Publications Gerhard KIRCHMAIR

2024

Preprints

N. Diaz-Naufal, L. Deeg, D. Zoepfl, C. Schneider, M. L. Juan, G. Kirchmair, A. Metelmann Kerr enhanced optomechanical cooling in the unresolved sideband regime, (2024-10-20), arXiv:2410.15435 arXiv:2410.15435 (ID: 721277)
D. Atanasova, I. Yang, T. Hönigl-Decrinis, D. Gusenkova, I. M. Pop, G. Kirchmair In-situ tunable interaction with an invertible sign between a fluxonium and a post cavity, (2024-09-11), arXiv:2409.07612 arXiv:2409.07612 (ID: 721273)
M. Zanner, R. Albert, E. I. Rosenthal, S. Casulleras-Guardia, I. Yang, C. Schneider, O. Romero-Isart, G. Kirchmair Spatial Addressing of Qubits in a Dispersive Waveguide, (2024-07-15), arXiv:2407.10617 arXiv:2407.10617 (ID: 721271)
A. Sharafiev, G. Kirchmair, M. L. Juan, M. Cattaneo Leveraging collective effects for thermometry in waveguide quantum electrodynamics, (2024-07-08), arXiv:2407.05958 arXiv:2407.05958 (ID: 721270) Toggle Abstract
We report a proof-of-principle experiment for a new method of temperature measurements in waveguide quantum electrodynamics (wQED) experiments, allowing one to differentiate between global and local baths. The method takes advantage of collective states of two transmon qubits located in the center of a waveguide. The Hilbert space of such a system forms two separate subspaces (bright and dark) which are coupled differently to external noise sources. Measuring transmission through the waveguide allows one to extract separately the temperatures of the baths responsible for global and local excitations in the system. Such a system would allow for building a new type of primary temperature sensor capable of distinguishing between local and global baths.
L. Deeg, D. Zoepfl, N. Diaz-Naufal, M. L. Juan, A. Metelmann, G. Kirchmair Optomechanical Backaction in the Bistable Regime, (2024-06-08), arXiv:2406.04217 arXiv:2406.04217 (ID: 721263)
J. Yang, T. E. Agrenius Gustafsson, V. Usova, O. Romero-Isart, G. Kirchmair Hot Schrödinger Cat States, (2024-06-05), arXiv:2406.03389 arXiv:2406.03389 (ID: 721262) Toggle Abstract
The observation of quantum phenomena often necessitates sufficiently pure states, a requirement that can be challenging to achieve. In this study, our goal is to prepare a non-classical state originating from a mixed state, utilizing dynamics that preserve the initial low purity of the state. We generate a quantum superposition of displaced thermal states within a microwave cavity using only unitary interactions with a transmon qubit. We measure the Wigner functions of these ``hot'' Schrödinger cat states for an initial purity as low as 0.06. This corresponds to a cavity mode temperature of up to 1.8 Kelvin, sixty times hotter than the cavity's physical environment. Our realization of highly mixed quantum superposition states could be implemented with other continuous-variable systems e.g. nanomechanical oscillators, for which ground-state cooling remains challenging.

2023

Article

D. Zöpfl, M. L. Juan, N. Diaz-Naufal, C. Schneider, L. Deeg, A. Sharafiev, A. Metelmann, G. Kirchmair Kerr Enhanced Backaction Cooling in Magnetomechanics, PRL 130 33601 (2023-01-17), http://dx.doi.org/10.1103/PhysRevLett.130.033601 doi:10.1103/PhysRevLett.130.033601 (ID: 720816) Toggle Abstract
Optomechanics is a prime example of light matter interaction, where photons directly couple to phonons, allowing the precise control and measurement of the state of a mechanical object. This makes it a very appealing platform for testing fundamental physics or for sensing applications. Usually, such mechanical oscillators are in highly excited thermal states and require cooling to the mechanical ground state for quantum applications, which is often accomplished by using optomechanical backaction. However, while massive mechanical oscillators are desirable for many tasks, their frequency usually decreases below the cavity linewidth, significantly limiting the methods that can be used to efficiently cool. Here, we demonstrate a novel approach relying on an intrinsically nonlinear cavity to backaction-cool a low frequency mechanical oscillator. We experimentally demonstrate outperforming an identical, but linear, system by more than 1 order of magnitude. Furthermore, our theory predicts that with this approach we can also surpass the standard cooling limit of a linear system. By exploiting a nonlinear cavity, our approach enables efficient cooling of a wider range of optomechanical systems, opening new opportunities for fundamental tests and sensing.

