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arXiv:1609.01418 · Physical Review Letters

Landau-Zener-Stueckelberg Physics with a Singular Continuum of States

D. M. Basko

Published Jan 6, 2017• 12 citations
arXivHTMLPDF

Abstract

This Letter addresses the dynamical quantum problem of a driven discrete energy level coupled to a semi-infinite continuum whose density of states has a square-root-type singularity, such as states of a free particle in one dimension or quasiparticle states in a BCS superconductor. The system dynamics is strongly affected by the quantum-mechanical repulsion between the discrete level and the singularity, which gives rise to a bound state, suppresses the decay into the continuum, and can produce Stueckelberg oscillations. This quantum coherence effect may limit the performance of mesoscopic superconducting devices, such as the quantum electron turnstile.

DOI
10.1103/physrevlett.118.016805

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This Letter addresses the dynamical quantum problem of a driven discrete energy level coupled to a semi-infinite continuum whose density of states has a square-root-type singularity, such as states of a free particle in one dimension or quasiparticle states in a BCS superconductor. The system dynamics is strongly affected by the quantum-mechanical repulsion between the discrete level and the singularity, which gives rise to a bound state, suppresses the decay into the continuum, and can produce Stueckelberg oscillations. This quantum coherence effect may limit the performance of mesoscopic superconducting devices, such as the quantum electron turnstile.
The Landau-Zener-Stueckelberg (LZS) effect in a model system of interacting tunneling particles is studied numerically and analytically. Each of N tunneling particles interacts with each of the others with the same coupling J. This problem maps onto that of the LZS effect for a large spin S=N/2.S=N/2.S=N/2. The mean-field limit $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$ corresponds to the classical limit $\stackrel{\ensuremath{\rightarrow}}{S}\ensuremath{\infty}$ for the effective spin. It is shown that the ferromagnetic coupling J>0J>0J>0 tends to suppress the LZS transitions. For $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$ there is a critical value of J above which the staying probability P does not go to zero in the slow sweep limit, unlike the standard LZS effect. For J<0J<0J<0 LZS transitions are boosted and P=0P=0P=0 for a set of finite values of the sweep rate for $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}.$ Various limiting cases such as strong and weak interaction, slow and fast sweep are considered analytically. It is shown that the mean-field approach works well for arbitrary N if the interaction J is weak.
We formulate a quantum mechanical system consisting of a single discrete state coupled to an infinite ladder of equally-spaced states, the coupling between the two being given by a Lorentzian profile. Various limits of this system correspond to well-known models from quantum optics, namely, the narrow resonance limit gives the Rabi system, the wide resonance limit gives the Bixon-Jortner system, the wide resonance, true continuum limit gives the Wigner-Weisskopf system, and the fixed resonance, true continuum limit gives a system that is typically studied by methods developed by Fano. We give a semi-analytical solution of the eigenvalue problem by reducing it to a transcendental equation, and demonstrate the aforementioned limiting behaviors. We then study the dynamics of the initial discrete state numerically, and show that it gives a wide range of behaviors in various limiting cases as predicted by our asymptotic theory including exponential decay, revivals, Rabi oscillations, and damped oscillations. The ability of this system to interpolate between such a rich set of behaviors and existing model systems, and the accessibility of a semi-analytical solution, make it a useful model system in quantum optics and related fields.
By performing experiments with thin-film resonators of NbSi, we elucidate a decoherence mechanism at work in disordered superconductors. This decoherence is caused by charged Two Level Systems (TLS) which couple to the conduction electrons in the BCS ground state; it does not involve any out-of-equilibrium quasiparticles, vortices, etc. Standard theories of mesoscopic disordered conductors enable making predictions regarding this mechanism, notably that decoherence should increase as the superconductor cross section decreases. Given the omnipresence of charged TLS in solid-state systems, this decoherence mechanism affects, to some degree, all experiments involving disordered superconductors. In particular, we show it easily explains the poor coherence observed in quantum phase slip experiments and may contribute to lowering the quality factors in some disordered superconductor resonators.
We formulate a quantum-mechanical system consisting of a single discrete state coupled to an infinite ladder of equally spaced states, with the coupling described by a Lorentzian profile. Various limiting cases of this system correspond to well-known models in quantum optics: the narrow-resonance limit yields the Rabi model, the wide-resonance limit yields the Bixon-Jortner model, the wide-resonance true continuum limit yields the Wigner-Weisskopf model, and the fixed-resonance true continuum limit yields a system typically studied using methods developed by Fano. We obtain a semianalytical solution to the eigenvalue problem by reducing it to a transcendental equation and demonstrate the limiting behaviors described above. We then investigate numerically the dynamics of the initial discrete state and show that, in various limiting regimes, the system exhibits a wide range of behaviors predicted by the asymptotic theory, including exponential decay, revivals, Rabi oscillations, and damped oscillations. The ability of the system to interpolate between such a rich variety of behaviors and established model systems, together with the accessibility of a semianalytical solution, makes it a useful model in quantum optics and related fields.
We formulate a quantum-mechanical system consisting of a single discrete state coupled to an infinite ladder of equally spaced states, with the coupling described by a Lorentzian profile. Various limiting cases of this system correspond to well-known models in quantum optics: the narrow-resonance limit yields the Rabi model, the wide-resonance limit yields the Bixon--Jortner model, the wide-resonance true continuum limit yields the Wigner--Weisskopf model, and the fixed-resonance true continuum limit yields a system typically studied using methods developed by Fano. We obtain a semianalytical solution to the eigenvalue problem by reducing it to a transcendental equation and demonstrate the limiting behaviors described above. We then investigate numerically the dynamics of the initial discrete state and show that, in various limiting regimes, the system exhibits a wide range of behaviors predicted by the asymptotic theory, including exponential decay, revivals, Rabi oscillations, and damped oscillations. The ability of the system to interpolate between such a rich variety of behaviors and established model systems, together with the accessibility of a semianalytical solution, makes it a useful model in quantum optics and related fields.