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.
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.
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.
The coupled dynamics of a nanomechanical resonator and superconducting quantum circuits are studied in three experiments, in the context of studying the quantum limit for force detection and quantum physics of macroscopic objects. In the first experiment, the dispersive mechanical resonance shift from the interaction with a Cooper-pair box qubit is studied. The measured coupling strength is large enough to satisfy one of the conditions required to perform many of the proposed quantum nanomechanical measurements. The resonance shift also probes the microwave-driven response of the qubit, showing Rabi oscillation and Landau-Zener tunneling, proving the coherent dynamics of the qubit. Second, the parametric excitation of nanomechanical motion is studied via experiments with a driven qubit. Degenerate parametric amplification and oscillation are demonstrated, with a new observation of nonlinear dissipation. The squeezing of the back-action noise from the detection amplifier is also observed, up to 4dB. It is the first demonstration using a qubit as an auxiliary system to modify the nanomechanical dynamics, showing a possible route for generation of nanomechanical quantum states. Finally, back-action cooling of nanomechanical motion has been investigated, which is implemented by capacitively coupling a high-Q coplanar waveguide microwave resonator to a nanomechanical resonator. The thermal state with 7.5 mechanical quanta on average is reached, a result that is ultimately limited due to increased bath heating with microwave power. The heating is consistent with a model based on two-level systems resonantly coupled to the nanomechanical mode. This additional heating suggests future efforts to improve coupling and for reducing two-level system density in materials employed to reach the motional ground state via back-action cooling.
The coupling of nanomechanical resonators to controllable quantum systems represents a growing and promising area of research. Recent advances in this field have brought to astonishing results, such as the initialization of a mechanical resonator into its quantum ground state and even the preparation of non-classical coherent states of motion. These achievements open up appealing scenarios to quantum information technologies and to the exploration of the quantum-classical boundary. From an application perspective, such quantum-mechanical hybrid systems provide a versatile and attractive tool for a variety of precision measurements, like ultra-sensitive detection of force, mass, and displacement. \n \nQuantum control over a mechanical resonator, or, conversely, the prospect of using resonator's motion for probing quantum states, both involve some tight requirements. First of all, the interaction between the mechanics and its quantum partner has to be large on the scale of the decoherence rates of the coupled systems. In most cases, the coupling mechanism has to be activated by engineering the resonator with electrodes, magnets, or mirrors, or by using tailored laser fields. For this reason, the search for a strong coupling typically competes with the requirement of overcoming decoherence effects. In addition, for quantum effects to be observable, strong coupling has to be accompanied by the preparation of zero entropy initial states, for instance by cooling the resonator into its ground state of motion. \n \nThe motivation pursued by this thesis is to contribute to the inspiring field of hybrid systems by walking through each of the aforementioned directions. We in fact demonstrate a promising system in which optically active quantum dots, embedded in fully self-assembled core-shell nanowires, are coupled to the nanowire motion. Mechanical vibrations of the nanowire modulate the quantum dot emission energy over a broad range exceeding 14 meV, by means of deformation potential coupling. In our system, therefore, both the coupling mechanism and the quantum states themselves are intrinsic to the resonator's structure. Besides revealing unusually strong, such a built-in opto-mechanical interaction produces a hybrid system whose inherent coherence is unspoiled by any functionalization or external field and whose fabrication is simpler than top-down techniques. \n \nWe further demonstrate the use of a quantum point contact as a displacement transducer to measure and control the low-temperature thermal motion of a nearby micromechanical cantilever. We show that by including the QPC in a suitable feedback loop, we are able to cool the cantilever's fundamental mechanical mode down to the level of the measurement noise, achieving a squashing of the QPC noise at high gain. Due to its off-board design, our system is particularly versatile and suitable to force-sensing applications. Since the QPC transducer is sensitive to local modifications of the nearby electric field, our approach is in principle compatible with any nanoscale resonator, without requiring any functionalization to activate the coupling. By improving the performance of the QPC as a one-dimensional conductor and the cantilever-QPC capacitive coupling, our system has the potential to achieve quantum-limited displacement resolution and ground state cooling. We then report on some ongoing attempts to overcome the current limitations of our system and couple mechanical motion to different mesoscopic transport devices. \n \nWe remark that our demonstration of an as-grown quantum-dot-in-nanowire hybrid system opens up bright prospects on future experiments, as also testified by the very recent ferment of the scientific community around this topic. We find that the opto-mechanical coupling rate is not far from the nanowire mechanical frequency. This fact makes our system particularly promising for the quantum non-demolition readout of a quantum dot state through a measurement of the nanowire position. On the other hand, we show that the coupling can be further optimized, and the nanowire mechanical heating rate reduced, thus disclosing the captivating perspective of using quantum dots to probe and control the mechanical state of a nanowire. In this context, it would be important to investigate a possible spin-oscillator coupling in our system, given the long coherence time offered by a spin state in a quantum dot. The wide range of control over the quantum dots emission energy and the ability to tune two neighboring dots into resonance pave the way to mechanically induced emitter-emitter coupling. In addition, our monolithic opto-mechanical system constitutes a good candidate for recent proposals of a tripartite hybrid system, which would integrate an optical cavity, a quantum two-level system and a mechanical resonator. The intrinsically strong coupling between the quantum dots and the nanowire motion would enhance the interaction between the mechanics and the cavity field, leading for instance to efficient cooling of the resonator to the ground state. Finally, the quantum dot sensitivity to the nanowire resonant vibration could also support the use of our system as an integrated force probe or as a nanomechanical mass sensor. In other words, the results reported in this dissertation constitute not only a relevant proof-of-principle, moreover they open up intriguing challenges for future research.