2022

Articles

R. Holzinger, R. Gutierrez Jauregui, T. Hönigl-Decrinis, G. Kirchmair, A. Asenjo Garcia, Helmut Ritsch Control of Localized Single- and Many-Body Dark States in Waveguide QED, Phys. Rev. Lett. 129 (2022-12-14), http://dx.doi.org/10.1103/PhysRevLett.129.253601 doi:10.1103/PhysRevLett.129.253601 (ID: 720918) Toggle Abstract
Subradiant states in a finite chain of two-level quantum emitters coupled to a one-dimensional reservoir are a resource for superior photon storage and their controlled release. As one can maximally store one energy quantum per emitter, storing multiple excitations requires delocalized states, which typically exhibit fermionic correlations and antisymmetric wave functions, thus making them hard to access experimentally. Here we identify a new class of quasilocalized dark states with up to half of the qubits excited, which only appear for lattice constants of an integer multiple of the wavelength. These states allow for a high-fidelity preparation and minimally invasive readout in state-of-the-art setups. In particular, we suggest an experimental implementation using a coplanar waveguide coupled to superconducting transmon qubits on a chip. With minimal free space and intrinsic losses, virtually perfect dark states can be achieved for a low number of qubits featuring fast preparation and precise manipulation.
T. Orell, M. Zanner, M. L. Juan, A. Sharafiev, R. Albert, S. Oleschko, G. Kirchmair, M. Silveri Collective bosonic effects in an array of transmon devices, Phys. Rev. A 105 (2022-06-01), http://dx.doi.org/10.1103/PhysRevA.105.063701 doi:10.1103/PhysRevA.105.063701 (ID: 720925) Toggle Abstract
Multiple emitters coherently interacting with an electromagnetic mode give rise to collective effects such as correlated decay and coherent exchange interaction, depending on the separation of the emitters. By diagonalizing the effective non-Hermitian many-body Hamiltonian we reveal the complex-valued eigenvalue spectrum encoding the decay and interaction characteristics. We show that there are significant differences in the emerging collective effects for an array of interacting anharmonic oscillators compared to those of two-level systems and harmonic oscillators. The bosonic decay rate of the most superradiant state increases linearly as a function of the filling factor and exceeds that of two-level systems in magnitude. Furthermore, with bosonic systems, dark states are formed at each filling factor. These are in strong contrast with two-level systems, where the maximal superradiance is observed at half-filling and with larger filling factors superradiance diminishes and no dark states are formed. As an experimentally relevant setup of bosonic waveguide QED, we focus on arrays of transmon devices embedded inside a rectangular waveguide. Specifically, we study the setup of two transmon pairs realized experimentally in Zanner et al. [Nat. Phys. 18, 538 (2022)] and show that it is necessary to consider transmons as bosonic multilevel emitters to accurately recover correct collective effects for the higher excitation manifolds.
M. Zanner, T. Orell, C. Schneider, R. Albert, S. Oleschko, M. L. Juan, M. Silveri, G. Kirchmair Coherent control of a symmetry-engineered multi-qubit dark state in waveguide quantum electrodynamics, Nature Phys. 18 (2022-03-14), http://dx.doi.org/10.1038/s41567-022-01527-w doi:10.1038/s41567-022-01527-w (ID: 720659) Toggle Abstract
Quantum information is typically encoded in the state of a qubit that is decoupled from the environment. In contrast, waveguide quantum electrodynamics studies qubits coupled to a mode continuum, exposing them to a loss channel and causing quantum information to be lost before coherent operations can be performed. Here we restore coherence by realizing a dark state that exploits symmetry properties and interactions between four qubits. Dark states decouple from the waveguide and are thus a valuable resource for quantum information but also come with a challenge: they cannot be controlled by the waveguide drive. We overcome this problem by designing a drive that utilizes the symmetry properties of the collective state manifold allowing us to selectively drive both bright and dark states. The decay time of the dark state exceeds that of the waveguide-limited single qubit by more than two orders of magnitude. Spectroscopy on the second excitation manifold provides further insight into the level structure of the hybridized system. Our experiment paves the way for implementations of quantum many-body physics in waveguides and the realization of quantum information protocols using decoherence-free subspaces.

