Optomechanical Interactions

Light exerts mechanical action on matter through various mechanisms, the most famous being radiation pressure, with the associated picture of a photon bouncing on a perfectly reflective movable mirror and transferring twice its momentum. But still today, unambiguously observing the effects of radiation pressure remains a challenge. In the quantum domain, the radiation pressure interaction between a moving mirror and light stored in a cavity accepts a simple Hamiltonian formulation. But this Hamiltonian description is sometimes oversimplified and underestimates or misses other mechanical effects of light accompanying radiation pressure in experiments. In this chapter, we will not only address radiation pressure but also other relevant optical forces such as the optical gradient force, electrostriction, or the photothermal and optoelectronic forces, which are key in micro- and nanoscale devices and must all be controlled on an equal footing to fully harness the technological and scientific potential of miniature optomechanical systems.

Early History and Fundamentals of Optomechanics

In its simplest form, optomechanics amounts to two complementary coupling effects: mechanical motion changes the path followed by light, but light (through radiation pressure) can drive the mechanical resonator into motion as well. Optomechanics allows one to control resonator motion by laser cooling down to the quantum ground state, or to control light by using back-action in optical measurements and in quantum optics. Its main applications are optomechanical sensors to detect tiny mechanical motions and weak forces, cold damping and laser cooling, and quantum optics. The objectives of this chapter are to provide a brief account of the history of the field, together with its fundamentals. We will in particular review both classical and quantum aspects of optomechanics, together with its applications to high-sensitivity measurements and to control or cool mechanical resonators down to their ground state, with possible applications for tests of quantum theory or for quantum information.

Atom Optomechanics

This chapter gives an introduction to optomechanics with ultracold atoms. The opening half deals with optomechanical atom–light interactions. Section 9.2 introduces atom trapping. Section 9.3 discusses the properties of trapped atoms as mechanical oscillators. Section 9.4 describes optomechanical interactions, treating the atoms as polarizable particles, a model used in section 9.5 to derive optomechanical coupling of atoms and a cavity field and briefly review cavity optomechanics experiments with atoms in the quantum regime. The second half deals with hybrid mechanical-atomic systems. We start with an overview of different coupling mechanisms, then focus on light-mediated interactions and derive the coupling of a membrane to an ensemble of laser-cooled atoms. Section 9.8 reviews experiments on sympathetic cooling of a membrane with cold atoms, with perspectives for mechanical quantum control discussed in section 9.9. Section 9.10 introduces the possibilities that arise if the mechanical oscillator is coupled to the atomic internal state.

Optomechanics and Quantum Measurement

After a quick review of the basic theory of quantum optomechanical systems, based largely on linearized Heisenberg–Langevin equations, this chapter focuses on selected topics related to quantum measurement and quantum optomechanics. Included are: a comprehensive discussion of the quantum limit on the added noise of a continuous position detector, following the quantum linear response approach; a detailed discussion of the role of noise correlations, and how these can be achieved in an optomechanical cavity (by using squeezed input light, or by modifying the choice of measured output quadrature); and a discussion of back-action evading measurements of a mechanical quadrature, discussing how this can be achieved in a two-tone driven cavity system. The chapter ends with a quick introduction to the theory of conditional continuous quantum measurement, and a discussion on how a back-action evading measurement can be used to produce conditional mechanical squeezed states.

Quantum Optomechanics: from Gravitational Wave Detectors to Macroscopic Quantum Mechanics

The quantum measurement process connects the quantum world and the classical world. The phrase ‘quantum measurement’ can have two meanings: measurement of a weak classical force, with the impact of quatum fluctuations on the measurement sensitivity, and the quantum mechanics of macroscopic objects: to try to prepare, manipulate and characterize the quantum state of a macroscopic quantum object through quantum measurement. Quantum noise leads to the Standard Quantum Limit (SQL), which provides the magnitude in which we must consider both measurement precision and measurement-induced back-action. The beginning of the chapter will be devoted to this thread of thought. The free-mass SQL actually provides a benchmark for the ‘quantum-ness’ of the system. We will show that a sub-SQL device can be used to prepare nearly pure quantum states and mechanical entanglement, as well as non-Gaussian quantum states that have no classical counterparts.

