# Gerhard KirchmairUniversity of Innsbruck | UIBK · Institute for Experimental Physics

Gerhard Kirchmair

Dr. Univ. Prof.

## About

79

Publications

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6,992

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Citations since 2017

Introduction

Additional affiliations

March 2013 - present

October 2010 - March 2013

January 2008 - September 2010

## Publications

Publications (79)

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 ther...

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 anti...

Subradiant excited states in finite chains of two-level quantum emitters coupled to a one-dimensional reservoir are a resource for superior photon storage and controlled photon manipulation. Typically, states storing multiple excitations exhibit fermionic correlations and are thus characterized by an anti-symmetric wavefunction, which makes them ha...

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 inte...

Superconducting qubits in a waveguide have long-range interactions mediated by photons that cause the emergence of collective states. Destructive interference between the qubits decouples the collective dark states from the waveguide environment. Their inability to emit photons into the waveguide render dark states a valuable resource for preparing...

Precise control over massive mechanical objects is highly desirable for testing fundamental physics and for sensing applications. A very promising approach is cavity optomechanics, where a mechanical oscillator is coupled to a cavity. Usually, such mechanical oscillators are in highly excited thermal states and require cooling to the mechanical gro...

Multiple atoms 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 atoms. By diagonalizing the effective non-Hermitian many-body Hamiltonian we reveal the complex-valued eigenvalue spectrum encoding the decay and interactio...

Understanding and mitigating loss channels due to two-level systems (TLS) is one of the main cornerstones in the quest of realizing long photon lifetimes in superconducting quantum circuits. Typically, the TLS to which a circuit couples are modeled as a large bath without any coherence. Here we demonstrate that the coherence of TLS has to be consid...

In this work, we propose how to load and manipulate chiral states in a Josephson junction ring in the so-called transmon regime. We characterize these states by their symmetry properties under time-reversal and parity transformations. We describe an explicit protocol to load and detect the states within a realistic set of circuit parameters and sho...

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 measuremen...

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 reali...

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...

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 cons...

Fast magnetic flux control is a crucial ingredient for circuit quantum electrodynamics (cQED) systems. So far, it has been a challenge to implement this technology with the high coherence 3D cQED architecture. In this paper, we control the magnetic field inside a superconducting waveguide cavity using a magnetic hose, which allows flux control of 3...

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...

In this work, we propose how to load and manipulate chiral states in a Josephson junction ring in the so called transmon regimen. We characterise these states by their symmetry properties under time reversal and parity transformations. We describe an explicit protocol to load and detect the states within a realistic set of circuit parameters and sh...

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...

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 inte...

The quantum wavefunction, despite continuous debates on its exact physical interpretation, is a fundamental concept in quantum physics and a useful tool to describe and simulate the state of a quantum system. While wavefunctions usually are not considered to be directly observable, in this work we show how the wavefunction of a single photon can be...

The possibility to operate massive mechanical resonators in the quantum regime has become central in fundamental sciences, in particular to test the boundaries of quantum mechanics. Optomechanics, where photons (e.g. optical, microwave) are coupled to mechanical motion, provide the tools to control mechanical motion near the fundamental quantum lim...

Qubits cannot exist without nonlinearity, but nonlinear elements in superconducting circuits lead to losses. A superconducting qubit has now been realized by nonlinearly coupling two microwave resonators, offering the promise of long coherence times.

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...

We propose a setup based on (solid-state) qubits coupled to a common multimode 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 nonlocal quantum gates, the simulation of...

Elektrische Halbleiterdioden sind ein Grundbaustein für alle Prozessoren oder Leuchtdioden. Deshalb findet man Dioden heutzutage in fast allen elektrischen Geräten. Sie fungieren als elektrische Einbahnstraßen, da sie den Stromfluss in eine Richtung zulassen und in die andere Richtung unterbinden. In vielen elektronischen Bausteinen spielen auch Ma...

Fast magnetic flux control is a crucial ingredient for circuit quantum electrodynamics (cQED) systems. So far it has been a challenge to implement this technology with the high coherence 3D cQED architecture. In this paper we control the magnetic field inside a superconducting waveguide cavity using a magnetic hose, which allows fast flux control o...

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...

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 distan...