2021

Articles

P. Heidler, C. Schneider, K. Kustura, C. Gonzalez-Ballestero, O. Romero-Isart, G. Kirchmair Non-Markovian Effects of Two-Level Systems in a Niobium Coaxial Resonator with a Single-Photon Lifetime of 10 ms, Phys. Rev. Applied 16 34024 (2021-09-13), http://dx.doi.org/10.1103/PhysRevApplied.16.034024 doi:10.1103/PhysRevApplied.16.034024 (ID: 720630) Toggle Abstract
Understanding and mitigating loss channels due to two-level systems (TLS) is one of the main corner stones in the quest of realizing long photon lifetimes in superconducting quantum circuits. Typically, the TLS to which a circuit couples are modelled as a large bath without any coherence. Here we demonstrate that the coherence of TLS has to be considered to accurately describe the ring-down dynamics of a coaxial quarter-waver resonator with an internal quality factor of $0.5\times10^9$ at the single-photon level. The transient analysis reveals an effective non-markovian dynamics of the combined TLS and cavity system, which we can accurately fit by introducing a comprehensive TLS model. The fit returns relaxation times around $T_1=0.8\,\mathrm{\mu s}$ for a total of $N\approx 2 \times 10^{8}$ TLS with power-law distributed coupling strengths. Despite the short-lived TLS excitations, we observe long-term effects on the cavity decay due to coherent elastic scattering between the resonator field and the TLS. The presented method is applicable to various systems and allows for a simple characterization of TLS properties.
R. Asensio-Perea, A. Parra-Rodriguez, G. Kirchmair, E. Solano, E. Rico Ortega Chiral states and nonreciprocal phases in a Josephson junction ring, Phys. Rev. B 103 224525 (2021-06-22), http://dx.doi.org/10.1103/PhysRevB.103.224525 doi:10.1103/PhysRevB.103.224525 (ID: 720583)
A. Sharafiev, M. L. Juan, O. Gargiulo, M. Zanner, S. Wögerer, J. García-Ripoll, G. Kirchmair Visualizing the emission of a single photon with frequency and time resolved spectroscopy, Quantum 5 474 (2021-06-10), http://dx.doi.org/10.22331/q-2021-06-10-474 doi:10.22331/q-2021-06-10-474 (ID: 720494) Toggle Abstract
At the dawn of Quantum Physics, Wigner and Weisskopf obtained a full analytical description (a photon portrait) of the emission of a single photon by a two-level system, using the basis of frequency modes (Weisskopf and Wigner, "Zeitschrift für Physik", 63, 1930). A direct experimental reconstruction of this portrait demands an accurate measurement of a time resolved fluorescence spectrum, with high sensitivity to the off-resonant frequencies and ultrafast dynamics describing the photon creation. In this work we demonstrate such an experimental technique in a superconducting waveguide Quantum Electrodynamics (wQED) platform, using single transmon qubit and two coupled transmon qubits as quantum emitters. In both scenarios, the photon portraits agree quantitatively with the predictions of the input-output theory and qualitatively with Wigner-Weisskopf theory. We believe that our technique allows not only for interesting visualization of fundamental principles, but may serve as a tool, e.g. to realize multi-dimensional spectroscopy in waveguide Quantum Electrodynamics.
E. I. Rosenthal, C. Schneider, M. Malnou, Z. Zhao, F. Leditzky, B. J. Chapman, W. Wustmann, X. Ma, D. A. Palken, M. Zanner, L. R. Vale, G. C. Hilton, J. Gao, G. Smith, G. Kirchmair, K. Lehnert Efficient and low-backaction quantum measurement using a chip-scale detector, Phys. Rev. Lett. 126 90503 (2021-03-03), http://dx.doi.org/10.1103/PhysRevLett.126.090503 doi:10.1103/PhysRevLett.126.090503 (ID: 720580) Toggle Abstract
Superconducting qubits are a leading platform for scalable quantum computing and quantum error correction. One feature of this platform is the ability to perform projective measurements orders of magnitude more quickly than qubit decoherence times. Such measurements are enabled by the use of quantum-limited parametric amplifiers in conjunction with ferrite circulators - magnetic devices which provide isolation from noise and decoherence due to amplifier backaction. Because these non-reciprocal elements have limited performance and are not easily integrated on-chip, it has been a longstanding goal to replace them with a scalable alternative. Here, we demonstrate a solution to this problem by using a superconducting switch to control the coupling between a qubit and amplifier. Doing so, we measure a transmon qubit using a single, chip-scale device to provide both parametric amplification and isolation from the bulk of amplifier backaction. This measurement is also fast, high fidelity, and has 70% efficiency, comparable to the best that has been reported in any superconducting qubit measurement. As such, this work constitutes a high-quality platform for the scalable measurement of superconducting qubits.
O. Gargiulo, S. Oleschko, J. Prat-Camps, M. Zanner, G. Kirchmair Fast flux control of 3D transmon qubits using a magnetic hose, Appl. Phys. Lett. 118 (2021-01-04), http://dx.doi.org/10.1063/5.0032615 doi:10.1063/5.0032615 (ID: 720099)

2020

Articles

D. Zöpfl, M. L. Juan, C. Schneider, G. Kirchmair Single-Photon Cooling in Microwave Magnetomechanics, PRL 125 23601 (2020-07-07), http://dx.doi.org/10.1103/PhysRevLett.125.023601 doi:10.1103/PhysRevLett.125.023601 (ID: 720518) Toggle Abstract
Cavity optomechanics, where photons are coupled to mechanical motion, provides the tools to control mechanical motion near the fundamental quantum limits. Reaching single-photon strong coupling would allow to prepare the mechanical resonator in non-Gaussian quantum states. Preparing massive mechanical resonators in such states is of particular interest for testing the boundaries of quantum mechanics. This goal remains however challenging due to the small optomechanical couplings usually achieved with massive devices. Here we demonstrate a novel approach where a mechanical resonator is magnetically coupled to a microwave cavity. We measure a single-photon coupling of g0/2π∼3 kHz, an improvement of one order of magnitude over current microwave optomechanical systems. At this coupling we measure a large single-photon cooperativity with C0≳10, an important step to reach single-photon strong coupling. Such a strong interaction allows us to cool the massive mechanical resonator to a third of its steady state phonon population with less than two photons in the microwave cavity. Beyond tests for quantum foundations, our approach is also well suited as a quantum sensor or a microwave to optical transducer.
P. Guimond, B. Vermersch, M. L. Juan, A. Sharafiev, G. Kirchmair, P. Zoller A Unidirectional On-Chip Photonic Interface for Superconducting Circuits, npj Quantum Information 6 (2020-03-27), http://dx.doi.org/10.1038/s41534-020-0261-9 doi:10.1038/s41534-020-0261-9 (ID: 720478) Toggle Abstract
We propose and analyze a passive architecture for realizing on-chip, scalable cascaded quantum devices. In contrast to standard approaches, our scheme does not rely on breaking Lorentz reciprocity. Rather, we engineer the interplay between pairs of superconducting transmon qubits and a microwave transmission line, in such a way that two delocalized orthogonal excitations emit (and absorb) photons propagating in opposite directions. We show how such cascaded quantum devices can be exploited to passively probe and measure complex many-body operators on quantum registers of stationary qubits, thus enabling the heralded transfer of quantum states between distant qubits, as well as the generation and manipulation of stabilizer codes for quantum error correction.

