Schrödinger’s Drum: Creating Quantum Superpositions in Mechanical Motion

Author: Denis Avetisyan

Researchers have proposed a novel method to generate macroscopic quantum superpositions-known as cat states-in a tiny mechanical resonator using light and magnetism.

A two-step protocol generates cat-like states of mechanical motion within an optomechanical system by first driving a magnon mode with microwave fields at frequencies $ω±=ωm±ωb$ to create a mechanically squeezed state, followed by the subtraction of phonons via a weak, red-detuned optical pulse conditioned on anti-Stokes photon detection.

This work details a scheme to create mechanical cat states via optomagnomechanical squeezing and phonon subtraction, opening avenues for enhanced quantum sensing and exploring macroscopic quantum phenomena.

Creating macroscopic quantum superpositions remains a central challenge in exploring the boundary between classical and quantum realms. Here, we present a theoretical framework, detailed in ‘Generation of mechanical cat-like states via optomagnomechanics’, for generating non-classical mechanical states via a hybrid opto- and magnomechanical system. Our approach utilizes squeezed states of motion and phonon subtraction induced by optical pulses to prepare a mechanical cat-like state, demonstrating a pathway to engineer macroscopic superposition. Could this scheme pave the way for novel quantum sensing technologies and tests of fundamental quantum mechanics?

Unveiling Quantum Superposition: The Foundation of Future Technologies

The pursuit of non-classical states, prominently including the Schrödinger’s cat state, represents a pivotal frontier in the development of quantum technologies. These states, defying the intuitive rules of classical physics, allow for the exploration of phenomena like superposition – where a quantum system exists in multiple states simultaneously – and entanglement, linking the fates of distant particles. Harnessing these uniquely quantum properties isn’t merely academic; it unlocks the potential for exponentially faster computation through quantum computers, ultra-sensitive sensors capable of detecting incredibly weak signals, and secure communication networks impervious to eavesdropping. The ability to reliably create, manipulate, and measure these complex states is therefore paramount, acting as a foundational requirement for realizing the transformative promise of a future powered by quantum mechanics and enabling capabilities far beyond the reach of classical systems.

Quantum states known as cat states dramatically illustrate the counterintuitive principles of superposition and entanglement. Unlike classical systems existing in a definite state, these states leverage superposition, allowing a quantum system-such as a superconducting circuit or the polarization of a photon-to exist as a combination of multiple states simultaneously, represented mathematically as a linear combination like $a|0\rangle + b|1\rangle$. Entanglement further complicates this picture, linking the fates of two or more quantum systems so that they share the same quantum state, even when separated by vast distances. In a cat state, this manifests as a superposition of macroscopically distinct states – akin to Schrödinger’s famous thought experiment – where the system exists as both $0$ and $1$ concurrently. This delicate balance, achieved through precise control of quantum interactions, is not merely a theoretical curiosity; it’s a fundamental resource for advancing technologies like quantum computing and ultra-sensitive sensors, where exploiting these non-classical correlations offers capabilities beyond the reach of classical systems.

The ability to reliably create and manipulate cat states – quantum superpositions of distinct quantum states – is paramount for realizing the full potential of quantum technologies. These fragile states, where a quantum bit exists as both 0 and 1 simultaneously, are not merely theoretical curiosities; they represent a pathway to enhanced computational power and precision sensing. In quantum information processing, cat states can serve as robust qubits, less susceptible to certain types of errors that plague traditional quantum bits. Moreover, their heightened sensitivity to external influences makes them ideal for building quantum sensors capable of detecting incredibly weak signals – from gravitational waves to minute magnetic fields. Achieving precise control over these superpositions, however, requires overcoming significant technical hurdles related to decoherence and maintaining the delicate quantum coherence necessary for computation and measurement. The ongoing pursuit of stable, controllable cat states is therefore central to the development of a new generation of quantum devices.

Exploring Alternative Platforms: Optomechanics and Magnomechanics

The established techniques for generating quantum superpositions known as Schrödinger cat states predominantly utilize two physical systems: superconducting circuits and trapped ions. Superconducting circuits, specifically transmon qubits, allow for strong, tunable interactions necessary for creating the required nonlinearities. Trapped ions, conversely, leverage precisely controlled laser interactions with individual ions to achieve similar results. Both approaches have demonstrated successful cat state generation and characterization, but are limited by the complexity of cryogenic infrastructure for superconducting circuits and the scalability challenges inherent in controlling large numbers of individually addressed ions. These limitations motivate exploration of alternative platforms, such as optomechanical and magnomechanical systems, for cat state preparation.

