Quantum information can be stored in micromechanical resonators, encoded as quanta of vibration known as phonons. The vibrational motion is then restricted to the stationary eigenmodes of the resonator, which thus serves as local storage for phonons. In contrast, we couple propagating phonons to an artificial atom in the quantum regime and reproduce findings from quantum optics, with sound taking over the role of light. Our results highlight the similarities between phonons and photons but also point to new opportunities arising from the characteristic features of quantum mechanical sound. The low propagation speed of phonons should enable new dynamic schemes for processing quantum information, and the short wavelength allows regimes of atomic physics to be explored that cannot be reached in photonic systems.
Quantum information can be stored in micromechanical resonators, encoded as quanta of vibration known as phonons. The vibrational motion is then restricted to the stationary eigenmodes of the resonator, which thus serves as local storage for phonons. In contrast, we couple propagating phonons to an artificial atom in the quantum regime and reproduce findings from quantum optics, with sound taking over the role of light. Our results highlight the similarities between phonons and photons but also point to new opportunities arising from the characteristic features of quantum mechanical sound. The low propagation speed of phonons should enable new dynamic schemes for processing quantum information, and the short wavelength allows regimes of atomic physics to be explored that cannot be reached in photonic systems.
Atoms, ions, and superconducting qubits are all examples of quantum objects, capable of producing and processing individual quanta of light, known as photons. Mechanical movement can be quantized in the same way as light, into particles of vibration known as phonons. Recent experiments have shown that quantum information generated in qubits can be converted to vibrations in mechanical resonators, which resemble miniature drum skins or piano strings. Such resonators restrict motion to their discrete and stationary modes, and thus serve as \emph{local storage units} for phonons. Here, we demonstrate the use of phonons as \emph{propagating carriers} of quantum information, by coupling them strongly to a superconducting qubit. The phonons thus serve the same role as itinerant photons have in the field of quantum optics. Due to the low speed of sound and a potential for very strong coupling, the use of propagating phonons as quantum carriers allows regimes to be explored which are difficult or impossible to reach with photons.
Quantum Processing
Quantum computers exploit the quantum-mechanical properties of materials to store and manipulate information stored in the quantum states of atoms or artificial atoms. Although there are a number of quantum platforms under investigation already, Gustafsson et al. present another, based on the propagation of sound waves on the surface of a crystal (see the Perspective by Ruskov and Tahan). The ability to tune the system and the slow propagation speeds of the acoustic waves offer new opportunities to control and process quantum information.
Science , this issue p. [207][1]; see also p. [165][2]
[1]: /lookup/doi/10.1126/science.1257219
[2]: /lookup/volpage/346/165?iss=6206
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.
Surface acoustic waves (SAWs) are mechanical vibrations that propagate on the surface of solids while dissipating little power, consequently enabling them to propagate freely over long distances. The speed and wavelength of SAWs are reduced a five order of magnitude compared to when light is used as a carrier at gigahertz frequencies. The unique properties of SAWs combined with the possibility to let them interact with artificial atoms, discovered and shown for the very first time in appended Paper I of this thesis, open up for exploration of new regimes of quantum physics. The appended Paper II is a book chapter providing an overview of many of the new areas of research, as well as going into depth of the method and significance of the results ofthe appended Paper I.The essential interaction between artificial atoms and SAWs was further investigated by using Autler-Townes splitting to achieve fast control of the interactions. The appended Paper IV, shows a transmitted field extinction of 80 %, and provides proof of concept for a SAW router in the quantum regime. In addition, due to the artificial atom's highly frequency dependent coupling to SAWs, electromagnetically induced transparency (EIT) could be observed in the appended Paper V. Furthermore, the EIT region was distinguished from the Autler-Townes splitting region by a threshold in the applied power. The results produce parallel findings to quantum optics, but are perhaps best described as part of a different field, quantum acoustics.Among the many possible areas of research emerging as an outcome of this work, a variety of potential quantum experiments would benefit greatly from a higher conversion efficiency between electric signals and SAWs. Due to this, focus was put on improving this conversion efficiency by studying superconducting unidirectional transducers (UDTs), making use of advances in classical SAW devices. The appended Paper III shows that 99.4~\\% of the acoustic power can be focused in a desired direction and that the conversion between electric signals and SAWs is greatly improved by using UDTs, thereby eliminating the largest source of loss of symmetric inter-digital transducers. There is, however, a trade-off between conversion efficiency and bandwidth. This finding allows tailoring of quantum experiments based on SAWs that may pave the way towards measuring quantum sound.
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).
One of the most fundamental phenomena occurring in nature is the interaction between single atoms and electromagnetic fields. This is studied in quantum optics to probe the quantum nature of the system. In appended Paper I, we demonstrated that an artificial atom can couple to propagating sound, which is the acoustic analogue of quantum optics. This thesis covers experiments where surface acoustic waves (SAWs) are used in superconducting circuits at gigahertz frequencies with the aim for quantum applications.Since SAWs are mechanical vibrations that propagate on the surface of solids and dissipate little power, they can propagate freely over long distances before and after they interact with the artificial atom. Their five order of magnitude slower speed and smaller wavelength than light at gigahertz frequencies, open up for exploring new regimes of quantum physics. In addition, the coupling between the artificial atom and the SAWs is promising for reaching ultrastrong coupling limits, which is hard in other types of systems. Many of the future applications are discussed in appended Paper II, together with a more detailed description of the theory and fabrication of the devices.Although the possibilities are many, a variety of potential experiments would benefit from higher conversion efficiency between electric signals and SAWs. Therefore, improvements of this conversion are studied in appended Paper III, making use of the many advances in classical SAW devices. More specifically, the conversion of unidirectional transducers (UDTs) on lithium niobate is studied and compared to symmetric interdigital transducers (IDTs). The results show that 99.4 % of the acoustic power can be focused in the desired direction and that the conversion between electric signals and SAWs is greatly improved by using UDTs, eliminating the largest contribution to loss of the IDTs. However, there is a trade-off between conversion efficiency and bandwidth. This knowledge allows us to better tailor potential quantum experiments based on SAWs, possibly towards measuring quantum sound.