2019

Articles

G. Kirchmair Designing nonlinearity, Nature Phys. 16 128 (2019-11-18), http://dx.doi.org/10.1038/s41567-019-0710-6 doi:10.1038/s41567-019-0710-6 (ID: 720590)
M. Schütz, B. Vermersch, G. Kirchmair, L. Vandersypen, J. I. Cirac, M. Lukin, P. Zoller Quantum Simulation and Optimization in Hot Quantum Networks, Phys. Rev. B 99 241302 (2019-06-27), http://dx.doi.org/10.1103/PhysRevB.99.241302 doi:10.1103/PhysRevB.99.241302 (ID: 720058) Toggle Abstract
We propose and analyze a setup based on (solid-state) qubits coupled to a common multi-mode transmission line, which allows for coherent spin-spin interactions over macroscopic on-chip distances, without any ground-state cooling requirements for the data bus. Our approach allows for the realization of fast deterministic quantum gates between distant qubits, the simulation of quantum spin models with engineered (long-range) interactions, and provides a flexible architecture for the implementation of quantum approximate optimization algorithms.

2018

Articles

J. Prat-Camps, P. Maurer, G. Kirchmair, O. Romero-Isart Circumventing Magnetostatic Reciprocity: A Diode for Magnetic Fields, Phys. Rev. Lett. 121 213903 (2018-11-20), http://dx.doi.org/10.1103/PhysRevLett.121.213903 doi:10.1103/PhysRevLett.121.213903 (ID: 719978) Toggle Abstract
Lorentz reciprocity establishes a stringent relation between electromagnetic fields and their sources. For static magnetic fields, a relation between magnetic sources and fields can be drawn in analogy to the Green’s reciprocity principle for electrostatics. So far, the magnetostatic reciprocity principle remains unchallenged and the magnetostatic interaction is assumed to be symmetric (reciprocal). Here, we theoretically and experimentally show that a linear and isotropic electrically conductive material moving with constant velocity is able to circumvent the magnetostatic reciprocity principle and realize a diode for magnetic fields. This result is demonstrated by measuring an extremely asymmetric magnetic coupling between two coils that are located near a moving conductor. The possibility to generate controlled unidirectional magnetic couplings implies that the mutual inductances between magnetic elements or circuits can be made extremely asymmetric. We anticipate that this result will provide novel possibilities for applications and technologies based on magnetically coupled elements and might open fundamentally new avenues in artificial magnetic spin systems.
P. R. Muppalla, O. Gargiulo, S. Mirzaei, B. Venkatesh, M. L. Juan, L. Grünhaupt, I. M. Pop, G. Kirchmair Bistability in a Mesoscopic Josephson Junction Array Resonator, Phys. Rev. B 97 24518 (2018-01-30), http://dx.doi.org/10.1103/PhysRevB.97.024518 doi:10.1103/PhysRevB.97.024518 (ID: 719817) Toggle Abstract
We present an experimental investigation of stochastic switching of a bistable Josephson junctions array resonator with a resonance frequency in the GHz range. As the device is in the regime where the anharmonicity is on the order of the linewidth, the bistability appears for a pump strength of only a few photons. We measure the dynamics of the bistability by continuously observing the jumps between the two metastable states, which occur with a rate ranging from a few Hz down to a few mHz. The switching rate strongly depends on the pump strength, readout strength and the temperature, following Kramer's law. The interplay between nonlinearity and coupling, in this little explored regime, could provide a new resource for nondemolition measurements, single photon switches or even elements for autonomous quantum error correction.

2017

Article

D. Zöpfl, C. Schneider, P. R. Muppalla, S. Kasemann, S. Partel, G. Kirchmair Characterization of low loss microstrip resonators as a building block for circuit QED in a 3D waveguide, AIP ADV 7 (2017-08-28), http://dx.doi.org/10.1063/1.4992070 doi:10.1063/1.4992070 (ID: 719818) Toggle Abstract
Here we present the microwave characterization of microstrip resonators made from aluminum and niobium inside a 3D microwave waveguide. In the low temperature, low power limit internal quality factors of up to one million were reached. We found a good agreement to models predicting conductive losses and losses to two level systems for increasing temperature. The setup presented here is appealing for testing materials and structures, as it is free of wire bonds and offers a well controlled microwave environment. In combination with transmon qubits, these resonators serve as a building block for a novel circuit QED architecture inside a rectangular waveguide.

