Macroscopic Quantum Tunneling Rate Research Articles

Enhancement of macroscopic quantum tunneling in the higher-order phase switches of Bi2212 intrinsic Josephson junctions

The macroscopic quantum tunneling (MQT) in the current-biased intrinsic Josephson junctions (IJJs) of high-Tc cuprates has attracted much attention for decades. Although the MQT for the phase switches from the zero to the first voltage state (1st SW) in the multiple-branched I-V curves is well explained by the conventional theory, the occurrence of MQT for the higher order switches such as the switch from the 1st to 2nd voltage state (2nd SW) has been still debated. Here, we present an experimental study on the phase switches of small IJJs fabricated from underdoped Bi2Sr2(Ca,Y)Cu2Oy. We observed the single photon transition between quantized energy levels in the 3rd phase switches at 59.15 GHz and 2 K. The comparison with the previous studies on the nearly optimal-doped Bi2Sr2CaCu2Oy clearly suggests a possibility that the MQT rate for the higher-order phase switches is commonly enhanced by the effective suppression of the energy barrier for the higher-order phase escape due to the phase-running state after the 1st SW, in spite of the large difference in a critical current density and Tc.

Determination of the dissipation in superconducting Josephson junctions

The results relative to macroscopic quantum tunneling rate, out of the metastable state of Josephson junctions, are examined in view of determining the effect of dissipation. We adopt a simple criterion in accordance to which the effect of dissipation can be evaluated by analyzing the shortening of the semiclassical traversal time of the barrier. In almost all the considered cases, especially those with relatively large capacitance values, the relative time shortening turns out to be about 20% and with a corresponding quality factor Q ≃ 5.5. However, beyond the specific cases here considered, still in the regime of moderate dissipation, the method is applicable also to different situations with different values of the quality factor. The method allows, within the error limits, for a reliable determination of the load resistance RL, the less accessible quantity in the framework of the resistively and capacitively shunted junction model, provided that the characteristics of the junction (intrinsic capacitance, critical current, and the ratio of the bias current to the critical one) are known with sufficient accuracy.

Enhanced Macroscopic Quantum Tunneling in Capacitively Coupled BiPb2201 Single-Layered Intrinsic Josephson Junctions

Macroscopic quantum tunneling (MQT) in an intrinsic Josephson junction (IJJ) stack of Bi1.9Pb0.1Sr1.39La0.63CuO6+δ (BiPb2201) has been investigated. For the first switch, from superconducting to the first resistive branch in current–voltage characteristics, the crossover between MQT and thermal activation (TA) takes place at 0.6 K. On the other hand, for the second switch, the MQT-TA crossover temperature is increased to 2.0 K. This result is interpreted as follows: the MQT rate of the second switch is enhanced by the charge coupling between adjacent IJJs as well as in Bi2Sr2CaCu2O8+δ. We consider that the enhancement of the MQT rate is a common feature among bismuth-cuprates with single and double CuO2 layers in their crystal structures.

Macroscopic quantum tunneling in quartic and sextic potentials: Application to a phase qubit

Macroscopic quantum tunneling of the phase is a fundamental phenomenon in the quantum dynamics of superconducting nanocircuits. The tunneling rate can be controlled in such circuits, where the potential landscape for the phase can be tuned with different external bias parameters. Precise theoretical knowledge of the macroscopic quantum tunneling rate is required in order to simulate and understand the experiments. We present a derivation, based on the instanton technique, of an analytical expression of the escape rate in general quartic and symmetric sextic potentials comprising two escape paths. These new potentials were recently realized when creating a noise-insensitive phase qubit in the camelback potential of a dc SQUID.

Macroscopic quantum tunneling induced by a spontaneous field in intrinsic Josephson junctions

We theoretically study macroscopic quantum tunneling (MQT) in capacitively coupled Josephson junctions in the case that one of the junctions is in the finite voltage state. We find that the system can be mapped into a one dimensional model with a spontaneous periodic perturbation and calculate the MQT rate by using the time-dependent WKB method. Then the MQT rate is found to be resonantly enhanced and the enhancement of MQT rate is found even off the resonant point.

