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arXiv:0812.0261 · Physical Review B

Cooling a micromechanical resonator by quantum back-action from a noisy qubit

Ying-Dan Wang, Yong Li, Fei Xue, Christoph Bruder, Kouichi Semba

Published Oct 6, 2009• 27 citations
arXivHTMLPDF

Abstract

We study the role of qubit dephasing in cooling a mechanical resonator by quantum back-action. With a superconducting flux qubit as a specific example, we show that ground-state cooling of a mechanical resonator can only be realized if the qubit dephasing rate is sufficiently low.
DOI
10.1103/physrevb.80.144508

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Using a semi-classical approach, we describe an on-chip cooling protocol for a micro-mechanical resonator by employing a superconducting flux qubit. A Lorentz force, generated by the passive back-action of the resonator's displacement, can cool down the thermal motion of the mechanical resonator by applying an appropriate microwave drive to the qubit. We show that this on-chip cooling protocol, with well-controlled cooling power and a tunable response time of passive back-action, can be highly efficient. With feasible experimental parameters, the effective mode temperature of a resonator could be cooled down by several orders of magnitude.
Using a semi-classical approach, we describe an on-chip cooling protocol for a micro-mechanical resonator by employing a superconducting flux qubit. A Lorentz force, generated by the passive back-action of the resonator's displacement, can cool down the thermal motion of the mechanical resonator by applying an appropriate microwave drive to the qubit. We show that this onchip cooling protocol, with well-controlled cooling power and a tunable response time of passive back-action, can be highly efficient. With feasible experimental parameters, the effective mode temperature of a resonator could be cooled down by several orders of magnitude.
For decades, quantum mechanics has been a hugely successful theory for understanding the microscopic world. Despite its seemingly non-physical predictions, such as superposition or cat states, the accuracy of the theory has been verified time and again for microscopic systems composed of single atoms or other quantum particles. Up till now, however, our understanding of how and if these quantum predictions scale to larger systems closer to our everyday perceptions, where we do not see quantum "weirdness", is an open question. One platform to pursue observation of quantum effects in a system composed of large ensembles of atoms rather than single particles is that of nanomechanical resonators. Several schemes have been proposed to observe quantum effects in these systems, eg [1],[41], but a common feature is the requirement that the mechanical resonator be at or near its quantum ground state, which has proved challenging to achieve. In this dissertation, a novel mechanical motion readout scheme using superconducting resonators is presented and shown to allow near quantum limited detection. In any strong measurement of a system, quantum mechanics dictates that the measurement will inherently produce some "back-action" on the measured system. It will be shown that for the measurement system presented, back-action forces can additionally be used to cool a single mode of a mechanical resonator to near its quantum ground state, with the lowest observed occu- pation factor at 3.8 ±1.3 quanta. This is a low enough occupation level that the nanoresonator is in its ground state statistically 21% of the time and opens up the possibility of preforming further quantum experiments. The system investigated in this dissertation is composed of a nanoscale mechanical resonator capacitively coupled to a superconducting coplanar waveguide resonator. The resonators were nanofabricated on a silicon substrate and cooled to low temperature in a dilution refrigerator system. Applying microwave signals to the device and measuring output spectra provided the means to both observe the mechanical motion and produce the back-action forces.
We propose an application of a single Cooper pair box (Josephson qubit) for active cooling of nanomechanical resonators. Latest experiments with Josephson qubits demonstrated that long coherence time of the order of microsecond can be achieved in special symmetry points. Here we show that this level of coherence is sufficient to perform an analog of the well known in quantum optics ``laser'' cooling of a nanomechanical resonator capacitively coupled to the qubit. By applying an ac driving to the qubit or the resonator, resonators with frequency of order 100 MHz and quality factors higher than 103{10}^{3}103 can be efficiently cooled down to their ground state, while lower-frequency resonators can be cooled down to micro-Kelvin temperatures. We also consider an alternative setup where dc-voltage-induced Josephson oscillations play the role of the ac driving and show that cooling is possible in this case as well.
Ground state cooling of a nanomechanical resonator coupled to a superconducting flux qubit is discussed. By inducing quantum interference to cancel unwanted heating excitations, ground state cooling becomes possible in the nonresolved regime. The qubit is modeled as a three-level system in Lambda configuration, and the driving fluxes are applied such that the qubit absorption spectrum exhibits electromagnetically induced transparency, thereby canceling the unwanted excitations. As our scheme allows the application of strong cooling fields, fast and efficient cooling can be achieved.