Applied Physics
Optomechanical systems typically consist of a mechanical oscillator or cantilever that can be driven by the optical radiation pressure of light. The light can either amplify the motion of the cantilever or be used to reduce the amount of vibration and effectively cool it. Recent work has demonstrated cooling to the extent that the number of vibrations, or phonons, in an oscillator can be quantized, even reaching the quantum-mechanical ground. Galland et al. introduce a method to introduce a single phonon into their mechanical oscillator. Starting off in the quantum-mechanical ground, they pump the system with a laser pulse that generates an entangled phonon-photon pair. Detection of the photon then heralds that a single-phonon state has been induced into the oscillator. The ability to deterministically control the number of vibrational quanta in such an optomechanical system has important implications for the likes of quantum information processing and quantum enhanced sensing applications.
Phys. Rev. Lett. 112 , 143602 (2014).
Applied Physics
Optomechanical systems typically consist of a mechanical oscillator or cantilever that can be driven by the optical radiation pressure of light. The light can either amplify the motion of the cantilever or be used to reduce the amount of vibration and effectively cool it. Recent work has demonstrated cooling to the extent that the number of vibrations, or phonons, in an oscillator can be quantized, even reaching the quantum-mechanical ground. Galland et al. introduce a method to introduce a single phonon into their mechanical oscillator. Starting off in the quantum-mechanical ground, they pump the system with a laser pulse that generates an entangled phonon-photon pair. Detection of the photon then heralds that a single-phonon state has been induced into the oscillator. The ability to deterministically control the number of vibrational quanta in such an optomechanical system has important implications for the likes of quantum information processing and quantum enhanced sensing applications.
Phys. Rev. Lett. 112 , 143602 (2014).
We show how to use the radiation pressure optomechanical coupling between a mechanical oscillator and an optical cavity field to generate in a heralded way a single quantum of mechanical motion (a Fock state). Starting with the oscillator close to its ground state, a laser pumping the upper motional sideband produces correlated photon-phonon pairs via optomechanical parametric down-conversion. Subsequent detection of a single scattered Stokes photon projects the macroscopic oscillator into a single-phonon Fock state. The nonclassical nature of this mechanical state can be demonstrated by applying a readout laser on the lower sideband to map the phononic state to a photonic mode and performing an autocorrelation measurement. Our approach proves the relevance of cavity optomechanics as an enabling quantum technology.
A multipartite quantum system is entangled when its state cannot be factorized into a product of states or a mixture of such products. Quantum information schemes that exploit this purely quantum mechanical feature have been devised initially for systems with two discrete quantum levels (i.e., qubits), and afterward, extended to continuous-variable (CV) systems characterized by observables with continuous spectra, such as the position and momentum of a particle, or the quadratures of an electromagnetic field. Optomechanical systems, such as a driven optical cavity with vibrating end-mirrors or a classical coherent field scattering sidebands off a freely suspended mirror, hold a promise of being candidates for CV quantum information processing applications. As in most other proposals, light is the information carrier; the difference lies in the choice of a micromirror as a quantum storage device. Desired quantum states can be encoded in acoustic modes. The optomechanical coupling, owing to which quantum state transfer between radiation and mirror is possible, is realized via the radiation pressure effect, which consists in momentum transfer between field and mirror during the scattering process. The use of the vibrational modes of a micromirror as a quantum state encoder system is somehow unexpected because this is a macroscopic ensemble of atoms expected to behave rather classically. However, there are proposals that show that, in principle, the vibrational occupation number of even such a large collection of atoms in a solid can be reduced close to zero, which signifies a clear transition from the classical to the quantum regime. Remarkable progress has been made to experimentally cool the resonator by a few orders of magnitude to quite low occupation numbers. However, in order to approach the quantum limit, one needs to integrate small, light, and flexible micromechanical elements into high-finesse cavities (which are typically much more rigid and massive), which is technically challenging. Furthermore, the mechanical quality factor has to be quite high, but present microfabrication techniques yield a mechanical quality factor scaling down for smaller and smaller microresonators. This chapter starts with developing a general framework for treating the dynamics of a driven optical cavity with a vibrating end-mirror system in which two cooling techniques have been recently demonstrated: (i) cold-damping quantum feedback, where the oscillator position is measured through a phase-sensitive detection of the cavity output and the resulting photocurrent is used for a real-time correction of the dynamics, and (ii) backaction or self-cooling, in which the off-resonant operation of the cavity results in a retarded back action on the mechanical system, and hence, in a “self”-modification of its dynamics. The two situations are illustrated in Fig. 24.1. Analytical results for the final phonon number are obtained for both schemes and their applicability within today's state-of-the-art laboratory setups is analyzed.
