Superconducting qubit–oscillator circuit beyond the ultrastrong-coupling regime
TL;DR: In this article, a circuit that pairs a flux qubit with an LC oscillator via Josephson junctions is proposed, and the energy eigenstate including the ground state is predicted to be highly entangled.
Abstract: A circuit that pairs a flux qubit with an LC oscillator via Josephson junctions pushes the coupling between light to matter to uncharted territory, with the potential for new applications in quantum technologies. The interaction between an atom and the electromagnetic field inside a cavity1,2,3,4,5,6 has played a crucial role in developing our understanding of light–matter interaction, and is central to various quantum technologies, including lasers and many quantum computing architectures. Superconducting qubits7,8 have allowed the realization of strong9,10 and ultrastrong11,12,13 coupling between artificial atoms and cavities. If the coupling strength g becomes as large as the atomic and cavity frequencies (Δ and ωo, respectively), the energy eigenstates including the ground state are predicted to be highly entangled14. There has been an ongoing debate15,16,17 over whether it is fundamentally possible to realize this regime in realistic physical systems. By inductively coupling a flux qubit and an LC oscillator via Josephson junctions, we have realized circuits with g/ωo ranging from 0.72 to 1.34 and g/Δ ≫ 1. Using spectroscopy measurements, we have observed unconventional transition spectra that are characteristic of this new regime. Our results provide a basis for ground-state-based entangled pair generation and open a new direction of research on strongly correlated light–matter states in circuit quantum electrodynamics.
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01 Jan 1958
TL;DR: In this article, it was shown that the ordinary semiclassical theory of the absorption of light by exciton states is not completely satisfactory (in contrast to the case of absorption due to interband transitions).
Abstract: It is shown that the ordinary semiclassical theory of the absorption of light by exciton states is not completely satisfactory (in contrast to the case of absorption due to interband transitions). A more complete theory is developed. It is shown that excitons are approximate bosons, and, in interaction with the electromagnetic field, the exciton field plays the role of the classical polarization field. The eigenstates of the system of crystal and radiation field are mixtures of photons and excitons. The ordinary one-quantum optical lifetime of an excitation is infinite. Absorption occurs only when "three-body" processes are introduced. The theory includes "local field" effects, leading to the Lorentz local field correction when it is applicable. A Smakula equation for the oscillator strength in terms of the integrated absorption constant is derived.
1,238 citations
TL;DR: In this paper, the authors provide an introductory guide to the central concepts and challenges in the rapidly accelerating field of superconducting quantum circuits, including qubit design, noise properties, qubit control and readout techniques.
Abstract: The aim of this review is to provide quantum engineers with an introductory guide to the central concepts and challenges in the rapidly accelerating field of superconducting quantum circuits. Over the past twenty years, the field has matured from a predominantly basic research endeavor to a one that increasingly explores the engineering of larger-scale superconducting quantum systems. Here, we review several foundational elements—qubit design, noise properties, qubit control, and readout techniques—developed during this period, bridging fundamental concepts in circuit quantum electrodynamics and contemporary, state-of-the-art applications in gate-model quantum computation.
969 citations
TL;DR: 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 as mentioned in this paper, and many higher-order effects, unusual and less familiar in traditional cavity quantum electrodynamics with natural atoms, have been experimentally observed.
909 citations
TL;DR: The time is ripe for describing some of the recent development of superconducting devices, systems and applications as well as practical applications of QIP, such as computation and simulation in Physics and Chemistry.
Abstract: During the last ten years, superconducting circuits have passed from being interesting physical devices to becoming contenders for near-future useful and scalable quantum information processing (QIP). Advanced quantum simulation experiments have been shown with up to nine qubits, while a demonstration of quantum supremacy with fifty qubits is anticipated in just a few years. Quantum supremacy means that the quantum system can no longer be simulated by the most powerful classical supercomputers. Integrated classical-quantum computing systems are already emerging that can be used for software development and experimentation, even via web interfaces. Therefore, the time is ripe for describing some of the recent development of superconducting devices, systems and applications. As such, the discussion of superconducting qubits and circuits is limited to devices that are proven useful for current or near future applications. Consequently, the centre of interest is the practical applications of QIP, such as computation and simulation in Physics and Chemistry.
