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arXiv:2012.11235 · Physical Review A

Effective quantum dynamics induced by a driven two-level-system bath

Katja Kustura, Oriol Romero‐Isart, Carlos Gonzalez-Ballestero

Published May 24, 2021• 3 citations
arXivHTMLPDF

Abstract

We derive a Born-Markov master equation describing the dissipation induced by a bath of lossy but coherently driven two-level systems (TLSs) coupled to a bosonic system via Jaynes-Cummings interaction. We analytically derive all the master-equation rates. We characterize these rates for the particular case of a single-mode system coupled to identical TLSs. We study the steady state of the system and its exotic properties stemming from the nonthermal stationary state of the driven TLS bath. These properties include dissipative amplification, bath-induced linear instability, and both coherent and dissipative squeezing. The master equation is valid for arbitrarily strong TLS driving and it can be generalized to include multilevel systems or other system-bath interaction terms, among others. Our work provides a tool to study and characterize TLS-induced decoherence, a key limiting factor in quantum technological devices based on, for instance, superconducting circuits, magnonic systems, or quantum acoustics.

DOI
10.1103/physreva.103.053709

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We derive a Born-Markov master equation describing the dissipation induced by a bath of lossy but coherently driven two-level systems (TLSs) coupled to a bosonic system via Jaynes-Cummings interaction. We analytically derive all the master-equation rates. We characterize these rates for the particular case of a single-mode system coupled to identical TLSs. We study the steady state of the system and its exotic properties stemming from the nonthermal stationary state of the driven TLS bath. These properties include dissipative amplification, bath-induced linear instability, and both coherent and dissipative squeezing. The master equation is valid for arbitrarily strong TLS driving and it can be generalized to include multilevel systems or other system-bath interaction terms, among others. Our work provides a tool to study and characterize TLS-induced decoherence, a key limiting factor in quantum technological devices based on, for instance, superconducting circuits, magnonic systems, or quantum acoustics.
We derive and analyze the Born-Markov master equation for a quantum harmonic oscillator interacting with a bath of independent two-level systems. This hitherto virtually unexplored model plays a fundamental role as one of the four ``canonical'' system-environment models for decoherence and dissipation. To investigate the influence of further couplings of the environmental spins to a dissipative bath, we also derive the master equation for a harmonic oscillator interacting with a single spin coupled to a bosonic bath. Our models are experimentally motivated by quantum-electromechanical systems and micron-scale ion traps. Decoherence and dissipation rates are found to exhibit temperature dependencies significantly different from those in quantum Brownian motion. In particular, the systematic dissipation rate for the central oscillator decreases with increasing temperature and goes to zero at zero temperature, but there also exists a temperature-independent momentum-diffusion (heating) rate.
We provide the exact non-Markovian master equation for a two-level system interacting with a thermal bosonic bath, and we write the solution of such a master equation in terms of the Bloch vector. We show that previous approximated results are particular limits of our exact master equation. We generalize these results to more complex systems involving an arbitrary number of two-level systems coupled to different thermal baths, providing the exact master equations also for these systems. As an example of this general case we derive the master equation for the Jaynes-Cummings model.
We study the decoherence dynamics of a superconducting qubit coupled to a quantum two-level system (TLS) in addition to its weak coupling to a background environment [1]. We identify two weak-coupling regimes, which differ by the relation between qubit and TLS decoherence times, and a strong coupling regime. We find expressions for the qubit decoherence rates in the weak-coupling regimes. For a weakly coupled and strongly dissipative TLS we find that the qubit dynamics is markovian, whereas for a weakly dissipative TLS the qubit dynamics shows non-markovian behavior. In the strong-coupling regime we study the driven qubit dynamics and we analyze the differences from standard Rabi-oscillations due to the coupling to the quantum TLS [2]. In doing so we identify signatures in the qubit dynamics that can be used to characterize the TLS. We also investigate the possibility of using environmental TLSs with long coherence times for quantum information processing [3]. By using the Josephson junction as a bus and the TLSs in the environment as qubits, we demonstrate that initialization, a universal set of quantum gates, and read-out of the TLSs can be implemented, even though the TLSs themselves cannot be directly accessed.
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 generalize a microscopic master equation method to study the dissipation dynamics of Jaynes-Cummings two-level system with a weak external driving. Using perturbative analysis to extend the damping bases theory, we derive the corrected Rabi oscillation and vaccum Rabi splitting analytically. The evolution of the decoherence factor of the weakly driven system reveals that the off-diagonal density matrix elements are oscillating at a frequency dependent on the driving strength and the initial population inversion. For highly-inverted systems at the weak-driving limit, this frequency reduces to twice the value for the non-driven system, showing the dissipation dynamics unable to be discovered using more conventional approaches.
We study a generic open quantum system where the coupling between the system and its environment is of an energy-preserving quantum nondemolition (QND) type. We obtain the general master equation for the evolution of such a system under the influence of a squeezed thermal bath of harmonic oscillators. From the master equation it can be seen explicitly that the process involves decoherence or dephasing without any dissipation of energy. We work out the decoherence-causing term in the high- and zero-temperature limits and check that they match with known results for the case of a thermal bath. The decay of the coherence is quantified as well by the dynamics of the linear entropy of the system under various environmental conditions. We make a comparison of the quantum statistical properties between QND and dissipative types of evolution using a two-level atomic system and a harmonic oscillator.