Metastable Flux States Research Articles

Initializing the flux state of multiwell inductively isolated Josephson junction qubits

We describe a technique for initializing the flux state of an inductively isolated Josephson junction, fulfilling an essential requirement for using the device as a qubit. By oscillating the applied magnetic flux with a specified amplitude and offset, we can select any of the allowed long-lived metastable flux states. We applied this technique to $\mathrm{Nb}\text{\ensuremath{-}}{\mathrm{Al}}_{2}{\mathrm{O}}_{3}\text{\ensuremath{-}}\mathrm{Nb}$ and $\mathrm{Al}\text{\ensuremath{-}}{\mathrm{Al}}_{2}{\mathrm{O}}_{3}\text{\ensuremath{-}}\mathrm{Al}$ devices with from 10 to over 100 distinct flux states at temperatures as low as $25\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$. In a ten-state system with an initial probability $p=0.13$ to be in the desired flux state, we achieved $p=0.999\phantom{\rule{0.2em}{0ex}}96$ after 50 oscillations at $22.6\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$. The technique is generally applicable to other systems with multiple metastable wells (including rf SQUIDs), requires no additional readout or bias lines, involves minimal energy dissipation, and appears to scale favorably with the number of qubits.

Macroscopic quantum device based on a rf SQUID system

The growing amount of theoretical interest in the area of quantum computing have stimulated in recent years research with the aim of developing a corresponding technology. Superconducting Josephson systems appear to be among the most promising candidates. We present the characterization of a fully integrated Josephson device consisting of an RF SQUID coupled to a readout system based on a dc SQUID sensor. We report measurements of the dc SQUID performances showing a high intrinsic responsivity and a low flux noise, giving a good signal to noise ratio in the small signal mode. In the classical regime data on the decay rate from the metastable flux states of RF SQUID are also reported. The low dissipation level and the good insulation of the probe from the external noise are encouraging in view of macroscopic quantum experiments. Work is in progress to improve the design of the device to increase its application capability toward the quantum regime.

Measurement of the effective dissipation in an rf SQUID system

We present an experimental study of the effective dissipation of a fully integrated ${\mathrm{N}\mathrm{b}/\mathrm{A}\mathrm{l}\mathrm{O}}_{x}/\mathrm{Nb}$ Josephson device consisting of a rf superconducting quantum interference device (SQUID) coupled to a readout system based on a dc SQUID sensor. In the classical regime data on the decay rate from the metastable flux states of rf SQUID are reported. The low dissipation level and the good insulation of the probe from the external noise are encouraging in view of building a macroscopic quantum device.

RF SQUID BASED DEVICES FOR MQC

We present different types of integrated planar SQUID devices in view of Macroscopic Quantum Coherence (MQC) experiments. These devices include an rf SQUID as a probe to test the MQC, coupled to a readout system based on a dc SQUID sensor. Both dc SQUID and flux transformer are in a gradiometric configuration to minimize the electromagnetic noise from environment. We report data on dc SQUID performances as well as preliminary results on the decay from the metastable flux state for rf SQUID-based devices above the crossover temeperature (classical limit).

Rf SQUID system for macroscopic quantum coherence experiments

We present the design of an integrated planar SQUID device in view of macroscopic quantum coherence (MQC) experiments. This device is made up by an rf SQUID, as a probe to test the MQC, and a readout system based on a dc SQUID sensor coupled to the probe. To minimize the electromagnetic noise from environment, gradiometric configuration of rf SQUID, dc SQUID and a flux transformer is included. Preliminary results on the decay from the metastable flux state for different rf SQUID-based devices in the classical limit are shown.

Josephson device for quantum experiments

We present the characterization of a fully integrated Josephson device consisting of a rf-superconducting quantum interference device (SQUID) coupled to a readout system based on a dc SQUID sensor. Particular care in the design is devoted to minimize the electromagnetic noise coming from the environment. We report data on dc SQUID performances as well as on the decay rate from metastable flux states of the rf SQUID in the classical regime. The low dissipation level and the good insulation of the probe from the external noise are encouraging in view of macroscopic quantum experiments.

Measurements of thermal switching between metastable flux states in a RF-SQUID with intermediate damping

Abstract Josephson devices and, in particular, RF-SQUIDs are ideal systems to test quantum phenomena at macroscopic level. In the view of an experiment of macroscopic quantum coherence, as a preliminary test we developed and fabricated on the same chip a set of thin-film RF-SQUIDs shunted with thin-film resistors of different values, to investigate the behavior of the RF-SQUIDs in different dissipation regimes. Here we present measurements on a moderately damped RF-SQUID, shunted with an 11 Ω resistor. In function of the temperature, we recorded the RF-SQUID characteristics (total magnetic flux vs applied magnetic flux) and studied the statistical distribution of the flux values at which the RF-SQUID switches from one metastable flux state to another. The RF-SQUID is read-out by a DC-SQUID integrated on the same chip.

Magnetic flux transitions in superconducting loops closed with a low-capacitance Josephson junction due to thermal activation

Superconducting rings that are interrupted by a weak superconducting junction can attain two different metastable flux states when they are placed in a magnetic field of appropriate strength. In this article we present the measurements of the mean lifetime of the flux states in the double well potential as a function of the temperature for two types of weak link devices, the evaporated planar ring and the point-contact device. It appears that the transition probability is too small compared to the classical activation theory of Kramers and its modern quantum versions. Two possible explanations of this discrepancy are discussed: (1) the adiabatic instead of isothermal behaviour during the stochastical flux transitions and (2) deviations from the sinusoidal supercurrent-phase relation. Another result obtained from our measurements is the deviation of the mean lifetimes over the flux states as a function of the applied magnetic flux from the quasi-Boltzmann distribution. It appears that this problem can be solved experimentally by using specially designed microwave filters.

