In the last two decades there has been an enormous progress in the experimental investigation of single quantum systems. This progress covers fields such as quantum optics, quantum computation, quantum cryptography, and quantum metrology, which are sometimes summarized as `quantum technologies'. A key issue there is entanglement, which can be considered as the characteristic feature of quantum theory. As disparate as these various fields maybe, they all have to deal with a quantum mechanical treatment of the measurement process and, in particular, the control process. Quantum control is, according to the authors, `control for which the design requires knowledge of quantum mechanics'. Quantum control situations in which measurements occur at important steps are called feedback (or feedforward) control of quantum systems and play a central role here. This book presents a comprehensive and accessible treatment of the theoretical tools that are needed to cope with these situations. It also provides the reader with the necessary background information about the experimental developments. The authors are both experts in this field to which they have made significant contributions. After an introduction to quantum measurement theory and a chapter on quantum parameter estimation, the central topic of open quantum systems is treated at some length. This chapter includes a derivation of master equations, the discussion of the Lindblad form, and decoherence – the irreversible emergence of classical properties through interaction with the environment. A separate chapter is devoted to the description of open systems by the method of quantum trajectories. Two chapters then deal with the central topic of quantum feedback control, while the last chapter gives a concise introduction to one of the central applications – quantum information. All sections contain a bunch of exercises which serve as a useful tool in learning the material. Especially helpful are also various separate boxes presenting important background material on topics such as the block representation or the feedback gain-bandwidth relation. The two appendices on quantum mechanics and phase-space and on stochastic differential equations serve the same purpose. As the authors emphasize, the book is aimed at physicists as well as control engineers who are already familiar with quantum mechanics. It takes an operational approach and presents all the material that is needed to follow research on quantum technologies. On the other hand, conceptual issues such as the relevance of the measurement process for the interpretation of quantum theory are neglected. Readers interested in them may wish to consult instead a textbook such as Decoherence and the Quantum-to-Classical Transition by Maximilian Schlosshauer. Although the present book does not contain applications to gravity, part of its content might become relevant for the physics of gravitational-wave detection and quantum gravity phenomenology. In this respect it should be of interest also for the readers of this journal.

https://iopscience.iop.org/article/10.1088/0264-9381/27/24/249002/pdf

Quantum Measurement and Control

All existing quantum-gravity proposals are extremely hard to test in practice. Quantum effects in the gravitational field are exceptionally small, unlike those in the electromagnetic field. The fundamental reason is that the gravitational coupling constant is about 43 orders of magnitude smaller than the fine structure constant, which governs light-matter interactions. For example, detecting gravitons—the hypothetical quanta of the gravitational field predicted by certain quantum-gravity proposals—is deemed to be practically impossible. Here we adopt a radically different, quantum-information-theoretic approach to testing quantum gravity. We propose witnessing quantumlike features in the gravitational field, by probing it with two masses each in a superposition of two locations. First, we prove that any system (e.g., a field) mediating entanglement between two quantum systems must be quantum. This argument is general and does not rely on any specific dynamics. Then, we propose an experiment to detect the entanglement generated between two masses via gravitational interaction. By our argument, the degree of entanglement between the masses is a witness of the field quantization. This experiment does not require any quantum control over gravity. It is also closer to realization than detecting gravitons or detecting quantum gravitational vacuum fluctuations.

Gravitationally Induced Entanglement between Two Massive Particles is Sufficient Evidence of Quantum Effects in Gravity.

Quantum control of complex objects in the regime of large size and mass provides opportunities for sensing applications and tests of fundamental physics. The realization of such extreme quantum states of matter remains a major challenge. We demonstrate a quantum interface that combines optical trapping of solids with cavity-mediated light-matter interaction. Precise control over the frequency and position of the trap laser with respect to the optical cavity allowed us to laser-cool an optically trapped nanoparticle into its quantum ground state of motion from room temperature. The particle comprises 108 atoms, similar to current Bose-Einstein condensates, with the density of a solid object. Our cooling technique, in combination with optical trap manipulation, may enable otherwise unachievable superposition states involving large masses.

https://science.sciencemag.org/content/sci/early/2020/01/29/science.aba3993.full.pdf

Cooling of a levitated nanoparticle to the motional quantum ground state.

The small mass and high coherence of nanomechanical resonators render them the ultimate mechanical probe, with applications that range from protein mass spectrometry and magnetic resonance force microscopy to quantum optomechanics. A notorious challenge in these experiments is the thermomechanical noise related to the dissipation through internal or external loss channels. Here we introduce a novel approach to define the nanomechanical modes, which simultaneously provides a strong spatial confinement, full isolation from the substrate and dilution of the resonator material's intrinsic dissipation by five orders of magnitude. It is based on a phononic bandgap structure that localizes the mode but does not impose the boundary conditions of a rigid clamp. The reduced curvature in the highly tensioned silicon nitride resonator enables a mechanical Q > 108 at 1 MHz to yield the highest mechanical Qf products (>1014 Hz) yet reported at room temperature. The corresponding coherence times approach those of optically trapped dielectric particles. Extrapolation to 4.2 K predicts quanta per milliseconds heating rates, similar to those of trapped ions. Soft phononic clamping dilutes the intrinsic dissipation of a mechanical resonator's material by five orders of magnitude, enabling a record value of the product between frequency and quality factor at room temperature, and mechanical coherence times otherwise only available in optical or Paul traps.