809 citations
TL;DR: The field of circuit quantum electrodynamics (QED) as discussed by the authors was initiated by Josephson-junction-based superconducting circuits and has become an independent and thriving field of research in its own right.
Abstract: Quantum-mechanical effects at the macroscopic level were first explored in Josephson-junction-based superconducting circuits in the 1980s. In recent decades, the emergence of quantum information science has intensified research toward using these circuits as qubits in quantum information processors. The realization that superconducting qubits can be made to strongly and controllably interact with microwave photons, the quantized electromagnetic fields stored in superconducting circuits, led to the creation of the field of circuit quantum electrodynamics (QED), the topic of this review. While atomic cavity QED inspired many of the early developments of circuit QED, the latter has now become an independent and thriving field of research in its own right. Circuit QED allows the study and control of light-matter interaction at the quantum level in unprecedented detail. It also plays an essential role in all current approaches to gate-based digital quantum information processing with superconducting circuits. In addition, circuit QED provides a framework for the study of hybrid quantum systems, such as quantum dots, magnons, Rydberg atoms, surface acoustic waves, and mechanical systems interacting with microwave photons. Here the coherent coupling of superconducting qubits to microwave photons in high-quality oscillators focusing on the physics of the Jaynes-Cummings model, its dispersive limit, and the different regimes of light-matter interaction in this system are reviewed. Also discussed is coupling of superconducting circuits to their environment, which is necessary for coherent control and measurements in circuit QED, but which also invariably leads to decoherence. Dispersive qubit readout, a central ingredient in almost all circuit QED experiments, is also described. Following an introduction to these fundamental concepts that are at the heart of circuit QED, important use cases of these ideas in quantum information processing and in quantum optics are discussed. Circuit QED realizes a broad set of concepts that open up new possibilities for the study of quantum physics at the macro scale with superconducting circuits and applications to quantum information science in the widest sense.
773 citations
References
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01 Jan 1963
TL;DR: In this article, it was shown that the semiclassical theory, when extended to take into account both the effect of the field on the molecules and the effects of the molecules on the field, reproduces the same laws of energy exchange and coherence properties as the quantized field theory, even in the limit of one or a few quanta in the field mode.
Abstract: This paper has two purposes: 1) to clarify the relationship between the quantum theory of radiation, where the electromagnetic field-expansion coefficients satisfy commutation relations, and the semiclassical theory, where the electromagnetic field is considered as a definite function of time rather than as an operator; and 2) to apply some of the results in a study of amplitude and frequency stability in a molecular beam maser. In 1), it is shown that the semiclassical theory, when extended te take into account both the effect of the field on the molecules and the effect of the molecules on the field, reproduces almost quantitatively the same laws of energy exchange and coherence properties as the quantized field theory, even in the limit of one or a few quanta in the field mode. In particular, the semiclassical theory is shown to lead to a prediction of spontaneous emission, with the same decay rate as given by quantum electrodynamics, described by the Einstein A coefficients. In 2), the semiclassical theory is applied to the molecular beam maser. Equilibrium amplitude and frequency of oscillation are obtained for an arbitrary velocity distribution of focused molecules, generalizing the results obtained previously by Gordon, Zeiger, and Townes for a singel-velocity beam, and by Lamb and Helmer for a Maxwellian beam. A somewhat surprising result is obtained; which is that the measurable properties of the maser, such as starting current, effective molecular Q, etc., depend mostly on the slowest 5 to 10 per cent of the molecules. Next we calculate the effect of amplitude and frequency of oscillation, of small systematic perturbations. We obtain a prediction that stability can be improved by adjusting the system so that the molecules emit all their energy h Ω to the field, then reabsorb part of it, before leaving the cavity. In general, the most stable operation is obtained when the molecules are in the process of absorbing energy from the radiation as they leave the cavity, most unstable when they are still emitting energy at that time. Finally, we consider the response of an oscillating maser to randomly time-varying perturbations. Graphs are given showing predicted response to a small superimposed signal of a frequency near the oscillation frequency. The existence of "noise enhancing" and "noise quieting" modes of operation found here is a general property of any oscillating system in which amplitude is limited by nonlinearity.
