arXiv subjects

L. Steffen

Publications and source records attributed to L. Steffen.

At least 19 recordsLinked to original sources

arXiv2013

Exploring the Effect of Noise on the Berry Phase

We make use of a superconducting qubit to study the effects of noise on adiabatic geometric phases. The state of the system, an effective spin one-half particle, is adiabatically guided along a closed path in parameter space and thereby acquires a geometric phase. By introducing artificial fluctuations in the control parameters, we measure the geometric contribution to dephasing for a variety of noise powers and evolution times. Our results clearly show that only fluctuations which distort the path lead to geometric dephasing. In a direct comparison with the dynamic phase, which is path-independent, we observe that the adiabatic geometric phase is less affected by noise-induced dephasing. This observation directly points towards the potential of geometric phases for quantum gates or metrological applications.

quant-ph↗

arXiv2013

Realization of Deterministic Quantum Teleportation with Solid State Qubits

Transferring the state of an information carrier from a sender to a receiver is an essential primitive in both classical and quantum communication and information processing. In a quantum process known as teleportation the unknown state of a quantum bit can be relayed to a distant party using shared entanglement and classical information. Here we present experiments in a solid-state system based on superconducting quantum circuits demonstrating the teleportation of the state of a qubit at the macroscopic scale. In our experiments teleportation is realized deterministically with high efficiency and achieves a high rate of transferred qubit states. This constitutes a significant step towards the realization of repeaters for quantum communication at microwave frequencies and broadens the tool set for quantum information processing with superconducting circuits.

quant-ph↗

arXiv2013

Probing Correlations, Indistinguishability and Entanglement in Microwave Two-Photon Interference

Interference at a beam splitter reveals both classical and quantum properties of electromagnetic radiation. When two indistinguishable single photons impinge at the two inputs of a beam splitter they coalesce into a pair of photons appearing in either one of its two outputs. This effect is due to the bosonic nature of photons and was first experimentally observed by Hong, Ou, and Mandel (HOM) [1]. Here, we present the observation of the HOM effect with two independent single-photon sources in the microwave frequency domain. We probe the indistinguishability of single photons, created with a controllable delay, in time-resolved second-order cross- and auto-correlation function measurements. Using quadrature amplitude detection we are able to resolve different photon numbers and detect coherence in and between the output arms. This measurement scheme allows us to observe the HOM effect and, in addition, to fully characterize the two-mode entanglement of the spatially separated beam splitter output modes. Our experiments constitute a first step towards using two-photon interference at microwave frequencies for quantum communication and information processing, e.g. for distributing entanglement between nodes of a quantum network [2, 3] and for linear optics quantum computation [4, 5].

quant-ph↗

arXiv2012

Geometric phases in superconducting qubits beyond the two-level-approximation

Geometric phases, which accompany the evolution of a quantum system and depend only on its trajectory in state space, are commonly studied in two-level systems. Here, however, we study the adiabatic geometric phase in a weakly anharmonic and strongly driven multi-level system, realised as a superconducting transmon-type circuit. We measure the contribution of the second excited state to the two-level geometric phase and find good agreement with theory treating higher energy levels perturbatively. By changing the evolution time, we confirm the independence of the geometric phase of time and explore the validity of the adiabatic approximation at the transition to the non-adiabatic regime.

quant-ph↗

arXiv2012

Experimental Monte Carlo Quantum Process Certification

Experimental implementations of quantum information processing have now reached a level of sophistication where quantum process tomography is impractical. The number of experimental settings as well as the computational cost of the data post-processing now translates to days of effort to characterize even experiments with as few as 8 qubits. Recently a more practical approach to determine the fidelity of an experimental quantum process has been proposed, where the experimental data is compared directly to an ideal process using Monte Carlo sampling. Here we present an experimental implementation of this scheme in a circuit quantum electrodynamics setup to determine the fidelity of two qubit gates, such as the cphase and the cnot gate, and three qubit gates, such as the Toffoli gate and two sequential cphase gates.

quant-ph↗

arXiv2011

Geometric Phase and Non-Adiabatic Effects in an Electronic Harmonic Oscillator

Steering a quantum harmonic oscillator state along cyclic trajectories leads to a path-dependent geometric phase. Here we describe an experiment observing this geometric phase in an electronic harmonic oscillator. We use a superconducting qubit as a non-linear probe of the phase, otherwise unobservable due to the linearity of the oscillator. Our results demonstrate that the geometric phase is, for a variety of cyclic trajectories, proportional to the area enclosed in the quadrature plane. At the transition to the non-adiabatic regime, we study corrections to the phase and dephasing of the qubit caused by qubit-resonator entanglement. The demonstrated controllability makes our system a versatile tool to study adiabatic and non-adiabatic geometric phases in open quantum systems and to investigate the potential of geometric gates for quantum information processing.

