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Microwave amplification with nanomechanical resonators
F. Massel, T. T. Heikkilä, J. -M. Pirkkalainen, S. U. Cho, H. Saloniemi, P. Hakonen, M. A. Sillanpää
TL;DR
The paper examines microwave amplification and the conditions under which its quantum limit can be reached. It describes amplification with a mechanically coupled system and reports a 0.6 dB signal-to-noise improvement corresponding to 20 added noise quanta.
Problem
The work addresses the quantum limit of noise added during signal amplification.
Method
The paper analyzes amplification in a coupled electromechanical system using a linearized description and experimentally characterizes its damping and amplification behavior.
Results
0.6 dB improvement to the signal-to-noise ratio corresponds to 20 added noise quanta, matching the expected thermal phonon number.
Takeaways & Limitations
The quantum limit can be reached in the absence of internal cavity losses and with a zero-temperature mechanical reservoir.
Takeaways & Limitations
For sufficiently large |ΓM|, the linearized description of the system physics breaks down.
Abstract
from arXiv · showhide
Sensitive measurement of electrical signals is at the heart of modern science and technology. According to quantum mechanics, any detector or amplifier is required to add a certain amount of noise to the signal, equaling at best the energy of quantum fluctuations. The quantum limit of added noise has nearly been reached with superconducting devices which take advantage of nonlinearities in Josephson junctions. Here, we introduce a new paradigm of amplification of microwave signals with the help of a mechanical oscillator. By relying on the radiation pressure force on a nanomechanical resonator, we provide an experimental demonstration and an analytical description of how the injection of microwaves induces coherent stimulated emission and signal amplification. This scheme, based on two linear oscillators, has the advantage of being conceptually and practically simpler than the Josephson junction devices, and, at the same time, has a high potential to reach quantum limited operation. With a measured signal amplification of 25 decibels and the addition of 20 quanta of noise, we anticipate near quantum-limited mechanical microwave amplification is feasible in various applications involving integrated electrical circuits.
resonators: Supplementary Information
The supplementary information identifies the authors and their affiliations at Aalto University and VTT Technical Research Centre of Finland.
- The paper lists F. Massel, T. T. Heikkilä, J.-M. Pirkkalainen, S. U. Cho, H. Saloniemi, P. Hakonen, and M. A. Sillanpää as authors.
- The authors are affiliated with the Low Temperature Laboratory at Aalto University and Microsystems and Nanoelectronics at VTT.
1 Description of the experiment
The experiment uses an on-chip meandering microwave cavity coupled to a suspended nanomechanical beam and operated in a dilution refrigerator. Characterization establishes the cavity and electromechanical parameters, while weak-probe measurements determine added noise.
- 1 Description of the experiment: The structures are fabricated using electron-beam lithography, 150 nm aluminum evaporation, focused-ion-beam beam etching, and a roughly 700 nm isotropic HF-vapor release etch.HF vapor is used instead of liquid oxide etchant to avoid damaging the aluminum film.
- 1 Description of the experiment: The device combines a 2-micrometre-wide, 45-millimetre-long meandering microstrip cavity with a suspended mechanical beam and a 9–12 nm vacuum slit.The cavity uses its lowest mode, approximately corresponding to a λ/2 transmission-line resonance.
- 1 Description of the experiment: The cavity model extracts its capacitance and inductance by simulating ideal Cg and Lg components and fitting their effect on the mode frequency.The effective stray capacitance is approximately C + Cc ≃ 24 fF.
- 1 Description of the experiment: The measured cavity response has an S11 full width at half maximum of (2π) × 6.0 MHz and a maximum resonant absorption of −5.5 dB.The final cavity parameters used in the paper are γc = (2π) × 6.2 MHz, γI = (2π) × 1.4 MHz, and γE = (2π) × 4.8 MHz.
2 Theoretical details
The theory models the cavity and mechanical resonator as coupled oscillators with external, internal, and mechanical baths, then linearizes their dynamics around a driven steady-state operating point. It derives signal gains and added-noise expressions, showing that reduced effective mechanical damping produces amplification and that the quantum limit is attainable under ideal conditions.
- Hamiltonian and reservoirs: The model describes coupled cavity and mechanical degrees of freedom, including their interaction and coupling to external, internal, and mechanical reservoirs.The external bath represents the transmission line, while internal and mechanical baths account for cavity dissipation and mechanical thermal noise.
- Steady state and linearization: A coherent pump drives the cavity, and the equations are linearized by separating stationary coherent fields from fluctuation operators.The stationary solution determines the amplifier operating point and effective fluctuation parameters.
- Steady state and linearization: The stationary equations yield three possible cavity-field solutions as functions of the pump, with the selected branch satisfying αs → 0 as αin → 0.This branch is used for the subsequent fluctuation analysis.
- Amplification: As γeff decreases toward zero, ΓM becomes large and the ΓM-dependent transfer coefficients produce amplification of the input signal.The maximum-gain condition corresponds to approaching γeff → 0+; crossing γeff = 0 marks the associated boundary.
- Noise and quantum limit: The amplifier treats internal cavity-loss noise and mechanical-bath noise as added noise, while transmission-line input noise is regarded as intrinsic input noise.The input-output relations distinguish signal gains from coefficients describing internal and mechanical noise contributions.
- Noise and quantum limit: The quantum limit can be reached without internal cavity losses and with a zero-temperature mechanical reservoir.Near optimal coupling Gopt = √γmγc and resonance, added noise increases linearly with mechanical-reservoir phonon number, with coefficient set by total-to-external losses.