Optomechanical and magnomechanical systems are emerging as viable platforms for generating non-classical states, such as Schrödinger cat states, due to their distinct advantages over traditional methods. Optomechanical systems utilize the radiation pressure of light to control the motion of a mechanical resonator, while magnomechanical systems employ microwave fields to manipulate the magnetization of a ferromagnetic material. Both approaches offer strong coupling between quantum and mechanical degrees of freedom, enabling precise control and measurement necessary for state preparation. Furthermore, these systems are potentially scalable and compatible with solid-state fabrication techniques, offering a pathway towards more compact and integrated quantum technologies. The long coherence times achievable in mechanical resonators also contribute to the feasibility of generating and maintaining these delicate quantum states.

Optomechanical and magnomechanical quantum control relies on the coupling of electromagnetic radiation – typically light in optomechanical systems or microwaves in magnomechanical systems – to the mechanical degrees of freedom of a physical resonator. This interaction allows for the manipulation of the resonator’s motional state using the electromagnetic field. Specifically, photons or phonons can be exchanged between the light/microwave field and the mechanical element, enabling coherent control and the creation of superposition states. The strength of this coupling, often quantified by the cooperativity parameter $C$, dictates the effectiveness of the quantum control; higher cooperativity facilitates stronger interactions and more precise state manipulation. This approach allows for the preparation of non-classical states, such as squeezed states and entangled states, by driving transitions between the mechanical resonator’s energy levels via the coupled electromagnetic field.

Magnon-Mediated Coupling: A Pathway to Squeezed States

The magnomechanical system leverages magnons, which are quantized collective excitations of the magnetic order within a material, to facilitate the coupling between mechanical and spin degrees of freedom. These spin waves, possessing both energy and momentum, act as intermediaries, enabling the transfer of information and energy between the mechanical resonator and the magnetic medium. Specifically, the interaction Hamiltonian includes terms describing the creation and annihilation of magnons, directly linking the mechanical displacement to changes in the magnetic state. This magnon-mediated coupling allows for the manipulation of both mechanical and spin dynamics, forming the basis for generating non-classical states of motion and exploring quantum phenomena in macroscopic systems.

Squeezing of the mechanical motion is achieved through the application of a two-tone driving field, a technique which reduces the quantum noise in one quadrature of the mechanical oscillator at the expense of increased noise in the orthogonal quadrature. This process generates a non-classical state known as a squeezed state, characterized by a squeezing parameter, $r$, of 1.25. A squeezing parameter greater than 1 indicates that the noise in the squeezed quadrature is reduced by a factor proportional to $1/r$ compared to a coherent state, enabling enhanced sensitivity in measurements dependent on minimized quantum noise.

Following the creation of a squeezed mechanical state, a cat-like state is generated via phonon subtraction. This process relies on the detection of anti-Stokes photons, which herald the removal of a single phonon from the initial squeezed state. The probability of successfully subtracting a single phonon, as indicated by the detection of an anti-Stokes photon, is measured at 1%. This low probability necessitates high-efficiency detection and careful calibration to reliably create and characterize the resulting superposed states, where the mechanical oscillator exists in a coherent superposition of the $ |0\rangle$ and $ |1\rangle$ states.

The Wigner function reveals a squeezed mechanical state resulting from the subtraction of single-phonon (a) and two-phonon (b) components, with specific parameters detailed in the text.

Modeling and Characterizing the Quantum State

Quantum Langevin Equations (QLEs) provide a framework for modeling the time evolution of the coupled magnon-mechanical system by incorporating both the deterministic dynamics governed by the system’s Hamiltonian and the stochastic forces arising from environmental interactions. These equations are specifically formulated as first-order differential equations for the system’s quadrature operators, accounting for the influence of thermal and quantum noise on the mechanical oscillator and the magnonic mode. The QLE approach allows for the calculation of correlation functions and spectral properties, which are essential for characterizing the quantum behavior of the system and predicting its response to external stimuli. Noise terms within the QLEs are treated as zero-mean Gaussian processes with correlation functions determined by the system’s dissipation rates and temperature, effectively modeling the decoherence mechanisms impacting the quantum state.

The covariance matrix (CM) is a key tool for characterizing the quantum fluctuations present in the coupled magnon-mechanical system. Specifically, the CM provides a complete description of the quantum state by defining the variances and covariances of the system’s quadrature amplitudes. Analysis of the CM allows for the quantification of noise and the determination of the system’s degree of quantum entanglement. Furthermore, the CM is essential for evaluating the efficiency of state preparation protocols; by comparing the measured CM to the theoretical ideal, one can assess the fidelity of generated quantum states, such as squeezed or entangled states, and optimize control parameters to minimize decoherence and maximize quantum performance.

The quantum state of the coupled system is fully described by the density matrix, which enables verification of non-classicality, specifically the generation of a quantum cat state. Experimental results demonstrate cat state generation with a mean thermal phonon number of 0.013, indicating a low level of thermal excitation. This performance is achieved under specific operating conditions: an optical cavity decay rate of 3 MHz and a magnomechanical coupling strength of 2 kHz. These parameters are critical for maintaining the coherence necessary for observing the desired quantum behavior and validating the state preparation process.

