Anton Frisk Kockum

Propagating phonons coupled to an artificial atom

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. The acoustic vibrations in a crystal can be used for quantum information processing. [Also see Perspective by Ruskov and Tahan] A sound proposition for quantum communication 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; see also p. 165

Microwave photonics with superconducting quantum circuits

In the past 20 years, impressive progress has been made both experimentally and theoretically in superconducting quantum circuits, which provide a platform for manipulating microwave photons. This emerging field of superconducting quantum microwave circuits has been driven by many new interesting phenomena in microwave photonics and quantum information processing. For instance, the interaction between superconducting quantum circuits and single microwave photons can reach the regimes of strong, ultra-strong, and even deep-strong coupling. Many higher-order effects, unusual and less familiar in traditional cavity quantum electrodynamics with natural atoms, have been experimentally observed, e.g., giant Kerr effects, multi-photon processes, and single-atom induced bistability of microwave photons. These developments may lead to improved understanding of the counterintuitive properties of quantum mechanics, and speed up applications ranging from microwave photonics to superconducting quantum information processing. In this article, we review experimental and theoretical progress in microwave photonics with superconducting quantum circuits. We hope that this global review can provide a useful roadmap for this rapidly developing field.

Giant cross-Kerr effect for propagating microwaves induced by an artificial atom

We investigate the effective interaction between two microwave fields, mediated by a transmon-type superconducting artificial atom which is strongly coupled to a coplanar transmission line. The interaction between the fields and atom produces an effective cross-Kerr coupling. We demonstrate average cross-Kerr phase shifts of up to 20 degrees per photon with both coherent microwave fields at the single-photon level. Our results provide an important step toward quantum applications with propagating microwave photons.

Quantum nondemolition detection of a propagating microwave photon.

The ability to nondestructively detect the presence of a single, traveling photon has been a long-standing goal in optics, with applications in quantum information and measurement. Realizing such a detector is complicated by the fact that photon-photon interactions are typically very weak. At microwave frequencies, very strong effective photon-photon interactions in a waveguide have recently been demonstrated. Here we show how this type of interaction can be used to realize a quantum nondemolition measurement of a single propagating microwave photon. The scheme we propose uses a chain of solid-state three-level systems (transmons) cascaded through circulators which suppress photon backscattering. Our theoretical analysis shows that microwave-photon detection with fidelity around 90% can be realized with existing technologies.

Breakdown of the Cross-Kerr Scheme for Photon Counting

We show, in the context of single-photon detection, that an atomic three-level model for a transmon in a transmission line does not support the predictions of the nonlinear polarizability model known as the cross-Kerr effect. We show that the induced displacement of a probe in the presence or absence of a single photon in the signal field, cannot be resolved above the quantum noise in the probe. This strongly suggests that cross-Kerr media are not suitable for photon counting or related single-photon applications. Our results are presented in the context of a transmon in a one-dimensional microwave waveguide, but the conclusions also apply to optical systems.

Deterministic quantum nonlinear optics with single atoms and virtual photons

We show how analogues of a large number of well-known nonlinear-optics phenomena can be realized with one or more two-level atoms coupled to one or more resonator modes. Through higher-order processes, where virtual photons are created and annihilated, an effective deterministic coupling between two states of such a system can be created. In this way, analogues of three-wave mixing, four-wave mixing, higher-harmonic and -subharmonic generation (i.e., up- and downconversion), multiphoton absorption, parametric amplification, Raman and hyper-Raman scattering, the Kerr effect, and other nonlinear processes can be realized. The effective coupling becomes weaker the more intermediate transition steps are needed. However, given the recent experimental progress in ultrastrong light-matter coupling, especially in the field of circuit quantum electrodynamics, we estimate that many of these nonlinear-optics analogues can be realized with currently available technology.

Probing the quantum vacuum with an artificial atom in front of a mirror

Quantum fluctuations of the vacuum are both a surprising and fundamental phenomenon of nature. Understood as virtual photons, they still have a very real impact, for instance, in the Casimir effects and the lifetimes of atoms. Engineering vacuum fluctuations is therefore becoming increasingly important to emerging technologies. Here, we shape vacuum fluctuations using a superconducting circuit analogue of a mirror, creating regions in space where they are suppressed. Moving an artificial atom through these regions and measuring the spontaneous emission lifetime of the atom provides us with the spectral density of the vacuum fluctuations. Using the paradigm of waveguide quantum electrodynamics, we significantly improve over previous studies of the interaction of an atom with its mirror image, observing a spectral density as low as 0.02 quanta, a factor of 50 below the mirrorless result. This demonstrates that we can hide the atom from the vacuum, even though it is exposed in free space.

Quantum nonlinear optics without photons

Spontaneous parametric down-conversion is a well-known process in quantum nonlinear optics in which a photon incident on a nonlinear crystal spontaneously splits into two photons. Here we propose an analogous physical process where one excited atom directly transfers its excitation to a pair of spatially-separated atoms with probability approaching one. The interaction is mediated by the exchange of virtual rather than real photons. This nonlinear atomic process is coherent and reversible, so the pair of excited atoms can transfer the excitation back to the first one: the atomic analogue of sum-frequency generation of light. The parameters used to investigate this process correspond to experimentally-demonstrated values in ultrastrong circuit quantum electrodynamics. This approach can be extended to realize other nonlinear inter-atomic processes, such as four-atom mixing, and is an attractive architecture for the realization of quantum devices on a chip. We show that four-qubit mixing can efficiently implement quantum repetition codes and, thus, can be used for error-correction codes.

Designing frequency-dependent relaxation rates and Lamb shifts for a giant artificial atom

In traditional quantum optics, where the interaction between atoms and light at optical frequencies is studied, the atoms can be approximated as pointlike when compared to the wavelength of light. So far, this relation has also been true for artificial atoms made out of superconducting circuits or quantum dots, interacting with microwave radiation. However, recent and ongoing experiments using surface acoustic waves show that a single artificial atom can be coupled to a bosonic field at several points wavelengths apart. Here, we theoretically study this type of system. We find that the multiple coupling points give rise to a frequency dependence in the coupling strength between the atom and its environment and also in the Lamb shift of the atom. The frequency dependence is given by the discrete Fourier transform of the coupling-point coordinates and can therefore be designed. We discuss a number of possible applications for this phenomenon, including tunable coupling, single-atom lasing, and other effects that can be achieved by designing the relative coupling strengths of different transitions in a multilevel atom.

Frequency conversion in ultrastrong cavity QED

We propose a new method for frequency conversion of photons which is both versatile and deterministic. We show that a system with two resonators ultrastrongly coupled to a single qubit can be used to realise both single- and multiphoton frequency-conversion processes. The conversion can be exquisitely controlled by tuning the qubit frequency to bring the desired frequency-conversion transitions on or off resonance. Considering recent experimental advances in ultrastrong coupling for circuit QED and other systems, we believe that our scheme can be implemented using available technology.