Why are classical theories often sufficient to describe the physics of our world even though everything around us is entirely composed of microscopic quantum systems? The boundary between these two fundamentally dissimilar theories remains an unsolved problem in modern physics. Position measurements of small objects allow us to probe the area where the classical approximation breaks down. In quantum mechanics, Heisenbergâ s uncertainty principle dictates that any measurement of the position must be accompanied by measurement induced back-action---in this case manifested as an uncertainty in the momentum. In recent years, cavity optomechanics has become a powerful tool to perform precise position measurements and investigate their fundamental limitations. The utilization of optical micro-cavities greatly enhances the interaction between light and state-of-the-art nanomechanical oscillators. Therefore, quantum mechanical phenomena have been successfully observed in systems far beyond the microscopic world. In such a cavity optomechanical system, the fluctuations in the position of the oscillator are transduced onto the phase of the light, while fluctuations in the amplitude of the light disturb the momentum of the oscillator during the measurement. As a consequence, correlations are established between the amplitude and phase quadrature of the probe light. However, so far, observation of quantum effects has been limited exclusively to cryogenic experiments, and access to the quantum regime at room temperature has remained an elusive goal because the overwhelming amount of thermal motion masks the weak quantum effects. This thesis describes the engineering of a high-performance cavity optomechanical device and presents experimental results showing, for the first time, the broadband effects of quantum back-action at room temperature. The device strongly couples mechanical and optical modes of exceptionally high quality factors to provide a measurement sensitivity ∼104 times below the requirement to resolve the zero-point fluctuations of the mechanical oscillator. The quantum back-action is then observed through the correlations created between the probe light and the motion of the nanomechanical oscillator. A so-called â variational measurementâ , which detects the transmitted light in a homodyne detector tuned close to the amplitude quadrature, resolves the quantum noise due to these correlations at the level of 10\% of the thermal noise over more than an octave of Fourier frequencies around mechanical resonance. Moreover, building on this result, an additional experiment demonstrates the ability to achieve quantum enhanced metrology. In this case, the generated quantum correlations are used to cancel quantum noise in the measurement record, which then leads to an improved relative signal-to-noise ratio in measurements of an external force. In conclusion, the successful observation of broadband quantum behavior on a macroscopic object at room temperature is an important milestone in the field of cavity optomechanics. Specifically, this result heralds the rise of optomechanical systems as a platform for quantum physics at room temperature and shows promise for generation of ponderomotive squeezing in room-temperature interferometers.
Nanoelectromechanical systems have many potential applications in nanoelec-tronics as well as in fundamental studies of quantum mechanics in mesoscopic sys-tems. Nanoelectromechanical systems have been touted as an extension of micro-electromechanical systems which would operate at higher frequencies and consume far less power due their higher quality factors. Since these systems can be cooled close to their ground states with existing cryogenic techniques, they are useful tools to study the quantum effects like backaction, coherent states and superposition in mesoscopic mechanical systems. Also there have been proposals to use these systems as qubits and buses in quantum computing. In this thesis I discuss the effects of the backaction of a superconducting single electron transistor that measures the position of a radio frequency nanomechanical resonator. One of the novel effects of this backaction is the cooling of the nanome-chanical resonator. The fact that a system can be cooled by merely coupling it to noisy non-equilibrium device is a counterintuitive phenomenon. Although backac-tion effects have been used to produce ultra-cold atoms, our results are the first demonstration of this cooling effect in a mesoscopic system. For a linear continuous position detection scheme, quantum mechanics places a lower limit on the product of position shot noise, Sx, and the backaction force noise, SF, which is given by, SxSF ≥ h̄
Experiments to probe the basic quantum properties of motional degrees of freedom of mechanical systems have developed rapidly over the last decade. One promising approach is to use hybrid electromechanical systems incorporating superconducting qubits and microwave circuitry. However, a critical challenge facing the development of these systems is to achieve strong coupling between mechanics and qubits while simultaneously reducing coupling of both the qubit and mechanical mode to the environment. Here we report measurements of a qubit-coupled mechanical resonator system consisting of an ultra-high-frequency nanoresonator and a long coherence-time superconducting transmon qubit, embedded in a superconducting coplanar waveguide cavity. It is demonstrated that the nanoresonator and transmon have commensurate energies and transmon coherence times are one order of magnitude larger than for all previously reported qubit-coupled nanoresonators. Moreover, we show that numerical simulations of this new hybrid quantum system are in good agreement with spectroscopic measurements and suggest that the nanoresonator in our device resides at low thermal occupation number, near its ground state, acting as a dissipative bath seen by the qubit. We also outline how this system could soon be developed as a platform for implementing more advanced experiments with direct relevance to quantum information processing and quantum thermodynamics, including the study of nanoresonator quantum noise properties, reservoir engineering, and nanomechanical quantum state generation and detection.