Michael Marthaler

Stabilizing the magnetic moment of single holmium atoms by symmetry

Single magnetic atoms, and assemblies of such atoms, on non-magnetic surfaces have recently attracted attention owing to their potential use in high-density magnetic data storage and as a platform for quantum computing. A fundamental problem resulting from their quantum mechanical nature is that the localized magnetic moments of these atoms are easily destabilized by interactions with electrons, nuclear spins and lattice vibrations of the substrate. Even when large magnetic fields are applied to stabilize the magnetic moment, the observed lifetimes remain rather short (less than a microsecond). Several routes for stabilizing the magnetic moment against fluctuations have been suggested, such as using thin insulating layers between the magnetic atom and the substrate to suppress the interactions with the substrate’s conduction electrons, or coupling several magnetic moments together to reduce their quantum mechanical fluctuations. Here we show that the magnetic moments of single holmium atoms on a highly conductive metallic substrate can reach lifetimes of the order of minutes. The necessary decoupling from the thermal bath of electrons, nuclear spins and lattice vibrations is achieved by a remarkable combination of several symmetries intrinsic to the system: time reversal symmetry, the internal symmetries of the total angular momentum and the point symmetry of the local environment of the magnetic atom.

Implementation of a quantum metamaterial using superconducting qubits

The key issue for the implementation of a metamaterial is to demonstrate the existence of collective modes corresponding to coherent oscillations of the meta-atoms. Atoms of natural materials interact with electromagnetic fields as quantum two-level systems. Artificial quantum two-level systems can be made, for example, using superconducting nonlinear resonators cooled down to their ground state. Here we perform an experiment in which 20 of these quantum meta-atoms, so-called flux qubits, are embedded into a microwave resonator. We observe the dispersive shift of the resonator frequency imposed by the qubit metamaterial and the collective resonant coupling of eight qubits. The realized prototype represents a mesoscopic limit of naturally occurring spin ensembles and as such we demonstrate the AC-Zeeman shift of a resonant qubit ensemble. The studied system constitutes the implementation of a basic quantum metamaterial in the sense that many artificial atoms are coupled collectively to the quantized mode of a photon field.

Bidirectional Single-Electron Counting and the Fluctuation Theorem

We investigate theoretically and experimentally the full counting statistics of bidirectional singleelectron tunneling through a double quantum dot in a GaAs/GaAlAs heterostructure and compare with predictions of the fluctuation theorem (FT) for Markovian stochastic processes. We observe that the quantum point contact electrometer used to study the transport induces nonequilibrium shot noise and dot-level fluctuations and strongly modifies the tunneling statistics. As a result, the FT appears to be violated. We show that it is satisfied if the back-action of the electrometer is taken into account, and we provide a quantitative estimate of this effect. PACS numbers: 73.23.-b,73.23.Hk,72.70.+m,05.70.Ln According to the second law of thermodynamics, the entropy of a macroscopic system driven out of equilibrium increases with time until equilibrium is reached. Thus the dynamics of such a system is irreversible. In contrast, for a mesoscopic system performing a random trajectory in phase space and measured during a sufficiently short time, the entropy may either increase or decrease. The ‘Fluctuation Theorem’ (FT), which relies only on the microreversiblity of the underlying equation of motion, states that the probability distribution P�(�S) for processes increasing or decreasing the en= (�)=  

Irreversibility on the Level of Single-Electron Tunneling

We present a low-temperature experimental test of the fluctuation theorem for electron transport through a double quantum dot. The rare entropy-consuming system trajectories are detected in the form of single charges flowing against the source-drain bias by using time-resolved charge detection with a quantum point contact. We find that these trajectories appear with a frequency that agrees with the theoretical predictions even under strong nonequilibrium conditions, when the finite bandwidth of the charge detection is taken into account. The second law of thermodynamics states that a macroscopic system out of thermal equilibrium will irreversibly move toward equilibrium driven by a steady increase of its entropy. This macroscopic irreversibility occurs despite the time-reversal symmetry of the underlying microscopic equations of motion. Also, a microscopic system will undergo an irreversible evolution on a long time scale, but, over a sufficiently short observation time � , both entropy-producing trajectories as well as their timereversed entropy-consuming counterparts occur. It is only because of the statistics of these occurrences that a longterm irreversible evolution is established. This phenomenon is described by the fluctuation theorem [1,2]. Irrespective of the description of the trajectories being system-specific, the fluctuation theorem (FT) relates the probabilities P� ð� SÞ for processes that change the entropy

