Dissipative Quantum Tunneling Research Articles

Quantum tunnelling and thermally driven transitions in a double-well potential at finite temperature

We explore dissipative quantum tunnelling, a phenomenon central to various physical and chemical processes, utilizing a model based on a double-well potential. This paper aims to bridge gaps in understanding the crossover from thermal activation to quantum tunnelling, a domain still shrouded in mystery despite extensive research. By numerically investigating a model derived from Caldeira–Leggett’s work on quantum Brownian motion, examining both Lindblad and stochastic Schrödinger dynamics, we offer new insights into the transition states in the crossover region. Contrary to a common belief that temperature strongly dampens all quantum effects, our findings reveal that under certain conditions temperature instead alters the nature of tunnelling from a deterministic and periodic process to a stochastic yet still very quantum phenomenon. This underscores the profound influence of quantum effects on transition rates and the critical role of temperature in modulating tunnelling behaviours. Additionally, we introduce a new model for quantum Brownian motion that takes Lindblad form and is formulated as a modification of the widely known model found in Breuer and Petruccione. In our approach, we remove the zero-temperature singularity resulting in a better description of low-temperature quantum Brownian motion near a potential minima. Despite these advancements, we recognize persistent challenges in accurately simulating the dynamics at extremely low temperatures for arbitrary potentials, particularly those that cannot be closely approximated locally by a quadratic function.

Disentangling 4f -radical coupling and dissipative Landau-Zener quantum tunneling in a continuously measured single-ion magnet spin transistor

Both radical-lanthanide exchange coupling and crystal-field tunnel splitting are responsible for the ground to first-excited Kramers doublet energy gap $\mathrm{\ensuremath{\Delta}}{E}_{\text{KD}}$ in an Ising $4f$ single-ion magnet coupled to a noninnocent ligand. However, these two mechanisms cannot be easily disentangled via spectroscopy alone because their interplay results in a single absorption line. Here we present a microscopic theory for the continuous measurement of the dissipative Landau-Zener transitions recently discussed for a ${\mathrm{TbPc}}_{2}$ spin transistor [Phys. Rev. Lett. 118, 257701 (2017)] and show how this quantum transport experiment can be used to disentangle the magnetic coupling and the tunnel splitting contributions to $\mathrm{\ensuremath{\Delta}}{E}_{\text{KD}}$. In addition, our model elucidates the microscopic origin of the decoherent spin tunneling observed in the ${\mathrm{TbPc}}_{2}$ spin transistor, by explicitly exposing the role played by phonon-mediated spin relaxation and sequential electron transport through the noninnocent ligand, in a time-dependent magnetic field.

Dissipative tunnelling by means of scaled trajectories

Dissipative quantum tunnelling through an inverted parabolic barrier is considered in the presence of an electric field. A Schrödinger–Langevin or Kostin quantum–classical transition wave equation is used and applied resulting in a scaled differential equation of motion. A Gaussian wave packet solution to the resulting scaled Kostin nonlinear equation is assumed and compared to the same solution for the scaled linear Caldirola–Kanai equation. The resulting scaled trajectories are obtained at different dynamical regimes and friction cases, showing the gradual decoherence process in this open dynamics. Theoretical results show that the transmission probabilities are always higher in the Kostin approach than in the Caldirola–Kanai approach in the presence or not of an external electric field. This discrepancy should be understood due to the presence of an environment since the corresponding open dynamics should be governed by nonlinear quantum equations, whereas the second approach is issued from an effective Hamiltonian within a linear theory.

Phonon assisted resonant tunneling and its phonons control

We observe a series of sharp resonant features in the tunnelling differential conductance of InAs quantum dots. We found that dissipative quantum tunnelling has a strong influence on the operation of nano-devices. Because of such tunnelling the current-voltage characteristics of tunnel contact created between atomic force microscope tip and a surface of InAs/GaAs quantum dots display many interesting peaks. We found that the number, position, and heights of these peaks are associated with the phonon modes involved. To describe the found effect we use a quasi-classical approximation. There the tunnelling current is related to a creation of a dilute instanton-anti-instanton gas. Our experimental data are well described with exactly solvable model where one charged particle is weakly interacting with two promoting phonon modes associated with external medium. We conclude that the characteristics of the tunnel nanoelectronic devices can thus be controlled by a proper choice of phonons existing in materials, which are involved.