quant-ph↗

arXiv2011

Benchmarking a Teleportation Protocol realized in Superconducting Circuits

Teleportation of a quantum state may be used for distributing entanglement between distant qubits in quantum communication and for quantum computation. Here we demonstrate the implementation of a teleportation protocol, up to the single-shot measurement step, with superconducting qubits coupled to a microwave resonator. Using full quantum state tomography and evaluating an entanglement witness, we show that the protocol generates a genuine tripartite entangled state of all three-qubits. Calculating the projection of the measured density matrix onto the basis states of two qubits allows us to reconstruct the teleported state. Repeating this procedure for a complete set of input states we find an average output state fidelity of 88%.

quant-ph↗

arXiv2011

Preparation of Subradiant States using Local Qubit Control in Circuit QED

Transitions between quantum states by photon absorption or emission are intimately related to symmetries of the system which lead to selection rules and the formation of dark states. In a circuit quantum electrodynamics setup, in which two resonant superconducting qubits are coupled through an on-chip cavity and driven via the common cavity field, one single-excitation state remains dark. Here, we demonstrate that this dark state can be excited using local phase control of individual qubit drives to change the symmetry of the driving field. We observe that the dark state decay via spontaneous emission into the cavity is suppressed, a characteristic signature of subradiance. This local control technique could be used to prepare and study highly correlated quantum states of cavity-coupled qubits.

quant-ph↗

arXiv2011

Observation of Resonant Photon Blockade at Microwave Frequencies using Correlation Function Measurements

Creating a train of single photons and monitoring its propagation and interaction is challenging in most physical systems, as photons generally interact very weakly with other systems. However, when confining microwave frequency photons in a transmission line resonator, effective photon-photon interactions can be mediated by qubits embedded in the resonator. Here, we observe the phenomenon of photon blockade through second-order correlation function measurements. The experiments clearly demonstrate antibunching in a continuously pumped source of single microwave photons measured using microwave beam splitters, linear amplifiers, and quadrature amplitude detectors. We also investigate resonance fluorescence and Rayleigh scattering in Mollow-triplet-like spectra.

quant-ph↗

arXiv2011

Photon State Tomography for Two-Mode Correlated Itinerant Microwave Fields

Continuous variable entanglement between two modes of a radiation field is usually studied at optical frequencies. As an important step towards the observation of entanglement between propagating microwave photons we demonstrate the experimental state reconstruction of two field modes in the microwave domain. In particular, we generate two-mode correlated states with a Josephson parametric amplifier and detect all four quadrature components simultaneously in a two-channel heterodyne setup using amplitude detectors. Analyzing two-dimensional phase space histograms for all possible pairs of quadratures allows us to determine the full covariance matrix and reconstruct the four-dimensional Wigner function. We demonstrate strong correlations between the quadrature amplitude noise in the two modes. Under ideal conditions two-mode squeezing below the standard quantum limit should be observable in future experiments.

quant-ph↗

arXiv2010

Experimental Tomographic State Reconstruction of Itinerant Microwave Photons

A wide range of experiments studying microwave photons localized in superconducting cavities have made important contributions to our understanding of the quantum properties of radiation. Propagating microwave photons, however, have so far been studied much less intensely. Here we present measurements in which we reconstruct the Wigner function of itinerant single photon Fock states and their superposition with the vacuum using linear amplifiers and quadrature amplitude detectors. We have developed efficient methods to separate the detected single photon signal from the noise added by the amplifier by analyzing the moments of the measured amplitude distribution up to 4th order. This work is expected to enable studies of propagating microwaves in the context of linear quantum optics.

quant-ph↗

arXiv2010

Multi-mode mediated exchange coupling in cavity QED

Microwave cavities with high quality factors enable coherent coupling of distant quantum systems. Virtual photons lead to a transverse exchange interaction between qubits, when they are non-resonant with the cavity but resonant with each other. We experimentally probe the inverse scaling of the inter-qubit coupling with the detuning from a cavity mode and its proportionality to the qubit-cavity interaction strength. We demonstrate that the enhanced coupling at higher frequencies is mediated by multiple higher-harmonic cavity modes. Moreover, in the case of resonant qubits, the symmetry properties of the system lead to an allowed two-photon transition to the doubly excited qubit state and the formation of a dark state.

