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arXiv:1811.09421 · Physical Review A

Cavity-free vacuum-Rabi splitting in circuit quantum acoustodynamics

Andreas Ask, Maria Ekström, Per Delsing, Göran Johansson

Published Jan 22, 2019• 37 citations
arXivHTMLPDF

Abstract

Artificial atoms coupled to surface acoustic waves (SAWs) have played a crucial role in the recent development of circuit quantum acoustodynamics. In this paper, we have investigated the interaction of an artificial atom and SAWs beyond the weak-coupling regime, focusing on the role of the interdigital transducer (IDT) that enables the coupling. We find a parameter regime in which the IDT acts as a cavity for the atom, rather than an antenna. In other words, the atom forms its own cavity. Similar to an atom coupled to an explicit cavity, this regime is characterized by vacuum-Rabi splitting, as the atom hybridizes with the phononic vacuum inside the IDT. This hybridization is possible because of the interdigitated coupling, which has a large spatial extension, and the slow propagation speed of SAWs. We work out a criterion for entering this regime from a model based on standard circuit-quantization techniques, taking only material parameters as inputs. Most notably, we find this regime hard to avoid for an atom on top of a strong piezoelectric material, such as lithium niobate (${\mathrm{LiNbO}}_{3}$). The SAW-coupled atom on top of ${\mathrm{LiNbO}}_{3}$ can thus be regarded as an atom-cavity-bath system. On weaker piezoelectric materials, the number of IDT electrodes needs to be large in order to reach this regime.

DOI
10.1103/physreva.99.013840

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Artificial atoms coupled to surface acoustic waves (SAWs) have played a crucial role in the recent development of circuit quantum acoustodynamics. In this paper, we have investigated the interaction of an artificial atom and SAWs beyond the weak-coupling regime, focusing on the role of the interdigital transducer (IDT) that enables the coupling. We find a parameter regime in which the IDT acts as a cavity for the atom, rather than an antenna. In other words, the atom forms its own cavity. Similar to an atom coupled to an explicit cavity, this regime is characterized by vacuum-Rabi splitting, as the atom hybridizes with the phononic vacuum inside the IDT. This hybridization is possible because of the interdigitated coupling, which has a large spatial extension, and the slow propagation speed of SAWs. We work out a criterion for entering this regime from a model based on standard circuit-quantization techniques, taking only material parameters as inputs. Most notably, we find this regime hard to avoid for an atom on top of a strong piezoelectric material, such as lithium niobate (LiNbO3{\mathrm{LiNbO}}_{3}LiNbO3​). The SAW-coupled atom on top of LiNbO3{\mathrm{LiNbO}}_{3}LiNbO3​ can thus be regarded as an atom-cavity-bath system. On weaker piezoelectric materials, the number of IDT electrodes needs to be large in order to reach this regime.
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.
The past 20 years has seen rapid developments in circuit quantum electrodynamics, where superconducting qubits and resonators are used to control and study quantum light-matter interaction at a fundamental level. The development of this field is strongly influenced by quantum information science and the prospect of realizing quantum computation, but also opens up opportunities for combinations of different physical systems and research areas. Superconducting circuits in the microwave domain offer a versatile platform for interfacing with other quantum systems thanks to strong nonlinearities and zero-point fluctuations, as well as flexibility in design and fabrication. Hybrid quantum systems based on circuit quantum electrodynamics could enable novel functionalities by exploiting the strengths of the individual components.This thesis covers experiments coupling superconducting circuits to surface acoustic waves (SAWs), mechanical waves propagating along the surface of a solid. Strong coupling can be engineered using the piezoelectric properties of GaAs substrates, and our experiments exploit this to investigate phenomena in quantum field-matter interaction. A key property of surface acoustic waves is the slow propagation speed, typically five orders of magnitude slower than light in vacuum, and the associated short wavelength. This enables the giant atom regime where the artificial atom in the form of a superconducting circuit is large compared to the wavelength of interacting SAW radiation, a condition which is difficult to realize in other systems. Experiments described in this thesis use these properties to demonstrate electromagnetically induced transparency for a mechanical mode, as well as non-Markovian interactions between an artificial giant atom and the SAW field. When the SAW field is confined to a resonant cavity, the short wavelength allows multimode spectra suitable for interacting with a frequency comb. We use a multimode SAW resonator to characterize the ensemble of microscopic two-level system defects with a two-tone spectroscopy approach. Finally, we introduce a hybrid superconducting-SAW resonator with applications in quantum information processing in mind. Experiments with this device demonstrate entanglement of SAW modes, and show promising results on the way to engineer cluster states for quantum computation in continuous variables.
Abstract The experimental investigation of quantum devices incorporating mechanical resonators has opened up new frontiers in the study of quantum mechanics at a macroscopic level. It has recently been shown that surface acoustic waves (SAWs) can be piezoelectrically coupled to superconducting qubits, and confined in high-quality Fabry–Perot cavities in the quantum regime. Here we present measurements of a device in which a superconducting qubit is coupled to a SAW cavity, realising a surface acoustic version of cavity quantum electrodynamics. We use measurements of the AC Stark shift between the two systems to determine the coupling strength, which is in agreement with a theoretical model. This quantum acoustodynamics architecture may be used to develop new quantum acoustic devices in which quantum information is stored in trapped on-chip acoustic wavepackets, and manipulated in ways that are impossible with purely electromagnetic signals, due to the 10 5 times slower mechanical waves.
Abstract We experimentally study a circuit quantum acoustodynamics system with a superconducting artificial atom coupled to both a two-dimensional surface acoustic wave resonator and a one-dimensional microwave transmission line. The strong coupling between the artificial atom and the acoustic wave resonator is confirmed by the observation of the vacuum Rabi splitting at the base temperature of dilution refrigerator. We show that the propagation of microwave photons in the microwave transmission line can be controlled by a few phonons in the acoustic wave resonator. Furthermore, we demonstrate the temperature effect on the measurements of the Rabi splitting and temperature induced transitions from high excited dressed states. We find that the spectrum structure of two-peak for the Rabi splitting could become into those of several peaks under some special experimental conditions, and gradually disappears with the increase of the environmental temperature T. The continuous quantum-to-classical crossover is observed around the crossover temperature T c, which is determined via the thermal fluctuation energy k B T and the characteristic energy level spacing of the coupled system. Experimental results agree well with the theoretical simulations via the master equation of the coupled system at different effective temperatures.
A scalable hybrid cavity quantum acoustodynamics (QAD) platform is proposed. The architecture integrates superconducting transmon qubits with phononic integrated circuits on a single chip made by a lithium niobate-on-sapphire substrate. The platform supports tightly confined and guided phononic modes in unsuspended waveguides and microring structures, while the superconducting qubits reside on the sapphire substrate. Efficient piezoelectric coupling between the phononic modes and transmon qubits can be achieved using interdigital transducers as part of the qubit’s shunt capacitance. Numerical calculations demonstrate the feasibility of achieving strong coupling between the phononic microring resonator and the transmon qubit. Remarkably, we show that a single pair of interdigital transducer fingers is sufficient to yield a coupling strength of g/2π≈1.3 MHz for the quasi-Love mode. This hybrid cavity QAD platform opens up new opportunities for quantum information processing and the study of novel quantum acoustic phenomena.