Computational multiqubit tunnelling in programmable quantum annealers.

Quantum tunnelling is a phenomenon in which a quantum state traverses energy barriers higher than the energy of the state itself. Quantum tunnelling has been hypothesized as an advantageous physical resource for optimization in quantum annealing. However, computational multiqubit tunnelling has not yet been observed, and a theory of co-tunnelling under high- and low-frequency noises is lacking. Here we show that 8-qubit tunnelling plays a computational role in a currently available programmable quantum annealer. We devise a probe for tunnelling, a computational primitive where classical paths are trapped in a false minimum. In support of the design of quantum annealers we develop a nonperturbative theory of open quantum dynamics under realistic noise characteristics. This theory accurately predicts the rate of many-body dissipative quantum tunnelling subject to the polaron effect. Furthermore, we experimentally demonstrate that quantum tunnelling outperforms thermal hopping along classical paths for problems with up to 200 qubits containing the computational primitive.

The influence of local phonon modes in a wide-band matrix on the tunnel current-voltage characteristics of quasi-zero-dimensional structures

Experimental results on the visualization of the density of states in InAs/GaSa(001) quantum dots that were obtained by tunnel atomic-force microscopy in an ultrahigh vacuum are presented. A one-dimensional (1D) model of dissipative quantum tunneling is proposed for describing experimental current-voltage characteristics of a tunnel contact between an atomic force microscope probe and the surface of InAs/GaAs (001) quantum dots. It was found that the influence of two local modes of the wide-band matrix on the probability of 1D dissipative tunneling leads to the appearance of several randomly spaced peaks in the field dependence. It was shown that the theoretical dependence agrees qualitatively with experimental the current-voltage characteristic of the atomic force microscope tip and the surface of InAs/GaAs(001) quantum dots.

ANALYTICAL BOUNCE SOLUTION IN A DISSIPATIVE QUANTUM TUNNELING

The analytical bounce solution is derived in terms of the polygamma function in the Caldeira–Leggett's dissipative quantum tunneling model. The classical action for the bounce solution lies between the upper and lower bounds in the full range of α, where α is a dissipation coefficient. The bounce peak point increases from 1 to 4/3 with the increase of α. In spite of various nice features, we have shown that the solution we have derived is not exact one by making use of the zero-mode argument in the linearized fluctuation equation. However, our solution can be a starting point for approximate computation of the prefactor in this model.

Two-dimensional tunnel correlations with dissipation

Tunneling of two particles in synchronous and asynchronous regimes is studied in the framework of dissipative quantum tunneling. The critical temperature T_c corresponding to a bifurcation of the underbarrier trajectory is determined. The effect of a heat bath local mode on the probability of two-dimensional tunneling transfer is also investigated. At certain values of the parameters, the degeneracy of antiparallel tunneling trajectories is important. Thus, four, six, twelve, etc., pairs of the trajectories should be taken into account (a cascade of bifurcations). For the parallel particle tunneling the bifurcation resembles phase transition of a first kind, while for the antiparallel transfer it behaves as second order phase transition. The proposed theory allows for the explanation of experimental data on quantum fluctuations in two-proton tunneling in porphyrins near the critical temperature.

Nonperturbative renormalization-group approach for quantum dissipative systems

We analyze the dissipative quantum tunneling in the Caldeira-Leggett model by the nonperturbative renormalization-group method. We classify the dissipation effects by introducing the notion of effective cutoffs. We calculate the localization susceptibility to evaluate the critical dissipation for the quantum-classical transition. Our results are consistent with previous semiclassical arguments, but give considerably larger critical dissipation.

