When operated in a dilution cryostat, a MHz-frequency nanomechanical device relies on active cooling to reach its quantum ground state. However, a proper understanding of its environmental interactions and mechanical quantum decoherence would require in-equilibrium cooling, with the thermal bath reaching sub-mK temperatures. This is very demanding and requires cooling via adiabatic nuclear demagnetization. The authors successfully demonstrate the technique, with a scheme to measure the temperature on-chip to verify equilibrium with the cryostat. An unexpected instability of unknown origin is observed at very low temperatures, presenting a strong limitation to progress in this field.
When operated in a dilution cryostat, a MHz-frequency nanomechanical device relies on active cooling to reach its quantum ground state. However, a proper understanding of its environmental interactions and mechanical quantum decoherence would require in-equilibrium cooling, with the thermal bath reaching sub-mK temperatures. This is very demanding and requires cooling via adiabatic nuclear demagnetization. The authors successfully demonstrate the technique, with a scheme to measure the temperature on-chip to verify equilibrium with the cryostat. An unexpected instability of unknown origin is observed at very low temperatures, presenting a strong limitation to progress in this field.
Abstract We report recent progress toward the realization of a sub-mK, low-vibration environment at the bottom stage of a dry dilution refrigerator for use in mechanical tests of quantum mechanics. Using adiabatic nuclear demagnetization, we have cooled a silicon cantilever force sensor to T≈1 T ≈ 1 mK. The temperature of the tip holder of the cantilever chip was determined via a primary magnetic flux noise thermometer. The quality factor of the cantilever continues to increase with decreasing temperature, reaching Q≈4⋅104 Q ≈ 4 · 10 4 at 2 mK. To demonstrate that the vibration isolation is not compromised, we report the detection of the thermal motion of the cantilever down to T≈20 T ≈ 20 mK, only limited by the coupling to the SQUID readout circuit. We discuss feasible improvements that will allow us to probe unexplored regions of the parameter space of continuous spontaneous localization models.
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.
Understanding the temporal and spatial dependence of temperature is critical in high-performance cryogenic devices. Typical thermometry techniques struggle to simultaneously combine high bandwidth, sensitivity and on-chip integration, limiting their ability to measure fast intra-device thermal fluctuations. Here, we demonstrate a time-resolved thermometry platform based on TiN kinetic inductance resonators integrated in a 22 nm FDSOI chip. By tracking temperature-dependent shifts in the resonant frequency, we achieve sub-millikelvin temperature sensitivity down to temperatures of 100 mK. Time-resolved on-chip pulsed heating experiments as a function of distance reveal an onset delay, consistent with a quasi-ballistic heat propagation velocity of 3.9 ± 0.1 mm μs−1. We also show that elevated temperatures increase net thermal conductance, shortening thermal relaxation times across all spatial separations. This behaviour manifests in two distinct regimes: a substrate-limited regime at 100 mK, where cooling rates vary with heater distance, and a Kapitza boundary-limited regime at 400 mK, where thermal relaxation becomes more spatially uniform. These measurements demonstrate kinetic inductance thermometry's ability to rapidly probe non-equilibrium temperature dynamics in cryogenic devices such as quantum processors.
Access to lower temperatures has consistently enabled scientific breakthroughs. Pushing the limits of \emph{on-chip} temperatures deep into the microkelvin regime would open the door to unprecedented quantum coherence, novel quantum states of matter, and also the discovery of unexpected phenomena. Adiabatic demagnetization is the workhorse of microkelvin cooling, requiring a dilution refrigerator precooling stage. Pulse-tube dilution refrigerators have grown enormously in popularity due to their vast experimental space and independence of helium, but their unavoidable vibrations are making microkelvin cooling very difficult. On-chip thermometry in this unexplored territory is also not a trivial task due to extreme sensitivity to noise. Here, we present a pulse-tube compatible microkelvin sample holder with on-board cooling and microwave filtering and introduce a new type of temperature sensor, the gate Coulomb blockade thermometer (gCBT), working deep into the microkelvin regime. Using on- and off-chip cooling, we demonstrate electronic temperatures as low as 224$\pm7μK,remainingbelow300μKfor27hours,thusprovidingsufficienttimeformeasurements.Finally,wegiveanoutlookforcoolingbelow50μ$K for a new generation of microkelvin transport experiments.
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.
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.