Thermal activation in the quantum regime and macroscopic tunnelling in the thermal regime in a metabistable system consisting of a superconducting ring interrupted by a weak junction: Part III: Macroscopic quantum tunnelling in the thermal regime

When an external magnetic flux close to half a flux quantum is applied to a superconducting ring containing a weak superconducting junction, a SQUID, there can exist two metastable magnetic flux states by a potential energy barrier. If the junction has a sufficiently small capacitance, at very low temperatures intrinsic stochastic magnetic flux transitions due to macroscopic quantum tunnelling from one metastable flux state into another and vice versa are observed. Experiments are described showing macroscopic quantum tunnelling effects in an evaporated Nb device performed in a glass dilution refrigerator. A statistical analysis of the sampled data is made showing the measured distribution of the flux transitions in agreement with a pure stochastic transition process with a Poisson distribution. The measurements of the mean lifetimes are — in two ways — out of keeping with the theoretical predictions of the dissipative two-state Boson model. Firstly, although at fixed temperature the mean lifetime depends exponentially on the bias in the potential energy, a thermal quasi-Boltzmann distribution has not been found. Secondly, the mean lifetime of the two flux states in case of zero bias, symmetrical potential energy, does not clearly show the predicted T 1−2α dependence. It is conjectured that the system may not behave perfectly isothermal, because when a flux transition takes place between the metastable potential wells some energy will be dissipated possibly causing a temporary temperature rise due to self-heating. This effect is discussed in part II in relation with the data of the thermal activation experiments obtained with the same type of devices.

Exactly solvable model for thermal activation and quantum tunneling in Ohmic systems.

Combining Kramers's energy diffusion (at temperature T ) with dissipative quantum tunneling (through a parabolic potential-energy barrier with curvature frequency ${\ensuremath{\omega}}_{b}$ and height ${U}_{b}$), a model for a localized metastable state (with harmonic frequency ${\ensuremath{\omega}}_{0}$) is formulated and solved exactly for its quasiequilibrium distribution \ensuremath{\rho}(E) and its decay rate \ensuremath{\Gamma}. It is shown that \ensuremath{\rho} remains locally extremely close to (although it essentially differs from) the Boltzmann distribution, unless the Ohmic friction coefficient \ensuremath{\lambda} is extremely small (of order \ensuremath{\Gamma}). Excluding this latter possibility, the ensuing decay rate is discussed for various temperature and friction regimes. It is shown to comprise several known results as special cases. First, an extended version of Bell's formula is shown to be valid in the strong-to-moderate friction regime. It involves the recently discovered crossover between thermal hopping and quantum tunneling at temperature ${T}_{0}$=\ensuremath{\Elzxh}\ensuremath{\kappa}${\ensuremath{\omega}}_{b}$/2\ensuremath{\pi}${k}_{B}$ (where \ensuremath{\kappa} is Kramers's viscosity correction factor). At high temperatures and very strong damping the result neatly reduces to Kramers's Smoluchovsky-limit formula. At zero temperature friction strongly suppresses the decay. Second, in the very weak friction regime \ensuremath{\Gamma} is shown to reduce to an extended version of Melnikov's formula. At high temperatures it equals Kramers's small-viscosity result, whereas at zero temperature and zero damping it attains the expected quantum value, the crossover again being at ${T}_{0}$. Third, in the classical limit (\ensuremath{\Elzxh}\ensuremath{\rightarrow}0) an extended version of B\"uttiker, Harris, and Landauer's [Phys. Rev. B 28, 1268 (1983)] result is recovered, now valid for any value of the damping. Finally, some remarks are made in relation to recent cryogenic measurements on metastable flux states.

Macroscopic quantum tunnelling in the r.f. SQUID with S-c-S point contacts

The experimental results on quantum decay of metastable flux states in the r.f. SQUID containing different S-c-S point contacts as the weak link are compared with various theoretical models. The formulae following from the RSJ model with weak and strong damping and the microscopic treatment of quantum effects in S-c-S junctions are analysed. It is concluded that only the latter theory provides a quantitative agreement with the experimental values.

Metabistability in superconducting rings interrupted by a weak junction

Under certain circumstances a superconducting ring containing a weak superconducting junction (a SQUID) has two metastable magnetic flux states separated by a potential barrier when an external magnetic field is applied of appropriate strength. If the junction has a small capacitance, even at low temperatures where kT is very much smaller than the barrier height ΔU intrinsic magnetic flux transitions are observed from one metastable flux state into an other and vice versa, or in other words a weak “persistent supercurrent” switches stochastically from one direction into the opposite. This flux transition mechanism at very low temperatures might be interpreted as due to macroscopic quantum tunnelling, a new macroscopic quantum effect.

On the conditional transition probabilities of the magnetic flux at low temperatures in a superconducting loop closed with a low-capacitance superconducting point contact

Abstract The conditional transition probabilities of the magnetic flux in a superconducting ring containing a weak link have been determined experimentally. We investigated earlier [1] the behaviour of the embraced magnetic flux as a function of the external magnetic field and time in situations in which the system could jump from a metastable flux state into another flux state and vice versa by classical thermal fluctuations over, or by quantum mechanical tunnelling through a potential barrier separating both flux states, depending on the temperature. For these low capacitance point contacts it was shown that stochastic, macroscopic quantum tunnelling could become dominant at lower temperatures. In order to investigate macroscopic quantum tunnelling in more detail we measured the conditional transition probabilities as a function of time for our devices and found an exponential phase incoherent behaviour, indicating that the phase relationship between the amplitudes for being on the different sides of the barrier can be neglected.