Nano-electro-mechanical devices are now rapidly approaching the point where it will be possible to observe quantum mechanical behavior. However, for such behavior to be visible it is necessary to reduce the thermal motion of these devices down to temperatures in the millikelvin range. Here we consider the use of feedback control for this purpose. We analyze an experimentally realizable situation in which the position of the resonator is continuously monitored by a Single-Electron Transistor. Because the resonator is harmonic, it is possible to use a classical description of the measurement process, and we discuss both the quantum and classical descriptions. Because of this the optimal feedback algorithm can be calculated using classical control theory. We examine the quantum state of the controlled oscillator, and the achievable effective temperature. Our estimates indicate that with current experimental technology, feedback cooling is likely to bring the required milliKelvin temperatures within reach.
Nano-electro-mechanical devices are now rapidly approaching the point where it will be possible to observe quantum mechanical behavior. However, for such behavior to be visible it is necessary to reduce the thermal motion of these devices down to temperatures in the millikelvin range. Here we consider the use of feedback control for this purpose. We analyze an experimentally realizable situation in which the position of the resonator is continuously monitored by a Single-Electron Transistor. Because the resonator is harmonic, it is possible to use a classical description of the measurement process, and we discuss both the quantum and classical descriptions. Because of this the optimal feedback algorithm can be calculated using classical control theory. We examine the quantum state of the controlled oscillator, and the achievable effective temperature. Our estimates indicate that with current experimental technology, feedback cooling is likely to bring the required milliKelvin temperatures within reach.
Cooled, low-loss nanomechanical resonators offer the prospect of directly observing the quantum dynamics of mesoscopic systems. However, the present state of the art requires cooling down to the milliKelvin regime in order to observe quantum effects. Here we present an active feedback strategy based on continuous observation of the resonator position for the purpose of obtaining these low temperatures. In addition, we apply this to an experimentally realizable configuration, where the position monitoring is carried out by a single-electron transistor. Our estimates indicate that with current technology this technique is likely to bring the required low temperatures within reach.
By coupling a single-electron transistor to a high-quality factor, 19.7-megahertz nanomechanical resonator, we demonstrate position detection approaching that set by the Heisenberg uncertainty principle limit. At millikelvin temperatures, position resolution a factor of 4.3 above the quantum limit is achieved and demonstrates the near-ideal performance of the single-electron transistor as a linear amplifier. We have observed the resonator's thermal motion at temperatures as low as 56 millikelvin, with quantum occupation factors of NTH = 58. The implications of this experiment reach from the ultimate limits of force microscopy to qubit readout for quantum information devices.
The application of quantum mechanics to macroscopic motion suggests many counterintuitive phenomena. While the quantum nature of the motion of individual atoms and molecules has long been successfully studied, an equivalent demonstration of the motion of a near-macroscopic structure remains a challenge in experimental physics. A nanomechanical resonator is an excellent system for such a study. It typically contains > 10 10 atoms, and it may be modeled in terms of macroscopic parameters such as bulk density and elasticity. Yet it behaves like a simple harmonic oscillator, with mass low enough and resonant frequency high enough for its quantum zero-point motion and single energy quanta to be experimentally accessible. In pursuit of quantum phenomena in a mechanical oscillator, two important goals are to prepare the oscillator in its quantum ground state, and to measure its position with a precision limited by the Heisenberg uncertainty principle. In this work we have demonstrated techniques that advance towards both of these goals. Our system comprises a 30 micron × 170 nm, 2.2 pg, 5.57 MHz nanomechanical resonator capacitively coupled to a 5 GHz superconducting microwave resonator. The microwave resonator and nanomechanical resonator are fabricated together onto a single silicon chip and measured in a dilution refrigerator at temperatures below 150 mK. At these temperatures the coupling of the motion to the thermal environment is very small, resulting in a very high mechanical Q, approaching ∼ 10 6 . By driving with a microwave pump signal, we observed sidebands generated by the mechanical motion and used these to measure the thermal motion of the resonator. Applying a pump tone red-detuned from the microwave resonance, we used the microwave field to damp the mechanical resonator, extracting energy and "cooling" the motion in a manner similar to optical cooling of trapped atoms. Starting from a mode temperature of ∼ 150 mK, we reached ∼ 40 mK by this "backaction cooling" technique, corresponding to an occupation factor only ∼ 150 times above the ground state of motion. We also determined the precision of our device in measurement of position. Quantum mechanics dictates that, in a continuous position measurement, the precision may be no better than the zero-point motion of the resonator. Increasing the coupling of the resonator to detector will eventually result in back-action driving of the motion, adding imprecision and enforcing this limit. We demonstrated that our system is capable of precisions approaching this limit, and identified the primary experimental factors preventing us from reaching it: noise added to the measurement by our amplifier, and excess dissipation appearing in our microwave resonator at high pump powers. Furthermore, by applying both red- and blue-detuned phase-coherent microwave pump signals, we demonstrated back-action evading (BAE) measurement sensitive to only a single quadrature of the motion. By avoiding the back-action driving in the measured quadrature, such a technique has the potential for precisions surpassing the limit of the zero-point motion. With this method, we achieved a measurement precision of ∼ 100 fm, or 4 times the quantum zero-point motion of the mechanical resonator. We found that the measured quadrature is insensitive to back-action driving by at least a factor of 82 relative to the unmeasured quadrature. We also identified a mechanical parametric amplification effect which arises during the BAE measurement. This effect sets limits on the BAE performance but also mechanically preamplifies the motion, resulting in a position resolution 1.3 times the zero-point motion. We discuss how to overcome the experimental limits set by amplifier noise, pump power and parametric amplification. These results serve to define the path forward for demonstrating truly quantum-limited measurement and non-classical states of motion in a nearly-macroscopic object.
Recent technological advances have enabled the creation of nanomechanical structures with resonance frequencies exceeding 2 GHz. The oscillators are nanomachined single‐crystal structures of silicon, designed to provide two distinct sets of coupled elements with very low and very high frequencies. At higher temperatures — in the so‐called classical regime, the response to an applied driving force is continuous. At millikelvin temperatures these nanomechanical oscillators enter the quantum regime of mechanical motion with a manifestly discrete response to the applied drive. The observed discrete response most likely results from the onset of the quantum regime in these macroscopic nanomechanical oscillators. These new experiments offer exciting prospects for the studies of quantum measurement and quantum computation, involving macroscopic quantum mechanical oscillators.
Measurement-based control has emerged as an important technique to prepare mechanical resonators in pure quantum states for applications in quantum information processing and quantum sensing. Conventionally this has required two separate channels, one for probing the motion and another one acting back on the resonator. In this work, we analyze and experimentally demonstrate a technique of single-laser feedback cooling, where one laser is used for both probing and controlling the mechanical motion. We show using an analytical model and experiments that feedback cooling is feasible in this mode as long as certain stability requirements are fulfilled. Our results demonstrate that, in addition to being more experimentally feasible construction, the interference effects of the single-laser feedback can actually be used to enhance cooling at some parameter regimes.
We consider the problem of controlling the motion of an atom trapped in an optical cavity using continuous feedback. In order to realize such a scheme experimentally, one must be able to perform state estimation of the atomic motion in real time. While in theory this estimate may be provided by a stochastic master equation describing the full dynamics of the observed system, integrating this equation in real time is impractical. Here we derive an approximate estimation equation for this purpose, and use it as a drive in a feedback algorithm designed to cool the motion of the atom. We examine the effectiveness of such a procedure using full simulations of the cavity QED system, including the quantized motion of the atom in one dimension.