The zero-point energy stored in the modes of an electromagnetic cavity has experimentally detectable effects, giving rise to an attractive interaction between the opposite walls, the static Casimir effect. A dynamical version of this effect was predicted to occur when the vacuum energy is changed either by moving the walls of the cavity or by changing the index of refraction, resulting in the conversion of vacuum fluctuations into real photons. Here, we demonstrate the dynamical Casimir effect using a Josephson metamaterial embedded in a microwave cavity at 5.4 GHz. We modulate the effective length of the cavity by flux-biasing the metamaterial based on superconducting quantum interference devices (SQUIDs), which results in variation of a few percentage points in the speed of light. We extract the full 4 × 4 covariance matrix of the emitted microwave radiation, demonstrating that photons at frequencies symmetrical with respect to half of the modulation frequency are generated in pairs. At large detunings of the cavity from half of the modulation frequency, we find power spectra that clearly show the theoretically predicted hallmark of the Casimir effect: a bimodal, "sparrow-tail" structure. The observed substantial photon flux cannot be assigned to parametric amplification of thermal fluctuations; its creation is a direct consequence of the noncommutativity structure of quantum field theory.Josephson junction | nanoelectronics | quantum mechanics A fundamental theoretical result of modern quantum field theory is that the quantum vacuum is unstable (1-6) under certain external perturbations that otherwise produce no consequences in a classical treatment (7). As a result of this instability, virtual fluctuations populating the quantum vacuum are converted into real particles by the energy provided by the perturbation. For example, the application of intense electrical fields extracts electron-positron pairs from a vacuum (Schwinger effect), the bending of space-time in the intense gravitational field at event horizons is responsible for the evaporation of black holes (Hawking radiation), the acceleration of an observer in the Minkowski vacuum results in the detection of particles (Unruh effect), and sudden changes in the boundary conditions of electromagnetic field modes or in the speed of light (index of refraction) create photons [dynamical Casimir effect (DCE)] (8). The DCE is a particular case of parametric amplification of vacuum fluctuations (3, 4, 6). To date, preliminary evidence for the analog of Hawking radiation has been obtained (9), whereas in the case of the DCE, a very recent experiment has reported production of photons by the nonadiabatic change of a boundary condition (10). Many other theoretical estimations and proposals for observing this effect in a variety of physical systems exist in the literature (11)(12)(13)(14)(15)(16)(17)(18)(19)(20).In this paper, we demonstrate the DCE by modulating the background in which the field propagates (3). We periodically change the index of refraction (which...

Hybrid quantum systems with inherently distinct degrees of freedom play a key role in many physical phenomena. Famous examples include cavity quantum electrodynamics [1], trapped ions [2], or electrons and phonons in the solid state. Here, a strong coupling makes the constituents loose their individual character and form dressed states. Apart from fundamental significance, hybrid systems can be exploited for practical purpose, noteworthily in the emerging field of quantum information control. A promising direction is provided by the combination between long-lived atomic states [2,3] and the accessible electrical degrees of freedom in superconducting cavities and qubits [4,5]. Here we integrate circuit cavity quantum electrodynamics [6,7] with phonons. Besides coupling to a microwave cavity, our superconducting transmon qubit [10] interacts with a phonon mode in a micromechanical resonator, thus representing an atom coupled to two different cavities. We measure the phonon Stark shift, as well as the splitting of the qubit spectral line into motional sidebands, which feature transitions between the dressed electromechanical states. In the time domain, we observe coherent conversion of qubit excitation to phonons as sideband Rabi oscillations. This is a model system having potential for a quantum interface, which may allow for storage of quantum information in long-lived phonon states, coupling to optical photons, or for investigations of strongly coupled quantum systems near the classical limit.Superconducting quantum bits based on Josephson junctions [5] have offered an unparalleled testing ground for quantum mechanics in relatively large systems. At the same time, Josephson devices constitute a promising implementation for quantum information processing. Basic quantum algorithms have indeed been recently demonstrated with phase [9] and transmon [10][11][12] qubits. The latter operate in the circuit cavity quantum electrodynamics (QED) architechture, in which the qubits couple to an on-chip [6] or 3-dimensional microwave cavity resonator [9]. The circuit QED setup, which enables coupling of qubits and non-destructive measurements of quantum states, can be regarded as the most feasible platform for quantum information.The forthcoming challenges in circuit QED include the construction of an interface to the storage and retrieval of qubit states in a long-lived quantum memory, as well as quantum communication [14] between spatially separated superconducting qubits. Hybrid quantum systems are showing promise for these goals because in principle one can combine the specific assets of each ingredient. Merger of macroscopic qubits with spin ensembles is intriguing due to the long lifetime of the latter [15, 16], but with the drawback of a difficult access and small coupling at the level of a single atomic degree of freedom.Micromechanical resonators were brought to the quantum regime of their motion only very recently [17, 18]. They have been suggested as a plausible interfacing medium for Josephson junction qubits [...

