Higher-Dimensional Systems Cool Oscillators More Efficiently Than Two-Level Regulators

Scientists are increasingly focused on optimising cooling processes within quantum networks, and a new study by Mrinmoy Samanta and Debkanta Ghosh from Harish-Chandra Research Institute, a CI of HBNI, working with Rivu Gupta from Dipartimento di Fisica “Aldo Pontremoli,” Università degli Studi di Milano, and Aditi Sen(De) from Harish-Chandra Research Institute, a CI of HBNI, demonstrates a significant advantage in utilising higher-dimensional auxiliary systems for this purpose. Their research establishes a fundamental limit to oscillator cooling when employing qubits as regulators, but reveals that increasing the dimensionality of these systems can substantially reduce the cooling cycles needed and facilitate the cooling of oscillators with greater initial energy. This collaborative work highlights the potential for near-perfect cooling in linear configurations and extends to hybrid continuous- and discrete-variable systems, offering a pathway towards more efficient and versatile quantum technologies.

Scientists have demonstrated a new approach to cooling quantum oscillators, revealing a fundamental limit to how effectively a two-level system can perform this task. The work establishes a ‘no-cooling theorem’ for qubits, the basic units of quantum information, when used as regulators for continuous-variable oscillators. This investigation quantifies cooling performance using the Uhlmann fidelity, assessing the ability to bring an oscillator, initialised in a general Gaussian state, close to its ground state. Beyond this limitation, researchers uncovered a significant advantage in utilising higher-dimensional quantum systems, termed ‘qudits’, for cooling purposes. This dimensional advantage manifests in two key ways: a reduction in the number of operational cycles needed for cooling and an enhanced ability to cool oscillators possessing higher initial energies. Shifting to higher-dimensional auxiliaries, specifically qutrits and beyond, circumvents the qubit limitation and unlocks a twofold dimensional advantage. The number of cycles required for efficient cooling demonstrably decreases with increasing auxiliary dimension, while simultaneously enabling the cooling of oscillators possessing higher initial energies. The study focuses on networks of oscillators cooled through repeated interactions with an auxiliary system, employing a technique involving unitary evolution followed by conditional measurement. Each oscillator, representing a resonator with frequency ωfi, is coupled to the regulator via a Jaynes-Cummings type interaction, allowing for energy exchange between them. Resonant conditions were assumed, setting oscillator and regulator frequencies to a common value of one, though this simplification does not limit the broader applicability of the analysis. The protocol is adaptable to hybrid quantum systems, seamlessly integrating both continuous- and discrete-variable components, which is particularly relevant for superconducting platforms, enabling scalable and efficient measurement-based cooling that surpasses existing techniques. While the benefits of increasing dimensionality eventually plateau at moderate levels, near-perfect cooling remains achievable in linear network configurations, unlike star networks which exhibit poorer performance. Investigations into network configurations revealed a stark contrast between linear and star networks; linear networks admit near-perfect cooling with unit fidelity and moderate success probability, whereas star networks exhibit poor performance even with small system sizes. Although the number of cycles needed to reach unit fidelity saturates as auxiliary dimension increases, utilising another oscillator as the auxiliary system can reduce this requirement to a single cycle. Optimal evolution times were derived for auxiliary states of varying dimensions, revealing that this time is determined solely by the desired measurement outcome and remains independent of the system’s initial state. Cooling a hybrid continuous- and discrete-variable system using a qudit auxiliary demonstrated near-unit cooling fidelity for both subsystems when the auxiliary dimension is four or higher. This dimensional advantage is further enhanced by employing higher-dimensional target qudits, requiring fewer cooling cycles. The resulting cooled states support the generation of non-Gaussian states, such as CAT states, and facilitate the production of hybrid CV-DV entanglement and N00N states, with increasing dimension allowing access to higher excitation manifolds. Such hybrid systems are increasingly important for generating entanglement, performing quantum teleportation, and advancing quantum sensing technologies. The researchers’ model differs from previous work by allowing full interaction between the oscillators and the auxiliary qudit, rather than restricting coupling to specific energy levels. The findings highlight that while increasing the auxiliary dimension does not indefinitely improve performance, it provides a crucial pathway towards efficient cooling, particularly for oscillators that are initially far from their lowest energy state. Scientists have long sought ways to harness the delicate quantum states of oscillators, the fundamental building blocks of many physical systems, for computation and sensing. Efficiently cooling oscillators is crucial for preserving quantum information, as thermal noise destroys the fragile coherence needed for quantum computation. While the benefit of increasing the auxiliary system’s dimensionality eventually plateaus, the initial gains are substantial, offering a clear pathway for near-perfect cooling in specific configurations. The study also highlights the importance of system geometry; linear arrangements perform better than ‘star’ configurations, a detail that will influence future designs. Ultimately, this work isn’t about a single breakthrough, but about refining the toolkit for building more robust and scalable quantum technologies.