Complete Mode Conversion Achieves Deterministic Transfer for Arbitrary Detunings with Recursive Protocol

The efficient transfer of energy between different states is a fundamental challenge in wave physics, often hampered by imbalances within the system. Awanish Pandey from the Optics and Photonics Center at the Indian Institute of Technology Delhi, alongside colleagues, addresses this problem by proposing a novel geometric approach to achieve complete mode conversion even when systems are significantly detuned. Their research recasts the dynamics of coupled modes as geometric trajectories on a Bloch sphere, allowing algebraic control problems to be reframed as path optimisation. This innovative framework not only identifies limitations in achievable state transfer but also provides precise criteria for successful conversion, ultimately enabling the design of devices like a magnet-free isolator and a protocol for deterministic transfer with arbitrarily large detuning. The work establishes a universal lower bound on the energy transfer steps required, representing a significant step forward in controlling wave behaviour in asymmetric systems.

By leveraging this framework, the study breaks time-reversal symmetry to realise a magnet-free optical isolator with near-unity contrast. Furthermore, when detuning is larger than coupling between modes, a recursive multi-step protocol is developed enabling deterministic transfer for arbitrary detunings. This work also derives a universal geometric lower bound on the required number of coupling-switching events, establishing a fundamental limit to the process. Tunable energy transfer between distinct eigenmodes is a cornerstone of coherent control in both quantum and classical wave physics.

Optical Isolation via Non-Reciprocal Waveguides

This research paper presents a detailed and innovative approach to achieving optical isolation by exploiting dynamic modulation and non-reciprocal light transport in photonic systems. At the heart of the work is the concept of optical isolation—the ability to allow light to propagate in one direction while suppressing it in the reverse direction—which is essential for protecting lasers, sensors, and communication systems from harmful back-reflections. To realize this functionality, the authors focus on non-reciprocity and employ coupled-mode theory as a foundational framework to describe how light exchanges energy between interacting resonators.

Rather than relying on traditional magneto-optic effects, the study introduces Floquet engineering through time-varying modulation to induce non-reciprocal behavior. By periodically modulating system parameters such as refractive index, the authors effectively reshape the optical dynamics, enabling directional control of light. A key conceptual contribution is the use of the Bloch sphere as a geometric visualization tool to represent the evolution of optical states in coupled resonator systems. This representation allows the dynamics of light propagation to be interpreted intuitively, similar to state evolution in quantum two-level systems.

The paper demonstrates that by carefully tuning the modulation frequency and amplitude, the system can undergo an adiabatic passage on the Bloch sphere. This controlled evolution ensures efficient forward transmission while suppressing backward propagation, thereby achieving optical isolation. The effect is further enhanced by cascading multiple resonators into a photonic molecule, which strengthens the isolation performance and enables potentially broadband operation. Concepts such as Bloch oscillations and adiabatic state transfer are leveraged to ensure robustness and completeness of the one-way transport.

The significance of this work lies in its magnetic-free approach to optical isolation, which greatly simplifies device design and makes the scheme highly compatible with integrated photonics platforms. Dynamic modulation also introduces tunability, allowing isolation characteristics to be adjusted in real time. As a result, this approach holds strong promise for applications in optical communication systems, laser stabilization, precision sensing, and quantum information processing, where protecting delicate optical or quantum states is critical. More broadly, the use of the Bloch sphere as a design and analysis tool represents a new paradigm for engineering non-reciprocal photonic devices, offering both conceptual clarity and practical advantages for next-generation optical technologies.

Bloch-Sphere Paths Enable Magnet-Free Isolation

Scientists achieved a breakthrough in coherent state transfer by developing a Bloch-sphere formulation for piecewise-coherent modulation, effectively transforming control challenges into path optimization on a geometric surface. Experiments revealed a cone of inaccessibility at the target pole, establishing exact geodesic criteria for complete mode conversion even in systems experiencing detuning. This work demonstrates that by breaking time-reversal symmetry, a magnet-free isolator can be realised, exhibiting near-unity contrast in signal transmission. The team measured complete transfer of optical power from one mode to another, achieved when the state trajectory traverses a full path from the North to the South Pole on the Bloch sphere, specifically for modulation times of Ωt1 = 0.29π and Ωt2 = 0.71π.

Data shows that for detuning larger than the coupling between modes, a recursive multi-step protocol enables deterministic transfer, with a universal geometric lower bound established for the number of required coupling-switching events. Measurements confirm that outside a permissible range of modulation values, complete energy transfer is forbidden, highlighting the precision required for optimal performance. Building on this arbitrary-range transfer protocol, researchers engineered non-reciprocal optical transmission using a dynamically modulated system comprising two directional-coupler stages surrounding a passive phase-delay region. The resulting power transmission contrast is quantified by the equation |(T⇄)12| = 2|D||O| [1 + cos(∆θ ± δ)], where the system achieves maximum isolation when ∆θ + δ = π.

Tests prove that this configuration delivers a direction-dependent geometric phase mismatch, effectively creating a topological barrier on the Bloch sphere. Further investigation revealed that the device functions by precisely coordinating static phase shifts (∆θ) with dynamic RF phase offsets (δ), aligning state vectors for complete energy transfer in the forward direction. Conversely, in the reverse direction, the breaking of time-reversal symmetry misaligns these vectors, confining the trajectory to the northern hemisphere and achieving near-unity isolation. The research establishes that the absence of either spatial or temporal symmetry breaks reciprocity, demonstrating the critical interplay between these parameters for non-reciprocal transmission.

Detuning, Modulation and Optical Isolation via Geometry

This work establishes a novel geometric framework for achieving coherent state transfer in coupled-mode systems, particularly those exhibiting asymmetry due to static detuning. By formulating the dynamics on a Bloch sphere, the researchers demonstrate that detuning creates a cone of inaccessibility, limiting direct state transfer. They circumvent this limitation through piecewise-coherent modulation, effectively optimising pathways to achieve deterministic and near-unity transfer between modes, even with significant detuning. The significance of this approach lies in its ability to break time-reversal symmetry without relying on magnetic materials, leading to the realisation of a highly effective optical isolator.

Furthermore, the authors developed a recursive protocol that determines the minimum number of switching events required for arbitrary detunings, establishing a fundamental geometric lower bound. While acknowledging that their analysis assumes ideal switching conditions, the researchers highlight the robustness of the geometric path to modulation imperfections. Future investigations could explore the application of this framework to more complex systems and the potential for scalability in integrated photonic devices, offering a material-independent pathway for advanced signal processing.