The Wigner function demonstrates squeezing of the mechanical mode, indicating non-classical behavior beyond vacuum fluctuations as detailed in the main text.

Towards a Quantum Future: Impact and Potential

The generation of quantum superpositions, known as Schrödinger cat states, is a cornerstone of many quantum technologies, but achieving robust and scalable production has remained a significant challenge. This research demonstrates a promising avenue through a magnomechanical approach, leveraging the unique properties of materials to create and control these delicate states. Unlike methods reliant on complex optical setups or cryogenic temperatures, this technique utilizes mechanical motion coupled with magnetic fields within a Yttrium-Iron-Garnet (YIG) system. This offers a pathway toward generating cat states with improved resilience to environmental noise and the potential for miniaturization and increased production rates. The ability to reliably create and manipulate these states is crucial for advancements in quantum sensing, where enhanced precision is paramount, as well as for realizing fault-tolerant quantum computation and exploring novel quantum information processing paradigms, potentially circumventing limitations inherent in current technologies utilizing bulk acoustic-wave resonators.

The exceptional coherence properties of Yttrium-Iron-Garnet (YIG) represent a significant advantage in the pursuit of stable quantum states. This ferromagnetic material exhibits remarkably low magnetic dissipation, allowing microwave magnons – quantized spin waves – to propagate with minimal loss of quantum information. This sustained coherence is crucial for maintaining the delicate superposition inherent in quantum systems, particularly in generating and manipulating complex states like the Schrödinger cat state explored in this research. Unlike many materials where vibrations and imperfections quickly degrade quantum coherence, YIG’s crystalline structure and magnetic properties offer a relatively noise-free environment for magnon confinement and interaction, potentially paving the way for longer coherence times and more robust quantum devices. The material’s compatibility with nanofabrication techniques further enhances its appeal for scalable quantum technologies, positioning YIG as a promising building block for future quantum sensors and processors.

The realization of this magnomechanical system presents a compelling pathway for advancements across several quantum technologies. Specifically, a functioning device promises enhanced capabilities in quantum sensing, allowing for the detection of incredibly weak signals and fields with unprecedented precision. Furthermore, the system’s potential extends to metrology, enabling more accurate and precise measurements of physical quantities at the quantum limit. Perhaps most significantly, this approach offers a fundamentally different strategy for quantum information processing, circumventing limitations inherent in current methods reliant on bulk acoustic-wave resonators. By leveraging the unique properties of magnons and mechanical motion, this technology could pave the way for more robust, scalable, and energy-efficient quantum computers and communication networks, ultimately broadening the scope of what’s achievable in the quantum realm.

The degree of mechanical mode squeezing is maximized by optimizing the positive coupling strength relative to the negative coupling strength, and is temperature-dependent, as demonstrated by varying both couplings and bath temperature.

The pursuit of generating non-classical states, as demonstrated in this work with the creation of mechanical cat-like states, echoes a fundamental principle of scientific inquiry. Every deviation from the expected, every apparent anomaly, holds the potential for deeper understanding. As Werner Heisenberg notably stated, “Not only does the new idea not come from the old, but it contradicts it.” This aligns perfectly with the exploration of squeezed states and phonon subtraction; the researchers intentionally manipulate a system to deviate from its classical behavior, leveraging those very deviations to reveal the quantum properties of the mechanical mode. The creation of such a state isn’t simply about achieving a desired outcome, but about pushing the boundaries of what’s considered possible and extracting knowledge from the unexpected.

Where Do We Go From Here?

The generation of mechanical cat-like states, as proposed, hinges on the precise choreography of squeezing and phonon subtraction. While theoretically sound, the practical realization presents a considerable challenge. Maintaining coherence throughout the optical pulse interactions, particularly in the presence of environmental noise, remains a significant hurdle. The sensitivity of the system to imperfections in fabrication and control parameters requires careful consideration; a slight deviation could easily destroy the fragile quantum superposition.

Future work might explore alternative methods for phonon subtraction, perhaps leveraging different quantum interactions or measurement schemes. Extending this framework to create more complex entangled states, or even utilizing these states for quantum sensing applications, is a logical progression. However, the true test lies in demonstrating the robustness of these states – their ability to withstand decoherence and remain non-classical under realistic conditions.

Ultimately, the pursuit of mechanical non-classicality is not merely about achieving a specific quantum state. It is about probing the fundamental limits of quantum mechanics in macroscopic systems. If a pattern cannot be reproduced or explained, it doesn’t exist.

Original article: https://arxiv.org/pdf/2512.10347.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/