Effects of a resonant cavity on macroscopic quantum tunneling of fluxons in long Josephson junctions

We investigate the effects of high-Q_c resonant cavity on macroscopic quantum tunneling (MQT) of fluxon both from a metastable state to continuum and from one degenerate ground-state of a double-well potential to the other. By using a set of two coupled perturbed sine-Gordon equations, we describe the tunneling processes in linear long Josephson junctions (LJJs) and find that MQT in the resonant cavity increases due to potential renomalization, induced by the interaction between the fluxon and cavity.Enhancement of the MQT rate in the weak-coupling regime is estimated by using the experimantally accessible range of the model parameters. The tunneling rate from the metastable state is found to increase weakly with increasing junction-cavity interaction strength. However, the energy splitting between the two degenerate ground-states of the double-well potential increases significantly with increasing both the interaction strength and frequency of the resonant cavity mode. Finally, we discuss how the resonant cavity may be used to tune the property of Josephson vortex quantum bits.

Theory of two-dimensional macroscopic quantum tunneling inYBa2Cu3O7−δJosephson junctions coupled to an LC circuit

We investigate classical thermal activation (TA) and macroscopic quantum tunneling (MQT) for a YBa2Cu3O7−δ (YBCO) Josephson junction coupled to an LC circuit theoretically. Due to the coupling between the junction and the LC circuit, the macroscopic phase dynamics can be described as the escape process of a fictitious particle with an anisotropic mass moving in a two-dimensional potential. We analytically calculate the escape rate including both the TA and MQT regime by taking into account the peculiar dynamical nature of the system. In addtion to large suppression of the MQT rate at zero temperature, we study details of the temperature dependence of the escape rate across a crossover region. These results are in an excellent agreement with recent experimental data for the MQT and TA rate in a YBCO biepitaxial Josephson junction. Therefore the coupling to the LC circuit is essential in understanding the macroscopic quantum dynamics and the qubit operation based on the YBCO biepitaxial Josephson junctions.

Double tunneling in polarization switching

We present a theory of quantum switching of polarization in hydrogen-bonded order–disorder ferroelectrics, and examine the macroscopic quantum-tunneling rate of the polarization reversal for nano-samples induced by microscopic tunneling of protons between the two wells in potentials of hydrogen bonds. We compute the rate of the electric polarization tunneling through the barrier between two minima of the free energy density of a system. By using the instanton approach, we calculate a barrier factor and a prefactor multiplying the exponential of the action integral for the tunneling splitting at zero applied electric field. We compute the tunneling rate of domain walls. We obtain the double tunneling effect, i.e., the polarization tunneling related to the proton tunneling between the two minima in potentials of hydrogen bonds.

Suppression of macroscopic quantum tunneling in a large Josephson junction coupled to a resonator

We employ a functional integral technique to calculate the macroscopic quantum tunneling rate at zero temperature of a current-biased Josephson junction weakly coupled to a resonator. We allow for the effects of environmental dissipation on both the junction and the resonator via baths of harmonic oscillators, and we consider both cases of weak and strong junction damping. The resonator can be, in principle, any quantum harmonic oscillator that couples to the junction bilinearly in either the coordinate or the velocity. The Josephson phase difference $\ensuremath{\phi}$ is the tunneling variable in this system, and the low-lying bound states in the junction's potential energy well are weakly metastable due to tunneling through a finite-width energy barrier. There has been some interest in using such biased junctions as qubits with the resonator providing multiqubit coupling. The main result of this work is that coupling to the resonator has a suppressive effect on the junction's tunneling: the stronger the coupling strength between the junction and resonator, the greater the reduction of the tunneling rate. Including damping to the junction also suppresses tunneling, a well-known result, but damping of the resonator actually reduces the magnitude of suppression; i.e., damping the resonator partially counteracts the suppression provided directly by the junction-resonator coupling. Details of the junction-resonator coupling yield interesting variations on this theme that may be useful for qubit design. For example, the coupling ${U}_{\mathit{int}}$ between a current-biased junction and an AlN dilatational resonator should depend on the angular frequency of the resonator ${\ensuremath{\omega}}_{R}$ in a power-law fashion [A. N. Cleland and M. R. Geller, Phys. Rev. Lett. 93, 070501 (2004)], specifically ${U}_{\mathit{int}}\ensuremath{\propto}{({\ensuremath{\omega}}_{R})}^{n}$, where $n=1∕2$. We find that for any value of $n$ in the range $0lnl1$ the junction's tunneling rate exhibits a nonmonotonic dependence on ${\ensuremath{\omega}}_{R}$, and for $n=1∕2$, the tunneling rate is maximally suppressed for ${\ensuremath{\omega}}_{R}∕{\ensuremath{\omega}}_{J}\ensuremath{\approx}1$, where ${\ensuremath{\omega}}_{J}$ is the bias current-dependent plasma frequency of the junction.