Dissipative quantum tunneling with non-perturbative renormalization group

Dissipative quantum tunneling with non-perturbative renormalization group

Enhanced field ionization of excited atoms by inhibiting the spontaneous emission in a solid-state microcavity

Enhanced field ionization of excited atoms was observed in a solid-state microcavity (${\mathrm{C}\mathrm{a}\mathrm{S}:\mathrm{E}\mathrm{u}}^{2+}$ thin-film electroluminescent devices) by inhibiting their spontaneous emission. By increasing the lifetime of the excited ${\mathrm{Eu}}^{2+}$ atoms using the microcavity effect, the field-ionization rate was enhanced approximately three times over that without the microcavity. The characteristic temperature dependence of the enhanced field-ionization rate suggested the generation process was dissipative quantum tunneling induced by strong electron-phonon coupling between localized electrons in the excited ${\mathrm{Eu}}^{2+}$ atoms and the surrounding lattice vibrations of the CaS host in the solid-state microcavity.

Dissipative quantum tunneling of two-level systems driven by dc-ac fields

The time-dependent average population in a two-level system interacting with an Ohmic boson bath and driven by a dc-ac field is obtained. The study is performed within the noninteracting-blip approximation and for the high-frequency driving case. The integro-differential master equation and the exact formal solution for the average transition probability are obtained. The dissipative quantum decay and the transition temperature from the coherent to the incoherent motion are investigated. The effect of the external electric field on the the dissipative two-level system is found to destroy its coherence.

Dissipative Quantum Tunneling and Magnetic Response of a Single Electron in a Four-Well Potential

We study dissipative tunneling of a single electron in a four-well semiconductor nanostructure threaded by a magnetic flux. The system under consideration allows us to investigate an influence of dissipation and irreversibility on two fundamental quantum-interference phenomena: tunneling and the Aharonov–Bohm effect at once. We calculate the steady-state magnetic moment of the particle (orbital paramagnetism) and study its temperature dependence. The existence of orbital paramagnetism is evidence for electron persistent tunneling between quantum dots as well as for the conservation of quantum coherence in the thermodynamic-equilibrium state.

Wigner Distribution Function for Open Quantum Systems

Using the modified biorthonormal Heisenberg equations of motion for non-Hermitian (NH) Hamilton operators, in order to imply a consistent Lie-algebraic structure and also the equivalence between the Heisenberg and Schrödinger pictures, we have obtained the analytical form of the Wigner distribution function which is unavoidable complex. Its imaginary part accounts for the influence of additional degrees of freedom, which are always present in the phenomenological representation of dissipative systems through (NH) Hamiltonians. Applications of the above formalism can be found, for instance, in dissipative macroscopic quantum tunneling (MQT) effect for Josephson junctions, and in the dissipative tunneling of trapped atoms in optical crystals.

Dissipative quantum tunneling of a single defect in a disordered metal.

We have studied the dynamics of single bistable defects in submicron disordered Bi wires at temperatures 0.1--2 K. The wires are sufficiently small so that the motion of a single defect can be detected as a random telegraph signal in the resistance time trace. The amplitude of the resistance jumps increases as the temperature is lowered due to the physics of universal conductance fluctuations. The defect transitions obey Poisson statistics and detailed balance, indicating that the defect is a two-state system. We interpret the signal as arising from incoherent tunneling of an atom or group of atoms between the two wells of a double-well potential. The temperature dependence of the tunneling rates agrees quantitatively with the predictions of dissipative quantum tunneling theory, which describes tunneling of a defect in the presence of strong dissipation from the electron bath. Our measurements exploit the previous discovery that the energy asymmetry \ensuremath{\varepsilon} of the defect varies with magnetic field. By varying both the temperature and magnetic field, we can probe the behavior of the tunneling rates spanning two very different regimes, from kT\ensuremath{\ll}\ensuremath{\varepsilon} to kT\ensuremath{\gg}\ensuremath{\varepsilon}. Data from a single defect at several values of magnetic field suggest that the defect-bath coupling constant \ensuremath{\alpha} and the renormalized tunneling matrix element ${\mathrm{\ensuremath{\Delta}}}_{\mathit{r}}$ are nearly independent of magnetic field. \textcopyright{} 1996 The American Physical Society.