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. Here we theoretically and experimentally show that a linear and isotropic electrically condu...

We present an experimental investigation of the switching dynamics of a stochastic bistability in a 1000 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 drive strength of only a few photons. We meas...

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 te...

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 res...

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 freq...

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 i...

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...

Die Kopplung von Quibits an Mikrowellenresonatoren ermöglicht eine hervorragende Kontrolle von Quantenzuständen. In Experimenten an der Universität Yale ist es jetzt gelungen, die Quanteninformation eines einzelnen supraleitenden Quantenbits auf ein Ensemble von Mikrowellenphotonen, die sich in einem Schrödinger-Katzen-Zustand befinden, zu übertrag...

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 stat...

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 by using a superconducting transmon
qubit coupled to a waveguide cavity resonator with a highly ideal off-resonant coupling. This disp...

We propose a new method to autonomously correct for errors of a logical qubit
induced by energy relaxation. This scheme encodes the logical qubit as a
multi-component superposition of coherent states in a harmonic oscillator, more
specifically a cavity mode. The sequences of encoding, decoding and correction
operations employ the non-linearity prov...

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,...

Off-resonant coupling of a superconducting transmon qubit to a
three-dimensional waveguide cavity provides a dispersive qubit/cavity
interaction much stronger than any decay rates in the system. Using a
two-cavity/single-qubit architecture, we utilize this interaction to
deterministically map a qubit state to a superposition of coherent
states in a...

Significant progress has recently been made in improving the coherence
of superconducting qubits by using the 3D cQED architecture. This
current design is static, not allowing for the modulation of couplings
and nonlinearities in situ. This limitation may prove to be an obstacle
toward scaling this implementation into more complex systems. We prese...

The ability to control the frequency of a superconducting qubit on
nanosecond timescales has been used, among other things, to generate
multi-qubit entanglement. The recently developed 3D cQED architecture
has yielded dramatic coherence improvements and novel methods of
entangling fixed-tuned qubits, but has until now has lacked the ability
to cont...

We demonstrate a new all-microwave controlled phase entangling gate for
the superconducting qubits in the three-dimensional circuit QED (3D
cQED) architecture. The gate exploits the strong coupling between qubits
and a cavity, wherein the cavity frequency dispersively shifts depending
on the qubit register state. We off-resonantly displace the cavi...

Typically, models of qubit-cavity interactions in superconducting
circuits have included terms strictly linear in amplitude of the cavity
modes. Due to ever-increasing experimental ability to realize larger
coupling strengths, induced nonlinearities in the cavity contribute
significantly to the dynamics and thus need to be accounted for. Such
nonli...

With trapped ions quantum information can be encoded in various two-level systems or quantum bits (qubits). Here, we present an overview on qubit encoding with Ca + and several state-of-the-art operations involving two and three qubits. The use of decoherence-free subspaces and encoding logical qubits using two physical qubits may offer an advantag...

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 \textit{i...

We introduce a new gate that transfers an arbitrary state of a qubit into a
superposition of two quasi-orthogonal coherent states of a cavity mode, 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 qu...

We present a semi-classical 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 multi-mode physics, is...

Superconducting transmon qubits have recently been studied within 3D
cavities. In addition to increasing the coherence times of the qubits
this has enabled a simple scheme for varying the quality factor Q (or
decay rate κ) of a cavity in situ. This decay rate plays an
important role in our understanding of a number of effects in circuit
quantum ele...

The design parameters of superconducting qubits inside resonant cavities
have evolved over time to minimize decoherence, allow fast pulses and
enable high fidelity readout. The two are often coupled so strongly that
the dispersive shift of the qubit due to a single photon in the cavity
(or AC Stark shift) is much larger than a linewidth. In this st...

Circuit QED employs the coupling of nonlinear elements to resonant modes
of an electronic circuit. We demonstrate that all resonant modes will
attain some degree of nonlinearity from even a single nonlinear element.
This can result in individually addressable transitions for each mode
and allow direct control of each quantum state. Furthermore, we...

Current research in superconducting circuit QED is working towards
combining an increasing number of cavities and qubits to investigate
larger scale quantum systems. Here we will discuss measurements on a
system consisting of two three-dimensional microwave resonators coupled
to a single transmon qubit. We demonstrate that each mode of the system
h...