2015

Articles

N. Friis, A. Melnikov, G. Kirchmair, H. J. Briegel Coherent controlization using superconducting qubits, Sci. Rep. 5 18036 (2015-12-15), http://dx.doi.org/10.1038/srep18036 doi:10.1038/srep18036 (ID: 719310) Toggle Abstract
Coherent controlization, i.e., coherent conditioning of arbitrary single- or multi-qubit operations on the state of one or more control qubits, is an important ingredient for the flexible implementation of many algorithms in quantum computation. This is of particular significance when certain subroutines are changing over time or when they are frequently modified, such as in decision-making algorithms for learning agents. We propose a scheme to realize coherent controlization for any number of superconducting qubits coupled to a microwave resonator. For two and three qubits, we present an explicit construction that is of high relevance for quantum learning agents. We demonstrate the feasibility of our proposal, taking into account loss, dephasing, and the cavity self-Kerr effect.
E. T. Holland, B. Vlastakis, R. W. Heeres, M. J. Reagor, U. Vool, Z. Leghtas, L. Frunzio, G. Kirchmair, M. H. Devoret, M. Mirrahimi, R. Schoelkopf Single-photon Resolved Cross-Kerr Interaction for Autonomous Stabilization of Photon-number States, Phys. Rev. Lett. 115 180501 (2015-04-26), http://dx.doi.org/10.1103/PhysRevLett.115.180501 doi:10.1103/PhysRevLett.115.180501 (ID: 719226) Toggle Abstract
Quantum states can be stabilized in the presence of intrinsic and environmental losses by either applying active feedback conditioned on an ancillary system or through reservoir engineering. Reservoir engineering maintains a desired quantum state through a combination of drives and designed entropy evacuation. We propose and implement a quantum reservoir engineering protocol that stabilizes Fock states in a microwave cavity. This protocol is realized with a circuit quantum electrodynamics platform where a Josephson junction provides direct, nonlinear coupling between two superconducting waveguide cavities. The nonlinear coupling results in a single photon resolved cross-Kerr effect between the two cavities enabling a photon number dependent coupling to a lossy environment. The quantum state of the microwave cavity is discussed in terms of a net polarization and is analyzed by a measurement of its steady state Wigner function.
G. Via, G. Kirchmair, O. Romero-Isart Strong Single-Photon Coupling in Superconducting Quantum Magnetomechanics, Phys. Rev. Lett. 114 143602 (2015-04-07), http://dx.doi.org/10.1103/PhysRevLett.114.143602 doi:10.1103/PhysRevLett.114.143602 (ID: 719099) Toggle Abstract
We show that the inductive coupling between the quantum mechanical motion of a superconducting microcantilever and a flux-dependent microwave quantum circuit can attain the strong single-photon nanomechanical coupling regime with feasible experimental parameters. We propose to use a superconducting strip, which is in the Meissner state, at the tip of a cantilever. A pick-up coil collects the flux generated by the sheet currents induced by an external quadrupole magnetic field centered at the strip location. The position-dependent magnetic response of the superconducting strip, enhanced by both diamagnetism and demagnetizing effects, leads to a strong magnetomechanical coupling to quantum circuits.
M. Dalmonte, S. Mirzaei, P. R. Muppalla, D. Marcos, P. Zoller, G. Kirchmair Dipolar Spin Models with Arrays of Superconducting Qubits, Phys. Rev. B 92 174507 (2015-01-13), http://dx.doi.org/10.1103/PhysRevB.92.174507 doi:10.1103/PhysRevB.92.174507 (ID: 719116) Toggle Abstract
We propose a novel platform for quantum many body simulations of dipolar spin models using current circuit QED technology. Our basic building blocks are 3D Transmon qubits where we use the naturally occurring dipolar interactions to realize interacting spin systems. This opens the way toward the realization of a broad class of tunable spin models in both two- and one-dimensional geometries. We illustrate the potential offered by these systems in the context of dimerized Majumdar-Ghosh-type phases, archetypical examples of quantum magnetism, showing how such phases are robust against disorder and decoherence, and could be observed within state-of-the-art experiments.
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2014

Article

L. Sun, A. Petrenko, Z. Leghtas, B. Vlastakis, G. Kirchmair, K. M. Sliwa, A. Narla, M. Hatridge, S. Shankar, J. Blumoff, L. Frunzio, M. Mirrahimi, M. H. Devoret, R. Schoelkopf Tracking Photon Jumps with Repeated Quantum Non-Demolition Parity Measurements, Nature 511 448 (2014-07-13), http://dx.doi.org/10.1038/nature13436 doi:10.1038/nature13436 (ID: 718654) Toggle Abstract
Quantum error correction (QEC) is required for a practical quantum computer because of the fragile nature of quantum information. In QEC, information is redundantly stored in a large Hilbert space and one or more observables must be monitored to reveal the occurrence of an error, without disturbing the information encoded in an unknown quantum state. Such observables, typically multi-qubit parities such as <XXXX>, must correspond to a special symmetry property inherent to the encoding scheme. Measurements of these observables, or error syndromes, must also be performed in a quantum non-demolition (QND) way and faster than the rate at which errors occur. Previously, QND measurements of quantum jumps between energy eigenstates have been performed in systems such as trapped ions, electrons, cavity quantum electrodynamics (QED), nitrogen-vacancy (NV) centers, and superconducting qubits. So far, however, no fast and repeated monitoring of an error syndrome has been realized. Here, we track the quantum jumps of a possible error syndrome, the photon number parity of a microwave cavity, by mapping this property onto an ancilla qubit. This quantity is just the error syndrome required in a recently proposed scheme for a hardware-efficient protected quantum memory using Schr\"{o}dinger cat states in a harmonic oscillator. We demonstrate the projective nature of this measurement onto a parity eigenspace by observing the collapse of a coherent state onto even or odd cat states. The measurement is fast compared to the cavity lifetime, has a high single-shot fidelity, and has a 99.8% probability per single measurement of leaving the parity unchanged. In combination with the deterministic encoding of quantum information in cat states realized earlier, our demonstrated QND parity tracking represents a significant step towards implementing an active system that extends the lifetime of a quantum bit.
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2013