/pdf/ultracoherent-nanomechanical-resonators-via-soft-clamping-1p0f4dwiix.pdf

Ultracoherent nanomechanical resonators via soft clamping and dissipation dilution.

Nanomechanical oscillators are at the heart of ultrasensitive detectors of force, mass and motion. As these detectors progress to even better sensitivity, they will encounter measurement limits imposed by the laws of quantum mechanics. If the imprecision of a measurement of the displacement of an oscillator is pushed below a scale set by the standard quantum limit, the measurement must perturb the motion of the oscillator by an amount larger than that scale. Here we show a displacement measurement with an imprecision below the standard quantum limit scale. We achieve this imprecision by measuring the motion of a nanomechanical oscillator with a nearly shot-noise limited microwave interferometer. As the interferometer is naturally operated at cryogenic temperatures, the thermal motion of the oscillator is minimized, yielding an excellent force detector with a sensitivity of 0.51 aN Hz(-1/2). This measurement is a critical step towards observing quantum behaviour in a mechanical object.

/pdf/nanomechanical-motion-measured-with-an-imprecision-below-the-59vq4yks02.pdf

Nanomechanical motion measured with an imprecision below the standard quantum limit

A position sensor is demonstrated that is capable of resolving the zero-point motion of a nanomechanical oscillator in the timescale of its thermal decoherence; it achieves an imprecision that is four orders of magnitude below that at the standard quantum limit and is used to feedback-cool the oscillator to a mean photon number of five.

/pdf/measurement-based-control-of-a-mechanical-oscillator-at-its-q8xrbqfqhw.pdf

Measurement-based control of a mechanical oscillator at its thermal decoherence rate

Extreme stresses can be produced in nanoscale structures; this feature has been used to realize enhanced materials properties, such as the high mobility of silicon in modern transistors. We show how nanoscale stress can be used to realize exceptionally low mechanical dissipation when combined with “soft-clamping”—a form of phononic engineering. Specifically, using a nonuniform phononic crystal pattern, we colocalize the strain and flexural motion of a free-standing silicon nitride nanobeam. Ringdown measurements at room temperature reveal string-like vibrational modes with quality ( Q ) factors as high as 800 million and Q × frequency exceeding 10 15 hertz. These results illustrate a promising route for engineering ultracoherent nanomechanical devices.

https://science.sciencemag.org/content/sci/360/6390/764.full.pdf

Elastic strain engineering for ultralow mechanical dissipation

One challenge of controlling quantum systems is striking a balance between the random disturbances caused by the act of measurement and stabilizing the system in a desired state. Researchers conduct an experiment in the so-called ``quantum feedback regime'' in which the disturbance due to a measurement is suppressed.

Appearance and Disappearance of Quantum Correlations in Measurement-Based Feedback Control of a Mechanical Oscillator

Mechanical resonators with high quality factors are widely used in precision experiments, ranging from gravitational wave detection and force sensing to quantum optomechanics Beams and membranes are well known to exhibit flexural modes with enhanced quality factors when subjected to tensile stress The mechanism for this enhancement has been a subject of debate, but is typically attributed to elastic energy being ``diluted'' by a lossless potential Here we clarify the origin of the lossless potential to be the combination of tension and geometric nonlinearity of strain We present a general theory of dissipation dilution that is applicable to arbitrary resonator geometries and discuss why this effect is particularly strong for flexural modes of nanomechanical structures with high aspect ratios Applying the theory to a nonuniform doubly clamped beam, we show analytically how dissipation dilution can be enhanced by modifying the beam shape to implement ``soft clamping,'' thin clamping, and geometric strain engineering, and derive the ultimate limit for dissipation dilution

https://link.aps.org/accepted/10.1103/PhysRevB.99.054107

Generalized dissipation dilution in strained mechanical resonators

Extreme stresses can be produced in nanoscale structures, a feature which has been used to realize enhanced materials properties, such as the high mobility of silicon in modern transistors. Here we show how nanoscale stress can be used to realize exceptionally low mechanical dissipation, when combined with “soft-clamping” - a form of phononic engineering. Specifically, using a non-uniform phononic crystal pattern, we colocalize the strain and flexural motion of a freestanding Si 3 N 4 nanobeam. Ringdown measurements at room temperature reveal string-like modes with quality $(\pmb{Q})$ factors as high as 800 million and $\mathbf{Q}\times$ frequency exceeding 1015Hz.

Amir H. Ghadimi

Papers

Measurement-based control of a mechanical oscillator at its thermal decoherence rate

Elastic strain engineering for ultralow mechanical dissipation

Appearance and Disappearance of Quantum Correlations in Measurement-Based Feedback Control of a Mechanical Oscillator

Generalized dissipation dilution in strained mechanical resonators

Elastic Strain Engineering for Ultralow Mechanical Dissipation