We study in the presence of dissipation the quantum phenomena of tunneling and especially interference around a Weyl-like or conical potential crossing due to the monopolar Berry gauge phase. It is pertinent to a wide range of physical and quantum chemical phenomena, and we microscopically motivate this model from the effective dynamics of collective degrees of freedom arising from a two-level system coupled to a bosonic bath. Using the instanton approach with symmetry analysis and advanced numerical methods, we are able to investigate the interplay between phase interference and dissipation by resolving the phase diagram of coherent tunneling with respect to the potential bias and dissipation. Under emergent mirror symmetry protection, the coherent tunneling exhibits Kramers degeneracy, nonmonotonic dependence on dissipation and a generic phase transition to no interference, before which an anomalous dissipation-enhanced regime persists.
We study in the presence of dissipation the quantum phenomena of tunneling and especially interference around a Weyl-like or conical potential crossing due to the monopolar Berry gauge phase. It is pertinent to a wide range of physical and quantum chemical phenomena, and we microscopically motivate this model from the effective dynamics of collective degrees of freedom arising from a two-level system coupled to a bosonic bath. Using the instanton approach with symmetry analysis and advanced numerical methods, we are able to investigate the interplay between phase interference and dissipation by resolving the phase diagram of coherent tunneling with respect to the potential bias and dissipation. Under emergent mirror symmetry protection, the coherent tunneling exhibits Kramers degeneracy, nonmonotonic dependence on dissipation and a generic phase transition to no interference, before which an anomalous dissipation-enhanced regime persists.
The Berry phase effect plays a central role in many mesoscale condensed matter and quantum chemical systems that are naturally under the environmental influence of dissipation. We propose and microscopically derive a prototypical quantum coherent tunneling model around a monopole or conical potential intersection in order to address the intriguing but overlooked interplay between dissipation and the topologically nontrivial Berry phase effect. We adopt the instanton approach with both symmetry analysis and accurate numerical solutions that consistently incorporate nonperturbative dissipation and the Berry phase. It reveals a unique and interesting dissipative quantum interference phenomenon with the Berry phase effect. The phase diagram of this tunneling exhibits Kramers degeneracy, nonmonotonic dependence on dissipation, and a generic dissipation-driven phase transition of quantum interference, before which an unconventional dissipation-enhanced regime of quantum tunneling persists.
For the realistic theoretical descriptions of quantum devices, we have to take the unavoidable coupling to their surrounding environment into account. A lot of effort in theoretical physics has been made to describe decoherence effects and the corresponding quantum to classical transition in the past. In these studies, baths are coupled to certain observables making their behavior more classical. In the most general case, a quantum device is affected by environments coupled to different observables. In this thesis, we study the differences emerging from coupling the bath to different observables. In particular, we investigate the situation, where two baths are coupled simultaneously to two conjugate variables (e.g. xˆ and pˆ, denoted dissipative frustration). We study how the interplay of these two baths can lead to interesting effects. After an introduction of the topic, we discuss the results of this thesis in Part II and Part III. In Part II, we study the effect of quantum tunneling in presence of a dissipative interaction with two Ohmic environments to the position xˆ and/or to the momentum pˆ of a particle. In chapter 2, we consider a symmetric double well potential which is important in the context of coherent state preparation, as its ground state is a superposition of being in the left and in the right well. Using the semiclassical approximation to calculate instanton paths within the path integral method, we find that momentum dissipation enhances the coherent tunnel splitting. In presence of dissipative couplings to xˆ and pˆ, the momentum dissipation acts in favor of the delocalization of the particle shifting the critical coupling strength of the dissipative phase transition induced by the position dissipation. Chapter 3 contains a study of the escape rate out of a metastable well in presence of dissipation. Here we find that the incoherent tunneling rate is exponentially enhanced in presence of momentum dissipation. We further show that the influence of momentum dissipation depends on the slope of the part of barrier the particle escaping through. In presence of both dissipative couplings, we find a non-monotonic behavior of the escape rate as a function of the dissipative couplings strengths. In Part III, we show that it is possible to realize the situation of "dissipative frustration" in Josephson junction chains. In particular, we introduce charge dissipation as a physical realization of the afore introduced momentum coupling. After presenting the circuit elements needed for charge dissipation, we study a chain of Josephson junctions affected by Ohmic baths coupled to the charge and/or the phase. Using a self-consistent harmonic approximation, we determine the phase diagram at zero temperature which exhibits a quantum phase transition between an ordered phase, corresponding to the superconducting state, and a disordered phase, corresponding to the insulating state with localized superconducting charge. Interestingly, we find that the critical line separating the two phases has a non-monotonic behavior as a function of the dissipative coupling strength. Moreover, within the self-consistent harmonic approximation, we analyze the dissipation induced crossover between a first and second order phase transition, showing that dissipative frustration increases the range in which the phase transition is second order. The non-monotonic behavior is also reflected in the purity of the system that quantifies the degree of correlation between the system and the environment, and in the logarithmic negativity as an entanglement measure that encodes the internal quantum correlations in the chain.