quant-ph↗

arXiv2010

Quantum-to-Classical Transition in Cavity Quantum Electrodynamics

The quantum properties of electromagnetic, mechanical or other harmonic oscillators can be revealed by investigating their strong coherent coupling to a single quantum two level system in an approach known as cavity quantum electrodynamics (QED). At temperatures much lower than the characteristic energy level spacing the observation of vacuum Rabi oscillations or mode splittings with one or a few quanta asserts the quantum nature of the oscillator. Here, we study how the classical response of a cavity QED system emerges from the quantum one when its thermal occupation -- or effective temperature -- is raised gradually over 5 orders of magnitude. In this way we explore in detail the continuous quantum-to-classical crossover and demonstrate how to extract effective cavity field temperatures from both spectroscopic and time-resolved vacuum Rabi measurements.

quant-ph↗

arXiv2010

Control and Tomography of a Three Level Superconducting Artificial Atom

A number of superconducting qubits, such as the transmon or the phase qubit, have an energy level structure with small anharmonicity. This allows for convenient access of higher excited states with similar frequencies. However, special care has to be taken to avoid unwanted higher-level populations when using short control pulses. Here we demonstrate the preparation of arbitrary three-level superposition states using optimal control techniques in a transmon. Performing dispersive read-out we extract the populations of all three levels of the qutrit and study the coherence of its excited states. Finally we demonstrate full quantum state tomography of the prepared qutrit states and evaluate the fidelities of a set of states, finding on average 96%.

quant-ph↗

arXiv2010

Measurements of the Correlation Function of a Microwave Frequency Single Photon Source

At optical frequencies the radiation produced by a source, such as a laser, a black body or a single photon source, is frequently characterized by analyzing the temporal correlations of emitted photons using single photon counters. At microwave frequencies, however, there are no efficient single photon counters yet. Instead, well developed linear amplifiers allow for efficient measurement of the amplitude of an electromagnetic field. Here, we demonstrate how the properties of a microwave single photon source can be characterized using correlation measurements of the emitted radiation with such detectors. We also demonstrate the cooling of a thermal field stored in a cavity, an effect which we detect using a cross-correlation measurement of the radiation emitted at the two ends of the cavity.

cond-mat.mes-hall↗

arXiv2009

Cavity QED with separate photon storage and qubit readout modes

We present the realization of a cavity quantum electrodynamics setup in which photons of strongly different lifetimes are engineered in different harmonic modes of the same cavity. We achieve this in a superconducting transmission line resonator with superconducting qubits coupled to the different modes. One cavity mode is strongly coupled to a detection line for qubit state readout, while a second long lifetime mode is used for photon storage and coherent quantum operations. We demonstrate sideband based measurement of photon coherence, generation of n photon Fock states and the scaling of the sideband Rabi frequency with the square root of n using a scheme that may be extended to realize sideband based two-qubit logic gates.

cond-mat.mes-hall↗

arXiv2009

Thermal Excitation of Multi-Photon Dressed States in Circuit Quantum Electrodynamics

The exceptionally strong coupling realizable between superconducting qubits and photons stored in an on-chip microwave resonator allows for the detailed study of matter-light interactions in the realm of circuit quantum electrodynamics (QED). Here we investigate the resonant interaction between a single transmon-type multilevel artificial atom and weak thermal and coherent fields. We explore up to three photon dressed states of the coupled system in a linear response heterodyne transmission measurement. The results are in good quantitative agreement with a generalized Jaynes-Cummings model. Our data indicates that the role of thermal fields in resonant cavity QED can be studied in detail using superconducting circuits.

cond-mat.mes-hall↗

arXiv2009

Dynamics of dispersive single qubit read-out in circuit quantum electrodynamics

The quantum state of a superconducting qubit nonresonantly coupled to a transmission line resonator can be determined by measuring the quadrature amplitudes of an electromagnetic field transmitted through the resonator. We present experiments in which we analyze in detail the dynamics of the transmitted field as a function of the measurement frequency for both weak continuous and pulsed measurements. We find excellent agreement between our data and calculations based on a set of Bloch-type differential equations for the cavity field derived from the dispersive Jaynes-Cummings Hamiltonian including dissipation. We show that the measured system response can be used to construct a measurement operator from which the qubit population can be inferred accurately. Such a measurement operator can be used in tomographic methods to reconstruct single and multiqubit states in ensemble-averaged measurements.

cond-mat.mes-hall↗