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arXiv:1206.2200 · Physical Review B

Damping and decoherence of Fock states in a nanomechanical resonator due to two-level systems

Laura G. Remus, M. P. Blencowe

Published Nov 15, 2012• 6 citations
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Abstract

We numerically investigate the decay of initial quantum Fock states and their superpositions for a mechanical resonator mode coupled to an environment comprising interacting, damped tunneling two-level system (TLS) defects. The cases of one, three, and six near-resonant, interacting TLS's are considered in turn, and it is found that, with even as few as three TLS's, the resonator's quantum decay behavior is indistinguishable from that due to coupling to an Ohmic oscillator bath.

DOI
10.1103/physrevb.86.205419

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We numerically investigate the decay of initial quantum Fock states and their superpositions for a mechanical resonator mode coupled to an environment comprising interacting, damped tunneling two-level system (TLS) defects. The cases of one, three, and six near-resonant, interacting TLS's are considered in turn, and it is found that, with even as few as three TLS's, the resonator's quantum decay behavior is indistinguishable from that due to coupling to an Ohmic oscillator bath.
Recent experiments on a range of engineered quantum systems have highlighted the important role of interacting two-level systems (TLSs) in modifying device properties and generating fluctuations. Focusing on the case of an oscillator coupled to a single near-resonant TLS, we explore how interactions between the TLS and lower-frequency thermally activated two-level fluctuators (TLFs) degrade the oscillator's coherence. Depending on the strength of the couplings, a single TLF can give rise to coherence oscillations that appear alongside, or supplant, Rabi oscillations of the oscillator-TLS system. Bath-driven transitions in the TLF cause irreversible coherence decay at a rate that is highly sensitive to both the couplings and the transition rate. For an ensemble of TLFs, we identify and characterise the different regimes of non-exponential phase-averaging-driven coherence decay that the oscillator can display. Using numerical calculations, we examine the extent to which systems with just a few TLFs differ from the limit of a large (continuum) TLF ensemble. Our work provides a theoretical framework for understanding the interplay of coherent TLS interactions and TLF-induced dephasing in quantum devices such as superconducting and phononic resonators.
We propose measurement-based conditional generation of the superposition of mesoscopic states of a nanomechanical resonator. We consider a two-level quantum mechanical system (qubit) coupled with a nanomechanical resonator through phonon exchange. An interaction, which produces shifts in the state of the nanomechanical resonator depending on the state of the qubit, is realized by driving the qubit through two resonant fields or a single field with controlled phase. The measurement of the state of the qubit produces superposition states of the nanomechanical resonator. We show that the quantum interference between the generated states in the superposition may lead to an arbitrary large displacement in the resonator. We also discuss decoherence of the generated states using the Wigner function.
Among the various nanoscale systems operating in the quantum limit, nanomechanical oscillators have emerged as particularly powerful platforms. They constitute highly sensitive sensors and can mediate interactions between light and localized quantum systems, playing a central role in various quantum information processing architectures. Due to their relatively large mass, they also serve as ideal platforms for investigating the transition between classical and quantum behavior. This thesis examines the dynamics of a nanomechanical oscillator coupled to a driven two-level system. The analysis focuses on the resolved sideband limit, where the twolevel system’s damping rate Γ is much smaller than the mechanical frequency ωm, and explores both the strong coupling (ωm ≫ g0 ≫ Γ) and ultra-strong coupling (g0 ∼ ωm ≫ Γ) regimes, where g0 denotes the coupling strength. These regimes enable coherent manipulation of the mechanical state while preserving its quantum coherence. Under blue-detuned driving of the two-level system and assuming low mechanical damping, the system exhibits a dynamical instability marked by the emergence of limit cycles in the mechanical oscillator. The onset of this regime is accompanied by pronounced fluctuations in the photon emission from the two-level system, indicated by a large deviation from Poissonian statistics. The phonon statistics display a similar behavior, offering an additional experimental signature. As the coupling strength approaches ωm, the mechanical oscillator reaches a steady state with non-classical feature. The phonon number distribution in this regime resembles that of Fock states, and the corresponding quasi-probability distribution in phase space displays negative regions, a signature of nonclassicality. A method is proposed to detect this non-classicality experimentally through measurements of the emitted light, from which the full quantum state of the coupled system can be reconstructed. The robustness of this approach is analyzed in the presence of realistic noise sources. The thesis further investigates the response of the system under two-tone driving. A tailored model is developed to describe this regime at strong coupling. When the driving frequencies are tuned to the first blue and red sidebands, the mechanical oscillator reaches a steady state exhibiting quadrature squeezing. In the case where both driving frequencies are red-detuned, the oscillator evolves into a superposition of coherent states, analogous to the behavior of a parametrically driven resonator. In both configurations, non-classical features become prominent when g0 approaches ωm. These results provide new insights into the generation and stabilization of non-classical and squeezed mechanical states. We outline feasible strategies for their detection, offering potential applications in hybrid quantum systems and foundational tests of quantum mechanics.
The dissipative quantum dynamics of a two-level system interacting with a structured reservoir consisting of a damped harmonic mode is investigated by means of the numerically exact path integral Monte Carlo method. This approach provides benchmark results in a broad range of parameter space, in particular, in those domains which are not accessible by approximate methods and alternative numerical schemes, that is, strong coupling between system and harmonic mode and from low to high temperatures. For low temperatures the numerical data are quantitatively in agreement with the noninteracting blip approximation only in the regimes of very weak and very strong coupling. It turns out that the entangled dynamics of the two-level system and the harmonic mode is relatively robust so that its signatures are observable up to relatively strong friction and high temperatures. Nonequilibrium initial preparations of the reservoir with respect to the initial state of the system give rise, for strong interactions, to a stepwise decay of the population, thus displaying coherent dynamics of the bath. The impact of an additional Ohmic bath coupled directly to the two-level system is studied as well, including the case where both reservoirs carry different temperatures.