Theory of macroscopic quantum tunneling in high-Tcc-axis Josephson junctions

We study macroscopic quantum tunneling (MQT) in $c$-axis twist Josephson junctions made of high-${T}_{c}$ superconductors in order to clarify the influence of the anisotropic order parameter symmetry (OPS) on MQT. The dependence of the MQT rate on the twist angle $\ensuremath{\gamma}$ about the $c$ axis is calculated by using the functional integral and the bounce method. Due to the $d$-wave OPS, the $\ensuremath{\gamma}$ dependence of standard deviation of the switching current distribution and the crossover temperature from thermal activation to MQT are found to be given by $\mathrm{cos}\phantom{\rule{0.2em}{0ex}}2\ensuremath{\gamma}$ and $\sqrt{\mathrm{cos}\phantom{\rule{0.2em}{0ex}}2\ensuremath{\gamma}}$, respectively. We also show that a dissipative effect resulting from the nodal quasiparticle excitation on MQT is negligibly small, which is consistent with recent MQT experiments using ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ intrinsic junctions. These results indicate that MQT in $c$-axis twist junctions becomes a useful experimental tool for testing the OPS of high-${T}_{c}$ materials at low temperature, and suggest high potential of such junctions for qubit applications.

Macroscopic quantum effect in intrinsic Josephson junctions containing magnetic flux

We formulate a quantum theory that can describe the macroscopic quantum tunneling (MQT) in intrinsic Josephson junction stacks. Both capacitive and inductive couplings between junctions in the stacks are considered. It is shown that the inductive coupling renormalizes the height of the potential barrier, while the capacitive coupling causes mass renormalization, when the switching event in the I–V characteristics is mapped onto the problem of a quasi-classical particle showing MQT. Both couplings enhance the MQT rate.

Detecting Current Noise with a Josephson Junction in the Macroscopic Quantum Tunneling Regime

We discuss the use of a hysteretic Josephson junction to detect current fluctuations with frequencies below the plasma frequency of the junction. These adiabatic fluctuations are probed by switching measurements observing the noise-affected average rate of macroscopic quantum tunneling of the detector junction out of its zero-voltage state. In a proposed experimental scheme, frequencies of the noise are limited by an on-chip filtering circuit. The third cumulant of current fluctuations at the detector is related to an asymmetry of the switching rates.

Enhanced Macroscopic Quantum Tunneling inBi2Sr2CaCu2O8+δIntrinsic Josephson-Junction Stacks

We have investigated macroscopic quantum tunneling in Bi(2)Sr(2)CaCu(2)O(8 + delta) intrinsic Josephson junctions at millikelvin temperatures using microwave irradiation. Measurements show that the escape rate for uniformly switching stacks of Nu junctions is about Nu(2) times higher than that of a single junction having the same plasma frequency. We argue that this gigantic enhancement of the macroscopic quantum tunneling rate in stacks is boosted by current fluctuations which occur in the series array of junctions loaded by the impedance of the environment.