Multistability and switching in a superconducting metamaterial

The field of metamaterial research revolves around the idea of creating artificial media that interact with light in a way unknown from naturally occurring materials. This is commonly achieved using sub-wavelength lattices of electronic or plasmonic structures, so-called meta-atoms. One of the ultimate goals for these tailored media is the ability to control their properties in situ. Here we show that superconducting quantum interference devices can be used as fast, switchable meta-atoms. We find that their intrinsic nonlinearity leads to simultaneously stable dynamic states, each of which is associated with a different value and sign of the magnetic susceptibility in the microwave domain. Moreover, we demonstrate that it is possible to switch between these states by applying nanosecond-long pulses in addition to the microwave-probe signal. Apart from potential applications for this all-optical metamaterial switch, the results suggest that multistability can also be utilized in other types of nonlinear meta-atoms.The field of metamaterial research revolves around the idea of creating artificial media that interact with light in a way unknown from naturally occurring materials. This is commonly achieved by creating sub-wavelength lattices of electronic or plasmonic structures, so-called meta-atoms, that determine the interaction between light and metamaterial. One of the ultimate goals for these tailored media is the ability to control their properties in-situ which has led to a whole new branch of tunable and switchable metamaterials.1–4 Many of the present realizations rely on introducing microelectromechanical actuators or semiconductor elements into their meta-atom structures.3 Here we show that superconducting quantum interference devices (SQUIDs) can be used as fast, intrinsically switchable meta-atoms. We found that their intrinsic nonlinearity leads to simultaneously stable dynamic states, each of which is associated with a different value and sign of the magnetic susceptibility in the microwave domain. Moreover, we demonstrate that it is possible to switch between these states by applying a nanosecond long pulse in addition to the microwave probe signal. Apart from potential applications such as, for example, an all-optical metamaterial switch, these results suggest that multi-stability, which is a common feature in many nonlinear systems, can be utilized to create new types of meta-atoms.

Spin torque switching of an in-plane magnetized system in a thermally activated region

The current dependence of the exponent of the spin torque switching rate of an in-plane magnetized system was investigated by solving the Fokker-Planck equation with low temperature and small damping and current approximations. We derived the analytical expressions of the critical currents, I_{c} and I_{c}^{*}. At I_{c}, the initial state parallel to the easy axis becomes unstable, while at I_{c}^{*} (\simeq 1.27 I_{c}) the switching occurs without the thermal fluctuation. The current dependence of the exponent of the switching rate is well described by (1-I/I_{c}^{*})^{b}, where the value of the exponent b is approximately unity for I < I_{c}, while b rapidly increases up to 2.2 with increasing current for I_{c} < I < I_{c}^{*}. The linear dependence for I < I_{c} agrees with the other works, while the nonlinear dependence for I_{c} < I < I_{c}^{*} was newly found by the present work. The nonlinear dependence is important for analysis of the experimental results, because most experiments are performed in the current region of I_{c} < I < I_{c}^{*}.

Strong coupling of spin qubits to a transmission line resonator

We propose a mechanism for coupling spin qubits formed in double quantum dots to a superconducting transmission line resonator. Coupling the resonator to the gate controlling the interdot tunneling creates a spin qubit-resonator interaction with a strength of tens of MHz. This mechanism allows operating the system at a symmetry point where decoherence due to charge noise is minimized. The transmission line can serve as the shuttle, allowing for fast two-qubit operations including the generation of qubit-qubit entanglement and the implementation of a controlled-phase gate.

Multiphoton dressing of an anharmonic superconducting many-level quantum circuit

We report on the investigation of a superconducting anharmonic multilevel circuit that is coupled to a harmonic readout resonator. We observe multiphoton transitions via virtual energy levels of our system up to the fifth excited state. The back-action of these higher-order excitations on our readout device is analyzed quantitatively and demonstrated to be in accordance with theoretical expectation. By applying a strong microwave drive we achieve multiphoton dressing within our anharmonic circuit which is dynamically coupled by a weak probe tone. The emerging higher-order Rabi sidebands and associated Autler-Townes splittings involving up to five levels of the investigated anharmonic circuit are observed. Experimental results are in good agreement with master-equation simulations.

Switching via quantum activation: A parametrically modulated oscillator

We study switching between period-two states of an underdamped quantum oscillator modulated at nearly twice its natural frequency. For all temperatures and parameter values switching occurs via quantum activation: it is determined by diffusion over oscillator quasienergy, provided the relaxation rate exceeds the rate of interstate tunneling. The diffusion has quantum origin and accompanies relaxation to the stable state. We find the semiclassical distribution over quasienergy. For T=0, where the system has detailed balance, this distribution differs from the distribution for T{yields}0; the T=0 distribution is also destroyed by small dephasing of the oscillator. The characteristic quantum activation energy of switching displays a typical dependence on temperature and scaling behavior near the bifurcation point where period doubling occurs.

Concentric transmon qubit featuring fast tunability and an anisotropic magnetic dipole moment

We present a planar qubit design based on a superconducting circuit that we call concentric transmon. While employing a straightforward fabrication process using Al evaporation and lift-off lithography, we observe qubit lifetimes and coherence times in the order of 10us. We systematically characterize loss channels such as incoherent dielectric loss, Purcell decay and radiative losses. The implementation of a gradiometric SQUID loop allows for a fast tuning of the qubit transition frequency and therefore for full tomographic control of the quantum circuit. Due to the large loop size, the presented qubit architecture features a strongly increased magnetic dipole moment as compared to conventional transmon designs. This renders the concentric transmon a promising candidate to establish a site-selective passive direct Z coupling between neighboring qubits, being a pending quest in the field of quantum simulation.