As with classical information processing, a quantum information processor requires bits (qubits) that can be independently addressed and read out, long-term memory elements to store arbitrary quantum states, and the ability to transfer quantum information through a coherent communication bus accessible to a large number of qubits. Superconducting qubits made with scalable microfabrication techniques are a promising candidate for the realization of a large-scale quantum information processor. Although these systems have successfully passed tests of coherent coupling for up to four qubits, communication of individual quantum states between superconducting qubits via a quantum bus has not yet been realized. Here, we perform an experiment demonstrating the ability to coherently transfer quantum states between two superconducting Josephson phase qubits through a quantum bus. This quantum bus is a resonant cavity formed by an open-ended superconducting transmission line of length 7 mm. After preparing an initial quantum state with the first qubit, this quantum information is transferred and stored as a nonclassical photon state of the resonant cavity, then retrieved later by the second qubit connected to the opposite end of the cavity. Beyond simple state transfer, these results suggest that a high-quality-factor superconducting cavity could also function as a useful short-term memory element. The basic architecture presented here can be expanded, offering the possibility for the coherent interaction of a large number of superconducting qubits.

Quantum entanglement is a phenomenon whereby systems cannot be described independently of each other, even though they may be separated by an arbitrarily large distance . Entanglement has a solid theoretical and experimental foundation and is the key resource behind many emerging quantum technologies, including quantum computation, cryptography and metrology. Entanglement has been demonstrated for microscopic-scale systems, such as those involving photons, ions and electron spins , and more recently in microwave and electromechanical devices. For macroscopic-scale objects, however, it is very vulnerable to environmental disturbances, and the creation and verification of entanglement of the centre-of-mass motion of macroscopic-scale objects remains an outstanding goal. Here we report such an experimental demonstration, with the moving bodies being two massive micromechanical oscillators, each composed of about 10 atoms, coupled to a microwave-frequency electromagnetic cavity that is used to create and stabilize the entanglement of their centre-of-mass motion. We infer the existence of entanglement in the steady state by combining measurements of correlated mechanical fluctuations with an analysis of the microwaves emitted from the cavity. Our work qualitatively extends the range of entangled physical systems and has implications for quantum information processing, precision measurements and tests of the limits of quantum mechanics.

Landau-Zener (LZ) tunneling can occur with a certain probability when crossing energy levels of a quantum two-level system are swept across the minimum energy separation. Here we present experimental evidence of quantum interference effects in solid-state LZ tunneling. We used a Cooper-pair box qubit where the LZ tunneling occurs at the charge degeneracy. By employing a weak nondemolition monitoring, we observe interference between consecutive LZ-tunneling events; we find that the average level occupancies depend on the dynamical phase. The system's unusually strong linear response is explained by interband relaxation. Our interferometer can be used as a high-resolution Mach-Zehnder-type detector for phase and charge.

A pair of conjugate observables, such as the quadrature amplitudes of harmonic motion, have fundamental fluctuations that are bound by the Heisenberg uncertainty relation. However, in a squeezed quantum state, fluctuations of a quantity can be reduced below the standard quantum limit, at the cost of increased fluctuations of the conjugate variable. Here we prepare a nearly macroscopic moving body, realized as a micromechanical resonator, in a squeezed quantum state. We obtain squeezing of one quadrature amplitude 1.1 AE 0.4 dB below the standard quantum limit, thus achieving a long-standing goal of obtaining motional squeezing in a macroscopic object. DOI: 10.1103/PhysRevLett.115.243601 PACS numbers: 42.50.Wk, 03.65.Ta, 42.50.Ct, 81.07.Oj The motion xðtÞ ¼ X 1 ðtÞ cosðω m tÞ þ X 2 ðtÞ sinðω m tÞ of a harmonic oscillator having the natural oscillating frequency ω m can be described by the quadrature amplitudes X 1 and X 2 which have slow fluctuations. The fluctuations, presented in units of the quantum zero-point fluctuation amplitude x zp , satisfy the Heisenberg uncertainty relation ΔX 1 ΔX 2 ≥ 1. One of the two can be prepared (¼ squeezed) below the value 1, at the expense of increased fluctuations in the other quadrature. In optics, squeezing of laser light was observed in early 1980s [1,2], not long after the possibility was realized.It has been a formidable challenge to obtain squeezing in the motional state of a macroscopic object. The possibility of squeezing in the oscillations of massive gravitational antennae was hypothesized a long time ago [3,4], but technological limitations are too severe for experimental realization. Other motional quantum-mechanical phenomena, on the other hand, have recently been experimentally demonstrated [5,6] in micromechanical resonators. The latter systems are nearly macroscopic in physical size, and therefore they provide an ideal test system for treating the borderline between quantum and classical. Of particular interest for these studies has been the cavity optomechanics setting coupling electromagnetic cavity mode and the oscillator motion [7]. Output of squeezed light [8][9][10] was recently observed, but this does not yet imply that the oscillator mode is squeezed.Here we report the first realization of squeezing of the motional state of a nearly macroscopic body, realized as a micromechanical resonator measuring 15 microns in diameter. We utilize the novel idea of dissipative squeezing [11][12][13] [see Fig. 1(a)], where the system is allowed to cool towards a squeezed low-energy state. This method has the great advantage of being able to create unconditional squeezing in the steady state. This is in contrast with many other plausible methods of squeezing generation [14][15][16][17][18][19][20]. Our approach is closely related to the quantum nondemolition measurements [21][22][23] which, however, are not able to generate true squeezing without feedback. At this point we mention that classical squeezing of thermal noise is routinely observed in mechanical system...

