Classical Oscillators May Simulate Quantum Systems, German Physicists Find

Researchers from the University of Konstanz have explored the potential of classical oscillators to simulate dissipative quantum systems. The study, published in the Physical Review Research, focused on a system of two coupled oscillators subject to stochastic fluctuations. The researchers demonstrated that these fluctuations could be engineered in the control apparatus of the systems, providing new insights into the quantum-classical analogy. The findings could have applications in nanomechanics, particularly in the control of levitated nanoparticles and nanostring resonators, and contribute to the understanding of the quantum-classical border.

Can Classical Oscillators Simulate Dissipative Qubits?

In a recent study published in the Physical Review Research, Lorenzo Bernazzani and Guido Burkard from the Department of Physics at the University of Konstanz, Germany, explored the potential of classical oscillators to simulate dissipative quantum systems. The researchers focused on a system composed of two coupled oscillators subject to stochastic fluctuations in its internal parameters.

The study aimed to answer whether the well-known classical analogy of the quantum dynamics of two-level systems (TLSs), or qubits, provided by two coupled oscillators, could be extended to simulate the dynamics of dissipative quantum systems. The analogy in the dissipation-free case has already been tested in multiple experimental setups, such as doubly clamped or cantilever string resonators and optically levitated particles.

A key result of this classical analogy is that the relaxation and decoherence times of the analog quantum system must be equal. However, the researchers showed that this fundamentally quantum feature could be implemented in the aforementioned classical systems by adding stochastic fluctuations in their internal parameters.

How Can Stochastic Fluctuations Be Engineered?

The researchers further demonstrated that these stochastic contributions could be engineered in the control apparatus of those systems. They discussed the application of this theory to levitated nanoparticles and to nanostring resonators.

The study is significant as it provides new insights about the quantum-classical analogy, drawing from the mapping of quantum evolution by means of classical oscillators. The researchers addressed the issue of the trivial form of the relaxation term in the Schrödinger equation for the simulated quantum two-level system (TLS).

In the quantum case, there are two relaxation times, the longitudinal T1 and the transverse T2. These are linked to the relaxation of the populations and of the coherences of the TLS state. The researchers showed how noise could induce dissipation mechanisms with such quantum features, which were not grasped by the previous classical model.

What is the Role of Quantum Phase in This Study?

The quantum phase is the defining concept of quantum mechanics, giving rise to quantum superpositions, interference phenomena, and many-body entanglement. The perturbation of microscopic quantum systems leads to the loss of phase coherence and, on a macroscopic scale, the emergence of our classical reality.

Decoherence is a detrimental aspect for quantum information systems. However, the interaction of quantum systems with the external degrees of freedom of the environment is unavoidable. The researchers complemented the attempt to suppress the coupling between the system and environment with the modeling of the effects of these interactions on the reduced system dynamics.

While an accurate model can be achieved in simple systems, the computational complexity scales exponentially with the system size. To cope with this, the simulation of dissipation is a valuable tool. The common approach consists of adding classical noise to the analog system. In this way, the open-quantum system that one is interested in simulating is mapped onto another system, more controllable, the dynamics of which is proven to be analogous.

What is the Significance of This Research?

This research is significant as it provides a new perspective on the quantum-classical analogy. By demonstrating that classical oscillators can simulate dissipative quantum systems, the study opens up new possibilities for the study and understanding of quantum dynamics.

The findings also have potential applications in the field of nanomechanics, particularly in the control of levitated nanoparticles and nanostring resonators. By showing how stochastic fluctuations can be engineered in the control apparatus of these systems, the research could pave the way for more precise control and manipulation of these systems.

Moreover, the study contributes to the ongoing quest for the nanoscale miniaturization of physical devices. The astounding degree of control that has been achieved in mechanical systems over the past years has fostered the hope to reach mesoscopic quantum superposition of massive objects and to study quantum effects of gravity in the laboratory.

What are the Future Implications of This Study?

The findings of this study have significant implications for the future of quantum mechanics and nanomechanics. By demonstrating that classical oscillators can simulate dissipative quantum systems, the research opens up new avenues for the study of quantum dynamics.

The ability to engineer stochastic fluctuations in the control apparatus of systems such as levitated nanoparticles and nanostring resonators could lead to advancements in the control and manipulation of these systems. This could, in turn, contribute to the development of more efficient and effective nanoscale devices.

Furthermore, the research could also contribute to our understanding of the elusive aspects of the quantum-classical border. By providing new insights into the quantum-classical analogy, the study could help uncover some of the elusive aspects of this border, thereby advancing our understanding of the fundamental principles of physics.