Landau-Zener tunneling, which describes the transition in a two-level system during a sweep through an anti-crossing, is a model applicable to a wide range of physical phenomena. Realistic quantum systems are affected by dissipation due to coupling to their environments. An important aspect of understanding such open quantum systems is the relative energy scales of the system itself and the system-environment coupling, which distinguishes the weak- and strong-coupling regimes. Using a tunable superconducting flux qubit, we observe the crossover from weak to strong coupling to the environment in Landau-Zener tunneling. Our results confirm previous theoretical studies of dissipative Landau-Zener tunneling in the weak and strong coupling limits. We devise a spin bath model that effectively captures the crossover regime. This work is relevant for understanding the role of dissipation in quantum annealing, where the system is expected to go through a cascade of Landau-Zener transitions before reaching the target state.
We study tunneling through a resonant level connected to two dissipative bosonic baths: one is the resistive environment of the source and drain leads, while the second comes from coupling to potential fluctuations on a resistive gate. We show that several quantum phase transitions (QPT) occur in such a model, transitions which emulate those found in interacting systems such as Luttinger liquids or Kondo systems. We first use bosonization to map this dissipative resonant level model to a resonant level in a Luttinger liquid, one with, curiously, two interaction parameters. Drawing on methods for analyzing Luttinger liquids at both weak and strong coupling, we obtain the phase diagram. For strong dissipation, a Berezinsky-Kosterlitz-Thouless QPT separates strong-coupling and weak-coupling (charge localized) phases. In the source-drain symmetric case, all relevant backscattering processes disappear at strong coupling, leading to perfect transmission at zero temperature. In fact, a QPT occurs as a function of the coupling asymmetry or energy of the resonant level: the two phases are (i) the system is cut into two disconnected pieces (zero transmission), or (ii) the system is a single connected piece with perfect transmission, except for a disconnected fractional degree of freedom. The latter arises from the competition between the two fermionic leads (source and drain), as in the two-channel Kondo effect.
The dissipative dynamics of a quantum bistable system coupled to a Ohmic heat bath is investigated beyond the spin-boson approximation. Within the path-integral approach to quantum dissipation, we propose an approximation scheme which exploits the separation of time scales between intra- and interwell (tunneling) dynamics. The resulting generalized master equation for the populations in a space localized basis enables us to investigate a wide range of temperatures and system-environment coupling strengths. A phase diagram in the coupling-temperature space is provided to give a comprehensive account of the different dynamical regimes.
The topic of the PhD project is a comparative study of phase dynamics and macroscopic quantum phenomena in moderately damped NbN, YBaCuO grain boundary (GB) Josephson junctions (JJs) and hybrid devices. This type of research activity responds to the needs of better identifying phase dynamics in JJs in the moderately damped regime, which is going to be more and more common in hybrid nanostructures. Issues on a more detailed understanding of coherence, dissipation and noise in the various devices have a relevant role in the progress of quantum circuits.
