Macroscopic Quantum Tunneling Escape Rate Research Articles

Two-dimensional macroscopic quantum tunneling in multi-gap superconductor Josephson junctions

Low-temperature characters of superconducting devices yield definite probes for different superconducting phenomena. We study the macroscopic quantum tunneling (MQT) in a Josephson junction, composed of a single-gap superconductor and a two-gap superconductor. Since this junction has two kinds to the superconducting phase differences, calculating the MQT escape rate requires the analysis of quantum tunneling in a multi-dimensional configuration space. Our approach is the semi-classical approximation along a 1D curve in a 2D potential- energy landscape, connecting two adjacent potential (local) minimums through a saddle point. We find that this system has two plausible tunneling paths; an in-phase path and an out-of-phase path. The former is characterized by the Josephson-plasma frequency, whereas the latter is by the frequency of the characteristic collective mode in a two-band superconductor, Josephson- Leggett mode. Depending on external bias current and inter-band Josephson-coupling energy, one of them mainly contributes to the MQT. Our numerical calculations show that the difference between the in-phase path and the out-of-phase path is manifest, with respect to the bias- current-dependence of the MQT escape rate. This result suggests that our MQT setting be an indicator of the Josephson-Leggett mode.

Theory of macroscopic quantum tunneling with Josephson-Leggett collective excitations in multiband superconducting Josephson junctions

Collective excitations reveal fundamental properties and potential applications of superconducting states. We theoretically study macroscopic quantum tunneling (MQT) in a Josephson junction composed of multiband superconductors, focusing on a phase mode induced by interband fluctuations: the Josephson-Leggett (JL) collective excitation mode. Using the imaginary-time path-integral method, we derive a formula for the MQT escape rate for low-temperature switching events. We clarify that the JL mode has two major effects on the MQT: (i) the zero-point fluctuations enhance the escape rate, and (ii) the quantum dissipation induced by the couplings to the gauge-invariant phase difference suppresses the quantum tunneling. We show that the enhancement exceeds the suppression for a wide range of junction parameters. This enhancement originates from the single-mode interaction between the tunneling variable and the interband fluctuations.

Inter-band phase fluctuations in macroscopic quantum tunneling of multi-gap superconducting Josephson junctions

We theoretically investigate macroscopic quantum tunneling (MQT) in a hetero Josephson junction formed by a conventional single-gap superconductor and a multi-gap superconductor. In such Josephson junctions, phase differences for each tunneling channel are defined, and the fluctuation of the relative phase differences appear which is referred to as Josephson–Leggett’s mode. We take into account the effect of the fluctuation in the tunneling process and calculate the MQT escape rate for various junction parameters. We show that the fluctuation of relative phase differences drastically enhances the escape rate.

Effect of strong coupling on collective macroscopic quantum tunneling in intrinsic Josephson junctions

We have theoretically investigated macroscopic quantum tunneling (MQT) for a stack of capacitively and inductively coupled intrinsic-junctions. By use of the functional integral method, we have analytically derived the MQT escape rate and found that the inductive coupling reduces the potential barrier height for the collective MQT process. Therefore, in the case of the strong inductive coupling, the relevant escape process is given by collective MQT.

TWO-DIMENSIONAL MACROSCOPIC QUANTUM DYNAMICS IN YBCO JOSEPHSON JUNCTIONS

We theoretically study classical thermal activation (TA) and macroscopic quantum tunneling (MQT) for a YBa2Cu3O7-δ( YBCO ) Josephson junction coupled with an LC circuit. The TA and MQT escape rate are calculated by taking into account the two-dimensional nature of the classical and quantum phase dynamics. We find that the MQT escape rate is largely suppressed by the coupling to the LC circuit. On the other hand, this coupling leads to the slight reduction of the TA escape rate. These results are relevant for the interpretation of a recent experiment on the MQT and TA phenomena in YBCO bi-epitaxial Josephson junctions.

Theory of two-dimensional macroscopic quantum tunneling in a Josephson junction coupled with an LC circuit

We investigate classical thermal activation (TA) and macroscopic quantum tunneling (MQT) for a Josephson junction coupled with an LC circuit theoretically. The TA and MQT escape rate are calculated analytically by taking into account the two-dimensional nature of the classical and quantum phase dynamics. We find that the MQT escape rate is largely suppressed by the coupling to the LC circuit. On the other hand, this coupling gives rise to slight reduction of the TA escape rate. These results are relevant for the interpretation of a recent experiment on the MQT and TA phenomena in grain boundary YBCO Josephson junctions.

Nonlocal macroscopic quantum tunneling and quantum terahertz electrodynamics in layered superconductors: Theory and simulations

We derive a quantum field theory of Josephson plasma waves (JPWs) in layered superconductors, which describes two types of interacting JPW bosonic quanta (one heavy and one lighter). We propose a mechanism of enhancement of macroscopic quantum tunneling (MQT) in stacks of intrinsic Josephson junctions. Due to the long-range interaction between junctions in layered superconductors, the calculated MQT escape rate $\ensuremath{\Gamma}$ has a nonlinear dependence on the number of junctions in the stack. We develop a numerical procedure, based on quantum field tunneling theory, to calculate $\ensuremath{\Gamma}$ for the stack of Josephson junctions. We also propose a simple analytical formula to estimate the MQT escape rate. Moreover, we demonstrate that the direct analogy between fluxon tunneling and tunneling of a quantum particle fails even for very thin junction stacks (about $1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ for ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$) and a field-theoretical approach is necessary. The theory developed here allows to quantitatively describe striking recent experiments in ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ stacks.

Collective macroscopic tunneling in intrinsic Josephson junctions

A theory for photon-assisted macroscopic quantum tunneling (MQT) in a stack of capacitively-coupled intrinsic Josephson junctions is proposed. The theory predicts how the quantized energy-levels in the N-junction stacked system distribute. Furthermore, the theory reveals that the MQT escape rate from the single-plasmon states to the uniform voltage ones under microwave irradiation is proportional to the square of the junction number (N2). This result is consistent with the recent observation in Bi-2212 intrinsic Josephson junctions.

Quantum Terahertz Electrodynamics and Macroscopic Quantum Tunneling in Layered Superconductors

We derive a quantum field theory of Josephson plasma waves (JPWs) in layered superconductors, which describes two types of interacting JPW bosonic quanta (one heavy and one lighter). We propose a mechanism of enhancement of macroscopic quantum tunneling (MQT) in stacks of intrinsic Josephson junctions. Because of the long-range interaction between junctions in layered superconductors, the calculated MQT escape rate Gamma has a nonlinear dependence on the number of junctions in the stack. We show that the crossover temperature between quantum and thermal escape increases when increasing the number of junctions. This allows us to quantitatively describe striking recent experiments in Bi2Sr2CaCu2O8+delta stacks.

Macroscopic quantum tunneling in globally coupled series arrays of Josephson junctions

We present a quantitative analysis of an escape rate for switching from the superconducting state to a resistive one in series arrays of globally coupled Josephson junctions. A global coupling is provided by an external shunting impedance. Such an impedance can strongly suppress both the crossover temperature from the thermal fluctuation to quantum regimes, and the macroscopic quantum tunneling (MQT) in short Josephson junction series arrays. However, in large series arrays we obtain an enhancement of the crossover temperature, and a giant increase of the MQT escape rate. The effect is explained by excitation of a spatial-temporal charge instanton distributed over a whole structure. The model gives a possible explanation of recently published experimental results on an enhancement of the MQT in single crystals of high-${T}_{c}$ superconductors.

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.