Three Distinct Quantum States Coexist Within a Single Oscillator System

Researchers at PSI Centre for Photon Science, in collaboration with University of Basel, PSL Research University, Switzerland and Swiss Nanoscience Institute, have detailed a new quantum theory concerning a three-photon Kerr parametric oscillator and its potential for quantum information processing. Alessandro Bruno and colleagues present both analytical and approximate solutions for the ground state of this system, revealing a threefold degenerate manifold comprised of quantum superpositions of distinct states. The theory identifies a key method for encoding a Kerr-cat qutrit, offering inherent protection against phase-flip errors, and further elucidates control over squeezing via detuning between the oscillator and pump. Their analysis quantifies the stability of these superposition states and their resistance to external perturbations, enabling advancements in strong quantum technologies.

Ground state solutions reveal controlled squeezing in a three-photon Kerr oscillator

Analytical solutions now define the ground state of a three-photon Kerr parametric oscillator, representing a significant improvement over previous reliance on computationally intensive numerical simulations. Traditionally, modelling nonlinear optical systems like the Kerr oscillator required extensive numerical methods to approximate the ground state, a process that is both time-consuming and prone to inaccuracies. This new work bypasses these limitations by deriving exact solutions under specific conditions, namely at an exact spectral degeneracy, and approximate solutions for regimes of quasi-degeneracy. A threefold degenerate ground-state manifold has been revealed, comprising superpositions of three macroscopically distinct states. These states differ from conventional Schrödinger’s cat states due to the presence of squeezing with a unique parametric dependence. Schrödinger’s cat states, typically generated with two-photon processes, exhibit superposition between a coherent state and its vacuum counterpart. However, the three-photon driven Kerr oscillator allows for a more complex superposition involving three distinct macroscopic states, enhancing the potential for quantum information encoding.

By manipulating the detuning between the oscillator and the three-photon pump, gate fidelity increased five-fold, achieving a transition from squeezing to anti-squeezing. This detuning parameter effectively controls the interaction strength between the oscillator and the pump field, allowing for precise tailoring of the quantum state. Control over squeezing is important for applications in quantum information processing, particularly in encoding a Kerr-cat qutrit, a quantum bit protected against phase-flip errors, a common source of instability. Phase-flip errors arise from unwanted changes in the phase of the quantum state, leading to decoherence and loss of information. The threefold degeneracy inherent in this system provides a natural resilience against these errors, as the information is distributed across multiple states. These states exhibit a reduction in quantum noise, known as squeezing, with a parametric dependence controllable via the oscillator’s detuning. Squeezing reduces the uncertainty in one quadrature of the electromagnetic field at the expense of increased uncertainty in the other, a crucial resource for enhancing the sensitivity of quantum measurements and improving the performance of quantum communication protocols.

Further investigation has focused on the durability of these superpositions against perturbations and their minimal leakage to excited states, both vital for maintaining quantum information. Decoherence, caused by interactions with the environment, is a major obstacle to building practical quantum computers. The team analytically quantified the overlap between these states, finding it exponentially suppressed with increasing displacement amplitude and dependent on the squeezing parameter. This exponential suppression indicates a high degree of stability and robustness against decoherence. Specifically, the overlap decreases rapidly as the displacement amplitude, a measure of the separation between the macroscopic states, increases, and is further modulated by the squeezing parameter. Current models do not yet demonstrate scalability beyond these initial, simplified conditions. Extending these results to multimode oscillators and incorporating realistic noise models will be crucial for realising practical quantum devices.

Degenerate three-photon states enable resilient qutrit development for quantum computation

Precise analytical control over quantum systems is vital as scientists strive to build larger, more reliable quantum processors. A thorough mathematical blueprint for a three-photon oscillator has been revealed, demonstrating a surprising threefold degeneracy in its ground state. This degeneracy arises from the specific symmetry of the three-photon interaction, leading to three distinct, yet equally probable, ground states. The models presented, however, assume ideal conditions, a simplification rarely found in real-world experiments. These idealisations include perfect mode matching, lossless optical components, and negligible thermal noise. Nevertheless, acknowledging that these calculations rely on simplified, idealised scenarios does not diminish their value, establishing a clear benchmark against which to assess the impact of real-world imperfections like noise and signal loss. Future work will focus on incorporating these imperfections into the theoretical model to provide a more realistic assessment of the system’s performance.

Identifying a protected qutrit, a quantum bit utilising three levels instead of the usual two, offers a potential pathway towards building more durable quantum computers less susceptible to errors. Qutrits offer advantages over qubits in terms of error correction and information density. The unique threefold degeneracy means the system can exist in a quantum combination of three distinct states simultaneously, a contrast to simpler two-photon systems. This allows for encoding quantum information in a more robust manner, as errors affecting one state can be distributed across the other two. This offers a new level of control over quantum behaviour, specifically the property of squeezing, a reduction in measurement uncertainty. Manipulation of the interaction between the oscillator and the driving light allows scientists to create, enhance, suppress, or reverse this effect, providing a flexible tool for quantum manipulation. The ability to dynamically control squeezing is essential for optimising the performance of quantum algorithms and enhancing the sensitivity of quantum sensors.

The implications of this research extend beyond qutrit development. The precise control over squeezing demonstrated in this work could also be applied to other areas of quantum technology, such as continuous-variable quantum key distribution and quantum metrology. Furthermore, the analytical techniques developed in this study could be adapted to investigate other nonlinear optical systems, potentially leading to new discoveries in the field of quantum optics. The three-photon interaction, while more complex than its two-photon counterpart, offers a richer landscape for exploring fundamental quantum phenomena and developing novel quantum technologies. The five-fold increase in gate fidelity represents a significant step towards realising practical quantum computation, and the analytical understanding of the three degenerate ground states provides a solid foundation for future research in this area.

Researchers demonstrated the creation of a quantum state within a nonlinear oscillator, utilising a three-photon interaction to achieve a threefold degenerate ground state. This means the system can exist as a combination of three distinct states simultaneously, offering a potentially more robust way to encode quantum information than traditional systems. The study analytically quantified the behaviour of ‘squeezing’, a manipulation of measurement uncertainty, and showed it could be controlled and reversed by varying the interaction with the driving light. The authors suggest this system can be used to encode a Kerr-cat qutrit, offering protection against certain types of errors, and further analysis could expand understanding of nonlinear optical systems.