Coupled quantized mechanical oscillators (1011.0473v2)

Abstract: The harmonic oscillator is one of the simplest physical systems but also one of the most fundamental. It is ubiquitous in nature, often serving as an approximation for a more complicated system or as a building block in larger models. Realizations of harmonic oscillators in the quantum regime include electromagnetic fields in a cavity [1-3] and the mechanical modes of a trapped atom [4] or macroscopic solid [5]. Quantized interaction between two motional modes of an individual trapped ion has been achieved by coupling through optical fields [6], and entangled motion of two ions in separate locations has been accomplished indirectly through their internal states [7]. However, direct controllable coupling between quantized mechanical oscillators held in separate locations has not been realized previously. Here we implement such coupling through the mutual Coulomb interaction of two ions held in trapping potentials separated by 40 um (similar work is reported in a related paper [8]). By tuning the confining wells into resonance, energy is exchanged between the ions at the quantum level, establishing that direct coherent motional coupling is possible for separately trapped ions. The system demonstrates a building block for quantum information processing and quantum simulation. More broadly, this work is a natural precursor to experiments in hybrid quantum systems, such as coupling a trapped ion to a quantized macroscopic mechanical or electrical oscillator [9-13].

• The paper demonstrates a direct, coherent coupling mechanism between 9Be+ ions using Coulomb interaction, achieving energy exchange in approximately 155 µs.
• The experimental methodology utilizes a precision-engineered cryogenic surface-electrode trap that minimizes heating and maintains quantum coherence.
• Results aligned with theoretical models, indicating significant potential for scaling multi-zone quantum processing and hybrid quantum network applications.

Coupled Quantized Mechanical Oscillators: An Analysis

The paper "Coupled Quantized Mechanical Oscillators" addresses the coupling of atomic ions trapped in separate potential wells, a notable advancement in quantum technologies that paves the way for further exploration in quantum information processing and quantum simulation. The researchers have realized direct controllable coupling through the Coulomb interaction of two ^9Be^+ ions held in trapping potentials separated by 40 µm, demonstrating energy exchange between the ions at the quantum level.

Theoretical Foundation

The coupling mechanism is grounded in the quantized interaction between motional modes of trapped ions, driven by their mutual Coulomb interaction. The Hamiltonian governing the interaction displays terms corresponding to the harmonic oscillator lowering and raising operators, establishing that the interaction is linear in the motional displacements of the ions. The coupling strength scales as an inverse cubic function of ion separation, necessitating precision in maintaining the resonance condition for optimal energy transfer.

Experimental Methodology

The ions were contained in a meticulously fabricated surface-electrode trap, cooled to cryogenic temperatures to minimize heating rates that could disrupt the quantum states. The researchers demonstrated energy exchange by preparing the ions in a state conducive to motional coupling and documenting the coherent swapping of energy consistent with theoretical models. The system exhibited an oscillatory energy transfer characterized by a coupling time of approximately 155 µs, alignment with theoretical predictions notwithstanding some deviation attributed to measurement uncertainties.

Numerical Insights and Observations

A key numerical result is the measured exchange time of 155 µs versus the predicted 162 µs, evidencing the experiment's sensitivity to parameters such as ion separation. The achieved coupling rate was shown to exceed the heating rate under cryogenic conditions, crucial for maintaining coherence. Further analysis showed the splitting between axial normal mode frequencies, with a measured minimum splitting of 3.0(5) kHz, reflecting the experimental system's commitment to fulfilling the resonance condition.

Implications and Future Directions

The implications for quantum computing are considerable, as direct coupling without co-location offers new avenues for multi-zone quantum processing architectures, potentially simplifying ion transport and minimizing decoherence mechanisms associated with such operations. Practically, this technique could enhance the capabilities of quantum-logic spectroscopy and enable metrological applications where multiple ion species or oppositely charged particles are involved.

From a theoretical perspective, the demonstrated system serves as a model for further studies involving hybrid quantum systems, such as integrating trapped ions with macroscopic mechanical oscillators or superconducting qubits for robust quantum information transfer. Continued advancement will likely focus on improving Raman laser intensity stability and minimizing beam direction-induced Debye-Waller factors for enhanced coherence.

Conclusion

"Coupled Quantized Mechanical Oscillators" effectively establishes a framework for the direct, coherent interaction of separated quantum systems, marking a significant milestone in realizing complex quantum networks. As device miniaturization and coupling fidelity see further refinement, the path forward promises substantial contributions to quantum computing and hybrid quantum interface development.