Superconducting circuits with Josephson junctions are promising candidates for developing future quantum technologies. Of particular interest is to use these circuits to study effects that typically occur in complex condensed-matter systems. Here we employ a superconducting quantum bit-a transmon-to perform an analogue simulation of motional averaging, a phenomenon initially observed in nuclear magnetic resonance spectroscopy. By modulating the flux bias of a transmon with controllable pseudo-random telegraph noise we create a stochastic jump of its energy level separation between two discrete values. When the jumping is faster than a dynamical threshold set by the frequency displacement of the levels, the initially separate spectral lines merge into a single, narrow, motional-averaged line. With sinusoidal modulation a complex pattern of additional sidebands is observed. We show that the modulated system remains quantum coherent, with modified transition frequencies, Rabi couplings, and dephasing rates. These results represent the first steps towards more advanced quantum simulations using artificial atoms.

The adiabatic manipulation of quantum states is a powerful technique that opened up new directions in quantum engineering—enabling tests of fundamental concepts such as geometrical phases and topological transitions, and holding the promise of alternative models of quantum computation. Here we benchmark the stimulated Raman adiabatic passage for circuit quantum electrodynamics by employing the first three levels of a transmon qubit. In this ladder configuration, we demonstrate a population transfer efficiency >80% between the ground state and the second excited state using two adiabatic Gaussian-shaped control microwave pulses. By doing quantum tomography at successive moments during the Raman pulses, we investigate the transfer of the population in time domain. Furthermore, we show that this protocol can be reversed by applying a third adiabatic pulse, we study a hybrid nondiabatic–adiabatic sequence, and we present experimental results for a quasi-degenerate intermediate level.

When a three-level quantum system is irradiated by an intense coupling field resonant with one of the three possible transitions, the absorption peak of an additional probe field involving the remaining level is split. This process is known in quantum optics as the Autler-Townes effect. We observe these phenomena in a superconducting Josephson phase qubit, which can be considered an "artificial atom" with a multilevel quantum structure. The spectroscopy peaks can be explained reasonably well by a simple three-level Hamiltonian model. Simulation of a more complete model (including dissipation, higher levels, and cross coupling) provides excellent agreement with all of the experimental data.

We investigate the quantum dynamics of a system of two coupled superconducting qubits under microwave irradiation. We find that, with the qubits operated at the charge co-degeneracy point, the quantum evolution of the system can be described by a new effective Hamiltonian which has the form of two coupled qubits with tunable coupling between them. This Hamiltonian can be used for experimental tests on macroscopic entanglement and for implementing quantum gates.Comment: 6 pages, 3 figure

Abstract. We review the physical phenomena that arise when quantum mechanical energy levels are modulated in time. The dynamics resulting from changes in the transition frequency is a problem studied since the early days of quantum mechanics. It has been of constant interest both experimentally and theoretically since, with the simple two-state model providing an inexhaustible source of novel concepts. When the transition frequency of a quantum system is modulated, several phenomena can be observed, such as Landau-Zener-Stückelberg-Majorana interference, motional averaging and narrowing, and the formation of dressed states with the presence of sidebands in the spectrum. Adiabatic changes result in the accumulation of geometric phases, which can be used to create topological states. In recent years, an exquisite experimental control in the time domain was gained through the parameters entering the Hamiltonian, and high-fidelity readout schemes allowed the state of the system to be monitored non-destructively. These developments were made in the field of quantum devices, especially in superconducting qubits, as a well as in atomic physics, in particular in ultracold gases. As a result of these advances, it became possible to demonstrate many of the fundamental effects that arise in a quantum system when its transition frequencies are modulated. The purpose of this review is to present some of these developments, from two-state atoms and harmonic oscillators to multilevel and many-particle systems.

We experimentally demonstrate robust superadiabatic population transfer close to the quantum speed limit.