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 archit...

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. With sequences of up to 100 gates and 6 qubits, the full time dynamics of a range of spin systems are digitally simu...

We studied the coherence times of transmon qubits using three-dimensional resonators. The three-dimensional (3D) superconducting resonant cavity is machined with aluminum alloy, whose quality factor is higher than 5 million at 10 mK inside a magnetic shield. The transmons are fabricated on sapphire substrates whose internal Q was not lower than 2 m...

The transmon is a simple superconducting qubit which has less dependence on the usual sources of 1/f noise, and has coherence which is mostly limited by a source of anomalous dissipation. The quality factors of transmon qubits on sapphire are observed to be ˜ 50,000, similar to that of transmission line resonators made with the same geometry. It is...

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...

Coupling internal and vibrational states of a string of trapped ions has proven to be an effective way of entangling the ions' internal states. This mechanism can be used for high-fidelity quantum gates, QND measurements of spin correlations and creation of large entangled states. However, spin-motion interactions are also of interest for the purpo...

We experimentally demonstrate a quantum walk on a line in phase space using one and two trapped ions. A walk with up to 23 steps is realized by subjecting an ion to state-dependent displacement operations interleaved with quantum coin tossing operations. To analyze the ion's motional state after each step we apply a technique that directly maps the...

A basic assumption behind the inequalities used for testing noncontextual hidden variable models is that the observables measured on the same individual system are perfectly compatible. However, compatibility is not perfect in actual experiments using sequential measurements. We discuss the resulting “compatibility loophole” and present several met...

The Dirac equation successfully merges quantum mechanics with special relativity. It provides a natural description of the electron spin, predicts the existence of antimatter and is able to reproduce accurately the spectrum of the hydrogen atom. The realm of the Dirac equation-relativistic quantum mechanics-is considered to be the natural transitio...

Laser-ion interactions that collectively couple the pseudo-spins of a string of trapped ions to one of the string's vibrational modes have been used by us to entangle a pair of 40Ca+ ions with very high fidelity. This gate mechanism allows for entangling ions without having recourse to ground state cooling. This opens the way to performing an entan...

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. Along this line, some types of hidden variable models ha...

We give a detailed description of the implementation of a Molmer-Sorensen gate entangling two Ca+ ions using a bichromatic laser beam near-resonant with a quadrupole transition. By amplitude pulse shaping and compensation of AC-Stark shifts we achieve a fast gate operation without compromising the error rate. Subjecting different input states to co...

We report on the first absolute transition frequency measurement at the 10;{-15} level with a single, laser-cooled 40Ca+ ion in a linear Paul trap. For this measurement, a frequency comb is referenced to the transportable Cs atomic fountain clock of LNE-SYRTE and is used to measure the 40Ca+ 4s ;{2}S_{1/2}-3d ;{2}D_{5/2} electric-quadrupole transit...

In an experiment using the odd calcium isotope Ca+43 , we combine the merits of a high-fidelity entangling operation on an optical transition (optical qubit) with the long coherence times of two ``clock'' states in the hyperfine ground state (hyperfine qubit) by mapping between these two qubits. For state initialization, state detection, global qub...

We report on an absolute frequency measurement with a single 40Ca+ ion in a linear Paul trap. A frequency comb referenced to the transportable Cs atomic fountain clock of LNE-SYRTE is used to measure the frequency of a laser exciting the 40Ca+ 4s 2S1/2 - 3d 2D5/2 electric-quadrupole transition. A transition frequency of nu_Ca+ = 411 042 129 776 393...

We report on the first absolute transition frequency measurement at the 10-15 level with a single, laser-cooled Ca+40 ion in a linear Paul trap. For this measurement, a frequency comb is referenced to the transportable Cs atomic fountain clock of LNE-SYRTE and is used to measure the Ca+40 4sS1/22-3dD5/22 electric-quadrupole transition frequency. Af...

We perform precision measurements of the branching
ratios of the 4p 2P3/2 level decay of a single
40Ca+ ion suspended in a linear Paul trap. High precision
is achieved by a novel technique based on monitoring the
population transfer when repeatedly pumping the ion between
different internal states. The branching fractions into the
4s 2S1/2, 3d 2D5/...