Articles

B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, R. Schoelkopf Deterministically encoding quantum information in 100-photon Schrödinger cat states, Science 342 610 (2013-09-26), http://dx.doi.org/10.1126/science.1243289 doi:10.1126/science.1243289 (ID: 718631) Toggle Abstract
In contrast to a single quantum bit, an oscillator can store multiple excitations and coherences, provided one has the ability to generate and manipulate complex multiphoton states. We demonstrate multiphoton control using a superconducting transmon qubit coupled to a waveguide cavity resonator with a highly ideal off-resonant coupling. This dispersive interaction is much greater than decoherence rates and higher-order nonlinearities to allow simultaneous manipulation of hundreds of photons. With a toolset of conditional qubit-photon logic, we map an arbitrary qubit state to a superposition of coherent states, known as a "cat state." We create cat states as large as 111 photons and extend this protocol to create superpositions of up to four coherent states. This control creates a powerful interface between discrete and continuous variable quantum computation and could enable applications in metrology and quantum information processing.
Z. Leghtas, G. Kirchmair, B. Vlastakis, R. Schoelkopf, M. H. Devoret, M. Mirrahimi Hardware-efficient autonomous quantum memory protection, Phys. Rev. Lett. 111 120501 (2013-09-20), http://dx.doi.org/10.1103/PhysRevLett.111.120501 doi:10.1103/PhysRevLett.111.120501 (ID: 718630) Toggle Abstract
We propose to encode a quantum bit of information in a superposition of coherent states of an oscillator, with four different phases. Our encoding in a single cavity mode, together with a protection protocol, significantly reduces the error rate due to photon loss. This protection is ensured by an efficient quantum error correction scheme employing the nonlinearity provided by a single physical qubit coupled to the cavity. We describe in detail how to implement these operations in a circuit quantum electrodynamics system. This proposal directly addresses the task of building a hardware-efficient quantum memory and can lead to important shortcuts in quantum computing architectures.
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Z. Leghtas, G. Kirchmair, B. Vlastakis, M. H. Devoret, R. Schoelkopf, M. Mirrahimi Deterministic protocol for mapping a qubit to coherent state superpositions in a cavity, Phys. Rev. A 87 042315 (2013-04-15), http://dx.doi.org/10.1103/PhysRevA.87.042315 doi:10.1103/PhysRevA.87.042315 (ID: 718629) Toggle Abstract
We propose and analyze a quantum gate that transfers an arbitrary state of a qubit into a superposition of two quasiorthogonal coherent states of a cavity mode (qcMAP), with opposite phases. This qcMAP gate is based on conditional qubit and cavity operations exploiting the energy-level dispersive shifts in the regime where they are much stronger than the cavity and qubit linewidths. The generation of multicomponent superpositions of quasiorthogonal coherent states, nonlocal entangled states of two resonators, and multiqubit Greenberger-Horne-Zeilinger states can be efficiently achieved by this gate.
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G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, R. Schoelkopf Observation of quantum state collapse and revival due to the single-photon Kerr effect, Nature 495 209 (2013-03-13), http://dx.doi.org/10.1038/nature11902 doi:10.1038/nature11902 (ID: 718628) Toggle Abstract
To create and manipulate non-classical states of light for quantum information protocols, a strong, nonlinear interaction at the single-photon level is required. One approach to the generation of suitable interactions is to couple photons to atoms, as in the strong coupling regime of cavity quantum electrodynamic systems. In these systems, however, the quantum state of the light is only indirectly controlled by manipulating the atoms. A direct photon–photon interaction occurs in so-called Kerr media, which typically induce only weak nonlinearity at the cost of significant loss. So far, it has not been possible to reach the single-photon Kerr regime, in which the interaction strength between individual photons exceeds the loss rate. Here, using a three-dimensional circuit quantum electrodynamic architecture, we engineer an artificial Kerr medium that enters this regime and allows the observation of new quantum effects. We realize a gedanken experiment in which the collapse and revival of a coherent state can be observed. This time evolution is a consequence of the quantization of the light field in the cavity and the nonlinear interaction between individual photons. During the evolution, non-classical superpositions of coherent states (that is, multi-component ‘Schrödinger cat’ states) are formed. We visualize this evolution by measuring the Husimi Q function and confirm the non-classical properties of these transient states by cavity state tomography. The ability to create and manipulate superpositions of coherent states in such a high-quality-factor photon mode opens perspectives for combining the physics of continuous variables with superconducting circuits. The single-photon Kerr effect could be used in quantum non-demolition measurement of photons, single-photon generation, autonomous quantum feedback schemes and quantum logic operations.
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2012