In the past several years, the field of optomechanics has progressed from proof-of-principle experiments to the realization of mechanical oscillators and measurements in the quantum regime. Mechanical oscillators are of great interest because they can have small dissipation rates, can couple to many different systems of interest, and are the fundamental elements of ultrasensitive force detectors. Coupling these mechanical oscillators to microwave or optical fields provides a twofold advantage. Firstly, information about mechanical position can be encoded in the interrogating field, enabling sensitive readout of the mechanical oscillator. Secondly, the radiation pressure force of that field can be used to control the state of the mechanical oscillator. Including a high-quality microwave or optical cavity enhances both of these effects, as the field strength is resonantly increased.\nThe major questions in the field of optomechanics in the last several years have dealt with using mechanical oscillators for ultrasensitive measurements and as tools for quantum information. Both of these goals have the prerequisite that we be able to read out the motion of the mechanical oscillator in a quantum efficient manner. To that end, we developed a nearly shot-noise limited microwave interferometer capable of measuring mechanical motion with an imprecision below that at the standard quantum limit. This achievement is not only a critical improvement for the electromechanical experiments we do, but is also an important tool for any experiment that encodes the information of interest in microwave fields. In order to use mechanical oscillators as tools for quantum information, the mechanical oscillator must also be cooled into the quantum regime and fully controllable by the interrogating fields. To this end, we used the radiation pressure of microwave fields to cool our macroscopic mechanical oscillator to less than one phonon. We also demonstrated coherent transfer between itinerant microwave states and the mechanical oscillator, even for incident fields with less than one photon of energy.\nThese accomplishments have set the foundation for further experiments to extend the quantum information abilities of optomechanical systems, couple diverse quantum systems via a mechanical intermediary, and potentially explore the foundations of quantum mechanics at macroscopic scales.
Phonon nonlinearities play an important role in hybrid quantum networks and on-chip quantum devices. We investigate the phonon statistics of a mechanical oscillator in hybrid systems composed of an atom and one or two standard optomechanical cavities. An efficiently enhanced atom-phonon interaction can be derived via a tripartite atom-photon-phonon interaction, where the atom-photon coupling depends on the mechanical displacement without practically changing a cavity frequency. This novel mechanism of optomechanical interactions, as predicted recently by Cotrufo et al. [Phys. Rev. Lett.118, 133603 (2017)10.1103/PhysRevLett.118.133603], is fundamentally different from standard ones. In the enhanced atom-phonon coupling, the strong phonon nonlinearity at a single-excitation level is obtained in the originally weak-coupling regime, which leads to the appearance of phonon blockade. Moreover, the optimal parameter regimes are presented both for the cases of one and two cavities. We compared phonon-number correlation functions of different orders for mechanical steady states generated in the one-cavity hybrid system, revealing the occurrence of phonon-induced tunneling and different types of phonon blockade. Our approach offers an alternative method to generate and control a single phonon in the quantum regime and could have potential applications in single-phonon quantum technologies.
The search for experimental demonstrations of the quantum behavior of macroscopic mechanical resonators is a fastly growing field of investigation and recent results suggest that the generation of quantum states of resonators with a mass at the microgram scale is within reach. In this chapter we give an overview of two important topics within this research field: cooling to the motional ground state, and the generation of entanglement involving mechanical, optical and atomic degrees of freedom. We focus on optomechanical systems where the resonator is coupled to one or more driven cavity modes by the radiation pressure interaction. We show that robust stationary entanglement between the mechanical resonator and the output fields of the cavity can be generated, and that this entanglement can be transferred to atomic ensembles placed within the cavity. These results show that optomechanical devices are interesting candidates for the realization of quantum memories and interfaces for continuous variable quantum communication networks.
Adding excitations on a coherent state provides an effective way to observe the nonclassical properties of radiation fields. Here, we describe and analyze how to apply this concept to the motional state of a mechanical oscillator and present a full scheme to prepare non-Gaussian phonon-added coherent states of the mechanical motion in cavity optomechanics. We first generate a mechanical coherent state using electromagnetically induced transparency. We then add a single phonon onto the coherent state via optomechanical parametric down-conversion combined with single-photon detection. We validate this single-phonon-added coherent state by using a red-detuned beam and reading out the state of the optical output field. This approach allows us to verify nonclassical properties of the phonon state, such as sub-Poissonian character and quadrature squeezing. We further show that our scheme can be directly implemented using existing devices, and is generic in nature and hence applicable to a variety of systems in opto- and electromechanics.