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 [...

The coupling of distinct systems underlies nearly all physical phenomena. A basic instance is that of interacting harmonic oscillators, giving rise to, for example, the phonon eigenmodes in a lattice. Of particular importance are the interactions in hybrid quantum systems, which can combine the benefits of each part in quantum technologies. Here we investigate a hybrid optomechanical system having three degrees of freedom, consisting of a microwave cavity and two micromechanical beams with closely spaced frequencies around 32 MHz and no direct interaction. We record the first evidence of tripartite optomechanical mixing, implying that the eigenmodes are combinations of one photonic and two phononic modes. We identify an asymmetric dark mode having a long lifetime. Simultaneously, we operate the nearly macroscopic mechanical modes close to the motional quantum ground state, down to 1.8 thermal quanta, achieved by back-action cooling. These results constitute an important advance towards engineering of entangled motional states.

Sensitive measurement of electrical signals is at the heart of modern science and technology. According to quantum mechanics, any detector or amplifier is required to add a certain amount of noise to the signal, equaling at best the energy of quantum fluctuations [1, 2]. The quantum limit of added noise has nearly been reached with superconducting devices which take advantage of nonlinearities in Josephson junctions [3, 4]. Here, we introduce a new paradigm of amplification of microwave signals with the help of a mechanical oscillator. By relying on the radiation pressure force on a nanomechanical resonator [5][6][7], we provide an experimental demonstration and an analytical description of how the injection of microwaves induces coherent stimulated emission and signal amplification. This scheme, based on two linear oscillators, has the advantage of being conceptually and practically simpler than the Josephson junction devices, and, at the same time, has a high potential to reach quantum limited operation. With a measured signal amplification of 25 decibels and the addition of 20 quanta of noise, we anticipate near Since the early days of quantum mechanics, the effect of quantum zero point fluctuations on measurement accuracy has been actively investigated. When measuring a position x of an object, one necessarily disturbs its subsequent motion by introducing a disturbance to the momentum p. The imprecision and disturbance are related by the fundamental limit ∆x∆p ≥ /2 owing to the Heisenberg uncertainty principle. A proper compromise between the two leads to the lowest added noise power per unit bandwidth ω/2 which equals the quantum fluctuations of the system itself at the signal frequency ω. On the other hand, if only one observable is measured, for example position, or a single quadrature such as either amplitude or phase of oscillations, noise in this measurement can be squeezed below the quantum limit at the expense of increased noise in the other quadrature. In this case, the amplifier is said to be phase-sensitive.While most modern transistors operate several orders of magnitude above the fundamental noise limit, superconducting Josephson junction parametric amplifiers [3, 4,8,9], working near the absolute zero of temperature, have found uses at the level of only a few added quanta at microwave frequencies.Approaching the quantum limit with a mechanical amplifier has remained fully elusive, moreover, there is little work whatsoever on amplifying electrical signals by mechanical means [10], foremost due to the typically small electromechanical interaction. In this work, we describe a way to approach quantum-limited microwave amplification, now with a mechanical device. Our system consists of a mechanical resonator affected by radiation pressure forces due to an electromagnetic field confined in a lithographically patterned thin-film microwave cavity. Depending on the configuration, it is capable of either phase-sensitive, or phase-insensitive amplification.Our system of two coupled linear oscillators form...

Coupling electromagnetic waves in a cavity and mechanical vibrations via the radiation pressure of photons is a promising platform for investigations of quantum–mechanical properties of motion. A drawback is that the effect of one photon tends to be tiny, and hence one of the pressing challenges is to substantially increase the interaction strength. A novel scenario is to introduce into the setup a quantum two-level system (qubit), which, besides strengthening the coupling, allows for rich physics via strongly enhanced nonlinearities. Here we present a design of cavity optomechanics in the microwave frequency regime involving a Josephson junction qubit. We demonstrate boosting of the radiation–pressure interaction by six orders of magnitude, allowing to approach the strong coupling regime. We observe nonlinear phenomena at single-photon energies, such as an enhanced damping attributed to the qubit. This work opens up nonlinear cavity optomechanics as a plausible tool for the study of quantum properties of motion.