Articles

A. P. Sears, A. Petrenko, G. Catelani, H. Paik, G. Kirchmair, L. Frunzio, L. I. Glazman, S. M. Girvin, R. Schoelkopf Photon shot noise dephasing in the strong-dispersive limit of circuit QED, Phys. Rev. B 86 180504 (2012-11-12), http://dx.doi.org/10.1103/PhysRevB.86.180504 doi:10.1103/PhysRevB.86.180504 (ID: 718627) Toggle Abstract
We study the photon shot noise dephasing of a superconducting transmon qubit in the strong-dispersive limit, due to the coupling of the qubit to its readout cavity. As each random arrival or departure of a photon is expected to completely dephase the qubit, we can control the rate at which the qubit experiences dephasing events by varying in situ the cavity mode population and decay rate. This allows us to verify a pure dephasing mechanism that matches theoretical predictions, and in fact explains the increased dephasing seen in recent transmon experiments as a function of cryostat temperature. We observe large increases in coherence times as the cavity is decoupled from the environment, and after implementing filtering find that the intrinsic coherence of small Josephson junctions when corrected with a single Hahn echo is greater than several hundred microseconds. Similar filtering and thermalization may be important for other qubit designs in order to prevent photon shot noise from becoming the dominant source of dephasing.
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S. E. Nigg, H. Paik, B. Vlastakis, G. Kirchmair, S. Shankar, L. Frunzio, M. H. Devoret, R. J. Schoelkopf, S. M. Girvin Black-Box superconducting circuit quantization, Phys. Rev. Lett. 108 240502 (2012-06-12), http://dx.doi.org/10.1103/PhysRevLett.108.240502 doi:10.1103/PhysRevLett.108.240502 (ID: 718196) Toggle Abstract
We present a semiclassical method for determining the effective low-energy quantum Hamiltonian of weakly anharmonic superconducting circuits containing mesoscopic Josephson junctions coupled to electromagnetic environments made of an arbitrary combination of distributed and lumped elements. A convenient basis, capturing the multimode physics, is given by the quantized eigenmodes of the linearized circuit and is fully determined by a classical linear response function. The method is used to calculate numerically the low-energy spectrum of a 3D transmon system, and quantitative agreement with measurements is found.
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2011

Articles

H. Paik, D. I. Schuster, L. S. Bishop, G. Kirchmair, G. Catelani, A. P. Sears, B. R. Johnson, M. J. Reagor, L. Frunzio, L. I. Glazman, S. M. Girvin, M. H. Devoret, R. J. Schoelkopf Observation of High Coherence in Josephson Junction Qubits Measured in a Three-Dimensional Circuit QED Architecture, Phys. Rev. Lett. 107 240501 (2011-12-05), http://dx.doi.org/10.1103/PhysRevLett.107.240501 doi:10.1103/PhysRevLett.107.240501 (ID: 718197) Toggle Abstract
Superconducting quantum circuits based on Josephson junctions have made rapid progress in demonstrating quantum behavior and scalability. However, the future prospects ultimately depend upon the intrinsic coherence of Josephson junctions, and whether superconducting qubits can be adequately isolated from their environment. We introduce a new architecture for superconducting quantum circuits employing a three-dimensional resonator that suppresses qubit decoherence while maintaining sufficient coupling to the control signal. With the new architecture, we demonstrate that Josephson junction qubits are highly coherent, with T2∼10 to 20 μs without the use of spin echo, and highly stable, showing no evidence for 1/f critical current noise. These results suggest that the overall quality of Josephson junctions in these qubits will allow error rates of a few 10-4, approaching the error correction threshold.
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B. P. Lanyon, C. Hempel, D. Nigg, M. Müller, R. Gerritsma, F. Zähringer, P. Schindler, J. T. Barreiro, M. Rambach, G. Kirchmair, M. Hennrich, P. Zoller, R. Blatt, C. F. Roos Universal Digital Quantum Simulation with Trapped Ions, Science 334 57 (2011-09-01), http://dx.doi.org/10.1126/science.1208001 doi:10.1126/science.1208001 (ID: 717768) Toggle Abstract
A digital quantum simulator is an envisioned quantum device that can be programmed to efficiently simulate any other local system. We demonstrate and investigate the digital approach to quantum simulation in a system of trapped ions. Using sequences of up to 100 gates and 6 qubits, the full-time dynamics of a range of spin systems are digitally simulated. Interactions beyond those naturally present in our simulator are accurately reproduced, and quantitative bounds are provided for the overall simulation quality. Our results demonstrate the key principles of digital quantum simulation and provide evidence that the level of control required for a full-scale device is within reach.
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R. Gerritsma, B. P. Lanyon, G. Kirchmair, F. Zähringer, C. Hempel, J. Casanova, J. J. García-Ripoll, E. Solano, R. Blatt, C. F. Roos Quantum simulation of the Klein paradox with trapped ions, Phys. Rev. Lett. 106 060503 (2011-02-11), http://dx.doi.org/10.1103/PhysRevLett.106.060503 doi:10.1103/PhysRevLett.106.060503 (ID: 717611) Toggle Abstract
We report on quantum simulations of relativistic scattering dynamics using trapped ions. The simulated state of a scattering particle is encoded in both the electronic and vibrational state of an ion, representing the discrete and continuous components of relativistic wave functions. Multiple laser fields and an auxiliary ion simulate the dynamics generated by the Dirac equation in the presence of a scattering potential. Measurement and reconstruction of the particle wave packet enables a frame-by-frame visualization of the scattering processes. By precisely engineering a range of external potentials we are able to simulate text book relativistic scattering experiments and study Klein tunneling in an analogue quantum simulator. We describe extensions to solve problems that are beyond current classical computing capabilities.