Theory of macroscopic quantum tunneling in high-Tc cuprate

To reveal macroscopic quantum tunneling (MQT) in high-Tc superconductor Josephson junctions is an important issue since there is a possibility to fabricate a superconducting quantum bit by use of high Tc junctions. Using the functional integral and the instanton theory, we analytically obtain the MQT rate (the inverse lifetime of the metastable state) for the c-axis twist Josephson junctions. In the case of the zero twist angle, the system shows the super-Ohmic dissipation due to the presence of the nodal quasiparticle tunneling. Therefore, the MQT rate is suppressed compared with the finite twist angle cases. Furthermore, the effect of the zero energy bound states (ZES) on the MQT in the in-plane junctions is theoretically investigated. We obtained the analytical formula of the MQT rate and showed that the presence of the ZES at the normal/superconductor interface leads to a strong Ohmic quasiparticle dissipation. Therefore, the MQT rate is noticeably inhibited compared with the c-axis junctions in which the ZES are completely absent.

Macroscopic quantum tunneling and dissipation in c-axis twist Josephson junctions

We study macroscopic quantum tunneling (MQT) in c-axis twist superconductor Josephson junctions. By using the functional integral method and the instanton theory we have obtained the analytical expression of the MQT rate (the inverse lifetime of the metastable state). In the case of the zero twist angle, we find that the system shows the super-Ohmic dissipation due to the presence of the nodal quasiparticle tunneling. Therefore, the MQT rate is strongly suppressed in compared with the finite twist angle cases.

Effect of zero-energy bound states on macroscopic quantum tunneling in high-Tcsuperconductor junctions

The macroscopic quantum tunneling (MQT) in the current biased high-Tc superconductor Josephson junctions and the effect of the zero energy bound states (ZES) on the MQT are theoretically investigated. We obtained the analytical formula of the MQT rate and showed that the presence of the ZES at the normal/superconductor interface leads to a strong Ohmic quasiparticle dissipation. Therefore, the MQT rate is noticeably inhibited in compared with the c-axis junctions in which the ZES are completely absent.

Zener Enhancement of Quantum Tunneling in a Two-Level Superconducting Circuit

We have investigated the macroscopic quantum tunneling (MQT) of the phase across a Josephson junction embedded in a superconducting circuit. This system is equivalent to a spin 1/2 particle in a potential energy well. The MQT escape rate of such a particle was recently predicted to be strongly modified when a crossing of its inner Zeeman levels occurs while tunneling. In this regime, we observe a significant enhancement of the MQT rate and compare it to theory.

Macroscopic quantum tunneling and quasiparticle dissipation ind-wave superconductor Josephson junctions

We examine the macroscopic quantum tunneling (MQT) in high-Tc superconductor Josephson junctions with a d-wave order parameter. Using microscopic Hamiltonian and the functional integral method, we analytically obtain the MQT rate (the inverse lifetime of the metastable state) for the c-axis twist Josephson junctions. In the case of the zero twist angle, the system shows the super-Ohmic dissipation due to the presence of the nodal quasiparticle tunneling. Therefore, the MQT rate is strongly suppressed in compared with the finite twist angle cases.

Traversal Time as Deduced from Decay Time Measurements inJosephson Junctions

The macroscopic quantum tunneling rate out of the metastable stateof a Josephson junction has been measured in a range of temperaturewhere the quantum contribution is comparable with the thermal escape.From such measurements the traversal time of the barrier has beendeduced and compared with the theoretical predictions of asemiclassical model.

Macroscopic Quantum Tunneling of a Bose-Einstein Condensate with Attractive Interaction

A Bose-Einstein condensate with attractive interaction can be metastable if it is spatially confined and if the number of condensate bosons $N_0$ is below a certain critical value $N_{\rm c}$. By applying a variational method and the instanton techinique to the Gross-Pitaevskii energy functional, we find analytically the frequency of the collective excitation and the rate of macroscopic quantum tunneling (MQT). We show that near the critical point the tunneling exponent vanishes according to $(1-N_0/N_c)^\frac{5}{4}$ and that MQT can be a dominant decay mechanism of the condensate for $N_0$ very close to $N_{\rm c}$.