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arXiv:cond-mat/9406043 · Physical Review Letters

Atomic Tunneling from a Scanning-Tunneling or Atomic-Force Microscope Tip: Dissipative Quantum Effects from Phonons

Ard A. Louis, James P. Sethna

Published Feb 20, 1995• 41 citations
arXivHTMLPDF

Abstract

We study the effects of phonons on the tunneling of an atom between two surfaces. In contrast to an atom tunneling in the bulk, the phonons couple very strongly and qualitatively change the tunneling behavior. This is the first example of Ohmic coupling from phonons for a two-state system. We propose an experiment in which an atom tunnels from the tip of an scanning-tunneling microscope, and show how its behavior would be similar to the macroscopic quantum coherence behavior predicted for SQUIDs. The ability to tune and calculate many parameters would lead to detailed tests of the standard theories.

DOI
10.1103/physrevlett.74.1363

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We study the effects of phonons on the tunneling of an atom between two surfaces. In contrast to an atom tunneling in the bulk, the phonons couple very strongly and qualitatively change the tunneling behavior. This is the first example of Ohmic coupling from phonons for a two-state system. We propose an experiment in which an atom tunnels from the tip of an scanning-tunneling microscope, and show how its behavior would be similar to the macroscopic quantum coherence behavior predicted for SQUIDs. The ability to tune and calculate many parameters would lead to detailed tests of the standard theories.
The atom tunneling across the potential barrier separating the surface and the tip of the scanning tunneling microscope is investigated by semiclassical methods, and by integrating numerically the time-dependent Schr\"odinger equation. It is shown that the barrier crossing is explained by the resonance phenomenon of quantum coherence oscillations, rather than by exponential decay. The occurrence of these resonances at the variation of the bias voltage is studied for the first two isomeric states of a Xe atom in a surface-tip potential of double-well shape. The resonant bias voltages for these two states practically coincide, and at the first common resonance the effect of the environmental temperature is discussed. The results provide a useful frame for understanding the mechanism of atom transfer in scanning tunneling microscopy.
The evolution of the quantum wave packet describing an atom trapped in the surface-tip junction of the scanning tunneling microscope is investigated by using the time-dependent Schroedinger equation, and by a quasi-classical Hamiltonian approach. The estimates concern a Xe atom in a biased double-well junction potential. The exact treatment shows that quantum coherence oscillations of the metastable ground state may occur at particular resonant values of the bias voltage. The effect of decoherence by partial localization is studied within the quasi-classical frame.
Phonon modes within pristine crystalline resonators now routinely reach the quantum ground state. Such systems are attractive for quantum information science applications, as advanced fabrication and processing can enable relatively long quantum coherence times, and precision control can be realized through optical, electrical, or qubit coupling. In many state-of-the-art systems, the phonon lifetime is limited by disorder. In particular, native oxides or damaged `dead layers' at surfaces can host two-level tunneling states that lead to a particularly problematic form of dissipation that increases at lower temperatures. As mechanical losses are driven down in systems such as micro-fabricated bulk acoustic wave resonators, tunneling states are expected to emerge as the dominant mechanism for phonon decoherence. A quantitative description of these mesoscopic systems therefore requires a framework that captures interactions between a selected phonon mode and a large ensemble of TLS. Here, we derive a quantum master equation for this coupled system, permitting the phonon decoherence produced by two-level tunneling states to be calculated. As an example, we estimate the lifetime of a variety of quantum states within quartz micro-resonators hosting a thin surface layer of tunneling states. We find that the phonon coherence time is maximized at low temperatures, in spite of increased mechanical dissipation, and that phonon-TLS coupling can be reduced for modes with strain nodes at the surfaces.
The problem of macroscopic quantum coherence in superconducting systems is studied theoretically. A two-level model of a SQUID with phonon-field coupling is considered. The probability of a transition, induced by a periodic perturbation, occurring between the lowest states of the two-well potential, describing the phase dependence of the energy in the SQUID, is calculated for a particular region of this coupling. Use is made of the conformity between this model and the resonance-level model. We also consider the strong-viscosity limit. It is shown that in this case the two-level model cannot be used to describe quantum interferometers.
The properties of a two-state chain interacting with a phonon bath is studied in this paper. We discuss the renormalization of the single pseudospin tunneling parameter by phonons' interaction, as well as other pseudospins' correlation. We find that for Ohmic dissipation, the correlation between pseudospins vanishes and the phonons' interaction induces the localization–delocalization transition. For our discussed super-Ohmic dissipation, the phonons' interaction only reduces the tunneling parameter and does not induce phase transition. In this case the pseudospins' correlation has its effect and reduces the tunneling parameter at weak coupling. In addition, some application of our results is also discussed.
Recently there has been interest in macroscopic systems which can be described in terms of the quantum dynamics of the same collective variables which describe their classical behavior. In particular, there has been considerable interest in the following questions: (1) Is it possible to observe unambiguous evidence of the quantum-mechanical nature of a macroscopic collective coordinate? (2) In what way is the quantum mechanics of a macroscopic variable different from that of a microscopic variable or, in other words, what is the effect of dissipation on the dynamics of a quantum-mechanical system? Spectroscopic evidence of the quantization of energy levels can be found by measuring the system's response to an applied ac perturbation, exploiting the quantum-mechanical relation between energy and frequency. The specific system studied is a superconducting quantum interference device (SQUID). It is shown that a time-varying magnetic field through the superconducting loop in a rf SQUID can cause transitions between different fluxoid states. The role of dissipation is discussed in detail, and it is shown that in the case that dissipation is characterized by linear damping in the classical limit, the photon-absorption process depends critically on the ratio of the resistance of the weak link to the fundamental unit of resistance h/e2{e}^{2}e2. .AE