Proceeding

C. F. Roos, R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt Quantum simulation of relativistic quantum physics with trapped ions, 22nd International Conference on Atomic Physics (Cairns, Australia, 2010-07-25) J. Phys. Conf. Ser. 264 012020 (2011-01-27), http://dx.doi.org/10.1088/1742-6596/264/1/012020 doi:10.1088/1742-6596/264/1/012020 (ID: 717471)

2010

Articles

F. Zähringer, G. Kirchmair, R. Gerritsma, E. Solano, R. Blatt, C. F. Roos Realization of a Quantum Walk with One and Two Trapped Ions, Phys. Rev. Lett. 104 100503 (2010-03-09), http://dx.doi.org/10.1103/PhysRevLett.104.100503 doi:10.1103/PhysRevLett.104.100503 (ID: 717148)
O. Gühne, M. Kleinmann, A. Cabello, J. Larson, G. Kirchmair, F. Zähringer, R. Gerritsma, C. F. Roos Compatibility and noncontextuality for sequential measurements, Phys. Rev. A 81 022121 (2010-02-26), http://dx.doi.org/10.1103/PhysRevA.81.022121 doi:10.1103/PhysRevA.81.022121 (ID: 717143)
R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, C. F. Roos Quantum simulation of the Dirac equation, Nature 463 71 (2010-01-07), http://dx.doi.org/10.1038/nature08688 doi:10.1038/nature08688 (ID: 716977)

2009

Articles

G. Kirchmair, F. Zähringer, R. Gerritsma, M. Kleinmann, O. Gühne, A. Cabello, R. Blatt, C. Roos State-independent experimental test of quantum contextuality, Nature 460 494 (2009), http://dx.doi.org/10.1038/nature08172 doi:10.1038/nature08172 (ID: 695207) Toggle Abstract
The question of whether quantum phenomena can be explained by classical models with hidden variables is the subject of a long-lasting debate. In 1964, Bell showed that certain types of classical models cannot explain the quantum mechanical predictions for specific states of distant particles, and some types of hidden variable models have been experimentally ruled out. An intuitive feature of classical models is non-contextuality: the property that any measurement has a value independent of other compatible measurements being carried out at the same time. However, a theorem derived by Kochen, Specker and Bell shows that non-contextuality is in conflict with quantum mechanics. The conflict resides in the structure of the theory and is independent of the properties of special states. It has been debated whether the Kochen–Specker theorem could be experimentally tested at all. First tests of quantum contextuality have been proposed only recently, and undertaken with photons and neutrons. But these tests required the generation of special quantum states and left various loopholes open. Here we perform an experiment with trapped ions that demonstrates a state-independent conflict with non-contextuality. The experiment is not subject to the detection loophole and we show that, despite imperfections and possible measurement disturbances, our results cannot be explained in non-contextual terms.
G. Kirchmair, J. Benhelm, F. Zähringer, R. Gerritsma, C. Roos, R. Blatt High-fidelity entanglement of 43Ca+ hyperfine clock states, Phys. Rev. A 79 020304 (2009), http://dx.doi.org/10.1103/PhysRevA.79.020304 doi:10.1103/PhysRevA.79.020304 (ID: 657856)
G. Kirchmair, J. Benhelm, F. Zähringer, R. Gerritsma, C. Roos, R. Blatt Deterministic entanglement of ions in thermal states of motion, 11 023002 (2009), http://dx.doi.org/10.1088/1367-2630/11/2/023002 doi:10.1088/1367-2630/11/2/023002 (ID: 655090)
M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. Villar, W. Hänsel, C. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, P. Laurent Absolute frequency measurement of the 40Ca+ 4s 2S1/2 - 3d 2D5/2 clock transition, Phys. Rev. Lett. 102 023002 (2009), http://dx.doi.org/10.1103/PhysRevLett.102.023002 doi:10.1103/PhysRevLett.102.023002 (ID: 650530)

Proceedings

M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. Villar, W. Hänsel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, D. Rovera, P. Laurent Absolute frequency measurement of the 40Ca+ S1/2-D5/2 clock transition, Proceedings of the 7th symposium on frequency standards and metrology 7th symposium on frequency standards and metrology (Pacific Grove, 2008-10-05) 108 (2009-10-28), (ID: 716779)
J. Benhelm, G. Kirchmair, R. Gerritsma, F. Zähringer, T. Monz, P. Schindler, M. Chwalla, W. Hänsel, M. Hennrich, C. F. Roos, R. Blatt Ca+ quantum bits for quantum information processing, Physica Scripta T137 014008 (2009-05-25), (ID: 716979)

2008

Articles

R. Gerritsma, G. Kirchmair, F. Zähringer, J. Benhelm, R. Blatt, C. Roos Precision measurement of the branching fractions of the 4p 2P3/2 decay of Ca II, Eur. Phys. J. D 50 13 (2008), http://dx.doi.org/10.1140/epjd/e2008-00196-9 doi:10.1140/epjd/e2008-00196-9 (ID: 621123)
J. Benhelm, G. Kirchmair, C. Roos, R. Blatt Experimental quantum information processing with 43Ca+ ions, Phys. Rev. A 77 062306 (2008), http://dx.doi.org/10.1103/PhysRevA.77.062306 doi:10.1103/PhysRevA.77.062306 (ID: 595124)
J. Benhelm, G. Kirchmair, C. Roos, R. Blatt Towards fault-tolerant quantum computing with trapped ions, Nature Phys. 4 463 (2008), http://dx.doi.org/10.1038/nphys961 doi:10.1038/nphys961 (ID: 578533)

2007

Article

J. Benhelm, G. Kirchmair, U. D. Rapol, T. Körber, C. Roos, R. Blatt Measurement of the hyperfine structure of the S1/2-D5/2 transition in 43Ca+, Phys. Rev. A 75 032506 (2007), http://dx.doi.org/10.1103/PhysRevA.75.032506 doi:10.1103/PhysRevA.75.032506 (ID: 461034) (local copy)