3,928 citations
TL;DR: It is shown that the strong coupling regime can be attained in a solid-state system, and the concept of circuit quantum electrodynamics opens many new possibilities for studying the strong interaction of light and matter.
Abstract: The interaction of matter and light is one of the fundamental processes occurring in nature, and its most elementary form is realized when a single atom interacts with a single photon. Reaching this regime has been a major focus of research in atomic physics and quantum optics1 for several decades and has generated the field of cavity quantum electrodynamics2,3. Here we perform an experiment in which a superconducting two-level system, playing the role of an artificial atom, is coupled to an on-chip cavity consisting of a superconducting transmission line resonator. We show that the strong coupling regime can be attained in a solid-state system, and we experimentally observe the coherent interaction of a superconducting two-level system with a single microwave photon. The concept of circuit quantum electrodynamics opens many new possibilities for studying the strong interaction of light and matter. This system can also be exploited for quantum information processing and quantum communication and may lead to new approaches for single photon generation and detection.
3,452 citations
TL;DR: The concept of entanglement plays an essential role in quantum physics as mentioned in this paper, and it is also essential to understand decoherence, the process accounting for the classical appearance of the macroscopic world.
Abstract: After they have interacted, quantum particles generally behave as a single nonseparable entangled system. The concept of entanglement plays an essential role in quantum physics. We have performed entanglement experiments with Rydberg atoms and microwave photons in a cavity and tested quantum mechanics in situations of increasing complexity. Entanglement resulted either from a resonant exchange of energy between atoms and the cavity field or from dispersive energy shifts affecting atoms and photons when they were not resonant. With two entangled particles (two atoms or one atom and a photon), we have realized new versions of the Einstein-Podolsky-Rosen situation. The detection of one particle projected the other, at a distance, in a correlated state. This process could be viewed as an elementary measurement, one particle being a ``meter'' measuring the other. We have performed a ``quantum nondemolition'' measurement of a single photon, which we detected repeatedly without destroying it. Entanglement is also essential to understand decoherence, the process accounting for the classical appearance of the macroscopic world. A mesoscopic superposition of states (``Schr\"odinger cat'') gets rapidly entangled with its environment, losing its quantum coherence. We have prepared a Schr\"odinger cat made of a few photons and studied the dynamics of its decoherence, in an experiment which constitutes a glimpse at the quantum/classical boundary. We have also investigated entanglement as a resource for the processing of quantum information. By using quantum two-state systems (qubits) instead of classical bits of information, one can perform logical operations exploiting quantum interferences and taking advantage of the properties of entanglement. Manipulating as qubits atoms and photons in a cavity, we have operated a quantum gate and applied it to the generation of a complex three-particle entangled state. We finally discuss the perspectives opened by these experiments for further fundamental studies.
2,303 citations
TL;DR: In this article, a single-Cooper-pair box with a gate electrode was used to control the coherent quantum state evolution, which modifies the energies of the two charge states non-adiabatically, bringing them into resonance.
Abstract: 5-7 as a candidate for a quantum bit or 'qubit'—the basic component of a quantum computer. Here we report the observation of quantum oscillations in a single- Cooper-pair box. By applying a short voltage pulse via a gate electrode, we can control the coherent quantum state evolution: the pulse modifies the energies of the two charge states non- adiabatically, bringing them into resonance. The resulting state— a superposition of the two charge states—is detected by a tunnelling current through a probe junction. Our results demon- strate electrical coherent control of a qubit in a solid-state
2,172 citations
TL;DR: Superconducting quantum bits (qubits) form the key component of these circuits and their quantum state is manipulated by using electromagnetic pulses to control the magnetic flux, the electric charge or the phase difference across a Josephson junction.
Abstract: Superconducting circuits are macroscopic in size but have generic quantum properties such as quantized energy levels, superposition of states, and entanglement, all of which are more commonly associated with atoms. Superconducting quantum bits (qubits) form the key component of these circuits. Their quantum state is manipulated by using electromagnetic pulses to control the magnetic flux, the electric charge or the phase difference across a Josephson junction (a device with nonlinear inductance and no energy dissipation). As such, superconducting qubits are not only of considerable fundamental interest but also might ultimately form the primitive building blocks of quantum computers.
1,561 citations