum systems are not merely observed, but actively programmed and harnessed for practical benefit.