In the last few years, studies of phase dynamics and macroscopic quantum phenomena have been extended to junctions composed of materials other than the traditional low critical temperature superconductors (LTS) and to novel types of structures with unconventional barriers composed for instance of graphene sheets or of grain boundaries. Progress in engineering new materials into junctions and in understanding and controlling the physics of interfaces may offer novel solutions for junctions of superior quality and complementary functionalities, and therefore may lead in the long run to improve also specific qubit performances.
For LTS JJs, once the barrier thickness and the critical current density (Jc) have been fixed, a reduction in its size unavoidably leads to a lowering of the critical current and determines a quite different phase dynamics re-normalized to the new scaling energy. Lower critical currents Ic result in lower Josephson energies EJ, and higher levels of dissipation are expected. The range of the energy dynamical parameters is significantly enlarged, and it is technologically easier to reproducibly realize nontrivial configurations. These devices are characterized by intermediate levels of dissipation (moderately damped regime) and by phase diffusion phenomena. The low Jc limit seems to be characteristic also of all futuristic nanohybrids devices incorporating nanowires, and the moderately damped regime (MDR) is intrinsically more common than it could be expected.
Measurements of switching current distribution (SCD) in these last years have turned to be standard tools to investigate phase dynamics in unconventional and hybrid systems and nanostructures. High critical temperature superconductors (HTS) are an example of unconventional systems, because of the d-wave order parameter symmetry and of the presence of low-energy quasiparticles, which are expected to induce high level of dissipation and as a consequence to spoil macroscopic quantum coherence. A comparative study in systems so different and complementary is of great interest.
During the PhD program, we have performed measurements of SCD, both in the thermal and quantum regime down to 20 mK, on moderately damped NbN/MgO/NbN JJs and on YBCO biepitaxial GB JJs. The NbN JJs exhibit a crossover from thermal activation (TA) to macroscopic quantum tunneling (MQT) regime at about 90 mK. After the MQT saturation, the width of the SCD follows the expected dependence in the TA regime. Deviations are evident in proximity and above the crossover temperature T* (about 1.6K) where we find effects of anti-correlation between the bath temperature and thermal fluctuations since the width of the histograms starts to collapse, and indications of a transition to a third regime called phase diffusion (PD) are evident, such as the change of the switching distributions symmetry.
Experimental data have been analyzed through numerical fitting of the switching probability and Monte Carlo simulations, and we found a good agreement with theoretical expectations based on multiple re-trapping processes, which strongly depend on the junction damping. The combined analysis of these three regimes allowed us to extract the fundamental parameters, which completely characterize the dynamics of such moderately damped NbN JJs. In addition, clear signatures of the PD regime have been detected and numerical methods have been developed to estimate the dissipation level in the MDR.
As a term of comparison, the studies on moderately damped systems have been also carried out on HTS junctions, which have different levels of intrinsic dissipation induced by low energy quasi-particles, and are for this reason of great impact as a reference.
In such JJs we have clearly observed a direct transition from the MQT to the PD regime. The width of the SCDs is constant below 100mK, which is a clearly indication of a quantum activation regime. Above 100mK the negative temperature derivative of the width is consistent with a diffusive motion due to multiple escape and re-trapping in the potential wells. Thermal behavior of the width has been fitted through numerical simulations, thus providing the estimate of the damping factor. These conclusions of a PD regime also in YBaCuO JJs are supported by data in presence of an externally applied magnetic field, and are consistent with the numerical outcomes.
Numerical simulations of the thermal behavior of the SCD width for different values of the quality factor ranging from 1 to 10 have been carried out. Such numerical simulations allow us to reconstruct a (Q, kBT/EJ) phase diagram summarizing the various activation regimes. The transition curve between the PD regime and the running state following thermal or quantum activation has been determined numerically by varying the damping factor Q as function of the ratio between the thermal energy and the Josephson energy. The result of the calculation is a universal curve. A phase diagram valid in a large range of dissipation conditions emerges as a functional guide to classify the switching behavior and to settle the fundamental junction parameters and energies in the MDR. It is therefore a reference for phase dynamics of novel types of junction and system for which the nature of the current induced transition from the superconducting to the normal state has not been completely clarified.