Coupling Superconducting Qubits to Electromagnetic and Piezomechanical Resonators

Quantum bits have been under intense development since the late 1990s, due to the discovery of a number of potential applications for engineered quantum systems to problems in computation or communication. As superconducting circuits provide a straightforward path to scaling up to large numbers of qubits and are exible in terms of their application to a range of different problems, This chapter focuses on the problem of coupling superconducting qubits to other systems, in particular to microwave frequency electromagnetic resonators as well as mechanical resonators. It begins by introducing the topics of piezoelectricity and its role in solid mechanics, then turns to a description of one flavour of superconducting qubit, the phase qubit. It then describes how the phase qubit can be used to control and measure a superconducting electromagnetic resonator, and concludes by describing how a phase qubit can also be used to control and measure a piezomechanical resonator.

Quantum Optomechanics Thermodynamics and Heat Engines

This chapter addresses topics in quantum thermodynamics, where optomechanics may contribute attractive experimental tests and additional understanding. Quantum thermodynamics can be defined as the study of thermodynamics when quantum mechanical noise coexists with thermal noise and has a significant impact on the dynamics. This chapter focuses on the example of an optomechanical quantum heat engine (QHE). Section 11.2 reviews some questions about quantum work. Section 11.3 then outlines the steps leading to the formulation of continuous measurements in terms of stochastic Schrödinger equations. Section 11.4 reviews the main characteristics of QHE, comparing thermodynamic processes and engine cycles in the classical and quantum regimes. The opportunities offered by quasiparticles in the operation of QHE justify reviewing their properties in some detail (section 11.5), before introducing the optomechanical QHE system (section 11.6). Section 11.7 discusses the properties of the engine, and section 11.8 expands the discussion to polariton based quantum heat pumps.

Optomechanics for Gravitational Wave Detection: From Resonant Bars to Next Generation Laser Interferometers

This chapter reviews the 40-year history that led to the first detection of gravitational waves, and goes on to outline techniques which will allow the detectors to be substantially improved. Following a review of the gravitational wave spectrum and the early attempts at detection, it emphasizes the theme of optomechanics, and the underlying physics of parametric transducers, which creates a connection between early resonant bar detectors and modern interferometers and techniques for enhancing their sensitivity. Developments are presented in an historical context, while themes and connections between earlier and later work are emphasized.

Optically Levitated Nanospheres for Cavity Quantum Optomechanics

This chapter introduces cavity quantum optomechanics with levitated nanospheres with some emphasis on preparing mesoscopic quantum superpositions and testing collapse models. It is divided into three parts: levitated quantum optomechanics: atoms vs. sphere; decoherence in levitated nanospheres; and wave-packet dynamics: coherence vs. decoherence. It is first shown how the master equation describing the dynamics of a polarizable object in a cavity along the cavity axis and that of the cavity mode is derived. Optical levitation is also discussed. It is then shown how most of the decoherence sources in levitated nanospheres can be cast into a relatively simple master equation describing position localization type of decoherence. Such decoherence tends to suppress the centre-of-mass position coherences. Finally, a discussion of wave-packet dynamics is given, with the motivation of using levitated nanospheres for matter-wave interferometry, that is, to create macroscopic quantum superpositions for testing quantum mechanics in unprecedented parameter regimes.

Dynamic and Multimode Electromechanics

These notes discuss electromechanical devices in the quantum regime, a topic closely related to cavity optomechanics. Both cavity optomechanics and quantum electromechanics have their roots in gravitational-wave detection. As such, most of their applications are associated with ultrasensitive sensing. In contrast, these notes deal with an emerging application of quantum electromechanics: signal processing. Such applications are a natural consequence of shrinking the mechanical elements from the metre-scale resonators used in gravitational wave detectors to the micron scale, where quantum effects are more evident. Indeed, MEMS are a crucial technology for classical information processing and modern wireless communication. The advent of quantum information processing, particularly with superconducting circuits, means that there is now a need for analogue signal processing functions operating at microwave frequencies and in the quantum regime. Electromechanical devices have now entered this regime as they can store, amplify, squeeze, entangle, temporally shape, and frequency convert microwave signals.