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arXiv:1808.02916 · Physical Review A

Analog quantum simulation of extremely sub-Ohmic spin-boson models

Mehdi Abdi, Martin Bodo Plenio

Published Oct 26, 2018• 13 citations
arXivHTMLPDF

Abstract

We propose a scheme for the quantum simulation of sub-Ohmic spin-boson models by color centers in free-standing hexagonal boron nitride (hBN) membranes. The electronic spin of a color center that couples to the membrane vibrational spectrum constitutes the physical model. The spin-motion coupling is provided by an external magnetic field gradient. In this Rapid Communication, we show that a class of spectral densities can be attained by engineering geometry and boundary conditions of the hBN resonator. We then put our focus on two extreme cases, i.e., $1/f$- and white-noise spectral densities. Spin coherence and polarization dynamics are studied. Our calculations show coherence revivals at periods set by the bath characteristic frequency signaling the non-Markovian nature of the baths. The nonequilibrium dynamics of the spin polarization exhibits a coherent localization, a property peculiar to the quantum phase transition in extremely sub-Ohmic spin-boson models. Our scheme may find application in understanding the sources of decoherence in solid-state quantum bits.

DOI
10.1103/physreva.98.040303

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We propose a scheme for the quantum simulation of sub-Ohmic spin-boson models by color centers in free-standing hexagonal boron nitride (hBN) membranes. The electronic spin of a color center that couples to the membrane vibrational spectrum constitutes the physical model. The spin-motion coupling is provided by an external magnetic field gradient. In this Rapid Communication, we show that a class of spectral densities can be attained by engineering geometry and boundary conditions of the hBN resonator. We then put our focus on two extreme cases, i.e., 1/f1/f1/f- and white-noise spectral densities. Spin coherence and polarization dynamics are studied. Our calculations show coherence revivals at periods set by the bath characteristic frequency signaling the non-Markovian nature of the baths. The nonequilibrium dynamics of the spin polarization exhibits a coherent localization, a property peculiar to the quantum phase transition in extremely sub-Ohmic spin-boson models. Our scheme may find application in understanding the sources of decoherence in solid-state quantum bits.
Employing the nonperturbative numerical renormalization group method, we study the dynamics of the spin-boson model, which describes a two-level system coupled to a bosonic bath with a spectral density J(omega) proportional to omega(s). We show that, in contrast with the case of Ohmic damping, the delocalized phase of the sub-Ohmic model cannot be characterized by a single energy scale only, due to the presence of a nontrivial quantum phase transition. In the strongly sub-Ohmic regime, s<<1, weakly damped coherent oscillations on short time scales are possible even in the localized phase--this is of crucial relevance, e.g., for qubits subject to electromagnetic noise.
We propose a general extended coherent state approach to the qubit (or fermion) and multimode boson coupling systems. The application to the spin-boson model with the discretization of a bosonic bath with arbitrary continuous spectral density is described in detail, and very accurate solutions can be obtained. The quantum phase transition in the nontrivial sub-Ohmic case can be located by the fidelity and the order-parameter critical exponents for the bath exponents s<1/2s<1/2s<1/2 can be correctly given by the fidelity susceptibility, demonstrating the strength of the approach.
The transition from weakly damped coherent motion to localization in the context of the spin-boson model has been the subject of numerous studies with distinct behavior depending on the form of the phonon-bath spectral density $J\left(\ensuremath{\omega}\right)\ensuremath{\propto}{\ensuremath{\omega}}^{s}$. Sub-Ohmic (s<1s<1s<1) and Ohmic (s=1s=1s=1) spectral densities show a clear localization transition at zero temperature and zero bias, while for super-Ohmic (s>1s>1s>1) spectral densities this transition disappears. In this paper, we consider the influence of the phonon-bath spectral density on the nonequilibrium dynamics of a quantum dot with electron-phonon interactions described by the extended Holstein model. Using the reduced density matrix formalism combined with the multilayer multiconfiguration time-dependent Hartree approach, we investigate the dynamic response, the time scales for relaxation, as well as the existence of multiple long-lived solutions as the system-bath coupling changes from the sub- to the super-Ohmic cases. Bistability is shown to diminish for increasing powers of sss similar to the spin-boson case. However, the physical mechanism and the dependence on the model parameters such as the typical bath frequency ${\ensuremath{\omega}}_{c}$ and the polaron shift $\ensuremath{\lambda}$ are rather distinct.
We investigate the dynamics of a large anisotropic spin whose easy-axis component is coupled to a bosonic bath with a spectral function . Such a spin complex might be realized in a single-molecular magnet. Using the non-perturbative renormalization group, we calculate the line of quantum-phase transitions (QPTs) in the sub-ohmic regime ( s <1). These QPTs only occur for integer spin J . For half-integer J , the low temperature fixed-point is identical to the fixed-point of the spin-boson model without quantum tunneling between the two levels. Short-time coherent oscillations in the spin decay prevail even into the localized phase in the sub-ohmic regime. The influence of the reorganization energy and the recurrence time on the decoherence in the absence of quantum tunneling is discussed.
The spin-boson model, describing a two-level system coupled to a bosonic bath, is extensively studied as a paradigmatic dissipative quantum system, exhibiting rich dynamical behavior and even a localization transition in the strong coupling regime. Here, we additionally consider dephasing as a source of Markovian dissipation on top of the non-Markovian dynamics due to an Ohmic bath, and investigate the dynamics of the spin. We show that the characteristic frequency of the spin dynamics, while strongly renormalized by the bosonic bath, changes in a simple fashion (or does not change at all) with dephasing. To obtain these results, we develop an exact nonperturbative method known as the stochastic Schr\"odinger equation, mimicking the Ohmic bath via a stochastic magnetic field combined with the Lindblad quantum master equation due to dephasing, which allows us to numerically compute the dynamics. Furthermore, we derive weak-coupling analytic results utilizing the well-known noninteracting blip approximation. Our findings are relevant to quantum simulation of the spin-boson model in the regime of strong coupling in trapped ions and circuit QED architectures among others.
A quantum two-level system immersed in a sub-Ohmic bath experiences enhanced low-frequency quantum statistical fluctuations which render the nonequilibrium quantum dynamics highly non-Markovian. Upon using the numerically exact time-evolving matrix product operator approach, we investigate the phase diagram of the polarization dynamics. In addition to the known phases of damped coherent oscillatory dynamics and overdamped decay, we identify a new third region in the phase diagram for strong coupling showing an aperiodic behavior. We determine the corresponding phase boundaries. The dynamics of the quantum two-state system herein is not coherent by itself but slaved to the oscillatory bath dynamics.