Dissipative Quantum Tunneling in Metals11The project supported in part by National Natural Science Foundation of China

The influence of a bath consisting of both conduction electrons and Debye phonons on quantum tunneling in metals is studied by the perturbation approach developed by the authors. We find that the renormalized tunneling parameter and the condition of localization transition are modified in comparison with the results of a bath consisting of conduction electrons.

Dynamical norm method for nonadiabatic macroscopic quantum tunneling.

We present a method for macroscopic quantum tunneling, named dynamical norm method, which works over a very wide range of situations between the adiabatic and the sudden limits. We examine the validity of the method by studying the effects of linear oscillator coupling on the tunneling rate through an Eckart barrier. We then apply the method to discussing the effects of a nuclear intrinsic excitation on fission. This method shows that the adiabaticity of the tunneling process is governed not only by the relative time scale of the tunneling degree of freedom and of environmental degrees of freedom, but also by the properties of the coupling between them. We also show that the dynamical norm factor which represents nonadiabatic effects in our method is closely related to the dissipation factor in the Caldeira-Leggett theory for dissipative quantum tunneling.

HOPPING AND DISSIPATIVE TUNNELING OF ORIENTATIONAL DEFECTS IN ICE

We have measured the dielectric relaxation time of orientational defects for H2O and D2O polycrystalline ice samples, in the temperature range 200–270 K, and over the frequency range 0.3–1000 kHz. Results are in good agreement with previous studies, and at T<240 K departures from the familiar Arrhenius law have been observed. We show that these deviations from classical rate theory can be well described within the framework of dissipative quantum tunneling (DQT) theory, assuming impurity-generated Bjerrum defects responsible for the observed dielectric relaxation process over the entire temperature range investigated. The temperature regions where quantum tunneling, crossover to thermal hopping, and quantum corrections to classical laws, respectively prevail are here reviewed. Particularly significant is the perfect agreement, near the crossover temperature Tc, of all our different samples with a universal scaling law, as predicted by DQT theory. The crossover temperature Tc, where quantum tunneling and thermal hopping merge, has been found close to 240 K and to 220 K for H2O and D2O ice respectively, thus showing the higher relevance of quantum effects in H2O ice. It is shown that the dielectric relaxation time of orientational defects for both H2O and D2O ice samples never attains a fully classical behaviour, even at their melting temperature.

Dissipative quantum tunneling of defects in a mesoscopic metal

We have studied the dynamics of single bistable defects in sub-micron Bi wires at temperatures 0.1–2 K. The defect motions can cause large changes in the sample resistance via universal conductance fluctuations. The dynamics are due to the defect particle, coupled to the electron bath, tunneling in a double-well potential with asymmetry ɛ. We clearly observe tunneling rates that increase as the temperature is lowered when kT≫ɛ, as predicted by the theory of dissipative quantum tunneling. Fits of the theory to the data yield a value of the defect-electron bath coupling constant α, that is defect-specific.

Dissipative quantum tunneling of a single defect in Bi.

We have studied the dynamics of single bistable defects in submicrometer Bi wires at temperatures 0.1--2 K. The defect motions cause measurable changes in the sample resistance via universal conductance fluctuations. The temperature dependence of the transition rates agrees quantitatively with the predictions of dissipative quantum tunneling theory, which describes tunneling of a defect in a double-well potential with strong dissipation from the electron bath. We report detailed measurements of a single defect as a function of magnetic field, and discuss the field dependence of the defect-potential asymmetry \ensuremath{\varepsilon}, the defect-bath coupling constant \ensuremath{\alpha}, and the renormalized tunneling matrix element ${\mathrm{\ensuremath{\Delta}}}_{\mathit{r}}$.